Miracle-dz/UniFAR-FTUs huggingface dataset:
Defect fusing rules in affine Toda field theory

The concept of fusing rules for defects in the a r ( 1 ) ? > affine Toda field theories is introduced in the classical and quantum contexts. This idea is employed in finding a new transmission matrix for the a 3 ( 1 ) ? > theory which obeys the triangle relations and the crossing-unitarity relations.
The defect variance of random spherical harmonics

The defect of a function is defined as the difference between the measure of the positive and negative regions. In this paper, we begin the analysis of the distribution of defect of random Gaussian spherical harmonics. By an easy argument, the defect is non-trivial only for even degree and the expected value always vanishes. Our principal result is evaluating the defect variance, asymptotically in the high-frequency limit. As other geometric functionals of random eigenfunctions, the defect may be used as a tool to probe the statistical properties of spherical random fields, a topic of great interest for modern cosmological data analysis.
The thermoelastic bending and thermal diffusion processes influence on photoacoustic signal generation using open photoacoustic cell technique

Thermal diffusion and thermoelastic bending are two consequences of heating generated on the sample surface. Both are employed in Open Photoacoustic Cell (OPC) technique to measure the thermal diffusivity of the sample. In this work, we explore the potential use of the OPC technique to study the effectiveness of thermoelastic bending process and thermal diffusion process on photoacoustic signal (S) generation in solids. More specifically, it is observed that if the thermoelastic bending process becomes more effective while the sample thickness is decreased, this information can be used to obtain a method to self-check the value of the thermal diffusivity parameter measured. The method is based on the measurement of the thermoelastic bending parameter as a function of the sample thickness (ls). The expected dependence of the thermoelastic bending parameter (C2) with the sample thickness, according to the theoretical model, is C2 ∝ ls−3. Our results for aluminum metallic samples give a C2 ∝ ls−2.8 dependenc.
General analytical treatment of optics in layered structures: Application to magneto-optics

We have derived compact and interpretable analytical expressions to describe the magneto-optics in layered structures for all orientations of magnetization and incident angle. In our approach, the multilayer system is considered as nonmagnetic and the magneto-optical effect is described by an induced electrical polarization. The electromagnetic waves radiated by this polarization are calculated via a propagative treatment and are also shown to directly derive from the Lorentz reciprocity theorem. The expressions of the magneto-optical components of the fields transmitted and reflected in the external media are easily interpretable. Only three relevant quantities are involved: the exciting field, the magnetization, and an extraction vector. The practical calculation is very simple in the framework of the first Born approximation as the 4\ifmmode\times\else\texttimes\fi{}4 matrix formalism is replaced by a 2\ifmmode\times\else\texttimes\fi{}2 matrix resolution. The whole approach is not restricted to magneto-optics and the case of a variety of other systems exhibiting weak induced polarizations originating from anisotropy, bianisotropy, nonlinearity, or inhomogeneity is treated. Higher-order approximations are also discussed and an analytical approximation for large induced polarizations in thin layers is derived.
The center of small quantum groups II: singular blocks

We generalize to the case of singular blocks the result in Bezrukavnikov and Lachowska [Quantum groups, Contemporary Mathematics 433 (American Mathematical Society, Providence, RI, 2007) 89–101] that describes the center of the principal block of a small quantum group in terms of sheaf cohomology over the Springer resolution. Then using the method developed in Lachowska and Qi [Int. Math. Res. Not. , Preprint, 2017, arXiv:1604.07380], we present a linear algebro‐geometric approach to compute the dimensions of the singular blocks and of the entire center of the small quantum group associated with a complex semisimple Lie algebra. A conjectural formula for the dimension of the center of the small quantum group at an l th root of unity is formulated in type A.
Thermal modelling for endocardiac radiofrequency ablation: comparison of hyperbolic bioheat equation and Pennes bioheat equation with finite element method

The objectives of this study are to model the endocardiac radiofrequency (RF) ablation procedure and to employ the Hyperbolic Bioheat Equation (HBE), which takes the thermal wave behaviour into account, comparing the results with those obtained using the common Pennes Bioheat Equation (BE) method. A complex model is created to cover particular endocardiac physical and geometry environment. Finite Element Method (FEM) is adopted to study the model with both BE and HBE methods. Different convection coefficients and voltages are applied to simulate different conditions. Lesion size, max temperature and specified position temperature are selected as criteria to evaluate the simulated results. The study found that during ablation, the lesion size difference ratio can reach 20% in some periods. The difference is obvious and cannot be neglected.
Taut foliations in surface bundles with multiple boundary components

