bluuebunny/crossref_metadata_2025 huggingface dataset:
Modular Design of Cys-loop Ligand-gated Ion Channels: Functional 5-HT3 and GABA ρ1 Receptors Lacking the Large Cytoplasmic M3M4 Loop
Authors: Jansen Michaela , Bali Moez , Akabas Myles H.
Published: January 2008

Cys-loop receptor neurotransmitter-gated ion channels are pentameric assemblies of subunits that contain three domains: extracellular, transmembrane, and intracellular. The extracellular domain forms the agonist binding site. The transmembrane domain forms the ion channel. The cytoplasmic domain is involved in trafficking, localization, and modulation by cytoplasmic second messenger systems but its role in channel assembly and function is poorly understood and little is known about its structure. The intracellular domain is formed by the large (>100 residues) loop between the α-helical M3 and M4 transmembrane segments. Putative prokaryotic Cys-loop homologues lack a large M3M4 loop. We replaced the complete M3M4 loop (115 amino acids) in the 5-hydroxytryptamine type 3A (5-HT3A) subunit with a heptapeptide from the prokaryotic homologue from Gloeobacter violaceus. The macroscopic electrophysiological and pharmacological characteristics of the homomeric 5-HT3A-glvM3M4 receptors were comparable to 5-HT3A wild type. The channels remained cation-selective but the 5-HT3A-glvM3M4 single channel conductance was 43.5 pS as compared with the subpicosiemens wild-type conductance. Coexpression of hRIC-3, a protein that modulates expression of 5-HT3 and acetylcholine receptors, significantly attenuated 5-HT–induced currents with wild-type 5-HT3A but not 5-HT3A-glvM3M4 receptors. A similar deletion of the M3M4 loop in the anion-selective GABA-ρ1 receptor yielded functional, GABA-activated, anion-selective channels. These results imply that the M3M4 loop is not essential for receptor assembly and function and suggest that the cytoplasmic domain may fold as an independent module from the transmembrane and extracellular domains.
The Muscle Chloride Channel ClC-1 Is Not Directly Regulated by Intracellular ATP
Authors: Zifarelli Giovanni , Pusch Michael
Published: January 2008

ClC-1 belongs to the gene family of CLC Cl− channels and Cl−/H+ antiporters. It is the major skeletal muscle chloride channel and is mutated in dominant and recessive myotonia. In addition to the membrane-embedded part, all mammalian CLC proteins possess a large cytoplasmic C-terminal domain that bears two so-called CBS (from cystathionine-β-synthase) domains. Several studies indicate that these domains might be involved in nucleotide binding and regulation. In particular, Bennetts et al. (J. Biol. Chem. 2005. 280:32452–32458) reported that the voltage dependence of hClC-1 expressed in HEK cells is regulated by intracellular ATP and other nucleotides. Moreover, very recently, Bennetts et al. (J. Biol. Chem. 2007. 282:32780–32791) and Tseng et al. (J. Gen. Physiol. 2007. 130:217–221) reported that the ATP effect was enhanced by intracellular acidification. Here, we show that in striking contrast with these findings, human ClC-1, expressed in Xenopus oocytes and studied with the inside-out configuration of the patch-clamp technique, is completely insensitive to intracellular ATP at concentrations up to 10 mM, at neutral pH (pH 7.3) as well as at slightly acidic pH (pH 6.2). These results have implications for a general understanding of nucleotide regulation of CLC proteins and for the physiological role of ClC-1 in muscle excitation.
Semi-linear wave equations
Authors: Struwe Michael
Published: January 2008

We survey existence and regularity results for semi-linear wave equations. In particular, we review the recent regularity results for the

u
5

{u^5}

-Klein Gordon equation by Grillakis and this author and give a self-contained, slightly simplified proof.
Nonunique tangent maps at isolated singularities of harmonic maps
Authors: White Brian
Published: January 2008

Shoen and Uhlenbeck showed that "tangent maps" can be defined at singular points of energy minimizing maps. Unfortunately these are not unique, even for generic boundary conditions. Examples are discussed which have isolated singularities with a continuum of distinct tangent maps.
User’s guide to viscosity solutions of second order partial differential equations
Authors: Crandall Michael G. , Ishii Hitoshi , Lions Pierre-Louis
Published: January 2008

The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking arguments. The range of important applications of these results is enormous. This article is a self-contained exposition of the basic theory of viscosity solutions.
A class of nonsymmetric harmonic Riemannian spaces
Authors: Damek Ewa , Ricci Fulvio
Published: January 2008

Certain solvable extensions of H-type groups provide noncompact counterexamples to a conjecture of Lichnerowicz, which asserted that "harmonic" Riemannian spaces must be rank 1 symmetric spaces.
Rational function certification of multisum/integral/“𝑞” identities
Authors: Wilf Herbert S. , Zeilberger Doron
Published: January 2008

The method of rational function certification for proving terminating hypergeometric identities is extended from single sums or integrals to multi-integral/sums and "q" integral/sums.
A counterexample to the Arakelyan conjecture
Authors: Erëmenko A.
Published: January 2008

A "self-similar" example is constructed that shows that a conjecture of N. U. Arakelyan on the order of decrease of deficiencies of an entire function of finite order is not true.
A characterization of convex hyperbolic polyhedra and of convex polyhedra inscribed in the sphere
Authors: Hodgson Craig D. , Rivin Igor , Smith Warren D.
Published: January 2008

We describe a characterization of convex polyhedra in

H
3

{H^3}

in terms of their dihedral angles, developed by Rivin. We also describe some geometric and combinatorial consequences of that theory. One of these consequences is a combinatorial characterization of convex polyhedra in

E
3

{E^3}

all of whose vertices lie on the unit sphere. That resolves a problem posed by Jakob Steiner in 1832.
Curvature, triameter, and beyond
Authors: Grove Karsten , Markvorsen Steen
Published: January 2008

