Search

We construct a two discrete parameter family of compact minimal surfaces embedded in the Berger sphere which may be considered as the analogue of the helicoidal Karcher-Scherk surfaces.

We construct a two discrete parameter family of compact minimal surfaces embedded in the Berger sphere which may be considered as the analogue of the helicoidal Karcher-Scherk surfaces. [ABSTRACT FROM AUTHOR]

This appendix gives a lower bound of the Billingsley-Hausdorff dimension of a level set related to Birkhoff average in the “non-compact” symbolic space $\mathbb{N}^{\mathbb{N}}$, defined by Gibbs measure.

We indicate some important simplifications and extensions of the analysis recently given by J. Benameur to derive blow-up estimates for strong solutions to 3D incompressible Navier–Stokes equations in homogeneous Sobolev spaces H ˙ s ( R 3 ) , s > 1 / 2 , in case of finite-time existence. [ABSTRACT FROM AUTHOR]

In 1985 Crapo introduced in [3] a new mathematical object that he called geometry of circuits. Four years later, in 1989, Manin and Schechtman defined in [13] the same object and called it discriminantal arrangement, the name by which it is known now a days. Those discriminantal arrangements B(n,k,A 0 ) are builded from an arrangement A 0 of n hyperplanes in general position in a k-dimensional space and their combinatorics depends on the arrangement A 0 . On this basis, in 1997 Bayer and Brandt (see [2]) distinguished two different type of arrangements A 0 calling very generic the ones for which the intersection lattice of B(n,k,A 0 ) has maximum cardinality and non-very generic the others. Results on the combinatorics of B(n,k,A 0 ) in the very generic case already appear in Crapo [3] and in 1997 in Athanasiadis [1] while the first known result on non-very generic case is due to Libgober and the first author in 2018. In their paper [12] they provided a necessary and sufficient condition on A 0 for which the cardinality of rank 2 intersections in B(n,k,A 0 ) is not maximal anymore. In this paper we further develop their result providing a sufficient condition on A 0 for which the cardinality of rank r, r ≥ 2, intersections in B(n,k,A 0 ) decreases. [ABSTRACT FROM AUTHOR]

Anantharaman and Le Masson proved that any family of eigenbases of the adjacency operators of a family of graphs is quantum ergodic (a form of delocalization) assuming the graphs satisfy conditions of expansion and high girth. In this paper, we show that neither of these two conditions is sufficient by itself to necessitate quantum ergodicity. We also show that having conditions of expansion and a specific relaxation of the high girth constraint present in later papers on quantum ergodicity is not sufficient. We do so by proving new properties of the Cartesian product of two graphs where one is infinite. [ABSTRACT FROM AUTHOR]

The paper summarizes the main core of the last results that we obtained in [8, 4, 17] on the regularity of the value function for a Bolza problem of a one-dimensional, vectorial problem of the calculus of variations. We are concerned with a nonautonomous Lagrangian that is possibly highly discontinuous in the state and velocity variables, nonconvex in the velocity variable and non coercive. The main results are achieved under the assumption that the Lagrangian is convex on the one-dimensional lines of the velocity variable and satisfies a local Lipschitz continuity condition w.r.t. the time variable, known in the literature as Property (S), and strictly related to the validity of the Erdmann–Du-Bois Reymond equation. Under our assumptions, there exists a minimizing sequence of Lipschitz functions. A first consequence is that we can exclude the presence of the Lavrentiev phenomenon. Moreover, under a further mild growth assumption satisfied by the minimal length functional, fully described in the paper, the above sequence may be taken with the same Lipschitz rank, even when the initial datum and initial value vary on a compact set. The Lipschitz regularity of the value function follows. [ABSTRACT FROM AUTHOR]

A new framework for the asymptotic analysis of incompressible flows of complex non-Newtonian materials is presented in this paper. It allows both to avoid redundant mathematical hypotheses and to dramatically reduce the amount of tedious formal calculations. The starting point of the proposed framework is a generic equation, easily adaptable to most problems of continuum mechanics, for which a thin-layer approximation is developed. We then show how to treat the so-called Gordon--Schowalter derivative, a general objective time derivative involved in non-Newtonian viscoelastic fluids. As a proof of concept of our framework, we apply it to theMaxwell viscoelasticmodel. [ABSTRACT FROM AUTHOR]

