In this paper we study microlocal regularity of a C 2 -solution u of the equation u t = f ( x , t , u , u x ) , where f ( x , t , ζ 0 , ζ ) is ultradifferentiable in the variables ( x , t ) ∈ R N × R and holomorphic in the variables ( ζ 0 , ζ ) ∈ C × C N . We proved that if C M is a regular Denjoy–Carleman class (including the quasianalytic case) then: WF M ( u ) ⊂ Char ( L u ) , where WF M ( u ) is

An important problem in analysis on fractals is the existence of a self-similar energy on finitely ramified fractals. The self-similar energies are constructed in terms of eigenforms, that is, eigenvectors of a special nonlinear operator. Previous results by C. Sabot and V. Metz give conditions for the existence of an eigenform. In this paper, I prove this type of result in a different way. The proof

Let K be a number field, and let C be a hyperelliptic curve over K with Jacobian J. Suppose that C is defined by an equation of the form y 2 = f ( x ) ( x − λ ) for some irreducible monic polynomial f ∈ O K [ x ] of discriminant Δ and some element λ ∈ O K . Our first main result says that if there is a prime p of K dividing ( f ( λ ) ) but not (2Δ), then the image of the natural 2-adic Galois representation

A central limit theorem and a moderate deviations principle for the ratio of geometric and p-generalized arithmetic mean are shown. Also a Berry–Esseen-type upper bound on the rate of convergence in the central limit theorem is proved. This has implications on the probabilistic version of the question of whether the inequality between geometric and p-generalized arithmetic mean can be reversed or improved

In this note, we study base point freeness up to taking p-power, which we will call p-power freeness. We first establish some criteria for p-power freeness as analogues of criteria for semi-ampleness. We then apply these results to three-dimensional birational geometry.

The number of different prime divisors of the order of a finite group G is bounded above by a quartic function of the maximum number of different prime divisors of the order of a single element in G. This improves earlier results of J. Zhang, T. M. Keller, and A. Moretó.

In this paper, we consider a family of closed hypersurfaces which shrink self-similarly with speed of quotient curvatures. We show that the only such hypersurfaces are shrinking spheres.

Based on singular analysis on manifolds with conical singularities, we establish the existence and nonexistence of solutions for a class of semilinear degenerate elliptic problems on conic manifolds with boundary by utilizing Galerkin method.

We classify connected graphs G whose binomial edge ideal is Gorenstein. In our proofs we use Frobenius type techniques and F-pure thresholds.

There have been a lot of works concerning the Strichartz estimates for the perturbed Schrödinger equation by potential. These can be basically carried out adopting the well-known procedure for obtaining the Strichartz estimates from the weighted L2 resolvent estimates for the Laplacian. In this paper we handle the Strichartz estimates without relying on the resolvent estimates. This enables us to consider

In this note we point out and correct a mistake in our paper “Global Lp estimates for degenerate Ornstein–Uhlenbeck operators with variable coefficients”, published in Math. Nachr. 286 (2013), no. 11–12, 1087–1101.

In this paper, we mainly discuss the existence of solutions for impulsive fractional differential equations. By applying variational methods and critical point theory, some new criteria to guarantee the impulsive fractional impulsive fractional differential equation has infinitely many solutions are established. Moreover, we improve and extend some previous results.

We study local well-posedness and orbital stability/instability of standing waves for a first order system associated with a nonlinear Klein–Gordon equation on a star graph. The proof of the well-posedness uses a classical fixed point argument and the Hille–Yosida theorem. Stability study relies on the linearization approach and recent results for the NLS equation with the δ-interaction on a star graph

In this paper we investigate the nuclear trace of vector-valued Fourier multipliers on the torus and its applications to the index theory of periodic pseudo-differential operators. First we characterise the nuclearity of pseudo-differential operators acting on Bochner integrable functions. In this regards, we consider the periodic and the discrete cases. We go on to address the problem of finding sharp

We prove that the Grand Lebesgue Space built on a unimodular locally compact topological group, equipped with bi-invariant Haar measure, forms a Banach algebra relative to the convolution.