In its most general form, the recognition problem in Riemannian geometry asks for the identification of an unknown Riemannian manifold via measurements of metric invariants on the manifold. We introduce a new infinite sequence of invariants, the first term of which is the usual diameter, and illustrate the role of these global shape invariants in a number of recognition problems.
New types of soliton solutions
Authors: Gesztesy F. , Karwowski W. , Zhao Z.
Published: January 2008

We announce a detailed investigation of limits of N-soliton solutions of the Korteweg-deVries (KdV) equation as N tends to infinity. Our main results provide new classes of KdV-solutions including in particular new types of soliton-like (reflectionless) solutions. As a byproduct we solve an inverse spectral problem for one-dimensional Schrödinger operators and explicitly construct smooth and real-valued potentials that yield a purely absolutely continuous spectrum on the nonnegative real axis and give rise to an eigenvalue spectrum that includes any prescribed countable and bounded subset of the negative real axis.
Prevalence: a translation-invariant “almost every” on infinite-dimensional spaces
Authors: Hunt Brian R. , Sauer Tim , Yorke James A.
Published: January 2008

We present a measure-theoretic condition for a property to hold "almost everywhere" on an infinite-dimensional vector space, with particular emphasis on function spaces such as

C
k

{C^k}

and

L
p

{L^p}

. Like the concept of "Lebesgue almost every" on finite-dimensional spaces, our notion of "prevalence" is translation invariant. Instead of using a specific measure on the entire space, we define prevalence in terms of the class of all probability measures with compact support. Prevalence is a more appropriate condition than the topological concepts of "open and dense" or "generic" when one desires a probabilistic result on the likelihood of a given property on a function space. We give several examples of properties which hold "almost everywhere" in the sense of prevalence. For instance, we prove that almost every

C
1

{C^1}

map on

R

n

{\mathbb {R}^n}

has the property that all of its periodic orbits are hyperbolic.
Factorizations of invertible operators and 𝐾-theory of 𝐶*-algebras
Authors: Zhang Shuang
Published: January 2008

Let

A

\mathcal {A}

be a unital

C

∗

{\text {C}}^{\ast }

-algebra. We describe K-skeleton factorizations of all invertible operators on a Hilbert

C

∗

{\text {C}}^{\ast }

-module

H

A

\mathcal {H}_\mathcal {A}

, in particular on

H

=

l
2

\mathcal {H}={l^2}

, with the Fredholm index as an invariant. We then outline the isomorphisms
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper K 0 left-parenthesis script upper A right-parenthesis approximately-equals pi Subscript 2 k Baseline left-parenthesis left-bracket p right-bracket Subscript 0 Baseline right-parenthesis approximately-equals pi Subscript 2 k Baseline left-parenthesis upper G upper L Subscript r Superscript p Baseline left-parenthesis script upper A right-parenthesis right-parenthesis">

K
0

(

A

)
≅

π

2
k

(

[
p

]
0

)
≅

π

2
k

(

G
L

r
p

(

A

)
)

{K_0}(\mathcal {A}) \cong {\pi _{2k}}({[p]_0}) \cong {\pi _{2k}}({GL}_r^p(\mathcal {A}))

and
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper K 1 left-parenthesis script upper A right-parenthesis approximately-equals pi Subscript 2 k plus 1 Baseline left-parenthesis left-bracket p right-bracket Subscript 0 Baseline right-parenthesis approximately-equals pi Subscript 2 k plus 1 Baseline left-parenthesis upper G upper L Subscript r Superscript p Baseline left-parenthesis script upper A right-parenthesis right-parenthesis">

K

1

(

A

)
≅

π

2
k
+
1

(

[
p

]
0

)
≅

π

2
k
+
1

(

G
L

r
p

(

A

)
)

{{K}_{1}}(\mathcal {A})\cong {{\pi }_{2k+1}}({[p]_0})\cong {{\pi }_{2k+1}}({GL}_r^p(\mathcal {A}))

for

k
≥
0

k \geq 0

, where

[
p

]
0

{[p]_0}

denotes the class of all compact perturbations of a projection p in the infinite Grassmann space

G
r

∞

(

A

)

{Gr}^{\infty }(\mathcal {A})

and

G
L

r
p

(

A

)

{GL}_r^p(\mathcal {A})

stands for the group of all those invertible operators on

H

A

{\mathcal {H}_\mathcal {A}}

essentially commuting with p.
A new result for the porous medium equation derived from the Ricci flow
Authors: Wu Lang-Fang
Published: January 2008

Given

R

2

{\mathbb {R}^2}

, with a "good" complete metric, we show that the unique solution of the Ricci flow approaches a soliton at time infinity. Solitons are solutions of the Ricci flow, which move only by diffeomorphism. The Ricci flow on

R

2

{\mathbb {R}^2}

is the limiting case of the porous medium equation when m is zero. The results in the Ricci flow may therefore be interpreted as sufficient conditions on the initial data, which guarantee that the corresponding unique solution for the porous medium equation on the entire plane asymptotically behaves like a "soliton-solution".
Relative 𝐾-cycles and elliptic boundary conditions
Authors: Gong Guihua
Published: January 2008

In this paper, we discuss the following conjecture raised by Baum-Douglas: For any first-order elliptic differential operator D on smooth manifold M with boundary

∂
M

\partial M

, D possesses an elliptic boundary condition if and only if

∂
[
D
]
=
0

\partial [D] = 0

in

K
1

(
∂
M
)

{K_1}(\partial M)

, where [D] is the relative K-cycle in

K
0

(
M
,
∂
M
)