The unstable Adams spectral sequence is a spectral sequence that starts fromalgebraic information about the mod 2 cohomology H* (X) of a space X as an unstable algebra over the Steenrod algebra A, and converges, in good cases, to the 2-localized homotopy groups of X. Bousfield and Don Davis looked at the case when X was either of the infinite matrix groups SO or U. Bousfield and Davis created algebraic spectral sequences and conjectured that they agreed with the unstable Adams spectral sequences for SO and U. To this end the following algebraic decomposition must hold ... where M1 ∈ M2 ∈ ⋯ is the well known dyadic filtration of the A-module H* (ℝP∞, ℤ/2) ≄ F2 [u] given by the dyadic expansion of the powers of u. This paper aims at showing that this decomposition holds for numerous values of s and t. [ABSTRACT FROM AUTHOR]

Thanks to a finite element method, we solve numerically parabolic partial differential equations on complex domains by avoiding the mesh generation, using a regular backgroundmesh, not fitting the domain and its real boundary exactly. Our technique follows the φ-FEM paradigm, which supposes that the domain is given by a level-set function. In this paper, we prove a priori error estimates in l²(H¹) and l∞(L2) norms for an implicit Euler discretization in time. We give numerical illustrations to highlight the performances of φ-FEM, which combines optimal convergence accuracy, easy implementation process and fastness. [ABSTRACT FROM AUTHOR]

Let R be a commutative noetherian local ring which is singular and has an isolated singularity. Let Dsg(R) be the singularity category of R in the sense of Buchweitz and Orlov. In this paper, we find real numbers t such that the complexity δt (G, X) in the sense of Dimitrov, Haiden, Katzarkov and Kontsevich vanishes for any split generator G of Dsg(R) and any object X of Dsg(R). In particular, the entropy ht(F) of an exact endofunctor F of Dsg(R) is not defined for such numbers t. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to showthat the modulus of smoothness and the K-functionals constructed from the Sobolev-type space corresponding to the Dunkl operator are equivalent on the interval (-1, 1). [ABSTRACT FROM AUTHOR]

Understanding the behavior of a black-box model with probabilistic inputs can be based on the decomposition of a parameter of interest (e.g., its variance) into contributions attributed to each coalition of inputs (i.e., subsets of inputs). In this paper, we produce conditions for obtaining unambiguous and interpretable decompositions of very general parameters of interest. This allows recovering known decompositions, holding under weaker assumptions than the literature states. [ABSTRACT FROM AUTHOR]

The last decade has seen an abundance of congruences for bℓ(n), the number of ℓ-regular partitions of n. Notably absent are congruences modulo 4 for b3(n). In this paper, we introduce Ramanujan type congruences modulo 4 for b3(2n) involving some primes p congruent to 11,13,17,19,23 modulo 24. [ABSTRACT FROM AUTHOR]

This paper studies the unique continuation problem for the heat equation. We prove a so-called conditional stability estimate for the solution. We are interested in local estimates that are Hölder stable with the weakest possible norms of data on the right-hand side. Such an estimate is useful for the convergence analysis of computational methods dealing with data assimilation. We focus on the case of a known solution at initial time and in some subdomain but that is unknown on the boundary. To the best of our knowledge, this situation has not yet been studied in the literature. [ABSTRACT FROM AUTHOR]

The optimal transport map between the standard Gaussian measure and an α-strongly log-concave probability measure is α-1/2-Lipschitz, as first observed in a celebrated theorem of Caffarelli. In this paper, we apply two classical covariance inequalities (the Brascamp--Lieb and Cramér--Rao inequalities) to prove a sharp bound on the Lipschitz constant of the map that arises from entropically regularized optimal transport. In the limit as the regularization tends to zero, we obtain an elegant and short proof of Caffarelli's original result. We also extend Caffarelli's theorem to the setting in which the Hessians of the log-densities of the measures are bounded by arbitrary positive definite commuting matrices. [ABSTRACT FROM AUTHOR]

