Miracle-dz/UniFAR-FTUs huggingface dataset:
Rasmussen invariant, Slice-Bennequin inequality, and sliceness of knots

We use recently introduced Rasmussen invariant to find knots that are topologically locally-flatly slice but not smoothly slice. We note that this invariant can be used to give a combinatorial proof of the slice-Bennequin inequality. Finally, we compute the Rasmussen invariant for quasipositive knots and show that most of our examples of non-slice knots are not quasipositive and, to the best of our knowledge, were previously unknown.
The approximation property does not imply the bounded approximation property

There is a Banach space which has the approxi- mation property but fails the bounded approximation property. The space can be chosen to have separable conjugate, hence there is a nonnuclear operator on the space which has nuclear adjoint. This latter result solves a problem of Grothendieck (2).
INTEGRAL and Multiwavelength Observations of the Blazar Mrk 421 during an Active Phase

A ToO observation of the TeV‐emitting blazar Mrk 421 with INTEGRAL was triggered in June 2006 by an increase of the RXTE count rate to more than 30 mCrab. The source was then observed with all INTEGRAL instruments with the exception of the spectrometer SPI for a total exposure of 829 ks. During this time several outbursts were observed by IBIS and JEM‐X. Multiwavelength observations were immediately triggered and the source was observed at radio, optical and X‐ray wavelengths up to TeV energies. The data obtained during these observations are analysed with respect to spectral evolution and correlated variability. Preliminary results of the analysis are presented in this poster.
Evidence That the Deuteron Is Not an Elementary Particle

If the deuteron were an elementary particle then the triplet n−p effective range would be approximately −ZR(I−Z), where R=4.31 F is the usual deuteron radius and Z is the probability of finding the deuteron in a bare elementary-particle state. This formula is model-independent, but has an error of the order of the range mπ−1=1.41 F of the n−p force, so it becomes exact only in the limit of small deuteron binding energy, i.e., R≫mπ−1. The experimental value of the effective range is not of order R and negative, but rather of order mπ−1 and positive, so Z is small or zero and the deuteron is mostly or wholly composite.
Bending martensite needles in Ni 65 Al 35 investigated by two-dimensional elasticity and high-resolution transmission electron microscopy

The bending and tapering of microtwin needles at the interface between two martensite laminates in ${\mathrm{Ni}}_{65}{\mathrm{Al}}_{35}$ are addressed. A theory is presented, based on the assumption that the microstructure is essentially stress-free; it predicts a linear relationship between the bending and tapering of the needles. The predictions of this theory are compared to experimental data obtained by high-resolution transmission electron microscopy. The agreement between theory and experiment is good, thus bridging the gap between continuum theory and discrete atomic structure, particularly in the region where the bending and tapering are largest.
Reduced norms of division algebras over complete discrete valuation fields of local-global type

Let [Formula: see text] be a complete discrete valuation field whose residue field [Formula: see text] is a global field of positive characteristic [Formula: see text]. Let [Formula: see text] be a central division [Formula: see text]-algebra of [Formula: see text]-power degree. We prove that the subgroup of [Formula: see text] consisting of reduced norms of [Formula: see text] is exactly the kernel of the cup product map [Formula: see text], if either [Formula: see text] is tamely ramified or of period [Formula: see text]. This gives a [Formula: see text]-torsion counterpart of a recent theorem of Parimala, Preeti and Suresh, where the same result is proved for division algebras of prime-to-[Formula: see text] degree.
Bi-Hamiltonian structure of a dynamical system introduced by Braden and Hone

We investigate the finite dimensional dynamical system derived by Braden and Hone in 1996 from the solitons of An−1 affine Toda field theory. This system of evolution equations for an Hermitian matrix L and a real diagonal matrix q with distinct eigenvalues was interpreted as a special case of the spin Ruijsenaars–Schneider models due to Krichever and Zabrodin. A decade later, Li re-derived the model from a general framework built on coboundary dynamical Poisson groupoids. This led to a Hamiltonian description of the gauge invariant content of the model, where the gauge transformations act as conjugations of L by diagonal unitary matrices. Here, we point out that the same dynamics can be interpreted also as a special case of the spin Sutherland systems obtained by reducing the free geodesic motion on symmetric spaces, studied by Pusztai and the author in 2006; the relevant symmetric space being . This construction provides an alternative Hamiltonian interpretation of the Braden–Hone dynamics. We prove that the two Poisson brackets are compatible and yield a bi-Hamiltonian description of the standard commuting flows of the model.
Existence, Uniqueness, and Regularity Results for Elliptic Equations with Drift Terms in Critical Weak Spaces