{K_0}(M,\partial M)

corresponding to D. We prove the "if" part of this conjecture for

d
i
m
(
M
)
≠
4
,
5
,
6
,
7

dim(M) \ne 4,5,6,7

and the "only if" part of the conjecture for arbitrary dimension.
Integration and approximation of multivariate functions: average case complexity with isotropic Wiener measure
Authors: Wasilkowski G. W.
Published: January 2008

We study the average case complexity of multivariate integration and

L

2

{L_{2}}

function approximation for the class

F
=
C
(
[
0
,
1

]

d

)

{F = C([0,1]^{d})}

of continuous functions of d variables. The class F is endowed with the isotropic Wiener measure (Brownian motion in Levy’s sense). Furthermore, for both problems, only function values are used as data.
On the distribution of sums of residues
Authors: Griggs Jerrold R.
Published: January 2008

We generalize and solve the

mod

q

{\bmod \;q}

]> analogue of a problem of Littlewood and Offord, raised by Vaughan and Wooley, concerning the distribution of the

2
n

{2^n}

sums of the form

∑

i
=
1

n

ε
i

a
i

{\sum _{i = 1}^n{\varepsilon _i}{a_i}}

, where each

ε
i

{\varepsilon _i}

is 0 or 1. For all q, n, k we determine the maximum, over all reduced residues

a
i

{a_i}

and all sets P consisting of k arbitrary residues, of the number of these sums that belong to P.
Borel actions of Polish groups
Authors: Becker Howard , Kechris Alexander S.
Published: January 2008

We show that a Borel action of a Polish group on a standard Borel space is Borel isomorphic to a continuous action of the group on a Polish space, and we apply this result to three aspects of the theory of Borel actions of Polish groups: universal actions, invariant probability measures, and the Topological Vaught Conjecture. We establish the existence of universal actions for any given Polish group, extending a result of Mackey and Varadarajan for the locally compact case. We prove an analog of Tarski’s theorem on paradoxical decompositions by showing that the existence of an invariant Borel probability measure is equivalent to the nonexistence of paradoxical decompositions with countably many Borel pieces. We show that various natural versions of the Topological Vaught Conjecture are equivalent with each other and, in the case of the group of permutations of

N

{\mathbb {N}}

, with the model-theoretic Vaught Conjecture for infinitary logic; this depends on our identification of the universal action for that group.
Quasipositivity as an obstruction to sliceness
Authors: Rudolph Lee
Published: January 2008

For an oriented linkL⊂S3=∂D4L\,\, \subset \,\,{S^3}\, = \,\,\partial {D^4}, letχs(L){\chi _s}{\text {(}}L{\text {)}}be the greatest Euler characteristicχ(F)\chi (F)of an oriented 2-manifoldF(without closed components) smoothly embedded inD4{D^4}with boundaryL. A knotKissliceifχs(K)=1{\chi _s}(K) = 1. RealizeD4{D^4}inC2{\mathbb {C}^2}as{(z,w):|z|2+|w|2≤1}\{ (z,w):|z{|^2} + |w{|^2} \leq 1\}. It has been conjectured that, ifVis a nonsingular complex plane curve transverse toS3{S^3}, thenχs(V∩S3)=χ(V∩D4){\chi _s}(V \cap {S^3}) = \chi (V \cap {D^4}). Kronheimer and Mrowka have proved this conjecture in the case thatV∩D4V \cap {D^4}is the Milnor fiber of a singularity. I explain how this seemingly special case implies both the general case and the "slice-Bennequin inequality" for braids. As applications, I show that various knots are not slice (e.g., pretzel knots likeP(−3,5,7)\mathcal {P}( - 3,5,7); all knots obtained from a positive trefoilO{2,3}O\{ 2,3\}by iterated untwisted positive doubling). As a sidelight, I give an optimal counterexample to the "topologically locally-flat Thom conjecture".
A counterexample to Borsuk’s conjecture
Authors: Kahn Jeff , Kalai Gil
Published: January 2008

Letf(d)f(d)be the smallest number so that every set inRd{R^d}of diameter 1 can be partitioned intof(d)f(d)sets of diameter smaller than 1. Borsuk’s conjecture was thatf(d)=d+1f(d) = d + 1. We prove thatf(d)≥(1.2)df(d) \geq (1.2)\sqrt dfor larged.
The genus-minimizing property of algebraic curves
Authors: Kronheimer P. B.
Published: January 2008

A viable and still unproved conjecture states that, if X is a smooth algebraic surface and C is a smooth algebraic curve in X, then C realizes the smallest possible genus amongst all smoothly embedded 2-manifolds in its homology class. A proof is announced here for this conjecture, for a large class of surfaces X, under the assumption that the normal bundle of C has positive degree.
Coupling and Harnack inequalities for Sierpiński carpets
Authors: Barlow Martin T. , Bass Richard F.
Published: January 2008

Uniform Harnack inequalities for harmonic functions on the pre-and graphical Sierpinski carpets are proved using a probabilistic coupling argument. Various results follow from this, including the construction of Brownian motion on Sierpinski carpets embedded in

R

d

{\mathbb {R}^d}

,

d
≥
3

d \geq 3

, estimates on the fundamental solution of the heat equation, and Sobolev and Poincaré inequalities.
Trace formulae and inverse spectral theory for Schrödinger operators
Authors: Gesztesy F. , Holden H. , Simon B. , Zhao Z.
Published: January 2008

We extend the well-known trace formula for Hill’s equation to general one-dimensional Schrödinger operators. The new function

ξ
\xi

, which we introduce, is used to study absolutely continuous spectrum and inverse problems.
The rigid analytic period mapping, Lubin-Tate space, and stable homotopy theory
Authors: Hopkins M. J. , Gross B. H.
Published: January 2008