Let M be a fibered 3-manifold with multiple boundary components. We show that the fiber structure of M transforms to closely related transversely oriented taut foliations realizing all rational multislopes in some open neighborhood of the multislope of the fiber. Each such foliation extends to a taut foliation in the closed 3-manifold obtained by Dehn filling along its boundary multislope. The existence of these foliations implies that certain contact structures are weakly symplectically fillable. Any closed, orientable 3-manifold can be realized by Dehn filling a 3-manifold which is fibered over S 1 [Alexander 1920; Myers 1978]. In other words, any closed oriented 3-manifold can be realized by Dehn filling a 3-manifold M0, where M0 has the form of a mapping torus M0D ST 0; 1U= ; where S is a compact orientable surface with nonempty boundary and is an equivalence relation given by . x; 1/ . h.x/; 0/ for some orientation-preserving homeomorphism hV S! S which fixes the components of@S setwise. Although we shall not appeal to this fact in this paper, it is interesting to note that it is possible to assume that h is pseudo-Anosov [Colin and Honda 2008] and hence M0 is hyperbolic [Thurston 1988]. It is also possible to assume that S has positive genus. Any nonorientable closed 3-manifold admits a double cover of this form. Taut codimension-one foliations are topological objects which have proved very useful in the study of 3-manifolds. The problem of determining when a 3-manifold contains a taut foliation appears to be a very difficult one. A complete classification exists for Seifert fibered manifolds [Brittenham 1993; Eisenbud et al. 1981; Jankins and Neumann 1985; Naimi 1994], but relatively little is known for the case of hyperbolic 3-manifolds. There are many partial results demonstrating existence
The absolute positive partial transpose property for random induced states

In this paper, we first obtain an algebraic formula for the moments of a centered Wishart matrix, and apply it to obtain new convergence results in the large dimension limit when both parameters of the distribution tend to infinity at different speeds. We use this result to investigate APPT (absolute positive partial transpose) quantum states. We show that the threshold for a bipartite random induced state on $\C^d=\C^{d_1} \otimes \C^{d_2}$, obtained by partial tracing a random pure state on $\C^d \otimes \C^s$, being APPT occurs if the environmental dimension $s$ is of order $s_0=\min(d_1, d_2)^3 \max(d_1, d_2)$. That is, when $s \geq Cs_0$, such a random induced state is APPT with large probability, while such a random states is not APPT with large probability when $s \leq cs_0 $. Besides, we compute effectively $C$ and $c$ and show that it is possible to replace them by the same sharp transition constant when $\min(d_1, d_2)^{2}\ll d$.
A note on functional inequalities for some Levy processes

By using a 2 approach like in (AL00), we establish a modified logarithmic Sobolev inequality for the law at time t for some Levy processes, which yields Poissonian con- fidence intervals in a Monte-Carlo method by means of a concentration inequality for Lipschitz functions. Actually, this result was already obtained in (Wu00) via a martingale representation (Clark-Ocone formulae).
Split metaplectic groups and their L-groups

We adapt the conjectural local Langlands parameterization to split metaplectic groups over local fields. When $\tilde G$ is a central extension of a split connected reductive group over a local field (arising from the framework of Brylinski and Deligne), we construct a dual group $\mathbf{\tilde G}^\vee$ and an L-group ${}^L \mathbf{\tilde G}^\vee$ as group schemes over ${\mathbb Z}$. Such a construction leads to a definition of Weil-Deligne parameters (Langlands parameters) with values in this L-group, and to a conjectural parameterization of the irreducible genuine representations of $\tilde G$. This conjectural parameterization is compatible with what is known about metaplectic tori, Iwahori-Hecke algebra isomorphisms between metaplectic and linear groups, and classical theta correspondences between $Mp_{2n}$ and special orthogonal groups.
On the surjectivity of the power maps of a class of solvable groups