We consider Dirichlet problems for linear elliptic equations of second order in divergence form on a bounded or exterior smooth domain $\Omega$ in $\mathbb{R}^n$, $n \ge 3$, with drifts $\mathbf{b}$ in the critical weak $L^n$-space $L^{n,\infty}(\Omega ; \mathbb{R}^n )$. First, assuming that the drift $\mathbf{b}$ has nonnegative weak divergence in $L^{n/2, \infty }(\Omega )$, we establish existence and uniqueness of weak solutions in $W^{1,p}(\Omega )$ or $D^{1,p}(\Omega )$ for any $p$ with $n' = n/(n-1) 0$ when the domain $\Omega$ is bounded. By duality, these results enable us to obtain a quite general uniqueness result as well as an existence result for weak solutions belonging to $\bigcap_{p< n' }W^{1,p}(\Omega )$. Finally, we prove a uniqueness result for exterior problems, which implies in particular that (very weak) solutions are unique in both $L^{n/(n-2),\infty}(\Omega )$ and $L^{n,\infty}(\Omega )$.
Nonisospectral scattering problems: A key to integrable hierarchies

We show that certain partial differential equations associated to nonisospectral scattering problems in 2+1 dimensions provide a key to associated integrable hierarchies of both ordinary and partial differential equations. This is illustrated using (an extension of) a known second-order and two new third-order nonisospectral scattering problems. These scattering problems allow us to derive new hierarchies of integrable partial differential equations, in both 1+1 and 2+1 dimensions, together with their underlying linear problems (isospectral and nonisospectral); and also new hierarchies of integrable ordinary differential equations, again with their underlying linear problems.
The global future stability of the FLRW solutions to the Dust-Einstein system with a positive cosmological constant

We study small perturbations of the Friedman–Lemaitre–Robertson–Walker (FLRW) solutions to the dust-Einstein system with a positive cosmological constant in the case that the space-like Cauchy hypersurfaces are diffeomorphic to 𝕋3. We show that the FLRW solutions are nonlinearly globally future-stable under small perturbations of their initial data. In our analysis, we construct harmonic-type coordinates such that the cosmological constant results in the presence of dissipative terms in the evolution equations. Our result extends those of [I. Rodnianski and J. Speck, The nonlinear future stability of the FLRW family of solutions to the irrotational Euler–Einstein system with a positive cosmological constant, J. Eur. Math. Soc. 15 (2013) 2369–2462; J. Speck, The nonlinear future stability of the FLRW family of solutions to the Euler–Einstein system with a positive cosmological constant, Selecta Math. 18 (2012) 633–715; C. Lubbe and J. A. Valiente Kroon, A conformal approach for the analysis of the nonlinear stability of pure radiation cosmologies, Ann. Phys. 328 (2013) 1–25], where analogous results were proved for the Euler–Einstein system under the equations of state , . The dust-Einstein system is the case cs = 0. The main difficulty that we overcome here is that the dust's energy density loses one degree of differentiability compared to the cases , which introduces many obstacles for closing the estimates. To resolve this difficulty, we commute the equations with a well-chosen differential operator and derive elliptic estimates that complement the energy estimates of [I. Rodnianski and J. Speck, The nonlinear future stability of the FLRW family of solutions to the irrotational Euler–Einstein system with a positive cosmological constant, J. Eur. Math. Soc. 15 (2013) 2369–2462; J. Speck, The nonlinear future stability of the FLRW family of solutions to the Euler–Einstein system with a positive cosmological constant, Selecta Math. 18 (2012) 633–715]. Our results apply in particular to small perturbations of the vanishing dust state containing vacuum regions.
Seiberg–Witten and Gromov invariants for
self-dual harmonic 2–forms

