. In a recent paper [9], Choe et al. obtained characterizations for bounded and compact differences of two weighted composition operators acting on standard weighted Bergman spaces over the unit disk in terms of Carleson measures. Then they extended the results to the ball setting. In this paper, we further generalize those results to the Bergman spaces with variable exponent. Our methods, when restricted to the case of constant exponent, are new and simpler. Moreover, boundedness and compactness of Toeplitz operators on variable exponent Bergman spaces are also characterized.
We establish that rational homology disk smoothings of weighted homogeneous surface singularities are always Q-Gorenstein by using their sandwiched structures.
We provide a method to calculate the integrations of some augmentations over finite-dimensional algebras, and prove that these integrations are Bochner integrations. Furthermore, let A be an algebra of type At, we show that there exists a Nakayama algebra A ' of type ->- A t = 1--> 2--> & centerdot; & centerdot; & centerdot; --> t such that the number & sharp;(mod(A)) of iso classes of indecomposable right Amodules, the dimension dim A ' of the Nakayama algebra A ' as a vector space, and the Bochner integrations (B) f[0,1]& times;t 2 Sigma ti=1 vpi d & micro; coincide. Here, p1,...,pt are all right maximal paths on the bound quiver of A ', and, for each 1 <= i <= t, vpi is the sum of all augmentations vvcorre-sponding to starting points v of all arrows on pi. Moreover, we consider some algebras of type D by a similar way.
Two notable classes of figurate numbers are those of polygonal numbers P lambda(n), and centered polygonal numbers C lambda(n), where lambda is the number of sides and n is the position in the sequence. A few years ago, numbers that are simultaneously polygonal concerning two different configurations (i.e., with a different number of sides) were characterized. Similarly, more recently, numbers that are both polygonal and centered polygonal have also been studied. In this article, we characterize the numbers that are simultaneously centered polygonal concerning two distinct configurations. Moreover, solving for certain families of Diophantine equations, we will provide a method for determining explicit examples of numbers that are simultaneously centered.
Motivated by [4], we study when the operator norm of the self-adjoint main character is minimized in the category of finitely generated discrete quantum groups. Specifically, we prove that the operator norm is minimized by the unitary free quantum groups FU(Q), and they are the only minimizers among the duals of free quantum groups.
. We study the mean-field limit of the relativistic Cucker- Smale (RCS) model on complete smooth Riemannian manifolds. The RCS model describes the collective dynamics of the relativistic Cucker- Smale particles on abstract manifolds, and it was first introduced as the generalization of the Cucker-Smale model in special relativity framework via a suitable ansatz for entropy, and using Boillat and Ruggeri's principle of subsystem [9] from the Euler equations for a gas mixture on Riemannian manifolds. In this paper, we derive a Vlasov-type kinetic RCS model on Riemannian manifolds using manifold counterpart of particlein-cell method and study its emergent dynamics. For the proposed kinetic model, we provide a priori velocity alignment estimate via the dissipation of total energy. We also adopt the concept of measure-valued solution to the kinetic RCS model in [4,32] and show the global existence of a unique measure-valued solution.
The aim of this paper is to establish the boundedness of a bilinear singular integral operator Te associated with generalized kernels and its corresponding commutator Teb1,b2 formed by b1, b2 is an element of BMO(Rn) and Te on product mixed Lebesgue spaces Lp(Rn) and product mixed generalized Morrey spaces up(Rn) pound. Via some known results for the operators Te and Teb1,b2, the authors prove that Te and from product spaces Lp1 (Rn) & times; Lp2(Rn) into spaces Lp(Rn). Furthermore, under assumption that Lebesgue measurable functions u1, u2 and u belong to the class Wp and meet u1u2 = u, the authors show that Te and Teb1,b2 are bounded from product spaces u1 pound p1 (Rn) & times; u2p2 pound (Rn) into spaces u pound p Teb1,b2 are bounded (Rn), respectively.
In this paper, we will investigate the boundedness of the commutators of the fractional Hardy operator H(ohm,beta(& centerdot;))of variable order beta(& centerdot;) with some rough kernel ohm is an element of L-s(Sn-1)(s > 1) and its dual operator H-ohm, beta(& centerdot;)(& lowast;) generated with the function b is an element of CMOq(& centerdot;)(R-n) on the grand variable Herz-Morrey spaces M K-center dot alpha(& centerdot;),K-u),K-theta lambda,p(& centerdot;) (Rn), respectively. It's worth noting that, compared with spaces BMO(Rn), the spaces CMOq(& centerdot;)(Rn) are not equipped with the property BMOq(& centerdot;)(R-n) approximate to BMO(R-n), which brings some difficulties to establish main results. Moreover, the corresponding results are also new even on the grand variable Herz spaces K-center dot alpha(& centerdot;),u),theta (p(& centerdot;)) (R-n).
Let T1M(2) be the unit tangent sphere bundle of an oriented Riemannian two-manifold M-2. In this paper we show that T1M(2) admits a one parameter family of bi-contact metric structures (eta 1(c), eta 2(c), gc), c > -1, where g(c) is a Kaluza-Klein metric and (r eta 1(c), eta 2(c), ) is a taut contact circle. If M2 has Gaussian curvature K = constant < 0, we get that T1M2 admits a one parameter family of bi-contact metric structures (eta 1(a),eta 2(a) g(a)), a > 0, where g(a) is a metric of Kaluza-Klein type and (rl1x, rl2x) is a taut contact hyperbola. Furthermore, we find that the Kaluza-Klein metric gc is a critical bi-contact metric, with respect to the Chern-Hamilton functional, if and only if c + 1 = |K| > 0. Finally, when the Gaussian curvature K = constant < 0 and M2 is compact, we show that T1M2 admits two H-1(1)-families of volume preserving contact Anosov vector fields, where H-1(1) denotes an equilateral hyperbola.