In this paper, we study the relative homological dimension based on the class of projectively coresolved Gorenstein flat modules (PGF-modules), that were introduced by Saroch and Stovicek in [26]. The resulting PGF-dimension of modules has several properties in common with the Gorenstein projective dimension, the relative homological theory based on the class ofGorenstein projective modules. In particular, there is a hereditary Hovey triple in the category of modules of finite PGF-dimension, whose associated homotopy category is triangulated equivalent to the stable category of PGF-modules. Studying the finiteness of the PGF global dimension reveals a connection between classical homological invariants of left and right modules over the ring, that leads to generalizations of certain results by Jensen [24], Gedrich and Gruenberg [17] that were originally proved in the realm of commutative Noetherian rings. [ABSTRACT FROM AUTHOR]

A conjecture by the second author, proven by Bonnafé--Rouquier, says that the multiplicity matrix for baby Verma modules over the restricted rational Cherednik algebra has rank one over Q when restricted to each block of the algebra. In this paper, we show that if H is a prime algebra that is a free Frobenius extension over a regular central subalgebra R, and the centre of H is normal Gorenstein, then each central quotient A of H by a maximal ideal m of R satisfies the rank-one property with respect to the Cartan matrix of A. Examples where the result is applicable include graded Hecke algebras, extended affine Hecke algebras, quantized enveloping algebras at roots of unity, non-commutative crepant resolutions of Gorenstein domains and 3 and 4 dimensional PI Sklyanin algebras. In particular, since the multiplicity matrix for restricted rational Cherednik algebras has the rank-one property if and only if its Cartan matrix does, our result provides a different proof of the original conjecture. [ABSTRACT FROM AUTHOR]

In this paper, we present certain results concerning the distribution of zeros of polynomials of a quaternionic variable and with quaternionic coefficients. We obtain ring shaped regions of Eneström--Kakeya type for the zeros of these polynomials and also extend some classical results from the complex to quaternionic setting. [ABSTRACT FROM AUTHOR]

In this paper, we consider a general single species model in a heterogeneous environment of n patches (n ≥ 2), where each patch follows a generalized logistic law. First, we prove the global stability of the model. Second, in the case of perfect mixing, i.e. when the migration rate tends to infinity, the total population follows a generalized logistic law with a carrying capacity which in general is different from the sum of the n carrying capacities. Next, we give some properties of the total equilibrium population and we compute its derivative at no dispersal. In some particular cases, we determine the conditions under which fragmentation and migration can lead to a total equilibrium population which might be greater or smaller than the sum of the n carrying capacities. Finally, we study an example of two-patch model where the first patch follows a logistic law and the second a Richard's law, we give a complete classification of the model parameter space as to whether dispersal is beneficial or detrimental to the sumof two carrying capacities. [ABSTRACT FROM AUTHOR]

In this paper, we study the alternating Euler T-sums and S-sums, which are infinite series involving (alternating) odd harmonic numbers, and have similar forms and close relations to the Dirichlet beta functions. By using the method of residue computations, we establish the explicit formulas for the (alternating) linear and quadratic Euler T-sums and eS-sums, from which, the parity theorems of Hoffman's double and triple t-values and Kaneko-Tsumura's double and triple T-values are further obtained. As supplements, we also show that the linear T-sums and S-sums are expressible in terms of colored multiple zeta values. Some interesting consequences and illustrative examples are presented. [ABSTRACT FROM AUTHOR]

The present paper deals with lines contained in a smooth complex cubic threefold. It is well-known that the set of lines of the second type on a cubic threefold is a curve on its Fano surface. Here we give a description of the singularities of this curve. [ABSTRACT FROM AUTHOR]

In this paper we define a continuous version of multiple zeta functions. They can be analytically continued tomeromorphic functions on ℂr with only simple poles at some special hyperplanes. The evaluations of these functions at positive integers (continuous multiple zeta values) satisfy the shuffle product. We give a detailed analysis about the depth structure of continuous multiple zeta values. There are also sumformulas for continuous multiple zeta values. Lastly we calculate some special continuous multiple zeta values in terms of special values of multiple polylogarithms. [ABSTRACT FROM AUTHOR]