The geometry of the Lubin-Tate space of deformations of a formal group is studied via an étale, rigid analytic map from the deformation space to projective space. This leads to a simple description of the equivariant canonical bundle of the deformation space which, in turn, yields a formula for the dualizing complex in stable homotopy theory.
Pointwise convergence of wavelet expansions
Authors: Kelly Susan E. , Kon Mark A. , Raphael Louise A.
Published: January 2008

In this note we announce that under general hypotheses, wavelet-type expansions (of functions in

L
p

{L^p}

,

1
≤
p
≤
∞

1 \leq p \leq \infty

, in one or more dimensions) converge pointwise almost everywhere, and identify the Lebesgue set of a function as a set of full measure on which they converge. It is shown that unlike the Fourier summation kernel, wavelet summation kernels

P
j

{P_j}

are bounded by radial decreasing

L
1

{L^1}

convolution kernels. As a corollary it follows that best

L
2

{L^2}

spline approximations on uniform meshes converge pointwise almost everywhere. Moreover, summation of wavelet expansions is partially insensitive to order of summation. We also give necessary and sufficient conditions for given rates of convergence of wavelet expansions in the sup norm. Such expansions have order of convergence s if and only if the basic wavelet

ψ
\psi

is in the homogeneous Sobolev space

H
h

−
s
−
d

/

2

H_h^{ - s - d/2}

. We also present equivalent necessary and sufficient conditions on the scaling function. The above results hold in one and in multiple dimensions.
A theory of characteristic currents associated with a singular connection
Authors: Harvey Reese , Lawson H. Blaine
Published: January 2008

This note announces a general construction of characteristic currents for singular connections on a vector bundle. It develops, in particular, a Chern-Weil-Simons theory for smooth bundle maps

α
:
E
→
F

\alpha :E \to F

which, for smooth connections on E and F, establishes formulas of the type
\[

ϕ
=

Res

ϕ

Σ
α

+
d
T
.

\phi = {\operatorname {Res}}_\phi {\Sigma _\alpha } + dT.

\]
Here

ϕ
\phi

is a standard charactersitic form,

Res
ϕ

{\operatorname {Res}_\phi }

is an associated smooth "residue" form computed canonically in terms of curvature,

Σ
α

{\Sigma _\alpha }

is a rectifiable current depending only on the singular structure of

α
\alpha

, and T is a canonical, functorial transgression form with coefficients in

L

loc

1

L_{{\text {loc}}}^1

. The theory encompasses such classical topics as: Poincaré-Lelong Theory, Bott-Chern Theory, Chern-Weil Theory, and formulas of Hopf. Applications include: a new proof of the Riemann-Roch Theorem for vector bundles over algebraic curves, a

C

∞

{C^{\infty }}

-generalization of the Poincaré-Lelong Formula, universal formulas for the Thom class as an equivariant characteristic form (i.e., canonical formulas for a de Rham representative of the Thom class of a bundle with connection), and a Differentiable Riemann-Roch-Grothendieck Theorem at the level of forms and currents. A variety of formulas relating geometry and characteristic classes are deduced as direct consequences of the theory.
Alexander’s and Markov’s theorems in dimension four
Authors: Kamada Seiichi
Published: January 2008

Alexander’s and Markov’s theorems state that any link type in

R
3

{R^3}

is represented by a closed braid and that such representations are related by some elementary operations called Markov moves. We generalize the notion of a braid to that in 4-dimensional space and establish an analogue of these theorems.
Open sets of diffeomorphisms having two attractors, each with an everywhere dense basin
Authors: Kan Ittai
Published: January 2008

We announce the discovery of a diffeomorphism of a three-dimensional manifold with boundary which has two disjoint attractors. Each attractor attracts a set of positive 3-dimensional Lebesgue measure whose points of Lebesgue density are dense in the whole manifold. This situation is stable under small perturbations.
The flag-transitive tilde and Petersen-type geometries are all known
Authors: Ivanov A. A. , Shpectorov S. V.
Published: January 2008

We announce the classification of two related classes of flag-transitive geometries. There is an infinite family of such geometries, related to the nonsplit extensions3[n2]2⋅Sp2n(2){3^{[\begin {array}{*{20}{c}} n \\ 2 \\ \end {array} ]}}^2 \cdot {\text {Sp}}_{2n}(2), and twelve sporadic examples coming from the simple groupsM22{M_22},M23{M_23},M24{M_24},He,Co1Co_{1},Co2Co_{2},J4{J_4},BM,Mand the nonsplit extensions3⋅M223 \cdot {M_22},323⋅Co2{3^{23}} \cdot Co_{2}, and34371⋅BM{3^{4371}} \cdot BM.
A report on Wiles’ Cambridge lectures
Authors: Rubin K. , Silverberg A.
Published: January 2008

In lectures at the Newton Institute in June of 1993, Andrew Wiles announced a proof of a large part of the Taniyama-Shimura Conjecture and, as a consequence, Fermat’s Last Theorem. This report for nonexperts discusses the mathematics involved in Wiles’ lectures, including the necessary background and the mathematical history.
Exceptional surgery on knots
Authors: Boyer S. , Zhang X.
Published: January 2008

Let M be an irreducible, compact, connected, orientable 3-manifold whose boundary is a torus. We show that if M is hyperbolic, then it admits at most six finite/cyclic fillings of maximal distance 5. Further, the distance of a finite/cyclic filling to a cyclic filling is at most 2. If M has a non-boundary-parallel, incompressible torus and is not a generalized 1-iterated torus knot complement, then there are at most three finite/cyclic fillings of maximal distance 1. Further, if M has a non-boundary-parallel, incompressible torus and is not a generalized 1- or 2-iterated torus knot complement and if M admits a cyclic filling of odd order, then M does not admit any other finite/cyclic filling. Relations between finite/cyclic fillings and other exceptional fillings are also discussed.
Singular continuous spectrum is generic
Authors: Del Rio R. , Jitomirskaya S. , Makarov N. , Simon B.
Published: January 2008

