Functional inequalities for time-changed symmetric α-stable processes

We establish sharp functional inequalities for time-changed symmetric \alpha-stable processes on {\mathrm{ℝ}}^d with d\ge \mathrm{1} and \alpha \in (\mathrm{0},\mathrm{2}), which yield explicit criteria for the compactness of the associated semigroups. Furthermore, when the time change is defined via the special function W(x)={(\mathrm{1}+\left|x\right|)}^{\beta } with \beta >\alpha we obtain optimal Nash-type inequalities, which in turn give us optimal upper bounds for the density function of the associated semigroups.     

Relative homological dimensions in recollements of triangulated categories

Let E be a proper class of triangles in a triangulated category C, and let (A, B, C) be a recollement of triangulated categories. Based on Beligiannis's work, we prove that A and C have enough E-projective objects whenever B does. Moreover, in this paper, we give the bounds for the E-global dimension of B in a recollement (A, B, C) by controlling the behavior of the E-global dimensions of the triangulated categories A and C: In particular, we show that the finiteness of the E-global dimensions of triangulated categories is invariant with respect to the recollements of triangulated categories.     

Convergence of complex martingale for a branching random walk in an independent and identically distributed environment

We consider anR^d-valued discrete time branching random walk in an independent and identically distributed environment indexed by time n∈N.Let W_n(z)(z∈C^d)be the natural complex martingale of the process.We show necessary and sufficient conditions for the L^α-convergence of W_n(z)forα>1,as well as its uniform convergence region.     

Super-biderivations on twisted N = 1 Schrödinger-Neveu-Schwarz algebra

Let \widetilde{tsns} denote the twisted N = 1 Schrodinger-Neveu-Schwarz algebra over the complex field ℂ. In this paper, we determine the superskewsymmetric super-biderivations of \widetilde{tsns}. Furthermore, we prove that every super-skewsymmetric super-biderivation of \widetilde{tsns} is inner.     

G-stable support τ-tilting modules

Motivated by τ-tilting theory developed by T. Adachi, O. Iyama, I. Reiten, for a nite-dimensional algebra Λwith action by a nite group G; we introduce the notion of G-stable support τ-tilting modules. Then we establish bijections among G-stable support τ-tilting modules over Λ; G-stable two-term silting complexes in the homotopy category of bounded complexes of nitely generated projective Λ-modules, and G-stable functorially nite torsion classes in the category of nitely generated left Λ-modules. In the case when Λ is the endomorphism of a G-stable cluster-tilting object T over a Hom-nite 2-Calabi-Yau triangulated category ℓ with a G-action, these are also in bijection with G-stable cluster-tilting objects in ℓ : Moreover, we investigate the relationship between stable support τ-tilitng modules over Λ and the skew group algebra ΛG:     

Superminimal surfaces in hyperquadric Q2

We study a superminimal surface M immersed into a hyperquadric Q₂ in several cases classified by two global defined functions {{\displaystyle \tau }}_X and {{\displaystyle \tau }}_Y, which were introduced by X. X. Jiao and J. Wang to study a minimal immersion f : M\to {{\displaystyle Q}}_{\mathrm{2}}. In case both {{\displaystyle \tau }}_X and {{\displaystyle \tau }}_Y are not identically zero, it is proved that f is superminimal if and only if f is totally real or i\circ f:M\to {ℂ\mathrm{P}}^{\mathrm{3}} is also minimal, where i:{{\displaystyle Q}}_{\mathrm{2}}\to {ℂ\mathrm{P}}^{\mathrm{3}} is the standard inclusion map. In the rest case that {{\displaystyle \tau }}_X\equiv \mathrm{0} or {{\displaystyle \tau }}_Y\equiv \mathrm{0}, the minimal immersion f is automatically superminimal. As a consequence, all the superminimal two-spheres in Q₂ are completely described.     

Mean-square estimate of automorphic L-functions

Let f be a holomorphic Hecke cusp form with even integral weight k≥2 for the full modular group,and letχbe a primitive Dirichlet character modulo q.Let Lf(s,χ)be the automorphic L-function attached to f andχ-We study the mean-square estimate of Lf(s,χ)and establish an asymptotic formula.     

Proper resolutions and Gorensteinness in extriangulated categories

Let(C,E,s)be an extriangulated category with a proper classξof E-triangles,and W an additive full subcategory of(C,E,s).We provide a method for constructing a proper W(ξ)-resolution(resp.,coproper W(ξ)-coresolution)of one term in an E-triangle inξfrom that of the other two terms.By using this way,we establish the stability of the Gorenstein category GW(ξ)in extriangulated categories.These results generalize the work of Z.Y.Huang[J.Algebra,2013,393:142–169]and X.Y.Yang and Z.C.Wang[Rocky Mountain J.Math.,2017,47:1013–1053],but the proof is not too far from their case.Finally,we give some applications about our main results.     