Author(s): Gerig, Chris | Advisor(s): Hutchings, Michael | Abstract: For a closed oriented smooth 4-manifold X with $b^2_+(X)g0$, the Seiberg-Witten invariants are well-defined. Taubes' "SW=Gr" theorem asserts that if X carries a symplectic form then these invariants are equal to well-defined counts of pseudoholomorphic curves, Taubes' Gromov invariants. In the absence of a symplectic form there are still nontrivial closed self-dual 2-forms which vanish along a disjoint union of circles and are symplectic elsewhere. This thesis describes well-defined counts of pseudoholomorphic curves in the complement of the zero set of such near-symplectic 2-forms, and it is shown that they recover the Seiberg-Witten invariants (modulo 2). This is an extension of Taubes' "SW=Gr" theorem to non-symplectic 4-manifolds.The main results are the following. Given a suitable near-symplectic form w and tubular neighborhood N of its zero set, there are well-defined counts of pseudoholomorphic curves in a completion of the symplectic cobordism (X-N, w) which are asymptotic to certain Reeb orbits on the ends. They can be packaged together to form "near-symplectic" Gromov invariants as a map on the set of spin-c structures of X. They are furthermore equal to the Seiberg-Witten invariants with mod 2 coefficients, where w determines the "chamber" for defining the latter invariants when $b^2_+(X)=1$. In the final chapter, as a non sequitur, a new proof of the Fredholm index formula for punctured pseudoholomorphic curves is sketched. This generalizes Taubes' proof of the Riemann-Roch theorem for compact Riemann surfaces.
The Laguerre Unitary Process

We define a new matrix-valued stochastic process with independent stationary increments from the Laguerre Unitary Ensemble, which in a certain sense may be considered a matrix generalisation of the gamma process. We show that eigenvalues of this matrix-valued process forms a spatiotemporal determinantal point process and give an explicit expression for the correlation kernel in terms of Laguerre polynomials. Furthermore, we show that in an appropriate long time scaling limit, this correlation kernel becomes identical to that of Dyson Brownian Motion.
On the structure of double complexes

We study consequences and applications of the folklore statement that every double complex over a field decomposes into so‐called squares and zigzags. This result makes questions about the associated cohomology groups and spectral sequences easy to understand. We describe a notion of ‘universal’ quasi‐isomorphism and the behaviour of the decomposition under tensor product and compute the Grothendieck ring of the category of bounded double complexes over a field with finite cohomologies up to such quasi‐isomorphism (and some variants).
Simulation error minimization identification based on multi‐stage prediction

Classical prediction error minimization (PEM) methods are widely used for model identification, but they are also known to provide satisfactory results only in specific identification conditions, e.g. disturbance model matching. If these conditions are not met, the obtained model may have quite different dynamical behavior compared with the original system, resulting in poor long range prediction or simulation performance, which is a critical factor for model analysis, simulation, model‐based control design. In the mentioned non‐ideal conditions a robust and reliable alternative is based on the minimization of the simulation error. Unfortunately, direct optimization of a simulation error minimization (SEM) criterion is an intrinsically complex and computationally intensive task. In this paper a low‐complexity approximate SEM approach is discussed, based on the iteration of multi‐step PEM methods. The soundness of the proposed approach is demonstrated by showing that, for sufficiently high prediction horizons, the k‐steps ahead (single‐ or multi‐step) PEM criteria converge to the SEM one. Identifiability issues and convergence properties of the algorithm are also discussed. Some examples are provided to illustrate the mentioned properties of the algorithm. Copyright © 2010 John Wiley & Sons, Ltd.
Critical temperature for kaon condensation in color-flavor-locked quark matter

We study the behavior of Goldstone bosons in color-flavor-locked (CFL) quark matter at nonzero temperature. Chiral symmetry breaking in this phase of cold and dense matter gives rise to pseudo-Goldstone bosons, the lightest of these being the charged and neutral kaons K + and K°. At zero temperature, Bose-Einstein condensation of the kaons occurs. Since all fermions are gapped, this kaon-condensed CFL phase can, for energies below the fermionic energy gap, be described by an effective theory for the bosonic modes. We use this effective theory to investigate the melting of the condensate: we determine the temperature-dependent kaon masses self-consistently using the two-particle irreducible effective action, and we compute the transition temperature for Bose-Einstein condensation. Our results are important for studies of transport properties of the kaon-condensed CFL phase, such as bulk viscosity.
Taylor dispersion of orientable Brownian particles in unbounded homogeneous shear flows