The content of this paper is a generalization of a theorem by Joseph Rabinoff: if P is a finite family of pointed and rational polyhedra in Nℝ such that there exists a fan in Nℝ that contains all the recession cones of the polyhedra of P, if k is a complete non-archimedean field, if S is a connected and regular k-analytic space (in the sense of Berkovich) and Y is a closed k-analytic subset of U P × k S which is relative complete intersection and contained in the relative interior of U P × k S over S, then the quasifiniteness of π : Y → S implies its flatness and finiteness; moreover, all the finite fibers of π have the same length. This namely gives a analytic justification to the concept of stable intersection used in the theory of tropical intersection. [ABSTRACT FROM AUTHOR]

This paper develops Rio's method [11] to prove the weak law of large numbers for maximal partial sums of pairwise independent random variables. The method allows us to avoid using the Kolmogorov maximal inequality. As an application, a weak law of large numbers for maximal partial sums of pairwise independent random variables under a uniform integrability condition is also established. The sharpness of the result is illustrated by an example. [ABSTRACT FROM AUTHOR]

In this paper, we analyse the long-time behavior of solutions to a coupled system describing the motion of a rigid disk in a 2D viscous incompressible fluid. Following previous approaches in [4, 15, 17] we look at the problem in the system of coordinates associated with the center of mass of the disk. Doing so, we introduce a further nonlinearity to the classical Navier Stokes equations. In comparison with the classical nonlinearities, this new termlacks time and space integrability, thus complicating strongly the analysis of the long-time behavior of solutions. We provide herein two refined tools: a refined analysis of the Gagliardo--Nirenberg inequalities and a thorough description of fractional powers of the so-called fluid-structure operator [2]. On the basis of these two tools we extend decay estimates obtained in [4] to arbitrary initial data and show local stability of the Lamb-Oseen vortex in the spirit of [7,8]. [ABSTRACT FROM AUTHOR]

The Grassmann convexity conjecture, formulated in [8], gives a conjectural formula for the maximal total number of real zeroes of the consecutiveWronskians of an arbitrary fundamental solution to a disconjugate linear ordinary differential equation with real time. The conjecture can be reformulated in terms of convex curves in the nilpotent lower triangular group. The formula has already been shown to be a correct lower bound and to give a correct upper bound in several small dimensional cases. In this paper we obtain a general explicit upper bound. [ABSTRACT FROM AUTHOR]

In this paper, we consider the asymptotic behavior of solutions of Monge--Ampère equations with general boundary value conditions in half spaces, which reveals the accurate effect of boundary value condition on asymptotic behavior and improves the result in [13]. [ABSTRACT FROM AUTHOR]

This paper concerns the energy conservation for the weak solutions to the Navier--Stokes--Maxwell system. Although theMaxwell equation with hyperbolic nature, we still establish a LqLp type condition guarantee validity of the energy equality for the weak solutions. We mention that there no regularity assumption on the electric field E. [ABSTRACT FROM AUTHOR]

We consider a one dimensional transport equation with varying vector field and a small viscosity coefficient, controlled by one endpoint of the interval. We give upper and lower bounds on the minimal time needed to control to zero, uniformly in the vanishing viscosity limit. We assume that the vector field varies on the whole interval except at one point. The upper/lower estimates we obtain depend on geometric quantities such as an Agmon distance and the spectral gap of an associated semiclassical Schrödinger operator. They improve, in this particular situation, the results obtained in the companion paper [38]. The proofs rely on a reformulation of the problem as a uniform observability question for the semiclassical heat equation together with a fine analysis of localization of eigenfunctions both in the semiclassically allowed and forbidden regions [40], together with estimates on the spectral gap [1, 33]. Along the proofs, we provide with a construction of biorthogonal families with fine explicit bounds, which we believe is of independent interest. [ABSTRACT FROM AUTHOR]

In this paper, we introduce some monotonicity rules for the ratio of integrals. Furthermore, we demonstrate that the function -- Tν, α β(s) is completely monotonic in s and absolutely monotonic in ν if and only if β 1, where Tν, α β(s) = Kν²(s) -- βKν-α(s)Kν+α(s) defined on s > 0 and Kν(s) is the modified Bessel function of the second kind of order ν. Finally, we determine the necessary and sufficient conditions for the functions s → Tµ,α1(s)/Tν, α,1(s), s → (Tν, α,1(s))/(2T(µ+ν)/2,α,1(s)), and ... Tν, α,1(s)/... ν, α,1 (s) to be monotonic in s ∈ (0, ∞) by employing the monotonicity rules. [ABSTRACT FROM AUTHOR]