Abstract Let G be a group containing a nilpotent normal subgroup N with central series { N j } {\{N_{j}\}} such that each N j / N j + 1 {N_{j}/N_{j+1}} is an 𝔽 {\mathbb{F}} -vector space over a field 𝔽 {\mathbb{F}} and the action of G on N j / N j + 1 {N_{j}/N_{j+1}} induced by the conjugation action is 𝔽 {\mathbb{F}} -linear. For k ∈ ℕ {k\in\mathbb{N}} we describe a necessary and sufficient condition for all elements from any coset xN, x ∈ G {x\in G} , to admit kth roots in G, in terms of the action of x on the quotients N j / N j + 1 {N_{j}/N_{j+1}} . This yields in particular a condition for surjectivity of the power maps, generalising various results known in special cases. For 𝔽 {\mathbb{F}} -algebraic groups we also characterise the property in terms of centralisers of elements. For a class of Lie groups, it is shown that surjectivity of the kth power map, k ∈ ℕ {k\in\mathbb{N}} , implies the same for the restriction of the map to the solvable radical of the group. The results are applied in particular to the study of exponentiality of Lie groups.
On general transformations and variational principles for the magnetohydrodynamics of ideal fluids. Part III. Stability criteria for axisymmetric flows

The general theory developed in Part I of the present series is here applied to axisymmetric solutions of the equations governing the magnetohydrodynamics of ideal incompressible fluids. We first show a helpful analogy between axisymmetric MHD flows and flows of a stratified fluid in the Boussinesq approximation. We then construct a general Casimir as an integral of an arbitrary function of two conserved fields, namely the vector potential of the magnetic field and the scalar field associated with the ‘modified vorticity field’, the additional frozen-in field introduced in Part I. Using this Casimir, sufficient conditions for linear stability to axisymmetric perturbations are obtained by standard Arnold techniques. We exploit Arnold's method to obtain sufficient conditions for nonlinear (Lyapunov) stability of the MHD flows considered. The appropriate norm is a sum of the magnetic and kinetic energies and the mean square vector potential of the magnetic field.
EXTENDED SOLUTIONS OF THE HARMONIC MAP EQUATION IN THE SPECIAL UNITARY GROUP

We classify all harmonic maps of finite uniton number from a Riemann surface into SU(n) in terms of certain pieces of the Bruhat decomposition of the subgroup of algebraic loops in SU(n). We give a description of the "Frenet frame data" for such harmonic maps in a given class.
Notes on graded symmetric cellular algebras

Let $A=\oplus_{i\in \mathbb{Z}}A_i$ be a finite dimensional graded symmetric cellular algebra with a homogeneous symmetrizing trace of degree $d$. We prove that $A_{-d}$ contains the Higman ideal $H(A)$ of the center of $A$ and $\dim H(A)\leq \dim A_{0}$ if $d\neq 0$, and provide a semisimplicity criterion of $A$ in terms of the centralizer of $A_0$, which is a graded version of \cite[Theorem 3.2]{L}.
Lectures on modular Deligne--Lusztig theory

These notes are based on a series of lectures given by the author at the Centre Bernoulli (EPFL) in July 2016. They aim at illustrating the importance of the mod-$\ell$ cohomology of Deligne--Lusztig varieties in the modular representation theory of finite reductive groups.
Variation of magnetization and the Landé g factor with thickness in Ni–Fe films

We have measured the Lande g factor, the effective magnetization Meff, the uniaxial anisotropy Hk, and the Gilbert damping parameter α, as a function of Permalloy film thickness from 2.5 to 50 nm. We used a pulsed inductive microwave magnetometer capable of generating dc bias fields of 35.2 kA/m (440 Oe). A significant decrease in g is observed with decreasing thickness below 10 nm. Also, Meff decreases with decreasing thickness consistent with a surface anisotropy constant of 0.196±0.025 mJ/m2. The decrease in g can arise from the orbital motion of the electrons at the interface not being quenched by the crystal field. We also compare our data to a model of an effective g factor suggesting that the decrease in g factor might also stem from the Ni–Fe interface with a Ta underlayer.
Invariant Gibbs measures of the energy for shell models of turbulence: the inviscid and viscous cases

Gaussian measures of Gibbsian type are associated with some shell model of turbulence; they are constructed by means of the energy, a conserved quantity for the 3D inviscid and unforced shell model. We prove the existence of a unique global flow for a stochastic viscous shell model with the property that these Gibbs measures are invariant for this flow. Moreover, we prove that the deterministic inviscid shell model has a stationary solution with respect to these measures.
Reductions of topologically massive gravity I: Hamiltonian analysis of second order degenerate Lagrangians