In a variety of contexts, we prove that singular continuous spectrum is generic in the sense that for certain natural complete metric spaces of operators, those with singular spectrum are a dense

G
δ

{G_\delta }

.
Zeta functions do not determine class numbers
Authors: de Smit Bart , Perlis Robert
Published: January 2008

We show that two number fields with the same zeta function, and even with isomorphic adele rings, do not necessarily have the same class number.
On the geometric and topological rigidity of hyperbolic 3-manifolds
Authors: Gabai David
Published: January 2008

A homotopy equivalence between a hyperbolic 3-manifold and a closed irreducible 3-manifold is homotopic to a homeomorphsim provided the hyperbolic manifold satisfies a purely geometric condition. There are no known examples of hyperbolic 3-manifolds which do not satisfy this condition.
Müntz spaces and Remez inequalities
Authors: Borwein Peter , Erdélyi Tamás
Published: January 2008

Two relatively long-standing conjectures concerning Müntz polynomials are resolved. The central tool is a bounded Remez type inequality for non-dense Müntz spaces.
Wiener’s Tauberian theorem in 𝐿₁(𝐺//𝐾) and harmonic functions in the unit disk
Authors: Ben Natan Y. , Benyamini Y. , Hedenmalm H. , Weit Y.
Published: January 2008

Our main result is to give necessary and sufficient conditions, in terms of Fourier transforms, on a closed ideal I in

L
1

(
G

/

/

K
)

{L^1}(G//K)

, the space of radial integrable functions on

G
=
S
U
(
1
,
1
)

G = SU(1,1)

, so that

I
=

L
1

(
G

/

/

K
)

I = {L^1}(G//K)

or

I
=

L
0
1

(
G

/

/

K
)

I = L_0^1(G//K)

—the ideal of

L
1

(
G

/

/

K
)

{L^1}(G//K)

functions whose integral is zero. This is then used to prove a generalization of Furstenberg’s theorem which characterizes harmonic functions on the unit disk by a mean value property and a "two circles" Morera type theorem (earlier announced by Agranovskiĭ).
A splitting property for subalgebras of tensor products
Authors: Ge Liming
Published: January 2008

We prove a basic result about tensor products of a

I

I

1

{\text {I}}{{\text {I}}_1}

factor with a finite von Neumann algebra and use it to answer, affirmatively, a question asked by S. Popa about maximal injective factors.
Not all free arrangements are 𝐾(𝜋,1)
Authors: Edelman Paul H. , Reiner Victor
Published: January 2008

We produce a one-parameter family of hyperplane arrangements that are counterexamples to the conjecture of Saito that the complexified complement of a free arrangement is

K
(
π
,
1
)

K(\pi ,1)

. These arrangements are the restriction of a one-parameter family of arrangements that arose in the study of tilings of certain centrally symmetric octagons. This other family is discussed as well.
A new series of dense graphs of high girth
Authors: Lazebnik F. , Ustimenko V. A. , Woldar A. J.
Published: January 2008

Let

k
≥
1

k \geq 1

be an odd integer,

t
=

⌊

k
+
2

4

⌋

{t = \left \lfloor {\tfrac {{k + 2}}{4}} \right \rfloor }

, and q be a prime power. We construct a bipartite, q-regular, edge-transitive graph

C
D
(
k
,
q
)

CD(k,q)

of order

υ
≤
2

q

k
−
t
+
1

\upsilon \leq 2{q^{k - t + 1}}

and girth

g
≥
k
+
5

g \geq k + 5

. If e is the the number of edges of

C
D
(
k
,
q
)

CD(k,q)

, then

e
=
Ω
(

υ

1
+

1

k
−
t
+
1

)

e = \Omega ({{\upsilon ^{1 + \frac {1}{{k - t + 1}}}}})

. These graphs provide the best known asymptotic lower bound for the greatest number of edges in graphs of order

υ
\upsilon

and girth at least g,

g
≥
5

g \geq 5

,

g
≠
11

g \ne 11

, 12. For

g
≥
24

g \geq 24

, this represents a slight improvement on bounds established by Margulis and Lubotzky, Phillips, Sarnak; for

5
≤
g
≤
23

5 \leq g \leq 23

,

g
≠
11

g \ne 11

, 12, it improves on or ties existing bounds.
How many zeros of a random polynomial are real?
Authors: Edelman Alan , Kostlan Eric
Published: January 2008

We provide an elementary geometric derivation of the Kac integral formula for the expected number of real zeros of a random polynomial with independent standard normally distributed coefficients. We show that the expected number of real zeros is simply the length of the moment curve

(
1
,

t
,

…

,

t

n

)

(1,\,t,\,\ldots \,,t^{n})

projected onto the surface of the unit sphere, divided by

π
\pi

. The probability density of the real zeros is proportional to how fast this curve is traced out. We then relax Kac’s assumptions by considering a variety of random sums, series, and distributions, and we also illustrate such ideas as integral geometry and the Fubini-Study metric.
Families of curves and weight distributions of codes
Authors: Schoof René
Published: January 2008

In this expository paper we show how one can, in a uniform way, calculate the weight distributions of some well-known binary cyclic codes. The codes are related to certain families of curves, and the weight distributions are related to the distribution of the number of rational points on the curves.
Orthomodularity in infinite dimensions; a theorem of M. Solèr
Authors: Holland Samuel S.
Published: January 2008

Maria Pia Solèr has recently proved that an orthomodular form that has an infinite orthonormal sequence is real, complex, or quaternionic Hilbert space. This paper provides an exposition of her result, and describes its consequences for Baer