This paper is concerned with the blow-up of solutions to the following hyperbolic-elliptic chemotaxis system: ... under homogeneous Neumann boundary conditions in a bounded domain Ω ⊂ ℝn, n ≥ 1, with smooth boundary and the function g is assumed to generalize the logistic source: g(s) ≤ as - b sγ for s > 0 with 1 < γ 2. For b < χ and some suitable conditions on parameters of problem, we prove that the solutions of this problemblow up in finite time. This result extend the obtained results for this problem. [ABSTRACT FROM AUTHOR]

The generalized Frobenius number is the largest integer represented in at most p ways by a linear combination of nonnegative integers of given positive integers a1, a2, ..., ak. When p = 0, it reduces to the classical Frobenius number. In this paper, we give the generalized Frobenius number when aj = (bn+j-1-1)/(b - 1) (b ≥ 2) as a generalization of the result of p = 0 in [16]. [ABSTRACT FROM AUTHOR]

Abstract We continue the analysis of algebras introduced by Georgescu, Nistor, and their coauthors, in order to study N -body type Hamiltonians with interactions. More precisely, let Y ⊂ X be a linear subspace of a finite-dimensional Euclidean space X , and v Y be a continuous function on X / Y that has uniform homogeneous radial limits at infinity. We consider, in this paper, Hamiltonians of the form H = − Δ + ∑ Y ∈ S v Y , where the subspaces Y ⊂ X belong to some given family S of subspaces. Georgescu and Nistor have considered the case when S consists of all subspaces Y ⊂ X , and Nistor and coauthors considered the case when S is a finite semilattice and Georgescu generalized these results to any family. In this paper, we develop new techniques to prove their results on the spectral theory of the Hamiltonian to the case where S is any family of subspaces also, and extend those results to other operators affiliated to a larger algebra of pseudodifferential operators associated with the action of X introduced by Connes. In addition, we exhibit Fredholm conditions for such elliptic operators. We also note that the algebras we consider answer a question of Melrose and Singer. [ABSTRACT FROM AUTHOR]

Abstract This paper considers boundary value problems for a class of singular elliptic operators that appear naturally in the study of asymptotically anti-de Sitter (aAdS) spacetimes. These problems involve a singular Bessel operator acting in the normal direction. After formulating a Lopatinskiı̌ condition, elliptic estimates are established for functions supported near the boundary. The Fredholm property follows from additional hypotheses in the interior. This paper provides a rigorous framework for mode analysis on aAdS spacetimes for a wide range of boundary conditions considered in the physics literature. Completeness of eigenfunctions for some Bessel operator pencils is shown. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study a set relative to singularities of plurisubharmonic functions. We prove that this set is countable under the condition h > 0 on B\ {0}. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an explicit parallel algorithm for finding common solutions to a system of variational inequalities over the set of common fixed points of a finite family of demi-contractive operators. Under suitable assumptions, we prove the strong convergence of this algorithm in the framework of a Hilbert space. The results obtained in this paper extend and improve the results of Tian and Jiang (2017), of Censor, Gibali and Reich (2012), and of many others. [ABSTRACT FROM AUTHOR]

In this paper, we develop in a more general mathematical context the notion of indistinguishability , which in graph theory has recently been investigated as a symmetry relation with respect to a fixed vertex subset. The starting point of our analysis is to consider a set Ω of functions defined on a universe set U and to define an equivalence relation ≡ A on U for any subset A ⊆ Ω in the following way: u ≡ A u ′ if a ( u ) = a ( u ′ ) for any function a ∈ A . By means of this family of relations, we introduce the indistinguishability relation ≈ on the power set P ( Ω ) as follows: for A , A ′ ∈ P ( Ω ) , we set A ≈ A ′ if the relations ≡ A and ≡ A ′ coincide. We use then the indistinguishability relation ≈ to introduce several set families on Ω that have interesting order, matroidal and combinatorial properties. We call the above set families the indistinguishability structures of the function system ( U , Ω ) . Furthermore, we obtain a closure system and an abstract simplicial complex interacting each other by means of three hypergraphs having relevance in both theoretical computer science and graph theory. The first part of this paper is devoted to investigate the basic mathematical properties of the indistinguishability structures for arbitrary function systems. The second part deals with some specific cases of study derived from simple undirected graphs and the usual Euclidean real line. [ABSTRACT FROM AUTHOR]