We present Skinner-Rusk and Hamiltonian formalisms of second order degenerate Clement and Sarioglu-Tekin Lagrangians. The Dirac-Bergmann constraint algorithm is employed to obtain Hamiltonian realizations of Lagrangian theories. The Gotay-Nester-Hinds algorithm is used to investigate Skinner-Rusk formalisms of these systems.
Representation field for orders of small ranks

A representation field for a non-maximal order H in a central simple algebra A is a subfield of the spinor class field of maximal orders which determines the set of spinor genera of maximal orders representing H. In our previous work we have proved the existence of the representation field for several important families of suborders, like commutative orders, while we have also found examples where the representation field fails to exist. In this article, we prove that the representation field is defined for any order H of rank 7 or lower. The same technique yields the existence of representation fields for any order in an algebra whose semi-simple reduction is commutative. We also construct a rank-8 order whose representation field is not defined.
A note on the rigidity of unmeasured lamination spaces

We show that every auto-homeomorphism of the unmeasured lamination space of an orientable surface of finite type is induced by a unique extended mapping class unless the surface is a sphere with at most four punctures or a torus with at most two punctures or a closed surface of genus 2.
Controllability of a linear system with persistent memory via boundary traction

We consider a linear viscoelastic system of Maxwell-Boltzmann type. Hence, viscosity contributes a memory term to the elastic equation. The system is controlled via the traction exerted on a part $\Gamma_1$ of the boundary of the body. We prove that if the associated elastic system (i.e. the elastic system without memory) is exactly controllable then the viscoelastic system is exactly controllable too. This is similar to the known result when the boundary deformation is controlled, but the proof is far more delicate since controllability under boundary traction corresponds to the fact that a certain sequence of functions is a Riesz-Fisher sequence, but not a Riesz sequence.
Extremal conformal structures on projective surfaces

We introduce a new functional $\mathcal{E}_{\mathfrak{p}}$ on the space of conformal structures on an oriented projective manifold $(M,\mathfrak{p})$. The nonnegative quantity $\mathcal{E}_{\mathfrak{p}}([g])$ measures how much $\mathfrak{p}$ deviates from being defined by a $[g]$-conformal connection. In the case of a projective surface $(\Sigma,\mathfrak{p})$, we canonically construct an indefinite K\"ahler--Einstein structure $(h_{\mathfrak{p}},\Omega_{\mathfrak{p}})$ on the total space $Y$ of a fibre bundle over $\Sigma$ and show that a conformal structure $[g]$ is a critical point for $\mathcal{E}_{\mathfrak{p}}$ if and only if a certain lift $\widetilde{[g]} : (\Sigma,[g]) \to (Y,h_{\mathfrak{p}})$ is weakly conformal. In fact, in the compact case $\mathcal{E}_{\mathfrak{p}}([g])$ is -- up to a topological constant -- just the Dirichlet energy of $\widetilde{[g]}$. As an application, we prove a novel characterisation of properly convex projective structures among all flat projective structures. As a by-product, we obtain a Gauss--Bonnet type identity for oriented projective surfaces.
Dirac-Kahler equation in curved space-time, relation between spinor and tensor formulations

A common view is that generalization of a wave equation on Riemannian space-time is substantially determined by what a particle is - boson or fermion. As a rule, they say that tensor equations for bosons are extended in a simpler way then spinor equations for fermions. In that context, a very interesting problem is of extension a wave equation for Dirac--K\"{a}hler field (Ivanenko--Landau field was historically first term, also the term a vector field of general type was used). The article relates a generally covariant tensor formalism to a spinor one when these both are applied to description of the Dirac-K\"ahler field in a Rimannian space-time. Both methods are taken to be equivalent and the tensor equations are derived from spinor ones. It is shown that, for characterization of Dirac-K\"ahler's tensor components, two alternative approaches are suitable: these are whether a tetrad-based pseudo tensor classification or a generally coordinate pseudo tensor one. By imposing definite restrictions on the the Dirac-K\"ahler function, we have produced the general covariant form of wave equations for scalar, pseudoscalar, vector, and pseudovector particles.
Tame majorant analyticity for the Birkhoff map of the defocusing nonlinear Schrödinger equation on the circle

