      }
                m_grid[gridIndexX][gridIndexY][gridIndexZ].Add(i);
            }
        }
    }

A:

You need to add another indexer.  You've initialized m_grid as a 3-dimentional array.  So any first-level element within m_grid is a 2-dimensional array.  And you're trying to set one of those elements to a 1-dimensional array:
m_grid[gridIndexX] = new ArrayList[Height];

In the above code, m_grid[gridIndexX] is of type ArrayList[][], so you have a type mis-match.
You'll need to set it to the proper type:
m_grid[gridIndexX] = new ArrayList[Height][];

I don't know if this alone will solve your problem, because it's difficult to discern whatQ:

Find the next blank column on specific ROW with VBA

I need some help I need to find the next blank column on specific row because my table has some headers and blank spaces on the bottom i try a lot of methods and doesn't work for me
I need to find the next blank column on the row number 5.

A:

Sheet3.Cells(4, Sheet3.Columns.Count).End(xlToLeft)

specifies the first blank cell in row 4 of Sheet3.


YMH}}_c(A,\Phi)=
\|F_A\|_{L^2}^2+\|d_A\Phi\|_{L^2}^2+\|\mu(\Phi)-c\|_{L^2}^2.
\label{edefymh}$$ A basic result in the theory is that one can rewrite the Yang–Mills–Higgs functional as $$\begin{aligned}
{{\cal YMH}}_c(A,\Phi) &= \|\Lambda F_A+\mu(\Phi)-c\|_{L^2}^2+
2\|{\overline}{\partial}_A\Phi\|_{L^2}^2+4\|F_A^{0,2}\|_{L^2}^2 \notag \\
&+2\int_X{\langle}\Lambda F_A,c{\rangle}\omega^{[n]}
+\int_X {\operatorname{Tr}}F_A\wedge F_A\wedge \omega^{[n-2]},
\label{eymh2}\end{aligned}$$ where $\omega=\omega_X$ and $\omega^{[k]}=\omega^k/k!$. (In the integrals of functions on $X$ appearing in the sequel we will implicitly use the volume form $\omega^{[n]}$.) From this we deduce that, if we fix $E$ and $c$, the pairs $(A,\Phi)$ which minimise ${{\cal YMH}}_c$ are precisely the solutions to equations (\[eiequs\]). (Indeed, the terms $\int_X{\langle}\Lambda F_A,c{\rangle}$ and $\int_X {\operatorname{Tr}}F_A\wedge F_A\wedge \omega^{[n-2]}$ only depend on $E$, the representation $\rho$ and $c$.) The equality (\[eymh2\]) can be proved using the Kaehler identities (see for example [@Br1]). This equality allows to find $L^2$ bounds on the curvature $F_A$ and the covariant derivative $d_A\Phi$ when $(A,\Phi)$ satisfies (\[eiequs\]).

####functional evaluated at $(A,\Phi)\in{{\curly A}}\times{{\curly S}}$: $${{\cal YMH}}_c(A,\Phi)=
\|F_A\|_{L^2}^2+\|d_A\Phi\|_{L^2}^2+\|\mu(\Phi)-c\|_{L^2}^2,
\label{eiestr}$$ Here $d_A\Phi$ is the covariant derivative defined in (\[edefda\]). Of course, if $F$ is a vector space and $K$ acts linearly on $F$, then the Yang–Mills–Higgs functional defined above coincides with the classical one given in \[edefymh\]. We then prove a formula generalising (\[eymh2\]) which allows to write the Yang–Mills–Higgs functional as $${{\cal YMH}}_c(A,\Phi)=\|\Lambda F_A+\mu(\Phi)-c\|_{L^2}^2+
2\|{\overline}{\partial}_A\Phi\|_{L^2}^2+4\|F_A^{0,2}\|_{L^2}^2+T,$$ where $T$ is a constant depending only on the topology of $E$, $F$ and the section $\Phi$ (and which consequently is invariant under deformations of $A$ and $\Phi$). This formula will be used to obtain bounds on the $L^2$ norms of $F_A$ and $d_A\Phi$ for $(A,\Phi)$ solving equations (\[eiequs\]) and for $\Phi$ satisfying some fixed homological constraints.

### Chapter 2: Hitchin–Kobayashi correspondence

In this chapter we prove


much likely, a good understanding of a gluing construction of THCs will be crucial in developping the latter two questions.

-   [**Interpretation of the invariants.**]{} We would like to find a description of the invariants in terms of enumerative geometry, just as is done with Gromov-Witten invariants.

-   [**Wall crossing.**]{} In this thesis we define invariants using the moduli spaces ${{\cal N}}_{\sigma}(B,c)$ and ${{\cal M}}_{\sigma}(B,c)$ when $c\in{{\mathbf i}}{{\Bbb R}}\setminus C_0$. It would be interesting to study the relation between the invariants obtained when $c$ belongs to different connected components of ${{\mathbf i}}{{\Bbb R}}\setminus C_0$. Presumably we could prove a result similar to Thaddeus theorem in [@Th].

Notations
---------

All the manifolds, bundles and morphisms in this thesis will be smooth unless otherwise stated. All vector spaces will be finitewith respect to $I(A)$ as a map from $X$ to ${{\cal F}}$ if and only if $\overline{\partial}_A\Phi=0$. \[compara\]

This follows from the formula ${\overline}{\partial}_A\Phi=(d\Phi+I(A)\circ d\Phi\circ I_X)/2$.

The Yang–Mills–Higgs functional {#YMHs}
-------------------------------

The biinvariant metric on ${{\frak k}}$ induces a norm $\|\cdot\|:{{\frak k}}\to{{\Bbb R}}$. Thanks to $K$-equivariance, we may combine $\|\cdot\|$ with the volume form $\omega_X^{[n]}$ to obtain an $L^2$ norm $\|\cdot\|_{L^2}:\Omega^0(E\times_{{\operatorname{Ad}}}{{\frak k}})\to{{\Bbb R}}$ and similarly on $\Omega^0(E\times_{{\operatorname{Ad}}}{{\frak k}}^*)$. We can do the same thing with the $K$-invariant metric $g_F$ on $F$, thus getting $\|\cdot\|_{L^2}:\Omega^0(T{{\cal F}}_v)\to{{\Bbb R}}$.

Fix a central element $c\in{{\frak k}}$. The [**Yang–Mills–Higgs**]{} functional ${{\cal YMH}}_c:{{\curly A}}\times{{\curly S}}\to{{\Bbb R}}$ is defined as $${{\cal YMH}}_c(A,\Phi)=\|F_A\|_{L^2}^2+\|d_A\Phi\|_{L^2}^2
+\|c-\mu(\Phi)\|_{L^2}^2,$$ where $\Phi\in{{\curly S}}$ is a section and $A\in{{\curly A}}$ a connection on $E$.

We will say that two sections $\Phi_0,\Phi_1\in{{\curly S}}$ are [**homotopic**]{} iff there exists a map $H_{\Phi}:X\times[0,1]\to{{\cal


which we will also call $\omega$, or $dx\wedge dy$. Define the function $f:S\to{{\Bbb R}}$ by $\omega=f(dx\wedge dy)$. Take on $S$ the metric coming from the one on $F$. From $\omega(\partial/\partial x,\partial/\partial y)=f$, $|\partial/\partial x|=|\partial/\partial y|$ and the fact that $\partial/\partial x$ is orthogonal to $\partial/\partial y$ (recall that $I_F$ is an isometry) we deduce that $$|\partial/\partial x|=|\partial/\partial y|=\sqrt{f}.
\label{normpar}$$

Write, for $i=1,2$, $d_{A^i}=d+A^i_x dx+A^i_y dy$ in the chosen trivialisation of $E|_U$, where $A^i_x$ and $A^i_y$ take values in ${{\frak k}}$. The corresponding curvatures in our trivialisation are $$F_{A^i}=\left(\frac{\partial A^i_y}{\partial x}
-\frac{\partial A^i_x}{\partial y}+[A^i_x,A^i_y]\right)dx\wedge dy.$$ We will consider the restriction of the sections on $U$ as maps $\Phi^i:U\to F$. Now we compute $$\int_{S}{\langle}\Lambda F_{A^i},\mu(\Phi^i){\rangle}_{{{\frak k}}}\omega=
\int_{S}\left{\langle}\frac{\partial A^i_y}{\partial x}
-\frac{\partial A^i_x}{\partial y}+[A^i_x,A^i_y],\mu(\Phi^i)
\right{\rangle}_{{{\frak k}}}dx\wedge dy.$$ Integrating by parts we see that this is equal to $$\begin{aligned}
&B_i+
\int_{S}(-{\langle}{\langle}d\mu(\Phi),\partial\Phi^i/\partialF}}_v$ with the induced Kaehler structures, and $f=d_A\Phi(x)$. With these identifications $f^{1,0}=\partial_A\Phi(x)$ and $f^{0,1}=\overline{\partial}_A\Phi(x)$ (see remark \[trucu2\]). As a consequence, $$\begin{aligned}
C_{[\Phi]}&=\frac{1}{2}(\|\partial_A\Phi\|^2_{L^2}
-\|\overline{\partial}_A\Phi\|^2_{L^2})-
\int_X {\langle}\Lambda F_A,\mu(\Phi){\rangle}\notag \\
&=\int_X(\Phi^*\tilde{\omega}_F^A
-\Phi^*{\langle}\pi_F^*\Lambda F_A,\mu(\Phi){\rangle})\wedge\omega^{[n-1]}=
\int_X\Phi^*\omega_F^A\wedge\omega^{[n-1]},\notag \end{aligned}$$ which by proposition \[nonlinka2\] depends only on $[\Phi]$. This proves proposition \[nonlinka\].

#### The Cartan complex

We are now going to prove proposition \[nonlinka2\]. We will use some results from [@BeGeV], especially from chapter 7. Define the graded algebra $$\Omega_K(F)=({{\Bbb C}}[{{\frak k}}]\otimes \Omega(F))^K,$$ where $\Omega(F)$ is the algebra of differential forms on $F$, and assign to $P\otimes\alpha\in\Omega_K(F)$ the degree $\deg(P\otimes\alpha)=2\deg(P)+\deg(\alpha)$. As usual $(\cdot)^K$ denotes the $K$ invariant elements under the action of $K$. (The action of $K$ on ${{\Bbb C}}[{{\frak k}}]\otimes \Omega(F)$ is by pullback both on ${{\Bbb C}}[{{\frak k}}]$ and on $\Omega(F)$.) If $\eta\in\Omega_K(F)$, let $$d_{{{\frak k}}}(\eta)(s)=d(\eta(s))+\iota({{\curly X}}_s)\eta(s),$$ where $s$ is any element


$K$ on $G$ on the left). This is a principal $G$ bundle. Let ${{\curly G}}_G=\Gamma(E_G\times_{{\operatorname{Ad}}}G)=\Gamma(E\times_{{\operatorname{Ad}}}G)$ be the gauge group of $E_G$. The group ${{\curly G}}_G$ is the complexification of ${{\curly G}}_K$.

[startsection[subsubsection]{}[3]{}[0pt]{} [-2]{}[****]{}]{} In this chapter the manifold $F$ will be assumed to be Kaehler. We will write its symplectic form $\omega_F$ and its complex structure $I_F\in{\operatorname{End}}(TF)$ (recall that both structures are invariant under the action of $K$ by hypothesis). Let ${{\cal F}}=E\times_K F$ be the associated bundle and let ${{\curly S}}=\Gamma({{\cal F}})$ the the set of sections of ${{\cal F}}$. The gauge group ${{\curly G}}_K$ acts on the left on ${{\cal F}}$, and hence acts also on ${{\curly S}}$. Since $F$ is Kaehler, the action of $K$ on $F$ extends to a unique holomorphic action of $G$ (see[@GS]). This allows to extend the action of ${{\curly G}}_K$ on ${{\curly S}}$ to an action of ${{\curly G}}_G$.