It is proved that two entire functions of finite order having Dirichlet series representation in some right-half plane are identically equal if they have sufficiently many common a-points. In addition, based on the idea of Li in [15], we give a slightly briefer proof of a question posed by Bombieri and Perelli in [3].

Let M1 and M2 be functions on [0,1] such that M 1 ( t 1 / p ) and M 2 ( t 1 / p ) are Orlicz functions for some p ∈ ( 0 , 1 ] . Assume that M 2 − 1 ( 1 / t ) / M 1 − 1 ( 1 / t ) is non-decreasing for t ≥ 1 . Let ( α i ) i = 1 ∞ be a non-increasing sequence of nonnegative real numbers. Under some conditions on ( α i ) i = 1 ∞ , sharp two-sided estimates for entropy numbers of diagonal operators T α

In his previous paper, the author proposed as a problem a purely inseparable analogue of the Abhyankar conjecture for affine curves in positive characteristic and gave a partial answer to it, which includes a complete answer for finite local nilpotent group schemes. In the present paper, motivated by the Abhyankar conjectures with restricted ramifications due to Harbater and Pop, we study a refined

The main aim of this paper is to generalize the classical concept of a positive operator, and to develop a general extension theory, which overcomes not only the lack of a Hilbert space structure, but also the lack of a normable topology. The concept of anti-duality carries an adequate structure to define positivity in a natural way, and is still general enough to cover numerous important areas where

We use Operator Ideals Theory and Gershgorin theory to obtain explicit information in terms of the symbol concerning the spectrum of pseudo-differential operators, on a smooth manifold Ω with boundary ∂ Ω , in the context of the non-harmonic analysis of boundary value problems introduced in [29] in terms of a model operator L . For symbols in the Hörmander class S 1 , 0 0 ( Ω ¯ × I ) , we provide a

Let G be a finite group and let K = x G be the conjugacy class of an element x of G. In this paper, it is proved that if N is a normal subgroup of G such that the coset x N is the union of K and K − 1 (the conjugacy class of the inverse of x), then N and the subgroup ⟨ K ⟩ are solvable. As an application, we prove that if there exists a natural number n ≥ 2 such that K n = K ∪ K − 1 , then ⟨ K ⟩ is solvable

We study invariance for eigenvalues of selfadjoint Sturm–Liouville operators with local point interactions. Such linear transformations are formally defined by H ω : = − d 2 d x 2 + V ( x ) + ∑ n ∈ I ω ( n ) δ ( x − x n ) or similar expressions with δ ′ instead of δ. In a probabilistic setting, we show that a point is either an eigenvalue for all ω or only for a set of ω's of measure zero. Using classical

In this note, we obtain new classification results for static and V-static manifolds under pinching conditions of two different kinds. Firstly, we prove a classification result in higher dimensions assuming a condition of nonnegative Ricci curvature. This extends some recently obtained gap results on the traceless Ricci tensor. Furthermore, we employ the construction of an Einstein manifold associated

In this paper, we study biharmonic hypersurfaces in a product L m × R of an Einstein space L m and a real line R . We prove that a biharmonic hypersurface with constant mean curvature in such a product is either minimal or a vertical cylinder generalizing a result of [36] and [17]. We derived the biharmonic equation for hypersurfaces in S m × R and H m × R in terms of the angle function of the hypersurface

In this note we are concerned with interior regularity properties of the p-Poisson problem Δ p ( u ) = f with p > 2 . For all 0 < λ ≤ 1 we constuct right-hand sides f of differentiability − 1 + λ such that the (Besov-) smoothness of corresponding solutions u is essentially limited to 1 + λ / ( p − 1 ) . The statements are of local nature and cover all integrability parameters. They particularly imply