∗

{\ast }

-rings, infinite-dimensional projective geometries, orthomodular lattices, and Mackey’s quantum logic.
Necessity and chance: deterministic chaos in ecology and evolution
Authors: May Robert M.
Published: January 2008

This is an outline of my Gibbs Lecture to the American Mathematical Society in January 1994; it is essentially a sign-posted guide to a stilldeveloping literature.
Critical points on the boundaries of Siegel disks
Authors: Rogers James T.
Published: January 2008

Let f be a polynomial map of the Riemann sphere of degree at least two. We prove that if f has a Siegel disk G on which the rotation number satisfies a diophantine condition, then the boundary of G contains a critical point.
Chemical shift assignment of the transmembrane helices of DsbB, a 20‐kDa integral membrane enzyme, by 3D magic‐angle spinning NMR spectroscopy
Authors: Li Ying , Berthold Deborah A. , Gennis Robert B. , Rienstra Chad M.
Published: January 2008

The Escherichia coli inner membrane enzyme DsbB catalyzes disulfide bond formation in periplasmic proteins, by transferring electrons to ubiquinone from DsbA, which in turn directly oxidizes cysteines in substrate proteins. We have previously shown that DsbB can be prepared in a state that gives highly resolved magic‐angle spinning (MAS) NMR spectra. Here we report sequential 13C and 15N chemical shift assignments for the majority of the residues in the transmembrane helices, achieved by three‐dimensional (3D) correlation experiments on a uniformly 13C, 15N‐labeled sample at 750‐MHz 1H frequency. We also present a four‐dimensional (4D) correlation spectrum, which confirms assignments in some highly congested regions of the 3D spectra. Overall, our results show the potential to assign larger membrane proteins using 3D and 4D correlation experiments and form the basis of further structural and dynamical studies of DsbB by MAS NMR.
Involvement of DPP‐IV catalytic residues in enzyme–saxagliptin complex formation
Authors: Metzler William J. , Yanchunas Joseph , Weigelt Carolyn , Kish Kevin , Klei Herbert E. , Xie Dianlin , Zhang Yaqun , Corbett Martin , Tamura James K. , He Bin , Hamann Lawrence G. , Kirby Mark S. , Marcinkeviciene Jovita
Published: January 2008

The inhibition of DPP‐IV by saxagliptin has been proposed to occur through formation of a covalent but reversible complex. To evaluate further the mechanism of inhibition, we determined the X‐ray crystal structure of the DPP‐IV:saxagliptin complex. This structure reveals covalent attachment between S630 and the inhibitor nitrile carbon (C–O distance <1.3 Å). To investigate whether this serine addition is assisted by the catalytic His‐Asp dyad, we generated two mutants of DPP‐IV, S630A and H740Q, and assayed them for ability to bind inhibitor. DPP‐IVH740Q bound saxagliptin with an ∼1000‐fold reduction in affinity relative to DPP‐IVWT, while DPP‐IVS630A showed no evidence for binding inhibitor. An analog of saxagliptin lacking the nitrile group showed unchanged binding properties to the both mutant proteins, highlighting the essential role S630 and H740 play in covalent bond formation between S630 and saxagliptin. Further supporting mechanism‐based inhibition by saxagliptin, NMR spectra of enzyme–saxagliptin complexes revealed the presence of three downfield resonances with low fractionation factors characteristic of short and strong hydrogen bonds (SSHB). Comparison of the NMR spectra of various wild‐type and mutant DPP‐IV:ligand complexes enabled assignment of a resonance at ∼14 ppm to H740. Two additional DPP‐IV mutants, Y547F and Y547Q, generated to probe potential stabilization of the enzyme–inhibitor complex by this residue, did not show any differences in inhibitor binding either by ITC or NMR. Together with the previously published enzymatic data, the structural and binding data presented here strongly support a histidine‐assisted covalent bond formation between S630 hydroxyl oxygen and the nitrile group of saxagliptin.
Relationship between adipokines and manifestations of childhood asthma
Authors: Kim Kyung W. , Shin Youn H. , Lee Kyung E. , Kim Eun S. , Sohn Myung H. , Kim Kyu‐Earn
Published: January 2008

Although the prevalences of asthma and obesity are increasing substantially in recent decades, very little is known about the possible association between them. We evaluated the roles of leptin, adiponectin, and resistin, which are adipokines produced by adipose tissue, on childhood asthma, and their association with pulmonary function and bronchial hyperresponsiveness. We studied 149 atopic asthmatic children, 37 non‐atopic asthmatic children, and 54 healthy children. Body mass index was calculated using height and weight, which were measured on the same day that pulmonary function tests and methacholine challenge tests were performed. Skin prick tests were performed, and total eosinophil count, total serum immunoglobulin E (IgE), serum eosinophil cationic protein, leptin, adiponectin, and resistin were measured in all subjects. Atopic asthmatics had lower resistin levels compared with non‐atopic asthma and control groups, but leptin and adiponectin did not show any difference among these three groups. Resistin demonstrated positive correlation with methacholine PC20 and negative correlations with eosinophil count and serum total IgE. Leptin and adiponectin showed associations with forced expiratory volume in 1 s or forced expiratory flow between 25–75%. Multiple regression analysis revealed that resistin was a significant predictive factor for asthma. There was no direct association between asthma and leptin or adiponectin. Our findings suggest that resistin may play a negative predictive role in asthma. Adiponectin and leptin showed close associations with pulmonary function and may have disease‐modifying effects in children with asthma.
Simulating the Air Bearing Pressure and Flying Height in a Humid Environment
Authors: Zhang Shuyu , Strom Brian , Lee Sung-Chang , Tyndall George
Published: January 2008