[startsection[subsubsection]{}[3]{}[0pt]{} [-2]{}[****]{}]{} \[accioGG\] Let ${{\curly C}}$ be the set of $G$-invariant complex structures on $E_G$ for which the map $d\pi_G:TE_G\to \pi_G^*TX$ is complex. We define a map ${{\mathbf C}}:{{\curly C}}\to{{\curly A}}$, called the [**Chern map**]{}, as follows. An invariant complex structure $I\in{{\curly C}}$ is mapped to the connection whose horizontal distribuition is $I(TE)\cap TE\subset TE$ (this makes sense, since the inclusion $E=E\times_K K\subset E\times_K G$ given by $K\subset G$ induces an inclusion $TE\subset TE_G$). (This distribuition is $K$ invariant and hence corresponds to a connection because $I$ is $G$-invariant.) The map ${{\mathbf C}}$ is a bijection. Its inverse sends any connection $A\in{{\curly A}}$ to the complex structure $I_{E_G}(A)$ on $E_G$


is analytically stable if and only if $\Psi_x$ is linearly proper. \[fita\]

Suppose first that $x$ is analytically stable. We have to prove that there exist two positive constants $C_1, C_2\in{{\Bbb R}}$ such that, for any $s\in{{\frak k}}$, $\|s\|\leq C_1\Psi_x(e^{{{\mathbf i}}s})+C_2$. Assume that there are not such constants. Then, we can find sequences $\{s_j\}\subset {{\frak k}}$ and $\{C_j\}\subset{{\Bbb R}}$ such that $\|s_j\|\to\infty$, $C_j\to\infty$ and, for any $j$, $\|s_j\|\geq C_j\Psi_x(e^{{{\mathbf i}}s_j})$. Let $u_j=s_j/\|s_j\|$. After passing to a subsequence, we can assume that $u_j\to s$. Take now any $t>0$. By our hypothesis, and making use of (4) in proposition \[propietats1\], $$\frac{1}{C_j}\geq\frac{\Psi_x(e^{{{\mathbf i}}s_j})}{\|s_j\|}
\geq \frac{(\|s_j\|-t)}{\|s_j\|}
\lambda_{t}(x;u_j)+\frac{C_{u_j}(x;t)}{\|s_j\|}.$$ Now, making $j\to\infty$, we obtain $0\geq \lambda_{t}(x;s)$, since, by the compactness of $B_{{{\frak k}}}(1)=\{s\in{{\frak k}}|\ \|s\|=1\}$, $C_{u_j}(x;t)$ is uniformly bounded. This is true for any $t>0$, so passingconsequence $G_x$ is also finite.

To prove the converse, let $x\in F$. Assume that $G_x$ is finite and that there exists $g\in G$ such that $\mu(gx)=0$. Then $G_{gx}$ is also finite and consequently so is $K_{gx}$. This implies that, for any $s\in{{\frak k}}$, ${{\curly X}}_{{{\mathbf i}}s}(gx)\neq 0$, so (lemma \[gradient\]), $\lambda(gx;s)>\mu_s(gx)=0$. This means that $gx$ is analytically stable, hence so is $x$.

It is an exercise to verify that the property on analitically stable points of $F$ of being simple (see subsection \[ssp\]) is equivalent to that of having finite stabiliser in $G$.

Using the results in this section one can also study the equation $\mu=c$, where $c\in{{\frak k}}^*$ is any central element. Indeed, $\mu-c$ is a moment map, and so one only has to consider the maximal weights $\lambda^{\mu-c}$ and


closed.

The relevance of this definition comes from this fact. While in general it is not possible to give an algebraic structure to the set of orbits $F/G$, if we restrict ourselves to the set $F^s$ of stable points, then we can give $F^s/G$ a very natural algebraic structure. (This is the content of Geometric Invariant Theory; see [@MFK].)

The main point of Kempf-Ness theory is that the condition of stability defined by Mumford coincides with the condition of analytic stability. The link between both definitions is given by the Hilbert-Mumford numerical criterion, which allows to decide whether $y\in F$ is stable.

A [**one parameter subgroups of $G$**]{} (1-PS for short) is a morphism $\alpha:{{\Bbb C}}^*\to G$.

The point $y\in F$ is stable if and only if for any 1-PS $\alpha$ anda Hermitian pairing ${\langle},{\rangle}:{{\frak g}}\times{{\frak g}}\to{{\Bbb C}}$ and a norm $|\cdot|$, both obtained by means of the auxiliar representation $\rho_a$. We will use the following $L^p$ norm on $\Omega^0(E\times_{{\operatorname{Ad}}}{{\frak g}})$: $$\|s\|_{L^p}=\left(\int_X |s(x)|^p\right)^{1/p},$$ and Sobolev norm $$\|s\|_{L^p_2}=\|s\|_{L^p}+\|d_A s\|_{L^p}
+\|\nabla d_A s\|_{L^p},$$ where $\nabla:\Omega^0(T^*X\otimes E\times_{{\operatorname{Ad}}}{{\frak g}})\to
\Omega^1(T^*X\otimes E\times_{{\operatorname{Ad}}}{{\frak g}})$ is $\nabla_{LC}\otimes d_A$, $\nabla_{LC}$ being the Levi-Civita connection. As usual, $L^p_2(E\times_{{\operatorname{Ad}}}{{\frak g}})$ will denote the completion of $\Omega^0(E\times_{{\operatorname{Ad}}}{{\frak g}})$ with respect to the norm $\|\cdot\|_{L^p_2}$.

[startsection[subsubsection]{}[3]{}[0pt]{} [-2]{}[****]{}]{} Suppose from now on that $(A,\Phi)$ is simple and $c$-stable. Our aim is to minimise $\Psi^c$ in ${{\curly G}}_G/{{\curly G}}_K$. Through the exponential map we can identify ${{\curly G}}_G/{{\curly G}}_K$ with $\Omega^0(E\times_{{\operatorname{Ad}}}{{\mathbf i}}{{\frak k}})$. Fix from now on $p>2n$ and define $${{\cal M}et^p_2}=L^p_2(E\times_{{\operatorname{Ad}}}{{\mathbf i}}{{\frak k}}).$$ The first thing to do is to restrict ourselves to the


that appear there are related to ours as follows: $\alpha_j=m_j$ for any $1\leq j\leq r-1$ and $\lambda_r=z-\sum_{j=1}^{r-1}m_j\frac{R^j}{R}$. We get, after integration (recall that the volume of $X$ has been normalized to 1): $$\int_{x\in X}
\mu(\Phi(x);-g_{\sigma,\chi}(x))=
{\operatorname{rk}}(V_0)\left(z-\sum_{j=1}^{r-1}m_j\frac{R^j}{R}\right)
+\sum_{j=1}^{r-1}m_j{\operatorname{rk}}(V_0\cap V^j).$$ Hence, the stability notion is as follows: for any filtration $0\subset V^1\subset\dots\subset V^{r-1}\subset V^r=V$ and any set of negative weights $\alpha_1,\dots,\alpha_{r-1}$ we must have $$\begin{aligned}
0 &< z\deg(V)+\sum_{j=1}^{r-1}m_j
\left(\deg(V^j)-\frac{R^j}{R}\deg(V)\right) \notag \\
  &+ \tau\left({\operatorname{rk}}(V_0)
\left(z-\sum_{j=1}^{r-1}m_j\frac{R^j}{R}\right)
+\sum_{j=1}^{r-1}m_j{\operatorname{rk}}(V_0\cap V^j)\right)-zc\ R.
\label{st1}\end{aligned}$$ (Observe that thanks to our assumption that ${\operatorname{Vol}}(X)=1$, ${\langle}{{\mathbf i}}\chi,c{\rangle}{\operatorname{Vol}}(X)=-zcR$.) If this is to be satisfied by all possible choices of $z$, then $$c=\frac{\deg(V)+\tau{\operatorname{rk}}(V_0)}{R}.$$ So, given the symplectic form $\tau\omega$, there is a unique central element $c\in{{\frak u}}(n;{{\Bbb C}})$ such that the pair can be $c$-stable. Putting the value of the central element inside (\[st1\]) we get $$\begin{aligned}
0 &<possible thanks to the $K$-equivariance of $\mu$).

Using the fact that $(A,\Phi)$ solves the equations (\[sequs\]), one can prove that (\[defo\]) is a complex, that is, $d_2\circ d_1=0$. (Just apply the chain rule to the identity expressing the gauge invariance of the set of solutions to (\[sequs\]).) The complex (\[defo\]) is called the deformation complex of ${{\cal M}}_{\sigma}(B,c)$ at $[(A,\Phi)]$. Denote $H^0_{A,\Phi}$, $H^1_{A,\Phi}$ and $H^2_{A,\Phi}$ its cohomology groups. Using again the fact that the pair $(A,\Phi)$ solves (\[sequs\]) one can prove that the complex (\[defo\]) is elliptic, so $H^0_{A,\Phi}$, $H^1_{A,\Phi}$ and $H^2_{A,\Phi}$ are finite dimensional vector spaces. We will use them to give local models of the moduli space ${{\cal M}}_{\sigma}(B,c)$.

### Index of the deformation complex {#locals}

Since the complex (\[defo\]) is elliptic, the operator $$d_1^*+d_2:C_1\to C_0\oplus C_2$$ is Fredholm,


that the complex ${{\cal C}^{\bullet}}_{\Phi}$ is the Dolbeaut complex shifted one unit to the right).

#### The index of the complex ${{\cal C}^{\bullet}}_{A,\Phi}$

We have ${\operatorname{Ind}}(d_1^*+d_2)=-{\operatorname{Ind}}({{\cal C}^{\bullet}}_A)-{\operatorname{Ind}}({{\cal C}^{\bullet}}_{\Phi})$. Summing up our results we obtain that the index $\dim H^1_{A,\Phi}-(\dim H^0_{A,\Phi}+\dim H^2_{A,\Phi})$ (complex dimensions are meant) of the operator $d_1^*+d_2$ is equal to $$-{\operatorname{Ind}}({{\cal C}^{\bullet}}_{A,\Phi})=
{\langle}c_1(\Phi^*T{{\cal F}}_v)-c_1({{{\frak g}}_E}),[X]{\rangle}+(n-\dim_{{{\Bbb R}}}{{\frak k}})(1-g).$$

Using the functoriality of the Chern classes we can write $${\langle}c_1(\Phi^*T{{\cal F}}_v),[X]{\rangle}={\langle}c_1^K(TF),B{\rangle},$$ where $c_1^K(TF)\in H^2_K(F)$ is the first equivariant Chern class of the tangent bundle $TF$, and $${\langle}c_1({{{\frak g}}_E}),[X]{\rangle}={\langle}(\pi^{F_K})^* c_1^K({{\frak g}}),B{\rangle},$$ where $c_1^K({{\frak g}})\in H^*_K(\{{\operatorname{pt}}\})$ is the first equivariant Chern class of the bundle ${{\frak g}}\to\{{\operatorname{pt}}\}$ viewed as a $K$ bundle using the adjoint action of $K$ on ${{\frak g}}$.

So the previous formula for the index of ${{\cal C}^{\bullet}}_{A,\Phi}$ may be rewritten asdimension of ${{\cal M}}_{\sigma}(c)$ is $${\langle}c^K_1(TF),B{\rangle}+(n-1)(1-g).$$

To finish the argument we deduce from the preceeding reasoning that $\Sigma_c^{{\operatorname{reg}}}(E)\subset\Sigma_c(E)$ is of the second category with respect to the $C^{\infty}$ topology. The idea is due to Taubes (see p. 36 in [@McDS1]) and goes as follows. One considers for any $K>0$ the set $\Sigma_c^{{\operatorname{reg}},K}(E)\subset\Sigma_c(E)$ of perturbations $\sigma$ such that for any $(A,\Phi)\in{{\cal M}}_{\sigma}(c)$ which satisfies $|d_A\Phi|_{C^0}\leq K$ the cohomology group $H^2_{A,\Phi}$ vanishes (that is, ${{\cal M}}_{\sigma}(c)$ is smooth at $(A,\Phi)$). We obviously have $$\Sigma_c^{{\operatorname{reg}}}(E)=\bigcap_{K>0}\Sigma_c^{{\operatorname{reg}},K}(E).$$ The set $\Sigma_c^{{\operatorname{reg}},K}(E)$ is open for any $K$. Indeed, its complementary is closed, since for any sequence $\sigma_n\in\Sigma_c(E)$ which converges to $\sigma$ and $(A_n,\Phi_n)\in{{\cal M}}_{\sigma_n}(c)$ which satisfy $|d_{A_n}\Phi_n|_{C^0}\leq K$ for any $n$, one can take a subsequence converging to $(A,\Phi)$ (using nonlinear elliptic bootstrapping, see p. 192


in [@McDS1]) and the property of being exhaustive is open. Then one uses the identity $$\Sigma_c^{{\operatorname{reg}},K}(E)=\Sigma_c(E)\cap \Sigma_c^{{\operatorname{reg}},K}(E)^l$$ and the preceeding arguments to deduce that $\Sigma_c^{{\operatorname{reg}},K}(E)$ is dense. This concludes the reasoning (see pp. 36-37 in [@McDS1] for more details on this last step).