This paper deals with the well-posedness for the fully nonlinear functional differential equation u ′ ( t ) ∈ A ( t ) u t in a general Banach space X, where { A ( t ) ; t ∈ [ a , b ) } is a family of operators whose domains are subsets of the so-called initial-history space X and whose ranges are subsets of the space X. The special case where A ( t ) ϕ = B ( t ) ϕ ( 0 ) + G ( t , ϕ ) for t ∈ [ a ,

We consider projective rational strong Calabi dream surfaces: projective smooth rational surfaces which admit a constant scalar curvature Kähler metric for every Kähler class. We show that there are only two such rational surfaces, namely the projective plane and the quadric surface. In particular, we show that all rational surfaces other than those two admit a destabilising slope test configuration

Given n disjoint intervals I j on R together with n functions ψ j ∈ L 2 ( I j ) , j = 1 , ⋯ n , and an n × n matrix Θ = ( θ j k ) , the problem is to find an L2 solution φ ⃗ = Col ( φ 1 , ⋯ , φ n ) , φ j ∈ L 2 ( I j ) , to the linear system χ Θ H φ ⃗ = ψ ⃗ , where ψ ⃗ = Col ( ψ 1 , ⋯ , ψ n ) , H = diag ( H 1 , ⋯ , H n ) is a matrix of finite Hilbert transforms with H j defined on L 2 ( I j ) , and

We study an initial boundary value problem of two-dimensional (2D) inhomogeneous incompressible nematic liquid crystal flows with nonnegative density. It is proved that there exists a unique global strong solution provided that the initial orientation satisfies a geometric condition.

In this paper, we introduce the notion of m-normal subgroups and show that the m-normal subgroups of connect locally compact groups and that of compact groups are closely related to Lie groups. As applications, we extend Theorem 3.8 in [D. Peng and W. He, Lower continuous topological groups, Topol. Appl. 265 (2019)] by giving a lower continuity criterion for dense subgroups of arbitrary topological

In this paper, the boundedness of the maximal function for an operator-valued weighted L1 space on the unit sphere of R d + 1 , in which the weight functions are invariant under finite reflection groups, is established. We use it to prove the boundedness of orthogonal expansions in h-harmonics and this result applies to various methods of summability. Furthermore, we obtain the corresponding pointwise

We define new norms for symmetric tensors over ordered normed spaces; these norms are defined by considering linear combinations of tensor products or powers of positive elements only. Relations between the different norms are studied. The results are applied to the problem of representing a finitely exchangeable distribution as a mixture of powers, i.e., mixture of distributions of i.i.d. sequences

In this paper, we establish a new abstract functional space X K , p ( · ) ( Ω ) where K is a uncertain weighted function and p is a variable exponent. Based on the properties of this space, we consider the existence and regularity of weak solutions for non-local fractional differential inclusion with homogeneous Dirichlet boundary conditions. Under a suplinear growth condition we obtain the existence

We study a family of two variables polynomials having moduli up to bilipschitz equivalence: two distinct polynomials of this family are not bilipschitz equivalent. However any level curve of the first polynomial is bilipschitz equivalent to a level curve of the second.

In this paper, we introduce the concept of generalized weak KKM mapping that is more general than many others encountered in the KKM theory. Then, two previous intersection theorems of the author are extended from weak KKM mappings to generalized weak KKM mappings. Applications of these results to set-valued equilibrium problems and minimax inequalities are given in the last two sections.

We consider an infinite strip Ω L = ( 0 , 2 π L ) d − 1 × R , d ≥ 2 , L > 0 , and study the control problem of the heat equation on Ω L with Dirichlet or Neumann boundary conditions, and control set ω ⊂ Ω L . We provide a sufficient and necessary condition for null‐controllability in any positive time T > 0 , which is a geometric condition on the control set ω. This is referred to as “thickness with

Let ( X , d , μ ) be a space of homogeneous type, with upper dimension μ, in the sense of R. R. Coifman and G. Weiss. Let η be the Hölder regularity index of wavelets constructed by P. Auscher and T. Hytönen. In this article, the authors introduce the local Hardy space h ∗ , p ( X ) via local grand maximal functions and also characterize h ∗ , p ( X ) via local radial maximal functions, local non‐tangential