The physical- and orientation-space transport of non-spherical, generally non-neutrally buoyant, Brownian particles in unbounded homogeneous shear flows is analysed with the goal of studying the respective effects of the orientational degrees of freedom of such particles upon their sedimentation and dispersion rates. In particular, the present contribution concentrates on the interaction between the Taylor dispersion mechanism (arising from coupling between the orientational dependence of the particle's translational velocity and the stochastic sampling of the orientation space via rotary Brownian diffusion) and the shear velocity field. Making use of a recent extension of generalized Taylor dispersion theory to homogeneous (unbounded) shear flows, the mean transport process in physical space is modelled by a convection–diffusion problem characterized by a pair of constant phenomenological coefficients, provided that the eigenvalues of the (constant) undisturbed velocity gradient are purely imaginary. The latter phenomenological coefficients – namely, U*, the average ‘slip velocity’ vector (of the particles relative to the ambient fluid), and D*, the dispersivity dyadic or, equivalently, the pair of dyadics $\bar{\bm M}$ and DC (or $\bar{\bm D}^c$), the average mobility and the Taylor (or modified Taylor) dispersivity, respectively – are evaluated both asymptotically (in the respective limits of small and large rotary Peclét numbers) as well as numerically (for arbitrary Peclét numbers). It is established that (up to a scalar multiplication factor, independent of Peclét number) the anisotropic portion of the average mobility is formally equivalent to the direct diffusive contribution to the particle stress in the context of suspension rheology. The analysis focuses mainly on the case of simple shear flow. The approximate calculation in the limit of large Peclét numbers, Pe [Gt ] 1, which makes extensive use of the ‘natural coordinates’ along Jeffery orbits previously introduced by Leal & Hinch, verifies that, if the external force is non-orthogonal to the direction along which (undisturbed) fluid velocity variations occur, two of the eigenvalues of Dc are proportional to Pe; moreover, one of these O(Pe) eigenvalues is negative. When the external force is parallel to the latter direction, the negative eigenvalue corresponds to the principal direction of contraction in the shear velocity field; this thus relates the non-positive nature of DC to the interaction between the Taylor dispersion mechanism and the (deterministic) convection within the shear field. Explicit results for the variation of the dyadics $\bar{\bm M}$, Dc and $\bar{\bm D}^{c}$ jointly with the respective magnitude of the shear rate and the deviation of the particle geometry from a spherical shape are presented for spheroidal particles. Among other things, it is demonstrated that the proposed definition of the modified Taylor dispersivity coefficient, $\bar{\bm D}^{c}$, does indeed yield a non-negative dyadic.
Equations in the Hadamard ring of rational functions

Let K be a number field. It is well known that the set of recurrencesequences with entries in K is closed under component-wise operations, and so it can be equipped with a ring structure. We try to understand the structure of this ring, in particular to understand which algebraic equations have a solution in the ring. For the case of cyclic equations a conjecture due to Pisot states the following: assume {an} is a recurrence sequence and suppose that all the an have a d th root in the field K ; then (after possibly passing to a finite extension of K ) one can choose a sequence of such d th roots that satisfies a recurrence itself. This was proved true in a preceding paper of the second author. In this article we generalize this result to more general monic equations; the former case can be recovered for g(X, Y ) = Xd − Y = 0. Combining this with the Hadamard quotient theorem by Pourchet and Van der Poorten, we are able to get rid of the monic restriction, and have a theorem that generalizes both results. Mathematics Subject Classification (2000): 11B37 (primary); 12E25, 13F25 (secondary).
On smooth and isolated curves in general complete intersection Calabi-Yau threefolds

Recently Knutsen found criteria for the curves in a complete linear system |L| on a smooth surface X in a nodal Ktrivial threefold Y0 to deform to a scheme of finitely many smooth isolated curves in a general deformation Yt of Y0. In this article we develop new methods to check whether the set of nodes of Y0 imposes independent conditions on |L|. As an application, we find new smooth isolated curves in complete intersection Calabi-Yau
The Benard-Von Karman instability : an experimental study near the threshold