Now, if $\sigma\in\Sigma^{{\operatorname{reg}}}_c(E)$, for any pair $(A,\Phi)\in
{\widetilde{{{\cal M}}}}_{\sigma}(c)$ the infinitesimal stabiliser $H^0_{A,\Phi}=0$ by corollary \[eslliure\] and the obstruction $H^2_{A,\Phi}=0$ as well. Hence we have a smooth Kuranish model of a neighbourhood of $[(A,\Phi)]$ in the moduli space ${{\cal M}}_{\sigma}(c)$. So we may apply corollary \[dimensio\] to compute the dimension of the moduli (recall that in our case the formula given in corollary \[dimensio\] reduces to formula (\[vir2\])). Finally, corollary \[orientacio\] implies that the moduli space ${{\cal M}}_{\sigma}(c)$ has a canonical orientation.

A similar argument proves that theelement. There exist a constant $\epsilon>0$ with the following property. Let $X={{\Bbb D}}_r\subset{{\Bbb C}}$ be the disk of radius $r>0$ with the standard metric. Consider a pair $(A,\Phi)$, where $A\in\Omega^1(X;{{\frak k}})$ is a connection one form on the trivial bundle $K\times X\to X$ and $\Phi:X\to F\times X$ is a section of the associated bundle. Suppose that the pair $(A,\Phi)$ is a $\lambda$-THC, that is, it satisfies the equations $$\left\{\begin{array}{l}
\overline{\partial}_A\Phi = 0  \\
\Lambda F_A+\lambda \mu(\Phi) = \lambda c,
\end{array}\right.
\label{eqlthc}$$ where $\lambda\in[0,1]$ is a real number. Suppose that ${{\cal YMH}}_c(A,\Phi)<\epsilon$. Then $$|d_A\Phi(0)|^2<C(1+r^{-2})(1+\|d_A\Phi\|^2_{L^2(X)}),$$ where $C$ is a constant independent of $A$, $\Phi$ and $\lambda$. \[schwartz\]

Throughout the proof $C$ will denote a constant independent of $A$, $\Phi$ and $\lambda$, and will not always be necessarily the same. Let $r'=\min(r,\sqrt{\epsilon/2\pi})$. We will prove


argument, we may assume that $\{x_1^n,\dots,x_N^n\}=\{x_1,\dots,x_N\}$ for all $n$. Let $$X_0=X\setminus\{x_1,\dots,x_N\}.$$ Gromov-Schwartz lemma \[schwartz\] implies the following. If $x\in X\setminus C_{k,n}$ then $$|d_{A_k}\Phi_k(x)|<1+2^n C,$$ where $C$ is independent of $k$ and $n$. As a consequence, for any $x\in X_0$ we have a bound for any $k$ $$|d_{A_k}\Phi_k(x)|<C(d(x,\{x_1,\dots,x_N\})),
\label{bdist}$$ where $C:{{\Bbb R}}_+\to{{\Bbb R}}_+$ is a continuous function.

From the bound on the curvature in (\[bounds\]) and lemma \[noncomf\] we deduce that for any $\epsilon>0$, there exists $r=r(\epsilon)$ such that for any $x\in X$ and $0\leq r'\leq r$ $$\|F_{\psi_{x,r}^*A}\|_{L^2({{\Bbb D}})}\leq\epsilon.$$ Taking this into account, we define $r_0=r(\delta)$, where $\delta$ is the constant in Uhlenbeck’s theorem \[Uhlenbeck\].

Cover $X$ with open balls of radius $r_0$ and take a finite cover $\{D_1,\dots,D_s\}$ such that the collection $\{D_1',\dots,D_s'\}$ of disks concentric with $\{D_1,\dots,D_s\}$ and with radius$\alpha_{k,l}\to\alpha_l$ is in $C^{\infty}$. Hence on $K$ the pair $(d+\alpha_l,\Phi_{0}^K)$ is a THC. Doing this for any $x\in X_0$ we get a smooth section $\Phi_{0}'$ defined on $X_0$ such that $(A_{0},\Phi_{0}')$ is a THC on $X_0$.

[startsection[subsubsection]{}[3]{}[0pt]{} [-2]{}[****]{}]{} Using theorem \[removal\] on removability of singularities we see that the pair $(A_{0},\Phi_{0}')$ extends to a pair $(A,\Phi_{0})$ defined on the whole $X$. Indeed, from construction we know that $A_{0}$ extends to a connection $A$ with $\|A\|_{L^p_1}\leq\infty$.

[startsection[subsubsection]{}[3]{}[0pt]{} [-2]{}[****]{}]{} The total energy ${{\cal YMH}}_{c_{0}}(A_{0},\Phi_{0})$ may be lower than ${{\cal YMH}}_{c_k}(A_k,\Phi_k)$ if bubbling occurs. Equivalently, the cohomology class ${\rho_E}_*{\Phi_0}_*[X_0]$ need not be $B$. The last step is to consider this possibility and to study the possible bubbling.

For that one does the following. Fix $x\in\{x_1,\dots,x_N\}$. We consider sequences $\{t_k\}\in{{\Bbb R}}$ and $\{z_k\}\in{{\Bbb C}}$ (on


which later certain conditions will be imposed) and the maps $\psi_k:{{\Bbb C}}\simeq T_xX\to X$ which send any $z\in{{\Bbb C}}$ to $$\psi_k(z)={\operatorname{exp}}(t_k^{-1}(z-z_k)).$$ (Note that in general $\psi_k$ may fail to be defined in the complementary of a disk in ${{\Bbb C}}$.) Suppose that $t_k\to\infty$ and that $t_k z_k^{-1}$ remains bounded. Then for any compact $K\subset{{\Bbb C}}$ and big enough $k$ (with respect to $K$) the THC $$(A_k'',\Phi_k'')=\psi_k(A_k,\Phi_k)$$ is defined on $K$. Furthermore, the energy ${{\cal YMH}}_{c_k}(A_k'',\Phi_k'')$ remains bounded. So we can apply the same reasoning as in the beginning and deduce that out of a set $y_1,\dots,y_M\subset{{\Bbb C}}$ the THCs $(A_k'',\Phi_k'')$ converge (after conveniently regauging) to a THC $(A_\infty'',\Phi_\infty'')$ defined on ${{\Bbb C}}\setminus
\{y_1,\dots,y_M\}$.

The connection $A_\infty''$ is (gauge equivalent to) the trivial one. This follows from the fact that, sinceorder to get smooth moduli spaces of simple curves we will have to restrict ourselves to curves with a fixed isotropy pair (see subsection \[comentaris\]).

Isotropy pairs
--------------

Let $s:\Sigma\to F$ be any smooth map. We define the [**isotropy pair**]{} of $s$, $(L(s),H(s))$, to be the pair of closed subgroups $L(s)\subset H(s)\subset S^1$ defined as follows $$\begin{aligned}
H(s) &:= \{\theta\in S^1|\ \theta\cdot s(\Sigma)=s(\Sigma)\} \\
L(s) &:= \{\theta\in H(s)|\ \theta|_{s(\Sigma)}={\operatorname{Id}}\}.\end{aligned}$$

Let $s:\Sigma\to F$ be a simple map, and let $g\in H(s)$ be any element. Let $\Sigma_i$ be the set of injective points of $s$, that is, $$\Sigma_i=\{x\in\Sigma|\ ds(x)\neq 0,\ \sharp s^{-1}s(x)=1\}.$$ The action of $g$ on $s(\Sigma)$ induces a holomorphic bijection $\gamma_i(g):\Sigma_i\to\Sigma_i$ which can be extended to a homeomorphism $\gamma(g):\Sigma\to\Sigma.$ Now, since the map $s$ is simple, the noninjective points $\Sigma\setminus\Sigma_i$ can only accumulate at


$H\times\Sigma_0$. So the element $c\in S^1$ found at the end of the reasoning does not belong to $H$, and hence the fact that $c\cdot s(\Sigma)=s(\Sigma)$ leads to a contradiction.

[startsection[subsubsection]{}[3]{}[0pt]{} [-2]{}[****]{}]{} The following lemma finishes the proof of the theorem.

Let $I=[0,1]$, and let $h:I^2\to I$ be a continuous map. There exists $c\in I$ such that $\sharp h^{-1}(c)=\infty$. \[tururut\]

The image $h(I^2)$ is an interval $[a,b]\subset I$. If $a=b$ we put $c=a=b$, and the proof is finished. Otherwise, let $a<c<b$. Assume that $C=h^{-1}(c)$ is a finite set of points. Let $x,y\in I^2$ such that $h(x)=a$ and $h(y)=b$. We can find a path $\gamma:I\to I^2\setminus C$ from $x$ to $y$. Now the sandwich principle implies that there exists $m\in I$ such that $h(\gamma(m))=c$, in contradiction with the definition of $C$. (In fact,on $s^*TF^L$, since they have the same symbol. Because the action of $S^1$ on $F$ is almost-free, we need only distinguish these possibilities.

[**Case 1.**]{} $L=S^1$, $\Gamma=\{1\}$. Let $F^{S^1}=F_1\cup\dots\cup F_r$ be the connected components of the fixed point set. Suppose that $A\in H_2(F_k;{{\Bbb Z}})\subset H_2(F;{{\Bbb Z}})$. Then by Riemann-Roch the moduli space has dimension $$\dim_{{\Bbb C}}{{\cal M}}_I^{S^1}(A)={\langle}c_1(TF_k),A{\rangle}+\dim_{{\Bbb C}}F_k.$$

[**Case 2.**]{} $L=\{1\}$, $\Gamma\neq\{1\}$. As we said in the preceeding section, there exist two fixed points $x_{\pm}\in{{\Bbb CP}}^1$ of the action of $\Gamma$. Since the map $s$ is $\Gamma$-equivariant, we have a natural lift of the action $\rho$ of $\Gamma$ on ${{\Bbb CP}}^1$ to $E=s^*TF\to{{\Bbb CP}}^1$. Let us write it $$\gamma:\Gamma\to{\operatorname{Aut}}(E),$$ where ${\operatorname{Aut}}(E)$ denotes the automorphisms of $E$ as vector bundle. The map $\gamma$ induces representations $\gamma_{\pm}$ of $\Gamma$ on the fibres


$E_{x_\pm}$ over $x_{\pm}$. The weights of this representation are $l$ times the weights of the representation of $S^1$ on $TF_{s(x_\pm)}$. Since the action of $S^1$ is almost-free, the weights of $S^1$ acting on $TF_{s(x_\pm)}$ belong to $\{-1,0,1\}$. Let $P_\pm$ (resp. $Z_\pm$, $N_\pm$) be the number of weights of the representation $\gamma_\pm$ which are equal to $1$ (resp. $0$, $-1$). Using the Riemann-Roch theorem and the Atiyah-Bott fixed point formula one can compute the dimension (\[ladimensio\]) in terms of $P_\pm$, $Z_\pm$, $N_\pm$ and $l$. Let us write the dimension $${\operatorname{Ind}}_{\gamma}(E)=\dim (H^0(E))^{\Gamma}-\dim (H^1(E))^{\Gamma}.$$ We will compute the dimensions ${\operatorname{Ind}}_{\gamma}(E)$ in the next two sections. The results obtained may be summarized in the following two theorems, which correspond respectively to theorems \[inds1\] and \[indtor\].