In this paper, we prove that every C1 generic diffeomorphism f on a compact smooth manifold M is partially hyperbolic if it has the pseudo-orbit tracing property. Moreover we show that every C1 generic vector filed phi on M with dimM = 3 is singular hyperbolic if it has the pseudo-orbit tracing property. This is a partial answer of the conjecture proposed by Abdenur and D & imath;az in [1].
A partial flag variety is a smooth projective homogeneous variety admitting an action of a maximal torus T. Schubert varieties form an interesting family of T-invariant subvarieties of the partial flag varieties. We study toric Schubert varieties in Grassmannians with respect to the action of a quotient of the torus T. Indeed, we present an explicit description of the fan of a toric Schubert variety in a Grassmannian, and as a corollary, we show that any Gorenstein toric Schubert variety in a Grassmannian is Fano.
We study the existence and asymptotic behavior of solutions to an epidemiological model of SEIRS type with diffusion and nonlinear incidence rates. We first prove the existence and uniqueness of nonnegative global weak solutions to the system by using the Galerkin approximate method and the quasi-positivity of the nonlinear term. Then, we prove the existence of a global attractor for the continuous semigroup generated by the problem. Some properties of the global attractor are investigated such as the upper bound for fractal dimension and the upper semicontinuity with respect to the rate constant for loss of immunity. We also give sufficient conditions for the existence, uniqueness and global exponential stability of nonnegative stationary solutions to the system, which particularly implies that the global attractor becomes a trivial one, i.e., it consists of only a unique nonnegative stationary solution.
In this paper, we classify non-degenerate helix surfaces on the unit tangent bundle of a pseudo-Riemannian surface with constant Gaussian curvature, equipped with a pseudo-Riemannian g-natural metric of Kaluza-Klein type. We further introduce the concept of lightlike screen-helix surfaces within a 3-dimensional Lorentzian manifold and explore some of their key properties. Additionally, we examine lightlike screen-helix surfaces on the unit tangent bundle of surfaces with constant Gaussian curvature.
. In order to construct Nijenhuis algebra, two types of dendriform-Nijenhuis (abbr. dN) bialgebras were introduced by Leroux in [Int. J. Math. Math. Sci. 49-52 (2004), 2595-2615], and then studied by Peng et al. in [J. Algebra 575 (2021), 78-126]. In this paper, we focus on the representations of dN-bialgebras. We find that these two types of dN-bialgebras correspond to left and right representations, respectively. Based on this, we refer to them as left and right dN-bialgebras. Further corresponding left and right representations can be explained by left and right dN-bipro duct bialgebras, respectively. The fact that left and right dN-bialgebras possess the same dN-associative Yang-Baxter equations is discovered. At last, classifications of quasitriangular left (resp., right) dN-bialgebras of low dimensions are given.
Given a bounded domain Q subset of Rn with n >= 2, let cb be a Young function satisfying the doubling condition with the constant K-phi < 2(n). If Omega is a John domain, we show that Omega supports a (phi(n), phi)-Poincare inequality. Conversely, if Omega supports a (phi(n), phi)-Poincare inequality with an additional assumption that it is a simply connected domain when n = 2 or a bounded domain which is quasiconformally equivalent to some uniform domain when n >= 3, then it is a John domain.
. We first discuss imbedding theorems for pseudo-definable spaces and definable Crmanifolds in this note. We prove them under more relaxed conditions than the previous studies. The second topic of this paper is definable groups. We prove several basic assertions on definable groups such as definable topological structures on definable groups and a definable Tietze extension theorem with a group action. We also scrutinize differential topological structures of definable Crgroups in a definably complete locally o-minimal expansion of an ordered field.
In this paper, we mainly discuss the normality and hyponormality of Toeplitz operators with non-harmonic symbols of the form a1zn1zm1 + a2zn2zm2 + a3zn3zm3on the harmonic Bergman space, where each akis a complex number, nk and mk are positive integers for k = 1, 2, 3.
This article investigates a class of generalized quasilinear elliptic equations involving convolution term and critical growth. Using variational methods, we establish the existence of ground state solutions. Our results extend and complement several existing findings in the literature.
Let F-q(d) be a d-dimensional vector space over a finite field(q)(F)with q elements. For x is an element of F-q(d), let parallel to x parallel to=x(1)(2)+& centerdot;& centerdot;& centerdot;+x(d)(2). By abuse ofterminology, we shall call parallel to & centerdot;parallel to a norm onF(q)(d). For a subsetE subset of F-q(d), let triangle(E) be the distance set onEdefined as triangle(E) :={parallel to x-y parallel to:x,y is an element of E}. The Mattila-Sjolin problem seeks the smallest exponent alpha >0 such that triangle(E) =F(q)for all subsetsE subset of F(q)(d)with|E| >= Cq(alpha). In this article, weconsider this problem for a variant of this norm, which generates a smallerdistance set than the norm parallel to & centerdot;parallel to.Namely, we replace the norm parallel to & centerdot;parallel to by the so-calledk-norm (1 <= k <= d), which can be viewed as a kind of deformationof parallel to & centerdot;parallel to. To derive our result on the Mattila-Sjolin problem for thek-norm,we use a combinatorial method to analyze various summations arisingfrom the discrete Fourier machinery. Even though our distance set issmaller than the one in the Mattila-Sjolin problem, for somekwe stillobtain the same result as that of Iosevich and Rudnev [15], which dealswith the Mattila-Sjolin problem. Furthermore, our result is sharp in allodd dimensions.