For a hard disk drive operating in a humid environment, the water vapor in the slider’s air bearing is typically compressed beyond its saturation vapor pressure, causing the vapor to condense. Consequently, the air bearing pressure decreases and the slider’s flying attitude adjusts to balance the forces from the suspension. A method for calculating this air bearing response to humid air is presented. Using two air bearing designs, several test cases are analyzed to illustrate the air bearing response for various temperatures and humidity levels. The calculated flying heights agree with those measured in commercial hard disk drives.
A Two-Parameter Function for Nanoscale Indentation Measurement of Near Surface Properties
Authors: Farhang K. , Seitzman L. E. , Feng B.
Published: January 2008

A two-parameter function for estimation of projected area in instrumented indentation measurement is obtained to account for indenter tip imperfection. Imperfection near indenter tip is modeled using a spherical function and combined with a linear function describing the edge boundary of the indenter. Through an analytical fusion technique, the spherical and linear functions are combined into a single function with two unknown geometric parameters of tip radius of curvature and edge slope. Data from indentation measurement of force and displacement, using a Berkovich tip and single crystal alumina and silica samples, are implemented in the proposed area function yielding estimated values of Young’s modulus. Results were compared with that obtained from Oliver and Pharr technique for deep as well as shallow indentation regimes. The estimates for Young’s modulus were found to agree quite favorably. More importantly, in contrast to the Oliver–Pharr technique, the use of the two-parameter function resulted in a significantly more accurate estimation of Young’s modulus for shallow indentation depth of 0–50nm. The error in estimation of Young’s modulus was found to be within 10% for indentation depths of 25–50nm and within 20% for indentation depths of 0–25nm.
Analyses of the Long-Term Performance and Tribological Behavior of an Axial Piston Pump Using Diamondlike-Carbon-Coated Piston Shoes and Biodegradable Oil
Authors: Kalin M. , Majdič F. , Vižintin J. , Pezdirnik J. , Velkavrh I.
Published: January 2008

This work reports on the performance enhancement of a real-scale hydraulic system consisting of diamondlike-carbon (DLC)-coated components in combination with biodegradable oil in long-term experiments under conditions simulating those in an actual application. The performance of a hydraulic axial piston pump with DLC-coated piston shoes was evaluated in a newly designed, dedicated hydraulic test system using fully formulated biodegradable, synthetic ester oil. For comparison, an equal but separated hydraulic system with a conventional commercial pump and stainless-steel shoe surfaces was tested. The tests were run at 85% of the maximum pump load and an oil temperature of around 80°C for a period of 2000h, which corresponds to more than 1yr of continuous 8h∕day operation in an application. A major abrupt oxidation-induced degradation of the oil did not occur in either system; however, the oil from the system comprising the DLC-coated shoes showed noticeably and consistently better results. The wear of the DLC-coated shoes, especially during the running in, was much lower than that in the conventional steel system. Only minor polishing wear was observed on the DLC shoe’s sliding surfaces during the test period, while on the steel shoe’s surfaces, many scratches were found and some erosion of the edges was detected.
Bearing Signature Analysis as a Medium for Fault Detection: A Review
Authors: Patil M. S. , Mathew Jose , RajendraKumar P. K.
Published: January 2008

Rolling element bearings find widespread domestic and industrial application. Defects in bearing unless detected in time may lead to malfunctioning of the machinery. Different methods are used for detection and diagnosis of the bearing defects. This paper is intended as a tutorial overview of bearing vibration signature analysis as a medium for fault detection. An explanation for the causes for the defects is discussed. Vibration measurement in both time domain and frequency domain is presented. Recent trends in research on the detection of the defects in bearings have been included.
A Numerical Model for Life Scatter in Rolling Element Bearings
Authors: Raje Nihar , Sadeghi Farshid , Rateick Richard G. , Hoeprich Michael R.
Published: January 2008

Fatigue lives of rolling element bearings exhibit a wide scatter due to the statistical nature of the mechanisms responsible for the bearing failure process. Life models that account for this dispersion are empirical in nature and do not provide insights into the physical mechanisms that lead to this scatter. One of the primary reasons for dispersion in lives is the inhomogeneous nature of the bearing material. Here, a new approach based on a discrete material representation is presented that simulates this inherent material randomness. In this investigation, two levels of randomness are considered: (1) the topological randomness due to geometric variability in the material microstructure and (2) the material property randomness due to nonuniform distribution of properties throughout the material. The effect of these variations on the subsurface stress field in Hertzian line contacts is studied. Fatigue life is formulated as a function of a critical stress quantity and its corresponding depth, following a similar approach to the Lundberg–Palmgren theory. However, instead of explicitly assuming a Weibull distribution of fatigue lives, the life distribution is obtained as an outcome of numerical simulations. A new critical stress quantity is introduced that considers shear stress acting along internal material planes of weakness. It is found that there is a scatter in the magnitude as well as depth of occurrence of this critical stress quantity, which leads to a scatter in computed fatigue lives. Further, the range of depths within which the critical stress quantity occurs is found to be consistent with experimental observations of fatigue cracks. The life distributions obtained from the numerical simulations are found to follow a two-parameter Weibull distribution closely. The L10 life and the Weibull slope decrease when a nonuniform distribution of elastic modulus is assumed throughout the material. The introduction of internal flaws in the material significantly reduces the L10 life and the Weibull slope. However, it is found that the Weibull slope reaches a limiting value beyond a certain concentration of flaws. This limiting value is close to that predicted by the Lundberg–Palmgren theory. Weibull slopes obtained through the numerical simulations range from 1.29 to 3.36 and are within experimentally observed values for bearing steels.
Influence of Solid Body Temperature on the Thermal EHL Behavior in Circular Contacts
Authors: Liu Xiaoling , Yang Peiran
Published: January 2008