Suppose that $\Gamma=S^1$. The degree of $E$ is$S^1$-invariant.

As a final comment, we recall that the function $f=\mu({{\mathbf i}})$ is an equivariantly perfect Morse function (see for example [@Ki]). It seems interesting to pursue these ideas relating lines of steepest descent and $S^1$-invariant holomorphic curves.

Index computations: $S^1$ actions
---------------------------------

Let us identify the projective line ${{\Bbb CP}}^1$ with the sphere $S^2$ and consider the standard embedding $S^2\to{{\Bbb R}}^3$. Define the morphism $$\rho:S^1\to{\operatorname{Aut}}({{\Bbb CP}}^1)$$ by sending any $\theta\in S^1$ to the rotation of angle $\theta$ and axis $x=y=0$. Let $x_+=(0,0,1)$ and $x_-=(0,0,-1)$ be the north and south pole. These are the fixed points of the action $\rho$.

Let $E\to{{\Bbb CP}}^1$ be a holomorphic vector bundle. Suppose that there is a lift $$\alpha:S^1\to{\operatorname{Aut}}(E)$$ of the action $\rho$ (${\operatorname{Aut}}(E)$ is defined to be the automorphisms of $E$ which are linear on fibres).


lift of the classifying map ${{\curly A}}/{{\curly G}}_0\times X\to BS^1$ of the bundle ${{\Bbb E}}_J$). This induces a map $\psi:{{{\cal F}}^{{{\Bbb E}}_J}}\to F_{S^1}$, and $\rho_{{{\Bbb E}}_J}^*$ is the morphism in cohomology induced by $\psi$. In lemma \[indepframe\] in the appendix we prove that $\rho_{{{\Bbb E}}_J}^*$ is independent of the choice of $\phi$. Let then $\mu_i:H^*_{S^1}(F)\to H^*({{\curly B}}_0)$, $i=0,2$, be the maps defined as $$\mu_2(\delta):={\operatorname{ev}}_J^*\rho_{{{\Bbb E}}_J}^*\delta/[X]\qquad\mbox{ and }
\qquad \mu_0(\delta):={\operatorname{ev}}_J^*\rho_{{{\Bbb E}}_J}^*\delta/[{\operatorname{pt}}],$$ where $\delta\in H^*_{S^1}(F)$, and $[X]\in H_2(X)$ (resp. $[{\operatorname{pt}}]\in H_0(X)$) is the fundamental class of $X$ (resp. the class of a point). Let finally $$\nu:H^*({{\curly A}}/{{\curly G}}_0)\to H^*({{\curly B}}_0)$$ be the map induced by the projection ${{\curly B}}_0\to{{\curly A}}/{{\curly G}}_0$.

Let us take a homology class $B\in H_2(F_{S^1})$ such that ${\pi_F}_*B=\eta(E)$, where $\pi_F:F_{S^1}\to BS^1$ is the projection and where $\eta$ isclasses which belong to the image of the map $\pi_2(F)\to H_2(F;{{\Bbb Z}})$).

When there is no bubbling the extended moduli spaces is automatically compact and hence there is fundamental class in the homology of the moduli spaces ${{\cal N}}$, ${{\cal M}}$. Therefore, we can define the invariants as in the introduction.

#### Second case

If we allow bubbling to occur, we need to control the strata added to the moduli spaces ${{\cal N}}$ and ${{\cal M}}$ in theorem \[compactificacio\]. The following three conditions will be assumed in the sequel, and they will be used when proving that these strata have codimension greater than two.

$(F,I)$ has to be [**positive**]{}. This means that for any $I$-holomorphic map $s:{{\Bbb CP}}^1\to F$ the pullback $s^*TF$ has positive degree $$\deg(s^*TF)>0.$$ \[cond1\]

This condition is fulfilled for example


Then we set the horizontal space at $[A]$ to be $$(T_{[A]}{{\curly A}}/{{\curly G}}_0)_h:={\operatorname{Ker}}d_1^*\cap ({\operatorname{Ker}}d_2)^{\bot},$$ where $d_2:\Omega^1({{\mathbf i}}{{\Bbb R}})\to\Omega^2({{\mathbf i}}{{\Bbb R}})$ is the exterior derivation. Now, using parallel transport along lines going through $-{{\mathbf i}}2\pi d\omega_X/{\operatorname{Vol}}(X)\in\Omega^2({{\mathbf i}}{{\Bbb R}})$ we get the desired retraction $$R:{{\curly A}}/{{\curly G}}_0\to{\operatorname{Jac}}_d(X).$$

Let ${{\curly G}}^{{{\Bbb C}}}={\operatorname{Map}}(X,{{\Bbb C}}^*)$. This is the complexification of ${{\curly G}}$ and it acts on ${{\curly A}}$ holomorphically (see \[setting\]). Each ${{\curly G}}^{{{\Bbb C}}}$ orbit in ${{\curly A}}$ contains exactly one ${{\curly G}}$ orbit giving an element in ${\operatorname{Jac}}_d(X)$ (this is the most simple case of Hitchin-Kobayashi correspondence).

The map $R$ factors through the projection ${{\curly A}}/{{\curly G}}_0\to{{\curly A}}/{{\curly G}}^{{{\Bbb C}}}$.

Suppose for simplicity that $d=0$. The vector field we have used to construct the retraction is the gradient of the Yang–Mills functional $YM(A)=\|F_A\|_{L^2}^2$. Now,depend on the chosen pseudocycle representative of $\beta$) and only depends on the bordism class of $f$.

This is a consequence of the preceeding lemma together with remark 7.1.1 and lemma 7.1.5 in [@McDS1].

For convenience, we extend the map $\Psi_f$ by zero to the rest of the homology of $M$.

### Definitions of the Hamiltonian Gromov-Witten invariants

#### The invariant $\Phi$ {#the-invariant-phi}

Let $p\in{{\Bbb N}}$ and let $c_{p+q}:(F^{p+q})_{S^1}=ES^1\times_{S^1}(F^{p+q})
\to (F_{S^1})^{p+q}=(ES^1\times_{S^1}F)^{p+q}$ be the natural map (we consider on $F^{p+q}$ the diagonal action of $S^1$). Given cohomology classes $\alpha_1,\dots,\alpha_p,\beta_1,\dots,\beta_q\in H^*_{S^1}(F)$ we will write $$c(\alpha_1,\dots,\alpha_p,\beta_1,\dots,\beta_q)=
c_{p+q}^*(\alpha_1\otimes\dots\otimes\alpha_p\otimes\beta_1\otimes
\dots\otimes\beta_q).$$ Let us consider the map $${{\overline}{{\operatorname{ev}}}}^{p,q}_J:{{\curly A}}\times{{\curly S}}^*\times X^p
\to {{\curly A}}\times E\times_{S^1}(F^{p+q})$$ which sends $(A,\Phi,(x_1,\dots,x_p))$ to $(A,\Phi(x_1),\dots,\Phi(x_p),\Phi(y_1),\dots,\Phi(y_q))$. This map is ${{\curly G}}_0$ equivariant, so it descends to give a map $${\operatorname{ev}}^{p,q}_J:{{\curly B}}_0\times X^p\to{{{\cal F}}^{p+q,{{\Bbb E}}_J}},$$ where ${{{\cal F}}^{p+q,{{\Bbb E}}_J}}={{\Bbb E}}_J\times_{S^1}(F^{p+q})$. On


${{\overline}{\phi}}\in H^0(V)$ are given by $H^0(\phi^*{{\curly O}}_{{{\Bbb P}}(V)}(-1))$. Now, since for any line bundle $L\to X$ we have ${{\curly O}}_{{{\Bbb P}}(V\otimes L)}(-1)={{\curly O}}_{{{\Bbb P}}(V)}(-1)\otimes \pi^*L$, and since ${{\Bbb P}}(V\otimes L)={{\Bbb P}}(V)$ canonically, by taking $L=\phi^*{{\curly O}}_{{{\Bbb P}}(V)}(1)$ we can lift $\phi$ to a nonzero section ${{\overline}{\phi}}\in H^0(V\otimes L)=H^0(L^E\otimes L\oplus L)$, unique up to ${{\Bbb C}}^*$ (indeed, then we have $\phi^*{{\curly O}}_{{{\Bbb P}}(V\otimes L)}(-1)={{\curly O}}$). Let ${{\overline}{\phi}}=({{\overline}{\phi}}_0,{{\overline}{\phi}}_1)$ in the splitting $H^0(L^E\otimes L\oplus L)=H^0(L^E\otimes L)\oplus H^0(L)$. Then ${{\overline}{\phi}}_0$ and ${{\overline}{\phi}}_1$ have no common zeros (if they had then the bundle $\phi^*{{\curly O}}_{{{\Bbb P}}(V\otimes L)}(-1)$ would be of positive degree; but by our choice of $L$ it has degree zero).

Of course, the converse is also true: since ${{\curly O}}$ is the unique line bundle of degree $0$ with a nonzero section,Math.*]{} [**5**]{} (1994) 1–52.

O. Garc[í]{}a–Prada, Seiberg-Witten invariants and vortex equations, [*Les Houches school on quantum symmetries*]{}, eds. A. Connes, K. Gawȩndzki, J. Zinn-Justin, (1995) 885–934.

D. Gilbarg, N.S. Trudinger, [*Elliptic partial differential equations of second order*]{}, 2nd. edition, Springer, Berlin.

M. Gromov, Pseudo-holomorphic curves in symplectic manifolds, [*Invent. Math.*]{} [**82**]{} (1985) 307–347.

V. Guillemin, S. Sternberg, Geometric Quantization and Multiplicities of Group Representations, [*Invent. Math.*]{} [**67**]{} (1982) 515–538.

N.J. Hitchin, The self-duality equations on a Riemann surface, [*Proc. Lond. Math. Soc.*]{} [**55**]{} 59–126.

A. Jaffe, C.H. Taubes, [*Vortices and Monopoles*]{}, Progress in Physics 2, Birkhauser (1980), Boston.

G.R. Kempf, L.A. Ness, The length of vectors in representation spaces, [*Algebraic Geometry*]{}, Proc., Copenhagen 1978 (K. Lonsted, ed.), LNM 732, Springer–Verlag.

F.C. Kirwan, [*Cohomology of quotients in symplectic and algebraic geometry*]{}, Math. Notes, Princeton University Press 1984.

S.


coincide, [math.AG/9804108]{}.

C.T. Simpson, Constructing variations of Hodge structure using Yang–Mills theory and applications to uniformisation, [*J. Amer. Math. Soc.*]{} [**1**]{} (1988) 867–918.

J.-C. Sikorav, Some properties of holomorphic curves in almost complex manifolds, in [*Holomorphic curves in symplectic geometry*]{}, Ed. by M. Audin and J. Lafontaine, pp. 165-189, Birkhaeuser, 1994.

R. Sjamaar, Holomorphic slices, symplectic reduction and multiplicities of representations, [*Ann. Math. II*]{}, [**141**]{} No.1 (1995) 87–129.

S. Smale, An infinite dimensional version of Sard’s theorem, [*Am. J. Math.*]{} [**87**]{} (1973) 213–221.

M. Thaddeus, Stable pairs, linear systems and the Verlinde formula, [*Invent. Math.*]{} [**117**]{} (1994) 317–353.

K. Uhlenbeck, Connections with $L^p$ bounds on curvature, [*Comm. Math. Phys.*]{} [**83**]{} (1982) 31–42.

K. Uhlenbeck, S.T. Yau, On the existence of Hermitian Yang-Mills connections in stable vector bundles, [*Comm. Pure Appl. Math.*]{} [**39**]{} (1986) 257–239, [**42**]{}703–707.

E. Witten, Two dimensional gravity and intersection theory on moduli space, [*Surveys in Diff. Geom.*]{} [**1**]{} (1991), 243-310.

J.G. Wolfson, Gromov’s compactness of pseudo-holomorphic curves and symplectic geometry, [*J. Diff. Geom.*]{} [**28**]{} (1988) 383–405.

[^1]: The prefix [*pseudo*]{} refers to the fact that the complex structure defined by $A$ need not be integrable, similarly to what happens in the theory of (pseudo)holomorphic curves. In this thesis, however, we will use the word [*holomorphic*]{} regardless the integrability of the complex structure.