The evolution of the velocity components of the wake behind a cylinder has been investigated in the range 40 L'evolution des composantes de la vitesse dans le sillage d'un cylindre est etudiee dans la gamme 40<Re<300 par anemometrie Laser Doppler a defilement de franges. Le parametre d'ordre (amplitude de la fluctuation de vitesse perpendiculaire) suit la loi de Landau. L'existence de plusieurs modes est verifiee et des effets tridimensionnels sont observes et interpretes lorsque deux modes co-existent. La dependance des grandeurs critiques en fonction du rapport d'aspect est egalement donnee
Blow ups and base changes of symmetric powers and Chow groups

Let $\Sym^m X$ denote the $m$-th symmetric power of a smooth projective curve $X$. Let $\wt{\Sym^m X}$ be the blow up of $\Sym^m X$ along some non-singular subvariety. In this note we are going to discuss when the pushforward homomorphism induced by the natural morphism from $\wt{\Sym^m X}$ to $\Sym^n X$ is injective at the level of Chow groups for $m\leq n$. Also we are going to prove that base changes of embeddings of one symmetric power into another, with respect to closed embeddings induces an injection at the level of Chow groups.
On the temporal decay of solutions to the two‐dimensional nematic liquid crystal flows

We consider the temporal decay estimates for weak solutions to the two‐dimensional nematic liquid crystal flows, and we show that the energy norm of a global weak solution has non‐uniform decay ∥u(t)∥L2+∥∇d(t)∥L2→0ast→∞,under suitable conditions on the initial data. We also show the exact rate of the decay (uniform decay) of the energy norm of the global weak solution.
Painlevé functions of the third kind

We explicitly construct the one‐parameter family of solutions, η (ϑ;ν,λ), that remain bounded as ϑ→∞ along the positive real ϑ axis for the Painleve equation of third kind w w′′= (w′)2−ϑ−1 w w′+2νϑ−1(w 3−w) +w 4−1, where, as ϑ→∞, η ∼ 1−λΓ (ν+1/2)2−2νϑ−ν−1/2 e −2ϑ. We further construct a representation for ψ (t;ν,λ) =−ln[η (t/2;ν,λ)], where ψ (t;ν,λ) satisfies the differential equation ψ′′+t −1ψ′= (1/2)sinh(2ψ)+2νt −1 sinh(ψ). The small‐ϑ behavior of η (ϑ;ν,λ) is described for ‖λ‖<π−1 by η (ϑ;ν,λ) ∼ 2σ Bϑσ. The parameters σ and B are given as explicit functions of λ and ν. Finally an identity involving the Painleve transcendent η (ϑ;ν,λ) is proved. These results for the special case ν=0 and λ=π−1 make rigorous the analysis of the scaling limit of the spin–spin correlation function of the two‐dimensional Ising model.
A mass‐fraction‐based interface‐capturing method for multi‐component flow

An interface‐capturing method based on mass fraction is developed to solve the Riemann problem in multi‐component compressible flow. Equations of mass fraction with modified form, which is derived from conservative equations of mass, are employed here to capture the interface. By introducing mass fraction into Euler equations system, as well as other conservative coefficients, a quasi‐conservative numerical model is created. Numerical examples show that the mass fraction model performs well not only in multi‐component fluids modeled by simple stiffened gas equation of state (EOS) but also in that modeled by complex Mie–Grüneisen EOS. Moreover, the mass fraction model is applied to Riemann problem with piecewise EOS; the expression of which depends on density. It is found that the mass fraction model can well adapt to the analytic change in piecewise EOS and produce accuracy solutions with fewer unknown quantities, and the model can be easily extended to m‐component fluid mixture by using only m + 4 equations with no additional conditions. Copyright © 2013 John Wiley & Sons, Ltd.
Dirac gamma-equation, classical gauge fields and Clifford algebra

An equation, we call Dirac γ -equation, is introduced with the help of the mathematical tools connected with the Cliﬀord algebra. This equation can be considered as a generalization of the Dirac equation for the electron. Some features of Dirac γ -equation are investigated (plane waves, currents, canonical forms). Furthermore, on the basis of local gauge invariance regarding unitary group, a system of equations is introduced consisting of Dirac γ -equation and the Yang-Mills or Maxwell equations. This system of equations describes a Dirac’s ﬁeld interacting with the Yang-Mills or Maxwell gauge ﬁeld. Characteristics of this system of equations are studied for various gauge groups and the liaison between the new and the standard constructions of classical gauge ﬁelds is discussed. , t to √ λ , . , i λ of the group the the , . , t , . , t (2.20) G ( t , . ,