We study some new summability properties of multilinear operators. We introduce the concepts of φ‐summing, φ semi‐integral and φ‐dominated multilinear maps generated by Orlicz functions. We prove a variant of Pietsch's domination theorem for φ‐summing operators, providing also a characterization of φ‐dominated operators in terms of factorizations. We analyze vector‐valued inequalities associated to

The main focus of this paper is to present a method to construct new stable equivalences of Morita type. Suppose that a B‐A‐bimodule N define a stable equivalence of Morita type between finite dimensional algebras A and B. Then, for any generator X of the A‐module category and any finite admissible set Φ of natural numbers, the Φ‐Beilinson–Green algebras G A Φ ( X ) and G B Φ ( N ⊗ A X ) are stably

We consider perturbed quadharmonic operators, Δ 4 + V , acting on sections of a Hermitian vector bundle over a complete Riemannian manifold, with the potential V satisfying a bound from below by a non‐positive function depending on the distance from a point. Under a bounded geometry assumption on the Hermitian vector bundle and the underlying Riemannian manifold, we give a sufficient condition for

We derive sharp quantitative bounds for eigenvalues of biharmonic operators perturbed by complex-valued potentials in dimensions one, two and three.

We study linear and algebraic structures in sets of bounded holomorphic functions on the ball which have large cluster sets at every possible point (i.e., every point on the sphere in several complex variables and every point of the closed unit ball of the bidual in the infinite dimensional case). We show that this set is strongly c -algebrable for all separable Banach spaces. For specific spaces including

This paper first defines operators that are “well-localized” with respect to a pair of accretive functions and establishes a global two-weight T b theorem for such operators. Then it defines operators that are “well-localized” with respect to a pair of accretive systems and establishes a local two-weight T b theorem for them. The proofs combine recent T b proof techniques with arguments used to prove

In this paper, we study the following chemotaxis system with singular sensitivity and logistic source u t = Δ u − χ ∇ · u v ∇ v + r u − μ u k , x ∈ Ω , t > 0 , v t = Δ v − v + u , x ∈ Ω , t > 0 , in a smooth bounded convex domain Ω ⊂ R n ( n ≥ 2 ) with the non-flux boundary, where χ , r , μ > 0 , k > 2 . The boundedness of solutions has been proved in the case that n ≥ 2 , k > 3 ( n + 2 ) n + 4 and

In this paper, we establish the L p -norm ( 1 < p ≤ ∞ ) algebraic decay rate of solutions and higher-order derivative of solutions for 3D generalized Hall-MHD system provided that the L1-norm of initial data is sufficiently small and the parameters α ∈ 5 4 , 2 , β ∈ 7 4 , 2 .

We prove the existence of at least three weak solutions to a mixed Dirichlet–Neumann boundary value problem for equations driven by the p ( z ) -Laplace operator in the principal part. Our approach is variational and use three critical points theorems.

Our aim in this paper is to establish Hardy–Sobolev inequality for Sobolev functions in central Herz–Morrey spaces. As an application, we are concerned with Sobolev-type integral representation for a C1-function on R N which vanishes on the unit ball.

In this paper, we consider the following weakly coupled nonlinear Schrödinger system − ε 2 Δ u 1 + V 1 ( x ) u 1 = | u 1 | 2 p − 2 u 1 + β | u 1 | p − 2 | u 2 | p u 1 , x ∈ R N , − ε 2 Δ u 2 + V 2 ( x ) u 2 = | u 2 | 2 p − 2 u 2 + β | u 2 | p − 2 | u 1 | p u 2 , x ∈ R N , where ε > 0 , β ∈ R is a coupling constant, 2 p ∈ ( 2 , 2 ∗ ) with 2 ∗ = 2 N N − 2 if N ≥ 3 and + ∞ if N = 1 , 2 , V1 and V2 belong