[^2]: The results of this subsection were first proved by Luis [Á]{}lvarez C[ó]{}nsul [@Al; @AlGP].

[^3]: We recall that a set of Baire of the second category is by definition any countable intersection of dense open subsets of a topological space.

[^4]: Recall that this means that they can be covered by countably


her report card earlier this week. There were plenty of B's and C's, with a couple of D+'s sprinkled in to remind me that I am not spending anywhere near enough time helping her with Algebra and Physics.

Apparently college may be a long shot for several of us. "Danger, Will Robinson!" We're going to need a plan B.

For his part, David has spent the week bailing water out of his own boat, and when he wasn't in late meetings or staying late to finish projects, he was running to the stake center to go to other meetings or hang lights for a youth dance. (There happens to be a youth speed-dating activity that he is helping to put on this Saturday. I am thinking of going just sowork to all!

One of my favorite aspects of the path was listening to the rushing waters of Boulder Creek flow beside you as you walk. Combined with the new fallen snow and views of the Rockies, the whole scene was quite breathtaking. Just another reason, Colorado is one of my favorite states.

Congrats to all the citizens of Boulder for having such a stellar recreational and commuting amenity as part of the city’s greenway system. I cannot wait to return to Boulder very soon to visit my son in grad school and to hike/bike additional segments of the path during other seasons of the year.


is doing is what should be under discussion.PeaceKMA

I see Eed is still defending the use of racial slurs.

Yet another example of the ridiculous right who now stoops to defending the use of these racial slurs.

<quoted text>You remain, as always, disgusting and misinformed. One must ask herself which came first, vile, hate-filled Greasy Obnoxious Pricks or Faux News. There's probably only one that has deep enough pockets to pay damages for what they've done to the nation.

That would be Obama and his disgusting, misinformed, vile, hate-filled Greasy Obnoxious Obamabots or MSNBC Non-News.

<quoted text>Still slinging slurs.Most people believe that people that resort to using racial slurs are below average intelligence & generally uneducated & uninformed.So we go from slurs to the "Obama is a Muslim" lie to the "apology tour"Minister Sue Ellery to announce its official name.

"Bob grew up across the train tracks right there, he went to West Leederville Primary and he went to Perth Mod each day to go to high school," Mr McGowan said.

"So obviously building a brand-new inner-city school where Bob's life and formative years were and naming it after Bob Hawke I think is entirely appropriate."

Australia's 23rd prime minister and Labor Party legend died on May 16, aged 89, at his home in Sydney.

Bob Hawke moved into this home in West Leederville in 1939 when he was just nine years old, after moving to Perth with his parents. ( ABC News: Madeline Palmer )

Mr Hawke was the longest-serving Labor Prime Minister, holding office from 1983 to 1991.

In 1939, at the age of


on-demand in a deeply personalized experience optimized for the contemporary, always-connected television fan."

As network executives grow accustomed to establishing deals for streaming television services, Apple may be able to revisit its television plans. Apple has been working on some kind of subscription TV service for several years, but executives have not been able to establish deals with content owners. Apple's latest streaming plans reportedly fell apart because media companies demanded more money than Apple wanted to charge for its TV service and were reluctant to unbundle channels.himself, someone who has grown a beard (i.e. gotten older, from boy to man) since Hamlet last saw him. Subverting the line at once confuses Hamlet's age further and makes us think of the line in more metaphorical terms. I become less interested in the fact the First Player is newly bearded, but more in Hamlet's assertion that the Player would "top" him in some way. He doesn't "beard" him by being more hirsute, but rather by being more emotionally available, and by doing more to reveal the King's treachery with a single scene than Hamlet has managed to do since the start of the play.

Hamlet next addresses the "lady" of the group, and in line with the production's Medievalism, "she" is played by a boy, a boy


from the explosive Hamlet.As long as we're making comparisons, Heston's Player definitely has more gravitas, while James' emotions are more overt and desperate, bigger and thus more theatrical (as opposed to cinematic). The speech ends with the Player's hands on his face, but when Hamlet takes them off, he is all smiles. And yet, he sniffles through the rest of the scene. The faked "trappings" of grief still required a certain measure of truth. Where James shines as the Player, however, is in how he milks the awkwardness of Hamlet's outbursts against Polonius - slightly amused, but still respectful. He takes sides in the most subtle way possible, an example Polonius might have been smart to follow, but his love for his own wit prevents him from evera torch that illuminates the Prince. And when the players come in (with many torches), the room, which might as well have been the dark of night, fills with light. Polonius' arrival and subsequent announcement of the players gives Hamlet the glimmer of an idea, and that arrival a new sense of purpose, all of it expressed with lighting as much as acting. Polonius reads from a parchment - Felix Aylmer is as amusing as usual - and doesn't know what to make of "He that plays the king shall be welcome."

In the absence of Rosencrantz & Guildenstern, there is a certain irony to Polonius being the bearer of news that will undo him and his corrupt king.From the Players' entrance, Hamlet enters a manic state, delivering lines


--TEST--
Test popen() and pclose function: basic functionality

--SKIPIF--
<?php
if(substr(PHP_OS, 0, 3) != 'WIN' )
  die("skip Not Valid for Linux");
?>

--FILE--
<?php
/*
 *  Prototype: resource popen ( string command, string mode )
 *  Description: Opens process file pointer.

 *  Prototype: int pclose ( resource handle );
 *  Description: Closes process file pointer.
 */

echo "*** Testing popen(): reading from the pipe ***\n";

$file_path = dirname(__FILE__);

$string = "Sample String";
$file_handle = popen(" echo $string", "r");
fpassthru($file_handle);
pclose($file_handle);

echo "*** Testing popen(): writing to the pipe ***\n";
$arr = array("ggg", "ddd", "aaa", "sss");
// popen("sort", "w") fails if variables_order="GPCS"
// this is set in the default INI file
// it doesn't seem to be changeable in the --INI-- section
//	also, doing: ini_set('variables_order', ''); doesn't work!
//
// the only solution is to either put the absolute path here, or
// remove variables_order= from PHP.iniyou gift. Go ahead and hang it on your wall, and when you’re ready, you can start penciling in as many bicycle adventures as you see fit.

When you join today, we’ll also send you a $10 gift certificate to our Cyclosource store. Feel free to use it on bicycle maps and/or touring gear. Also keep in mind that as a member, you’ll always get up to 30% off Adventure Cycling Route maps, as well as a number of discounts from our affiliate partners. When used wisely, these discounts can pay for the membership and then some!

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Inc, there have been times of severe chills. In fact, but typically only when the benefits outweigh the risks.

ClinVet International Pty Ltd is a contract research facility providing professional research services to the animal health industry.

Blåsor på tungspetsen - baby oil ica. Inläggsnavigering

You need the latest version of Adobe Flash Player to view this video. Click here to download. You oil seeing ica message either because your Flash Player is outdated or because your browser does baby support HTML5 player. Gift of the year! Selena Gomez seex tape released!

WAC Lighting HR-3LED-H18D1-ICA Tesla 3-Inch New Construction Airtight Housing LED - - enen.aleprizz.se Food safety incidents in Poisonous Jinhua ham. In , several small producers of Jinhua hams (from Jinhua, Zhejiang) operated out of season and produced hams during warmerthe former needs to be done by operators and is quite time-consuming. Although there are studies [@ticket1; @ticket2; @ticket3; @workflow1; @workflow2; @workflow3] that suggest recovery actions for operators, most rely on trouble tickets, which do not always include sufficient information to precisely determine recovery commands. As such, we still cannot free operators from the task of recovering from failures in spite of much research on the topic.

Towards automatic recovery, we are aiming toward developing a method of automatically generating the recovery commands directly from logs. If the automatic generation of recovery commands is successful, the whole recovery process can be accomplished automatically just by executing the commands with RBA tools. Since logs and recovery commands usually accumulate in the equipment, we take an approach in which we use such


reliability over the threshold, which is denoted with the green broken line in Figure \[graph\], should be one. As far as this experiment is concerned, we conclude that we should set the threshold of reliability to at least 0.86.

![Number of successes/failures (red solid line/dotted blue line) and ratio of successes (broken green line) under given reliability. Under condition that threshold of reliability is above 0.86 (vertical black dotted line), ratio of successes becomes one, which means all estimated recovery commands satisfying this condition could be executed safely.[]{data-label="graph"}](graph_gnu.pdf)

Related work {#related_work}
============

Trouble-ticket-based method
---------------------------

To the best our knowledge, this is the first paper that addresses the estimation of recovery commands without manually predefining recovery actions. Most previous research on failure recovery relied on trouble tickets, which are reports of failure operation written indevelopment of US foreign and defense policy. He is best remembered of the Strategic Defense Initiative (SDI or "Star Wars"). The Iran-Contra affair involved running arms to Iran in order to get money to support the Contras in Nicaragua. mcfarlane and his successor, Admiral John Poindexter, were heavily involved in both the Iran and Nicaragua sides of the scandal. mcfarlane was serving as an assistant to Secretary of State Alexander Haig, in 1981, when he authored Taking the War ...

Excerpt
...Contrary to what has been widely reported and thought, the late Alexander Haig made precisely the right move in asserting his authority after the attempted assassination against President Reagan on March 30, 1981, according to a former national security ...
Source Info
American Spectator
http://spectator.org/blog/2010/02/24/al-haig-acted-properly-after-1

China mourns the death of General Alexander Haig.


});

  it('should run a --version command', function() {
    doc_opts.argv = '--version';
    return cli.run(doc_opts, run_options).then((code) => {
      h.expect(code).to.eql(0);
      h.expect(outputs[0]).to.match(version_regex);
    });
  });
});
Q:

Integrate Jekyll to run into WebStorm on Windows

Is it possible to run Jekyll as External Tool into WebStorm? (same for RubyMine, IntelliJ IDEA, ...)
The most obvious thing is to run the jekyll.bat file:

...but this doesn't work.

A:

I haven't found any solution so after some trial+error I discover this working configuration:

In this example I am using: RubyInstaller + gem install jekyll.
If you prefer using straight Ruby+DevKit then Program and Parameters paths must be changed according.


It is typically performed by wedging a forearm, especially a bony part of it, into the Achilles tendon, while leveraging the foot and the leg over the forearm serving as a fulcrum. This causes severe pressure on the Achilles tendon, and often also results in an ankle lock, since the ankle is being used as a point of leverage. Similarly, some ankle locks also cause a compression lock on the Achilles tendon, and hence the term "Achilles lock" is often also used to describe such ankle locks.

Biceps slicer
A biceps slicer (also called a biceps lock or biceps crusher) is a compression lock that involves pressing the biceps into the humerus. An effective biceps slicer can be applied by putting an arm or leg as a fulcrum on theliked to stack in towers like champagne flutes) were clearly long gone. For a moment, Quinn stood at the table, contemplating whether she would stoop so low as to swig straight from the bottle of pinot grigio only inches from her fingertips. But before she could take the plunge, Quinn felt someone touch her elbow.

She turned from the spread before her, thirsty and irritated and vulnerable, her composure thin. It was the worst possible state for her to be in when she spun around to find Bennet Van Eps standing before her. Of course, she knew that he was coming, but his proximity was still a shock. Quinn hadn't seen him in five years, but he hadn't changed a bit. Same quirky smile, one cheek creased as if


ashes of Lorelei Barnes. "I have something for you."

"I believe that you do," Tiffany said quietly. "I'm actually here because—"

There was a quick patter of light footsteps. A little gasp. "Mom?"

Tiffany's face crumpled and she fell to her knees, arms out for Lucy as her child raced across the space between them. When the girl threw herself against Tiffany, all doubt about her lineage was erased.

"Oh, baby." Tiffany buried her face in Lucy's hair and pressed her close, hands tugging at her arms, her dress, the blunt ends of her hair. It was as if she was drinking her in, memorizing each line and curve with the urgent stroke of her fingers—a blind woman fumbling for sight. "Oh, honey," she cried. "I've missed you so much."

Lucy pushed backan insignificant amount of time. What now? she thought. But the future was determinedly opaque.