For the defocusing nonlinear Schrödinger equation on the circle, we construct a Birkhoff map Φ which is tame majorant analytic in a neighborhood of the origin. Roughly speaking, majorant analytic means that replacing the coefficients of the Taylor expansion of Φ by their absolute values gives rise to a series (the majorant map) which is uniformly and absolutely convergent, at least in a small neighborhood. Tame majorant analytic means that the majorant map of Φ fulfills tame estimates. The proof is based on a new tame version of the Kuksin–Perelman theorem (2010 Discrete Contin. Dyn. Syst. 1 1–24), which is an infinite dimensional Vey type theorem.
Existence of Unpredictable Solutions and Chaos

In paper [1] unpredictable points were introduced based on Poisson stability, and this gives rise to the existence of chaos in the quasi-minimal set. This time, an unpredictable function is determined as an unpredictable point in the Bebutov dynamical system. The existence of an unpredictable solution and consequently chaos of a quasi-linear system of ordinary differential equations are verified. This is the first time that the description of chaos is initiated from a single function, but not on a collection of them. The results can be easily extended to different types of differential equations. An application of the main theorem for Duffing equations is provided.
Lie groupoids and algebroids applied to the study of uniformity and homogeneity of material bodies

A Lie groupoid, called \textit{material Lie groupoid}, is associated in a natural way to any elastic material. The corresponding Lie algebroid, called \textit{material algebroid}, is used to characterize the uniformity and the homogeneity properties of the material. The relation to previous results in terms of $G-$structures is discussed in detail. An illustrative example is presented as an application of the theory.
Numerical models of hydromagnetic dynamos

The magnetic induction equation is solved numerically in a sphere for a variety of prescribed fluid flows. The models considered are the so-called ‘αω dynamos’, in which both small-scale turbulence and large-scale shearing play a significant role. Solutions are obtained by marching the finite–difference equations forward in time from some initial field. For a critical value of the magnetic Reynolds number Rm solutions which neither grow nor decay are found. Further calculations are performed with a ‘cut-off effect’ in which an attempt is made to simulate the effect of the Lorentz forces on the turbulence. For supercritical values of R, the magnetic field now stabilizes a t a finite value instead of increasing indefinitely. The form of the final field is compared with that produced at critical Rm in the absence of the cut-off effect.
Metastability for parabolic equations with drift: Part i

We provide a self-contained analysis, based entirely on pde methods, of the exponentially long time behavior of solutions to linear uniformly parabolic equations which are small perturbations of a transport equation with vector field having a globally stable point. We show that the solutions converge to a constant, which is either the initial value at the stable point or the boundary value at the minimum of the associated quasi-potential. This work extends previous results of Freidlin and Wentzell and Freidlin and Koralov and applies also to semilinear elliptic pde.
A constructive proof of Tarski's theorem on quantifier elimination in the theory of ACF

Assume that $ACF$ denotes the theory of algebraically closed fields. The renowned theorem of A. Tarski states that $ACF$ admits quantifier elimination. In this paper we give a constructive proof of Tarski's theorem on quantifier elimination in $ACF$. This means that for a given formula $\varphi$ of the language of fields we construct a quantifier-free formula $\varphi'$ such that $ACF\vdash\varphi\leftrightarrow\varphi'$. We devote the last section of the paper to show some applications of this constructive version in mathematics and physics.
Non-Koszulness of Operads and Positivity of Poincaré Series

We prove that the operad of mock partially associative $n$-ary algebras is not Koszul, as conjectured by the second and the third author in 2009, and utilise the Zeilberger's algorithm for hypergeometric summation to demonstrate that non-Koszulness of that operad cannot be established by hunting for negative coefficients in the inverse of its Poincare series.
$\infty$-Operads as Analytic Monads

We develop an $\infty$-categorical version of the classical theory of polynomial and analytic functors, initial algebras, and free monads. Using this machinery, we provide a new model for $\infty$-operads, namely $\infty$-operads as analytic monads. We justify this definition by proving that the $\infty$-category of analytic monads is equivalent to that of dendroidal Segal spaces, known to be equivalent to the other existing models for $\infty$-operads.