The Douady space of compact subvarieties of a Kähler manifold is equipped with the Weil–Petersson current, which is everywhere positive with local continuous potentials, and of class C ∞ when restricted to the locus of smooth fibers. There a Quillen metric is known to exist, whose Chern form is equal to the Weil–Petersson form. In the algebraic case, we show that the Quillen metric can be extended

We consider a class of L2‐supercritical inhomogeneous nonlinear Schrödinger equations with potential in three dimensions. In the focusing case, using a recent method of Dodson and Murphy, we first study the energy scattering below the ground state for the equation with radially symmetric initial data. We then establish blow‐up criteria for non‐radial solutions to the equation. In the defocusing case

In this paper, we consider the following fractional Kirchhoff equation with critical nonlinearity a + b ∫ R 3 ( − Δ ) s 2 u 2 d x ( − Δ ) s u + V ( x ) u = Q ( x ) f ( u ) + | u | 2 s ∗ − 2 u , x ∈ R 3 , where a , b > 0 , ( − Δ ) s is the fractional Laplace operator with s ∈ ( 3 4 , 1 ) , V vanishes at infinity and 2 s ∗ = 6 3 − 2 s . Under appropriate assumptions on f, we prove the existence of positive

Meromorphic solutions of non‐linear differential equations of the form f n + P ( z , f ) = h are investigated, where n ≥ 2 is an integer, h is a meromorphic function, and P ( z , f ) is differential polynomial in f and its derivatives with small functions as its coefficients. In the existing literature this equation has been studied in the case when h has the particular form h ( z ) = p 1 ( z ) e α

In this article we make a classification of four‐dimensional gradient almost Ricci solitons with harmonic Weyl curvature. We prove first that any four‐dimensional (not necessarily complete) gradient almost Ricci soliton ( M , g , f , λ ) with harmonic Weyl curvature has less than four distinct Ricci‐eigenvalues at each point. If it has three distinct Ricci‐eigenvalues at each point, then ( M , g )

We give a possible extension of definition of shears and overshears in the case of two non commutative (quaternionic) variables in relation with the associated vector fields and flows. We define the divergence operator and determine the vector fields with divergence. Given the non‐existence of quaternionic volume form on H2, we define automorphisms with volume to be time‐one maps of vector fields with

In this article we prove upper bounds for the Laplace eigenvalues λ k below the essential spectrum for strictly negatively curved Cartan–Hadamard manifolds. Our bound is given in terms of k2 and specific geometric data of the manifold. This applies also to the particular case of non-compact manifolds whose sectional curvature tends to − ∞ , where no essential spectrum is present due to a theorem of

Let T : Y → X be a bounded linear operator between two real normed spaces. We characterize compactness of T in terms of differentiability of the Lipschitz functions defined on X with values in another normed space Z. Furthermore, using a similar technique we can also characterize finite rank operators in terms of differentiability of a wider class of functions but still with Lipschitz flavour. As an

In this paper we consider a LES model for the approximation of large scales of the 3D Boussinesq equations. We analyze the convergence rate, in appropriate norms, of the unique regular weak solution of the regularized Boussinesq equations towards a weak solution of the original Boussinesq system.

We consider the Riemann problem for a two-dimensional steady pressureless relativistic Euler equations. The delta shock wave is discovered in the Riemann solutions. It is shown that Dirac delta function develops in the state variable describing the number density of particles. By virtue of a suitable generalized Rankine–Hugoniot relation and entropy condition, we establish the existence and uniqueness

Topological measures and quasi-linear functionals generalize measures and linear functionals. We define and study deficient topological measures on locally compact spaces. A deficient topological measure on a locally compact space is a set function on open and closed sets which is finitely additive on compact sets, inner regular on open sets, and outer regular on closed sets. Deficient topological

In this paper, motivated by a question posed by H. de Alba and D. T. Hoang, we introduce strongly biconvex graphs as a subclass of weakly chordal and bipartite graphs. We give a linear time algorithm to find an induced matching for such graphs and we prove that this algorithm indeed gives a maximum induced matching. Applying this algorithm, we provide a strongly biconvex graph whose (monomial) edge