When he came, Bennet pulled a chair up to their circle and sat on the very edge of it so that he could rest his elbows on his knees and lean close. The set of his mouth was serious and he clutched a small black backpack in his hands as if it contained something precious. Liz wanted to shake him, to rip the bag from his hands so she could upend it on the floor and see what was inside. But she crossed her arms over her chest and forced herself to remain still, silent.

"Donovan Richter is dead," Bennet said without preamble. "There was a car accident about a mile down the road from


a Hawaii resort, where room prices start from $899, during a partial government shutdown sparked by quibbling over budget bills and funding for Trump’s long-desired border wall.

Also on rt.com Nancy Pelosi fights ‘Trump Shutdown’ with #Resistance luxury vacation in Hawaii

With the Democrats having won back control of the House of Representatives in the November midterms, Pelosi will likely once again become Speaker of the House when the new congress officially convenes on Thursday — despite some rumblings that younger, more progressive members of the party wanted to mount an effort to oust her.

Like this story? Share it with a friend!all four target genes (**Figure [4](#F4){ref-type="fig"}**). Notably, cell numbers estimated using *gapA* transcripts as the target were significantly lower than those estimated for *rfbE* (Steel-Dwass, *P* = 0.0019) and *eae* (Steel-Dwass, *P* = 0.0002). The same trends were also found for *E. coli* ATCC 700728 inactivated with 70% isopropanol-inactivated and incubated on petri dishes (data not shown) and heat killed cells in suspension (**Supplementary Figure [S3](#SM1){ref-type="supplementary-material"}**).

![**Detection of isopropanol-treated dead *E. coli* O157:H7 on plants by RT-qPCR.** Cell numbers were estimated by RT-qPCR targeting *gapA* (♢), *eae* (□), *lpfA* (△), and *rfbE* (○) transcripts compared to standard curves constructed using cDNA from known quantities of viable, exponential-phase *E. coli* ATCC 700728 cells. Each point represents the mean ± standard deviation of three independent replicates.](fmicb-07-00223-g004){#F4}

Because cell death might result in


• Momentum is your friend—and so are slight declines. • Always look ahead.Your bike goes where your eyes go. • Sit upright. Rotate your pelvis back so you're not falling toward the handlebar. • Ease into it. Resist the urge to push off the bar into the upright position.

Why was there never a sequel to Breaking Away?
Because no one—not even Steve Tesich himself, who won a Best Original Screenplay Oscar for the script—could ever, ever, ever beat the first one. If someone tried, we'd all end up asking for a refund. (Refund?!!) Of note: A year after the 1979 film's debut, Tesich and director Peter Yates teamed up for a TV series that served as a prequel and was cancelled after seven episodes; you can catch it on(1924 and '25) in revenge for some stolen grapes. We can say with authority that while he was out riding on June 3, 1927, the great champion was done in by Nona, Decima, and Morta Parcae.

A Part of Hearst Digital Media
Bicycling participates in various affiliate marketing programs, which means we may get paid commissions on editorially chosen products purchased through our links to retailer sites.


Lexicomp Lexi-Interat Online (Lexi-Comp, Inc., Hudson, USA) software which categorizes potential DDIs according to clinical significance in five types (A, B, C, D and X). Categories C, D and X are of clinical concern and always require medical attention (therapy monitoring, therapy modification or avoiding combination). We found that 80.9% of patients had at least one potential category C interaction while there were no D and X interactions. Most frequently encountered potential DDI (n = 176) included antidiabetic drugs and thiazide or thiazide like diuretics. Patients with diabetes are exposed to a large number of potential clinically significant DDIs that may require appropriate monitoring. Using databases of DDIs could be helpful in reducing the risk of potential clinically significant DDIs.Antichrist and 666? Will things get worse? What is the solution? Dr. Thiel answers these questions and more. A written article of related interest is titled “Totalitarian controls getting closer–The Guardian pushing internet censorship.”

Internet Control, Famine of the Word, and 666 On October 1, 2016, the USA officially relinquished control over the Internet Corporation for Assigned Names and Numbers (ICANN), despite objections from certain political leaders and former military officials. Might this lead to more censorship, imposition on non-biblical ‘community standards,’ and loss of first amendment rights? Could this transfer of control have any prophetic ramifications? Will the internet be a factor in the ‘short work’ of Romans 9:28 and the coming ‘famine of the word’ that the Prophet Amos warned about? Will internet control be something that


January 17, 2014

4/4 married while I was playing in the AHL) or that she's dumb (she's an Ivy League and graduate school grad), just know I'm embarrassed — Ben Scrivens (@ben_scrivens) January 17, 2014

5/4 I am to say that you are an Edmontonian. Way to make my family feel welcome. — Ben Scrivens (@ben_scrivens) January 17, 2014

Ben Scrivens is a native of Spruce Grove, a neighbouring community of Edmonton.

Vasquez-Peddie responded to the Oilers goalie Thursday night on Twitter.

Hi @scrivens_30. It was a tongue-in-cheek blog. Not an attack. The weather in Canada kind of sucks compared to L.A. — Tony Vasquez-Peddie (@AVPreports) January 17, 2014

Following the exchange, many Twitter users came to Scrivens’ defence.

#LeafsTwitterNation supports your ripping into @AVPreports for tasteless comments about Wife,Jenny. Welcome home Ben @scrivens_30 #SEAofBLUEHere are answers to our most commonly asked questions. If you cannot find an answer here, send us an email.

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John Du Prez (born Trevor Jones; 14 December 1946 in Sheffield, England) is a musician, conductor, and composer. Du Prez was a member of the 1980s multi-hit Salsa-driven pop band Modern Romance and has since written several film scores including Oxford Blues (1984), Once Bitten, Teenage Mutant Ninja Turtles (1990), and the final Carry On film,  Carry On Columbus (1992). He contributed to The Wild (2006) soundtrack.

Early life and education
Du Prez originally hails from Sheffield, England. He received his MA (Oxon), B.Mus., ARCM, and was a Trevelyan Scholar at Christ Church, Oxford. In 1976 he joined the staff of the London University's Music Department before becoming a full-time composer. He would then begin a 30-year working relationship with Eric Idle.

Career
Du Prez has often worked with


recording and production standpoint, the bulk of Modern Romance's music was produced by Tony Visconti; they were signed by the record labels WEA and Ronco. Du Prez and Modern Romance performed their hit single, High Life, on the Russell Harty Television Show in 1983, with Cleo Rocos as backing vocalist.

In 2006 Du Prez featured on the Warner CD Modern Romance: The Platinum Collection, a compilation featuring the best of Modern Romance.

Selected filmography (composer)

Monty Python's The Meaning of Life (1983)
A long time friend of Eric Idle, Du Prez composed the score for Monty Python's The Meaning of Life in 1983, while still a member of Modern Romance (band). The film stars John Cleese, Terry Gilliam, Graham Chapman, Idle, and Michael Palin. It is directed by - and also featurescharacters. We’ve seen them together but we’ve also seen them apart. We understand why it is their relationship has dissolved. So when they meet again after all that time, it really feels like something has been lost, but we understand why it had to happen and that’s sad too. They’ve moved on and the love that once brought them close together now keeps them apart. She asks him if he wants to go outside and meet their daughter, but he knows he can’t, because that’s a part of their lives that has ended. There’s some things in life that can only go one way and once it’s gone, there’s nothing to back to.

Compare that to the ending of La La Land. They kind of break up but then


me care about something being lost if I don’t understand how it is we got where we are. It just leads to me awkwards wondering why they aren’t still together.

All of this really narrows down the real issue that I have with this film. It’s not the romanticism, because we sure as hell need that sometimes, and it’s not the escapism because we sure as hell need that right now. It’s the fact that I don’t really care about the characters and what it is they’re doing. Who are these people other than spunky youths who want to follow their dreams? It makes sense to me that a film about nostalgia would end with the two characters being nostalgic for each other and the past they had together.be r(4). Let b be (-93)/(-2)*16/j. Solve -28*w = -b*w - 15 for w.
-5
Let z(y) = -2*y**3 - 5*y**2 - 2*y - 11. Suppose -38*f = -37*f + 3. Let v be z(f). Solve -3*g = v - 10 for g.
2
Suppose 0 = 3*h - 0*h - 6. Let w be 0 + (-6 - -23) + 11/(-1). Solve 4*t + h*t = w for t.
1
Suppose -11*w - 15989 = -15989. Solve 19*x + 60 + 35 = w for x.
-5
Let v = 8715 - 8565. Solve -v = 157*m - 132*m for m.
-6
Suppose c + 7*h - 12 = 6*h, -2*h - 8 = 0. Suppose 6 = -c*d + 70. Solve 7*j = 5*j - d for j.
-2
Let f be (-13 - -1)/(3/6). Let b =


the United States even before the notice to report to the police, which he claimed was the triggering event; and 5) Camaj's and Dhima's testimony of the repressiveness of the Albanian government is at odds with the U.S. State Department Profile of Asylum Claims and Country Conditions, released in May 2001, which described the 1997 elections as "adequately reflect[ing] the will of the people" and stated that "[b]oth major political parties trace their roots to the communist regime and repudiate it thoroughly."

13
The IJ also found the documentation submitted by Dhima to be insufficient to salvage his credibility. The IJ questioned the certificate that purportedly came from the chairman of the Democratic Party because the certificate consisted of "unsubstantiated rhetoric, unsupported by any evidence of how the maker cameYou own Falzer's Tool Coating Company, a high-tech firm specializing in the coating of cutting tools (e., drill bits, cutting blades) to provide...

You own Falzer’s Tool Coating Company, a high-tech firm specializing in the coating of cutting tools (e.g., drill bits, cutting blades) to provide longer life before re-sharpening is needed. You are concerned that the competition continues to develop new coating methods and new applications of coating in different industries. You want to create a work environment where employees offer more new product ideas, and suggest new industries where these ideas might be applied. What type of compensation plan will you recommend? What are some of the problems you need to be aware of?


its published data, which should not be
exceeded under the worst probable conditions.
These values are chosen by the device manufacturer to provide
acceptable serviceability of the device, taking no responsibility for
equipment variations, environmental variations, and the effects of
changes in operating conditions due to variations in the
characteristics of the device under consideration and of all other
electronic devices in the equipment.”

Here is where it gets really boring, but I threw this up for comparison
Analog says that their absolute maximum ratings won't kill the part instantly but it will degrade over time:

Stresses above those listed under Absolute Maximum Ratings may cause
permanent damage to the device. This is a stress rating only;
functional operation of the device at these or any other conditions
above those indicated in the operational section of this specification
is not implied. Exposurebeen tested, and there are programmes planned in Scotland and Wales.

Initial limiting testing of firefighters and control room staff has already begun at Glasgow Airport, according to the FBU.

Of the 3,000 fire and rescue staff in isolation, 2,600 are firefighters or work in control rooms.

In Bedfordshire, 12% of staff are off work - the highest proportion in the country.

In London, 10% are self-isolating, which is equal to 472 firefighters or controllers.

Meanwhile, West Yorkshire is short of nearly 16% of its control room staff.


1. Introduction {#sec1}
===============

Under physiological conditions the oral cavity accommodates a variety of different bacteria living in an ecological system \[[@B1]--[@B4]\]. However, disturbances or changes in conditions can induce shifts of benign microflora towards pathologies such as caries.

Microorganisms in the oral cavity are organized as a biofilm \[[@B5]\]. Dental biofilm, called plaque, is a histologically structured, dense, felted mass of bacteria in their self-produced extracellular polymeric matrix \[[@B6], [@B7]\].

The ability to form this matrix modifies the local environment, which in turn enables life even for microorganisms which are not usually viable within the oral cavity. Such modifications involve pH-value, redox potential, and possible gene transfer \[[@B8], [@B9]\]. A gradient of decreasing bacterial metabolism and increasing doubling rate is created from the top of the biofilm to the bottom. Thisgradient plays a key role in antibiotic resistance and presents a selective advantage for biofilm microorganisms \[[@B6], [@B7], [@B10]\].