In a recent paper, Hamidi and Jahangiri [C. R. Acad. Sci. Paris, Ser. I 352 (2014) 17–20] introduced and investigated the class of bi-close-to-convex functions, and determined the estimates for the general Taylor–Maclaurin coefficients of the functions therein. This note mainly aims to point out and correct the errors of the main result in the above-mentioned paper. [ABSTRACT FROM AUTHOR]

In this paper, we prove the theorem announced in the title. [ABSTRACT FROM AUTHOR]

In this paper, we disprove a recent monotonicity conjecture of C. Procesi on the generating function for monotone walks on the symmetric group, an object which is equivalent to the Weingarten function of the unitary group. [ABSTRACT FROM AUTHOR]

In this paper, we derive the Γ-limit of some optimal material distribution problems as the exponent goes to infinity [ABSTRACT FROM AUTHOR]

In this paper we study the motion of a rigid body driven by Newton’s law immersed in a stationary incompressible Stokes flow occupying a bounded simply connected domain. The aim is that of trajectory tracking of the solid by the means of a control in the form of Dirichlet boundary data on the outside boundary of the fluid domain. We show that it is possible to exactly achieve any smooth trajectory for the solid that stays away from the external boundary, by the means of such a remote control. The proof relies on some density methods for the Stokes system, as well as a reformulation of the solid equations into an ODE. [ABSTRACT FROM AUTHOR]

The Erdős–Lax Theorem states that if P(z) = ∑nν=1 aνzν is a polynomial of degree n having no zeros in |z| < 1, then max |z|=1 |P'(z)| ≤ n/2 max |z|=1 |P(z)|. (1) In this paper, we prove a sharpening of the above inequality (1). In order to prove our result we prove a sharpened form of the well-known Theorem of Laguerre on polynomials, which itself could be of independent interest. [ABSTRACT FROM AUTHOR]

In this paper, we address the problem of estimating a covariance matrix of a multivariate Gaussian distribution, from a decision theoretic point of view, relative to a Stein type loss function. We investigate the case where the covariance matrix is invertible and the case when it is non–invertible in a unified approach. [ABSTRACT FROM AUTHOR]

In this paper, we formulate and prove the so-called p-adic non-commutative analytic subgroup theorem. This result is seen as the p-adic analogue of a recent theorem given by Yafaev in [11]. [ABSTRACT FROM AUTHOR]

An abstract group G is called totally 2-closed if H = H(2),Ω for any set Ω with G ∼= H ≤ Sym(Ω), where H(2),Ω is the largest subgroup of Sym(Ω) whose orbits on Ω × Ω are the same orbits of H. In this paper, we classify the finite soluble totally 2-closed groups. We also prove that the Fitting subgroup of a totally 2-closed group is a totally 2-closed group. Finally, we prove that a finite insoluble totally 2-closed group G of minimal order with non-trivial Fitting subgroup has shape Z · X, with Z = Z(G) cyclic, and X is a finite group with a unique minimal normal subgroup, which is nonabelian. [ABSTRACT FROM AUTHOR]

In this paper, we show that there are solutions of degree r of the equation of Pell–Abel on some real hyperelliptic curve of genus g if and only if r > g . This result, which is known to the experts, has consequences, which seem to be unknown to the experts. First, we deduce the existence of a primitive kdifferential on an hyperelliptic curve of genus g with a unique zero of order k(2g −2) for every (k, g ) 6= (2, 2). Moreover, we show that there exists a non Weierstrass point of order n modulo a Weierstrass point on a hyperelliptic curve of genus g if and only if n > 2g . [ABSTRACT FROM AUTHOR]