Spectral gap of Boltzmann measures on unit circle

We give a two sided estimate on the spectral gap for the Boltzmann measures μ_h on the circle. We prove that the spectral gap is greater than 1 for any h\in ℝ and the spectral gap tends to the positive infinity as h\to \infty with speed \left|h\right|.     

Matchings extend to Hamiltonian cycles in hypercubes with faulty edges

We consider the problem of existence of a Hamiltonian cycle containing a matching and avoiding some edges in an n-cube {{\displaystyle Q}}_n, and obtain the following results. Let n\ge \mathrm{3},\hspace{0.17em}M\subset E({{\displaystyle Q}}_n), and F\subset E({{\displaystyle Q}}_n)\backslash M with \mathrm{1}\le \left|F\right|\le \mathrm{2}n-\mathrm{4}-\left|M\right|. If M is a matching and every vertex is incident with at least two edges in the graph {{\displaystyle Q}}_n-F, then all edges of M lie on a Hamiltonian cycle in {{\displaystyle Q}}_n-F. Moreover, if \left|M\right|=\mathrm{1} or \left|M\right|=\mathrm{2}, then the upper bound of number of faulty edges tolerated is sharp. Our results generalize the well-known result for \left|M\right|=\mathrm{1}.     

Equivalence of operator norm for Hardy-Littlewood maximal operators and their truncated operators on Morrey spaces

We will prove that for 1相似文献   

Radon transforms on Siegel-type nilpotent Lie groups

Let \mathfrak{N}:={{\displaystyle H}}_n\times {ℂ}^n be the Siegel-type nilpotent group, which can be identified as the Shilov boundary of Siegel domain of type II, where {{\displaystyle H}}_n denotes the set of all n\times n Hermitian matrices. In this article, we use singular convolution operators to define Radon transform on \mathfrak{N} and obtain the inversion formulas of Radon transforms. Moveover, we show that Radon transform on \mathfrak{N} is a unitary operator from Sobolev space W^n;2 into L²(\mathfrak{N}):     

The second moment of GL(3) × GL(2) L- functions at special points from GL(3) forms

For a fixed even SL(\mathrm{2},\mathbb{Z}) Hecke{Maass form f, we get an estimate for the second moment of L(s,{{\displaystyle \phi }}_j\times f) at special points, where {{\displaystyle \phi }}_j runs over an orthogonal basis of Hecke{Maass cusp forms for {{\displaystyle \mathrm{S}\mathrm{L}}}_{\mathrm{3}}(\mathbb{Z}).     

Grothendieck rings of a class of Hopf algebras of Kac-Paljutkin type

We construct the Grothendieck rings of a class of 2n²dimensional semisimple Hopf Algebras H_2n²,which can be viewed as a generalization of the 8 dimensional Kac-Paljutkin Hopf algebra H8.All irreducible H_2n²-modules are classified.Furthermore,we describe the Grothendieck rings r(H_2n²)by generators and relations explicitly.     

Oscillatory hyper Hilbert transforms along variable curves

For n = 2 or 3 and x\in {ℝ}^n, we study the oscillatory hyper Hilbert transform{{\displaystyle T}}_{\alpha ,\beta }f(x)={{\displaystyle \int }}_{ℝ}f(x-\Gamma (t,x)){\mathrm{e}}^{{-i\left|t\right|}^{-\beta }}{\left|t\right|}^{-\mathrm{1}-\alpha }\mathrm{d}talong an appropriate variable curve \mathrm{\Gamma }(t,x) in {ℝ}^n (namely, \mathrm{\Gamma }(t,x) is a curve in {ℝ}^n for each fixed x), where \alpha >\beta >\mathrm{0}. We obtain some L^p boundedness theorems of {{\displaystyle T}}_{\alpha ,\beta }, under some suitable conditions on \alphaand \beta. These results are extensions of some earlier theorems. However, {{\displaystyle T}}_{\alpha ,\beta }f(x) is not a convolution in general. Thus, we only can partially employ the Plancherel theorem, and we mainly use the orthogonality principle to prove our main theorems.     

Quasi-periodic solutions for class of Hamiltonian partial differential equations with fixed constant potential

We consider Hamiltonian partial differential equations u_tt +|∂_x|u+ σu = f(u), x ∈ T, t ∈?, with periodic boundary conditions, where f(u) is a real-analytic function of the form f(u) = u⁵ + o(u⁵) near u = 0, σ ∈ (0, 1) is a fixed constant, and \mathbb{T}=?/\mathrm{2}\pi \mathbb{Z}T= R/2πZ. A family of quasi-periodic solutions with 2-dimensional are constructed for the equation above with σ ∈ (0, 1)\ ?. The proof is based on infinite-dimensional KAM theory and partial Birkhoff normal form.