Undisturbed bacterial colonization and growth within the oral cavity lead to biofilm induced caries, gingivitis, and periodontitis \[[@B11]\].*Streptococcus mutans* is the main etiological agent of dental caries caused by dental biofilm. It adheres to a proteinous layer, the acquired pellicle, already present on the enamel. The pellicle consists of preadsorbed salivary proteins, lipids, and glycolipids \[[@B12], [@B13]\].

Since initial adhesion is the first step in biofilm development, research has focused on strategies to prevent initial microbial colonization and subsequently reduce or inhibit biofilm formation. Avoiding initial colonization is merely impossible, therefore it is necessary to develop other methods to prevent caries. Secondary caries is a major problem in restoration dentistry which


the negative control (*P* \< 0.05). However, pairwise comparisons yielded no statistically significant differences among the materials ([Figure 3](#fig3){ref-type="fig"}). In [Figure 4](#fig4){ref-type="fig"}, exemplary epifluorescence microscopy images of adherent bacteria on a glass ionomer material (A) and on the negative control (B) are shown. On the glass ionomer material, more dead cells (red) could be observed, whereas on bovine enamel, more viable bacteria could be counted (green cells).

4. Discussion {#sec4}
=============

Today secondary caries remains one of the principal reasons for the limited longevity of indirect restoration \[[@B23]\], a serious problem which causes additional costs and is unpleasant for the patient.

Luting cements with antimicrobial potential may protect teeth from secondary caries. Modern glass ionomer cements are suggested to obtain antimicrobial efficacy. Additionally, they release fluoride ions, which help to remineralize initialseems to be the least effective. This tendency could be due to the different additives of material A (Zn-tartrate) and C (silver-containing glass) compared to glass ionomers without additives (material B). Shashibhushan et al. \[[@B29]\] reported that zinc ions released by glass ionomer cements can interfere with substrate transport into the cell and so block important enzyme functions. Yet the most obvious explanation for the observed antimicrobial effects of the cement materials could be the release of fluoride as previous authors have suggested \[[@B17]--[@B19]\]. Koo et al. \[[@B27]\] indicate that fluoride ions are mostly bacteriostatic. However, under certain circumstances such as a high concentration, fluoride ions can also generate a bactericidal effect. Furthermore, other ingredients should also be taken into consideration as pointed out by Geurtsen \[[@B28]\].

The determination


Many New York City public schools lack dedicated laboratories and the equipment needed for students to perform hands-on experiments in the life sciences. Not surprisingly, most of these schools are located in sections of the City in which most of the students are minorities underrepresented in the life and health sciences. To address the needs of these students we have, with the support of a Phase I SEPA grant, developed and pilot tested two New York City science performance standards-specific portable laboratory kits, Microlab II and Molecules and Health. These kits contain all the equipment and other materials needed to perform relatively sophisticated life science experiments in a room that has only tables and electrical outlets. The kits are suitable for use by life and health sciences studentselection came during the county GOP convention where Paul delegates dominated, winning as many as half of the 1,382 delegates nominated to the state convention May 2-4 in Sparks..... "This is the grass roots taking a stand to change the direction of the party from the county level," said Carl Bunce, Nevada chairman of Paul's campaign and a delegate. "This is bigger than just Ron Paul. This is about liberty and openness and fairness and changing the party.".... Still, the Paul factor could complicate things at the state convention for Mitt Romney, the GOP front-runner who won the Feb. 4 GOP presidential caucus in Nevada with 50 percent of the vote.... The 2012 state GOP convention will elect 28 delegates to the Republican National Convention this summer in


also facilitates the formation of super elongation complex (SEC) containing active P-TEFb and additional elongation factors and transcription coactivators \[[@B41], [@B42]\]. These factors include AFF4, ENL, AF9, and elongation factor ELL2 \[[@B42]\]. The AFF4 protein emerges as the central scaffold that recruits other factors through direct interactions. AFF4 binds cyclin T1, ELL2, and ENL or AF9 acting as a bridge that links this complex to P-TEFb \[[@B43]\]. Through the bridging functions of Tat and AFF4, P-TEFb and ELL2 combine to form a bifunctional elongation complex that greatly activates HIV-1 transcription \[[@B42], [@B44]\]. Without Tat, AFF4 can mediate the ELL2-P-TEFb interaction, albeit inefficiently. Tat overcomes this limitation by bringing more ELL2 to P-TEFb and stabilizing ELL2 in a process that requires active P-TEFb \[[@B42]\].

4. CDK9 Phosphorylation {#sec4}
=======================

Activity of P-TEFbQ:

How to start evaluating a cold IObservable

I thought, that cold IObservables, like the one returned from Observable.Create are evaluated whenever a subscription to them is made. I made a subscription. The IObservable did not evaluate.
class Program
{
    static IObservable<int> HotSource()
    {
        return Observable.Generate<int, int>(0, x => x <= 100, x => x + 1, x => x);
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I kinase inhibitor but not by CRM197. With blockade of TGF-beta receptor, Ang II-mediated hypertrophy was converted into cell proliferation, which was blocked by CRM197. In summary, this is the first demonstration that HB-EGF shedding-dependent EGFR transactivation, along with activation of TGF-beta signaling pathways, mediates Ang II-induced renal tubular epithelial cell hypertrophy.process if the triangle lies completely behind the
camera or outside the screen bounds.

I believe the main reason my engine looks so good is because it uses satellite
photos for textures - they hint at a lot of 3D detail that isn't expressed by
the triangles. I render only 1 or 2 thousand triangles per frame, but they
pretend to be a lot more, if you don't look at the ridges too closely. Try the
m and i keys to look under the hood.

~~~
JoelPM
Thanks for the explanation - very cool!

------
inudor
mousewheel for tilt doesn't work in my MacBook Pro. Have a look at,
<http://www.judahfrangipane.com/blog/?p=237> or
<http://brandonaaron.net/code/mousewheel/docs>

for ideas on how to solve it.

~~~
cousin_it
Thanks! I think I fixed it. Clear your cache and try again.

~~~
bradleyland
Nice work. It's working on my MBP now.

------
drKarl
[http://kosmosnimki.ru/3d/index.html?x=235543&y=5030526](http://kosmosnimki.ru/3d/index.html?x=235543&y=5030526)

Barcelona, where I live :)

~~~
cousin_it
Ooh you're lucky.


Youtube’s problems, CG crowds) drops them and then picks them up again later, seemingly without any thought of drawing the arguments together into once place. I’m not even sure what his conclusion is, as there are so many ‘potential’ conclusions one can draw from this video depending on your own preconceived opinions. In short, I think this is a pretty bad video and I feel the need to say my piece about it.

I don’t intend to address all or even most of the points he raises because he doesn’t put enough effort into the majority of comments to actually warrant a response. However, I think it is worth addressing some of his larger claims because they mirror arguments that have been floating around online for years and so
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/***** Selena *****/
/*-----------------*/

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figure.effect-selena p {
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2007 was carried out. Using a structured questionnaire, the respondents' socio-demographic data were obtained, as well as their knowledge of breast cancer and of what breast cancer examination screens for, and self-reported data on their having ever received CBE during the current antenatal period. The knowledge of breast cancer was poor. Although 99% of the women had heard of breast cancer, only 34% of them knew what breast examination screened for, whilst only 1 and 2% had received CBE by doctors and nurses, respectively, during the current antenatal period. No breast abnormalities or suspicious nodes were detected during the antenatal CBEs. The level of practice of routine antenatal CBE by health-care providers is very low in our setting. Health-care providers should perform a thorough breast examination at thelooking at him and could be such a positive influence on so many children's lives, yet he chooses not to. To me this is a tragedy. There is so much more to life than making money - I believe a part of him sells his soul for that. I also heard his comments about MMA which were totally delusional. Let's be real, if Floyd didn't KO Ronda the first 30 seconds chances are she takes him down and submits him. A blue belt with wrestling will take Floyd down and terrorize him. These are just facts."

DeBlass isn't the first martial artist to speak out about Mayweather over the last few weeks. Demetrious Johnson spoke openly about how he would destroy the boxing champ within 15 seconds,while featherweight title


of all common mode signals at the tip and ring voltage taps and a compensation circuit is also connected between the tip and ring voltage taps and is responsive to the output of the control circuit for compensating for non-symmetrical current, the non-symmetrical current being introduced between the tip and ring voltage taps by normal operation of the control circuit, thereby, a threshold of ground fault current limiting action is substantially constant under all operating conditions. The d.c. amplifier is conveniently manufacturable in integrated circuit technology along with the remaining amplifiers in the active impedance line feed circuit.

Claim:

What is claimed is:

1. An active impedance line feed circuit including tip and ring amplifiers being responsive to a control signal being proportional to currents in tip and ring feed resistorsforwhich are usuallyprovided in the form of a film resistor network residing on an electrically insulating substrate. The line feed circuit disclosed in the U.S. Pat. No. 4,571,460 includes a d.c. amplifier having an input directly connected to the tip and ringterminals by a pair of matched resistors. An output of the d.c. amplifier is resistively connected to tip and ring voltage taps and also coupled via a unidirectional resistive current path to an input of the ring amplifier circuit.

In operation, the d.c. amplifier reduces fault current and associated circuit heating in a case of a low resistive fault connection from the ring lead of the two wire communication line to ground. This condition is usually referred to as aground fault. Also in normal operation, the d.c. amplifier


terminal 3 and an output terminal 5 of a ring amplifier circuit 40. The tip and ring amplifier circuits 20 and 40 are typically powered from a battery in a telephone system, not shown, common to a plurality of linecircuits. A tip voltage divider 14 includes a tip voltage tap 6 and is connected in series between the terminals 4 and 3. A ring voltage divider 15 includes a ring voltage tap 7 and is connected in series between the terminals 2 and 5. A controlcircuit at 60 includes a differential input of an amplifier 231, connected across the voltage taps 6 and 7, as shown. An output of the control circuit at 60 is connected to a supervision and transmit lead for providing a.c. information signals andsupervisorysignals to the associated telephone system. The output of the control circuit 60 is also resistively connected to a non-inverting input of the tip amplifier circuit 20, as is a bias voltage source V.

Resistors 45 and 48 are connected in series between the outputs of the tip and ring amplifier circuits 20 and 40, and a junction of the resistors 45 and 48 is connected to an inverting input of the ring amplifier circuit 40. It is usual thatohmic values for the resistors 45 and 48 be similar so that the ring amplifier circuit 40 will operate as an inverse follower with a gain of one with respect to signals at the terminal 4. Operating a.c. impedance and d.c. resistance characteristics ofthe outputs of the tip and ring


Q:

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Getting gif from url by curl: gif loose animation

I have a function which download an image from $url.
It's work from jpg, png, and gif but gif files looses animation (it become a static picture)
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other side of the Raj's northern border. A confidential memo revealed the total absence of reliable intelligence. 'We are without the means of obtaining prompt and reliable reports on what goes on in Turkestan. We do not know what party is in the ascendant.'

The despatch of a mission to Turkestan had been discussed on several occasions over the previous months. The first question was whether it should be official or unofficial: both options carried considerable risks. There was a further debate over whether or not to send a team of Indian soldiers to accompany the mission. The viceroy felt that sending troops 'would excite the liveliest suspicions in Afghanistan and might upset the whole situation.' After much discussion, the project was deemed so risky that it was quietly(and less glamorous) side of espionage, yet it was vitally important. The exodus of British nationals from Russia meant there was very little news of what was taking place inside the country. Information about daily life was urgently required. To this end, Dukes began supplying Mansfield Cumming with monthly reports describing the hardships faced by the populace.

The catastrophic decline in living standards became apparent as soon as he stepped off the train in Petrograd. The streets were strewn with garbage and pervaded with the stench of dead and decaying corpses of horses. The inhabitants presented a picture of human misery. 'Lines of wretched people standing patiently, disposing of personal belongings or of food got by foraging in the country.'