In order to investigate the influence of the body temperature of contacting solids on the lubrication performance of machine components, such as gears and roller bearings, a full numerical solution for the thermal elastohydrodynamic lubrication (EHL) problem in circular contacts under steady state has been achieved. The analysis assumed that the body temperature is different from the temperature of the supplied lubricating oil. The effects of the body temperature, the slide-roll ratio, and the velocity parameter have been discussed. Results show that if the entrainment velocity is not very high, the solid body temperature plays a dominant role in the EHL behavior; however, the influence of the body temperature decreases as the entrainment velocity increases.
ASTROPHYSICAL ASPECTS IN THE STUDIES OF SOLAR COSMIC RAYS
Authors: MIROSHNICHENKO L. I. , PEREZ-PERAZA J. A.
Published: January 2008

This review paper comprises main concepts, available observational data and recent theoretical results related to astrophysical aspects of particle acceleration at/near the Sun and extreme capacities of the solar accelerator(s). We summarize underground and ground-based observations of solar cosmic rays (SCR) accumulated since 1942, direct spacecraft measurements of solar energetic particles (SEP) near the Earth's orbit, indirect information on the SCR variations in the past, and other relevant astrophysical, solar and geophysical data. The list of the problems under discussion includes: upper limit spectrum (ULS) for solar cosmic rays; maximum energy (rigidity), Em(Rm), of particles accelerated at/near the Sun; production of the flare neutrinos; energetics of SCR and solar flares; production of flare neutrons and gamma rays; charge states and elemental abundances of accelerated solar ions; coronal mass ejections (CME's) and extended coronal structures in acceleration models; magnetic reconnection in acceleration scenarios; size (frequency) distributions of solar proton events (SPE) and stellar flares; occurrence probability of giant flares; archaeology of solar cosmic rays. The discussion allows us to outline a series of interesting conceptual and physical associations of SCR generation with the high-energy processes at other stars. The most reliable estimates of various parameters are given in each of research fields mentioned above; a set of promising lines of future studies is highlighted. A great importance of SCR data for resolving some general astrophysical problems is emphasized.
PLANE SYMMETRIC GRAVITATIONAL COLLAPSE
Authors: SHARIF M. , AHMAD ZAHID
Published: January 2008

In this paper, we derive the general formulation by considering two arbitrary plane symmetric space–times using Israel's method. As an example, we apply this formulation to known plane symmetric space–times. We take the Taub's static metric in the interior region whereas Kasner's nonstatic metric in the exterior region. It is shown that the plane collapses in some cases whereas it expands in some others.
ULTRAVIOLET PROPERTIES OF f(R)-GRAVITY
Authors: CODELLO ALESSANDRO , PERCACCI ROBERTO , RAHMEDE CHRISTOPH
Published: January 2008

We discuss the existence and properties of a nontrivial fixed point in f(R)-gravity, where f is a polynomial of order up to six. Within this seven-parameter class of theories, the fixed point has three ultraviolet-attractive and four ultraviolet-repulsive directions; this brings further support to the hypothesis that gravity is nonperturbatively renormalizable.
Metal Binding Affinity and Selectivity in Metalloproteins: Insights from Computational Studies
Authors: Dudev Todor , Lim Carmay
Published: January 2008

This review highlights insights gained from computational studies on protein-metal recognition. We systematically dissect the various factors governing metal binding affinity and selectivity in proteins starting from (a) the intrinsic properties of the metal and neighboring metal cations (if present), to (b) the primary coordination sphere, (c) the second coordination shell, (d) the protein matrix, (e) the bulk solvent, and (f) competing non-protein ligands from the surrounding biological environment. The results herein reveal the fundamental principles and the molecular bases underlying protein-metal recognition, which serve as a guide to engineer novel metalloproteins with programmed properties.
Stressful Life Events and Pemphigus
Authors: Morell-Dubois S. , Carpentier O. , Cottencin O. , Queyrel V. , Hachulla E. , Hatron P.-Y. , Delaporte E.
Published: January 2008

Background: Stress might be a triggering factor causing pemphigus. We studied 11 consecutive cases of pemphigus over 5 years. Objective: Studying and looking for a link between severe life events and the history of the disease. Methods: An epidemiological retrospective and prospective study was carried out, including an interview and a collection of the clinical history; then the life events were integrated into the clinical history with the patient blind. Two scales were used: Paykel’s inventory (assessing the negative impact of life events) and the Mini International Neuropsychiatric Interview DSM-IV (MINI). Results: 10 patients out of 11 were included. With the MINI, 2 patients presented anxiety. Paykel’s inventory showed type 3 life events for numerous patients, life event type 4 for 7 patients and type 5 for 3 patients, happening from 1 to 6 months before the first signs or worsening of pemphigus. We found stressful life events before the start or worsening of pemphigus for all patients with no other risk factors. Conclusion: Stressful life events can worsen or trigger off a pemphigus. Psychological care, associated with the immunosuppressive treatment, should entail a better management of these patients.
Multiple Skin Cysts in Nevoid Basal Cell Carcinoma Syndrome: A Case Report and Review of the Literature
Authors: Motegi Sei-ichiro , Nagai Yayoi , Tamura Atsushi , Ishikawa Osamu
Published: January 2008

We report a 72-year-old man with nevoid basal cell carcinoma syndrome (NBCCS) who presented with 25 skin cysts on his trunk and extremities. Fourteen of 25 skin cysts (56%) were observed on his hands. Histological examination demonstrated that most of the excised cysts had an epithelial wall with typical epidermal keratinization. However, 4 skin cysts (4/16; 25%) showed a corrugated or festooned inner surface of wall without a granular cell layer, which resembled an odontogenic keratocyst, a characteristic feature of skin cysts in NBCCS. A review of the literature suggested that acral localization of skin cysts is a distinctive feature of NBCCS. In addition, the histological findings of skin cysts resembling an odontogenic keratocyst might be a hallmark of NBCCS.