The opulent palaces that lined the Moika lay deserted, for


Afghanistan in the above files. The most detailed published account of the Afghan offensive and the British Indian defence is written by Molesworth, Afghanistan. A copy of the treaty (and negotiations) can be found on-line: http://www.iranicaon-line.org/articles/anglo-afghan-treaty-of-1921-the-outcome-of-
peace-negotiations-following-the-third-anglo-afghan-war

Part Three: The Professional Spy

13: Master of Disguise

Dukes writes about his mission in ST25 and Red Morrow. A number of his intelligence reports are to be found in the NA. See ADM 223/637 and ADM 1/8563/208. See also FO/371/4375; it contains many documents from the Political Intelligence Department on the situation inside Russia. FO/608/195/7 has many reports on conditions inside Soviet Russia. FO/236/59 contains Mr Woodhouse's report on conditions in Petrograd.

Ransome, Autobiography; Six Weeks; Signalling; Chambers, Last Englishman. Ransome's principal intelligence report, 'Report on the State of Russia', can be foundof 1186488?
2, 3, 1831
What are the prime factors of 458768?
2, 53, 541
List the prime factors of 269495.
5, 53899
What are the prime factors of 15581775?
3, 5, 11, 17, 101
What are the prime factors of 53691?
3, 11, 1627
List the prime factors of 359383.
31, 11593
What are the prime factors of 6345202?
2, 19, 166979
What are the prime factors of 7051?
11, 641
List the prime factors of 8622062.
2, 4311031
What are the prime factors of 509452?
2, 127363
List the prime factors of 664654.
2, 23, 14449
List the prime factors of 3167276.
2, 7, 113117
What are the prime factors of 159040?
2, 5, 7, 71
What are the prime factors of 108319?
19, 5701
What are the prime factors of 682826?
2, 223, 1531
What are the prime factors of 235406?
2, 117703
List the prime factors of 1130023.
1130023
List the prime factors of 434444.
2, 313, 347
What are


Purification of a MalE-SoxS fusion protein and identification of the control sites of Escherichia coli superoxide-inducible genes.
In Escherichia coli, the soxRS genes effect the cell's defence against superoxide by activating the transcription of more than 14 genes, including zwf, sodA, nfo, micF and fumC. Previous work from other laboratories has indicated that SoxR is the sensor of oxidative stress and induces synthesis of SoxS, which in turn activates transcription of the regulon's target genes. Although SoxS appears to be a DNA-binding protein, its ability to bind to the promoter regions of target genes has not been demonstrated. To facilitate purification and characterization of SoxS, we constructed a fusion of soxS to malE, which encodes maltose-binding protein, and demonstrated that the in vivo expression of the MalE-SoxS fusion proteinnot.) Some even argued Alice had included the recipe as a publicity stunt.

HASHISH FUDGE(which anyone could whip up on a rainy day)

This is the food of paradise — of Baudelaire’s Artificial Paradises: it might provide an entertaining refreshment for a Ladies’ Bridge Club or a chapter meeting of the DAR. In Morocco it is thought to be good for warding off the common cold in damp winter weather and is, indeed, more effective if taken with large quantities of hot mint tea. Euphoria and brilliant storms of laughter; ecstatic reveries and extensions of one’s personality on several simultaneous planes are to be complacently expected. Almost anything Saint Theresa did, you can do better if you can bear to be ravished by ‘un évanouissement reveillé‘.

Take 1 teaspoon black peppercorns,


fourth beat of each measure.

The results showed that when the image was flashed on that missed beat, the subjects identified the inverted image much faster than when the image was flashed at times out of synch with the beat or when the images were presented in silence. Somehow, the brain’s decision making was accelerated by the external auditory rhythm and heightened at precise points in synchrony with the beat. Since the power of rhythm in boosting cognitive performance was evident on the missing beat when no sound was presented, the effect could not have had anything to do with the sound of the drumbeat acting as a stimulus. Mental processing must have fallen into a rhythm of heightened expectation and superior performance on the anticipated beat.

Next the researchersobtain the assistance of counsel in two ways:  (1) by continuing their interrogation after he requested counsel, and (2) by eliciting a confession through an illusory promise of leniency.  We affirm.

I.

2
In September, 1986, the Indiana State Police questioned Lord about a missing person, Frederick Michael Thompson.  The police became suspicious of Lord because he was one of the last people seen with Thompson and because Lord's account of the events of September 5-6, 1986, contained some general inconsistencies.  On September 24, 1986, a county employee found Thompson's body, with a bullet wound to the back of the head, in a cistern beside an abandoned farmhouse.1  Following this discovery, the police returned to further question Lord, at which time they advised him of his


  Record at 33.  In resolving this ambiguity, the court determined that Lord's statement appeared to be in the nature of queries regarding future access to counsel for a court hearing rather than a request for counsel at that time, and, thus was not " '... sufficiently emphatic to constitute an invocation of the right.' "   Id. (citing Heald v. State, 492 N.E.2d 671, 676 (Ind.1986)).

22
The Indiana Supreme Court affirmed without deciding whether Lord had invoked his right to counsel.  After explicating the trial court's ruling and stating grounds therefor, the Court first distinguished Heald2 and then subjected Lord's contention to harmless error analysis:

23
If we would assume for the sake of argument that appellant should not have been interrogated following his statement concerninga petition for writ of habeas corpus is plenary.  United States ex rel. Partee v. Lane, 926 F.2d 694, 700 (7th Cir.1991), cert. denied, --- U.S. ----, 112 S.Ct. 1230, 117 L.Ed.2d 464 (1992);  United States ex rel. Simmons v. Gramley, 915 F.2d 1128, 1133 (7th Cir.1990).  We presume the state court's findings of historical fact to be correct unless not fairly supported by the record, Baskin v. Clark, 956 F.2d 142, 145 (7th Cir.), cert. denied, --- U.S. ----, 113 S.Ct. 109, 121 L.Ed.2d 67 (1992);  however, we review de novo questions of law and mixed questions of law and fact.  See 28 U.S.C. Sec. 2254(d);  Brewer v. Aiken, 935 F.2d 850, 855 (7th Cir.1991).

A.

27
We turn first to Lord's claim that


Lord was convicted are set forth in the opinion of the Indiana Supreme Court affirming the conviction, Lord v. State, 531 N.E.2d 207, 208-209 (Ind.1988), and need not be repeated here

2
 In Heald, the defendant interrupted the police during the Miranda warnings to say she wanted to see an attorney.  The policeman then indicated that he wished to finish giving the warnings, which he did.  Heald was then asked if she wished to talk to counsel, but she specifically waived her right to counsel at that time.  Here, by contrast, the supreme court found that Lord "at no time, pursuant to a direct question by the police, expressly waived his right to counsel following his statement [concerning counsel]."  Lord, 531 N.E.2d at 209

3
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Managing IT as a Business Summary

A Survival Guide for CEOs

Managing IT is a demanding process even for the most experienced ones.

We sum up the main discoveries in “Managing IT as a Business” and present a comprehensive summary that you can use in your daily endeavors.

Who Should Read “Managing IT as a business”? And Why?

We prescribe this one-of-a-kind guidebook to leaders, managers, economists, and students who march to become successful, and influential on the market. Written in an easily-digestible manner, “Managing IT as a Business” deservedly obtains the primacy – the book of tomorrow. Filled with investment tips, budget organization, strategies, you will not be wasting your time.

About Mark D. Lutchen

Mark D. Lutchen currently heads the


like a commodity, that almost the entire business community had it. In fact, going from No one to No (?), was a tough time for the conventional minds, who thought that nothing could overshadow IT. With no room to spare, a new methodology was born and conveyed with the transparency of a single article. Despite the efforts to put IT in the driver’s seat, everyone realized that it was not going to happen.

Here’s what you should consider:

Maybe we have underestimated the power of creativity, and traditional marketing techniques to gain a competitive edge. Strategically, it was no longer possible to rely on IT capabilities, and thus the market was preparing itself for another turn of events.

In fact, companies which failed to predict the pros and cons of ITand coordinate them perfectly is not enough to avoid collapse.

Like this summary? We’d Like to invite you to download our free 12 min app, for more amazing summaries and audiobooks.

Our Critical Review

As the title indicates, the emphasis falls on IT and speaks to CEOs from all industries to transform their mindsets. The process of allowing the CIOs to express themselves more freely will foster other departments to reach their goals. As such we believe that this book is perfect for leaders of today.


the freedom
of all on this mainland; for, by looking to that action, the Greeks
took courage to venture other battles for safety, becoming pupils of
the men of Marathon. The first prize of valour, then, we must bestow on
them: the second on those who fought at Artemisium, and round the Isle
of Salamis.”[13]

The battle of Marathon marks an important crisis in the history of
Greece, and of the civilized world. The later contests of the Persian
war at Thermopylæ and Salamis and Platæa, important as they were,
were not played for so deep a stake; for the chief of the Grecian
nations were then pledged to the war, and were besides encouraged by
knowing the Persian power not insuperable. The panegyric of Plato is
not overcharged. We have given the frank confession of Herodotus,
that up to thatwas to decide
whether Europe should remain Christian, or the Cross sink under the
Crescent. The light and active Saracens, whose defensive armour was
merely a quilted jacket, and their weapons arrows and javelins, rushed
fiercely to the attack; but they made little impression on the solid
battalions of the Franks, bristling with spear–points, and protected
by their close–locked shields. The latter were no match for their
assailants in agility of manœuvring, but the weighty arm and steady
foot made up for this deficiency. The Saracen cavalry charged up to
their ranks in vain; they were compelled to rein their horses round,
and when wearied and broken by their fruitless efforts, the Christians
advanced and routed them with great slaughter. In the heat of the
battle, Eudes, Duke of Aquitaine, led his troops round upon the enemy’s
camp, overthrowing all before


shields before their breasts, forth at once they go,
  Their lances in the rest, levelled fair and low;
  Their banners and their crests waving in a row,
  Their heads all stooping down toward the saddle bow.
  The Cid was in the midst, his shout was heard afar,
  ‘I am Ruy Diaz, the champion of Bivar;
  Strike among them, gentlemen, for sweet mercies’ sake!’
  There where Bermuez fought, amidst the foe they break;
  Three hundred bannered knights, it was a gallant show:
  Three hundred Moors they killed, a man with every blow.
  When they wheeled and turned, as many more lay slain,
  You might see them raise their lances, and level them again,
  There you might seethe cause, the
result of that hatred and contempt of their general which all felt.
He would have re–established their confidence by showing kindness and
courage; it was then too late. He addressed the Pacha of Buda, and
other chiefs; they kept silence in despair. ‘And you,’ he said to the
Tartarian chief, ‘will not you help me?’ The Khan replied that he
knew the King of Poland, and that there was no safety with him but in
flight, of which he immediately set the example. The Spahis were now
in extremity. The Poles broke and overthrew them, the grand standard
disappeared, and the Vizir ran away and communicated his own fears to
all. The dismay spread rapidly to the wings, which were assailed at
once by the various nations of the Christian army, the king animating
all by his


the fayth? what availeth the
prowesse that thou hast made in tyme passed whan thyne end sheweth that
thou hast doon wyckednes? O fals avaryce, and ardeur of concupiscence,
he is not the fyrst that by the is comen to myschyef! by the Adam was
to God dysobeysaunt, and the noble cyte of Troy the grande put to uttre
ruyne and destructyon! Thus in thys manere Ganellon brought gold and
sylver, wyn wymmen and other richesses as tofore he had enterprysed.
Whan Charles sawe al this, he thought that al way doon in good entent,
and equyte, and wythout barat.[42] The gret lordes and knyghtes toke
the wyn for them, and Charles toke onely the gold and sylver, and the
moyen people took the hethen wymmen. Themperour gaf consente to the
wordes of Ganellon. For he spake moche wysely,appear
to have gained the advantage, and their spirits were heightened by a
reinforcement of fifty–three Athenian triremes, bringing news that the
detachment sent round Eubœa had been overtaken by a storm and totally
destroyed. But they were severely handled in the last engagement;
and the news of the battle of Thermopylæ determined them to retreat
nearer to their homes. Previous to his departure, Themistocles engraved
these words upon the rocks at the watering place of Artemisium: “Men
of Ionia, you do ill in making war upon your fathers, and helping to
enslave Greece.[46] By all means therefore come over to us, or, if that
cannot be, remain neuter, and persuade the Carians to do the same. But
if the necessity which compels you to the part you are engaged in is
such as to make a secession impracticable, yet,