Stability is a basic property of dynamical systems. In this paper we analyze the stability of multidimensional systems and present new sufficient conditions for the asymptotic stability in terms of linear matrix inequalities. We treat both the discrete-time and continuous-time cases and also propose variants that require linear matrix inequalities of more moderate size.

Copulas are becoming an essential tool in analyzing data thus encouraging interest in related questions. In the early stage of exploratory data analysis, say, it is helpful to know local copula bounds with a fixed value of a given measure of association. These bounds have been computed for Spearman’s rho, Kendall’s tau, and Blomqvist’s beta. The importance of another two measures of association, Spearman’s

We propose an incremental aggregated proximal alternating direction method of multipliers (IAPADMM) for solving a class of nonconvex optimization problems with linear constraints. The new method inherits the advantages of the classical alternating direction method of multipliers and the incremental aggregated proximal method, which have been well studied for structured optimization problems. With some

In this paper we classify the irreducible Harish-Chandra bimodules with full support over filtered quantizations of conical symplectic singularities under the condition that none of the slices to codimension 2 symplectic leaves has type E8. More precisely, consider the quantization 𝒜⋋ with parameter ⋋. We show that the top quotient \( \overline{\mathrm{HC}}\left(\mathcal{A}\lambda \right) \) of the

The rank n symplectic oscillator Lie algebra 𝔤n is the semidirect product of the symplectic Lie algebra 𝔰𝔭2n and the Heisenberg algebra Hn. In this paper, we first study weight modules with finite-dimensional weight spaces over 𝔤n. When the central charge \( \dot{z} \) ≠ 0, it is shown that there is an equivalence between the full subcategory 𝒪𝔤n \( \left[\dot{z}\right] \) of the BGG category

We construct some counterexamples to the statements [1, 2.3.6] claiming maximal inequalities for the spaces \( B_{p,q}^{s}(𝕉^{n}) \) and \( F_{p,q}^{s}(𝕉^{n}) \) and propose a condition for these inequalities to hold. We consider some weighted inequality on a bounded interval \( I \) of the real axis that involves \( f\in C_{0}^{\infty}(I) \) and the derivative of \( f \).

We prove that each homeomorphism \( \varphi:D\to D^{\prime} \) of Euclidean domains in \( 𝕉^{n} \), \( n\geq 2 \), belonging to the Sobolev class \( W^{1}_{p,\operatorname{loc}}(D) \), where \( p\in[1,\infty) \), and having finite distortion induces a bounded composition operator from the weighted Sobolev space \( L^{1}_{p}(D^{\prime};\omega) \) into \( L^{1}_{p}(D) \) for some weight function \(

We study the class of systems of differential equations defined by one class of matrix quasielliptic operators and establish solvability conditions for the systems and boundary value problems on \( {𝕉}^{n}_{+} \) in the special scales of weighted Sobolev spaces \( W^{l}_{p,\sigma} \). We construct the integral representations of solutions and obtain estimates for the solutions.

This is a survey paper about affine Hecke algebras. We start from scratch and discuss some algebraic aspects of their representation theory, referring to the literature for proofs. We aim in particular at the classification of irreducible representations. Only at the end we establish a new result: a natural bijection between the set of irreducible representations of an affine Hecke algebra with parameters

Graham and Winkler derived a formula for the determinant of the distance matrix of a full-dimensional set of n+1 points {x0,x1,…,xn} in the Hamming cube Hn=({0,1}n,ℓ1). In this article we derive a formula for the determinant of the distance matrix D of an arbitrary set of m+1 points {x0,x1,…,xm} in Hn. It follows from this more general formula that det(D)≠0 if and only if the vectors x0,x1,…,xm are

W. C. Lang determined wavelets on Cantor dyadic group by using Multiresolution analysis method. In this paper we have given characterization of wavelet sets on Cantor dyadic group which provides another method for the construction of wavelets. All the wavelets originating from wavelet sets are not necessarily associated with a multiresolution analysis. We have also established relation between multiresolution

We prove that certain possibly non-smooth Hermitian metrics are Griffiths-semipositively curved if and only if they satisfy an asymptotic extension property. This result answers a question of Deng–Ning–Wang–Zhou in the affirmative.

Let S be a Damek–Ricci space and Δ be the Laplace–Beltrami operator of S. We explore the behaviour of heat propagator in S in large time to illustrate the differences with the corresponding results in Rn. In particular we study the relation between the limiting behaviour of the ball-averages as radius tends to ∞ and that of the the heat propagator as time goes to ∞ and use this relation for characterization

In this paper, we introduce the notions of proximal Berinde g-cyclic contractions of two non-self-mappings and proximal Berinde g-contractions, called proximal Berinde g-cyclic contraction of the first and second kind. Coincidence best proximity point theorems for these types of mappings in a metric space are presented. Some examples illustrating our main results are also given. Our main results extend

We generalize the concepts of normalized duality mapping, J-orthogonality and Birkhoff orthogonality from normed spaces to smooth countably normed spaces. We give some basic properties of J-orthogonality in smooth countably normed spaces and show a relation between J-orthogonality and metric projection on smooth uniformly convex complete countably normed spaces. Moreover, we define the J-dual cone

In this work we study the Ulam–Hyers stability of a differential equation. Its proof is based on the Banach fixed point theorem in some space of continuous functions equipped with the norm $\|\cdot \|_{\infty }$ . Moreover, we get some results on the Ulam–Hyers stability of a weakly singular Volterra integral equation using the Banach contraction principle in the space of continuous functions $C([a

For a positive integer r, a distance-r independent set in an undirected graph G is a set I⊆V(G) of vertices pairwise at distance greater than r, while a distance-r dominating set is a set D⊆V(G) such that every vertex of the graph is within distance at most r from a vertex from D. We study the duality between the maximum size of a distance-2r independent set and the minimum size of a distance-r dominating

For lattice paths in strips which begin at (0,0) and have only up steps U:(i,j)→(i+1,j+1) and down steps D:(i,j)→(i+1,j−1), let An,k denote the set of paths of length n which start at (0,0), end on heights 0 or −1, and are contained in the strip −⌊k+12⌋≤y≤⌊k2⌋ of width k, and let Bn,k denote the set of paths of length n which start at (0,0) and are contained in the strip 0≤y≤k. We establish a bijection

The main aim of this paper is to show that one can construct (𝔤,K)-modules of O(p,q) associated with the finite-dimensional representation of 𝔰𝔩2 by quantizing the moment map on the symplectic vector space (ℂp+q)ℝ and using the fact that (O(p,q),SL2(ℝ)) is a dual pair. Then one obtains the K-type formula, the Gelfand–Kirillov dimension and the Bernstein degree of them for all non-negative integers

In this paper, we study the spectral property of the self-affine measure μR,𝒟 generated by an expanding real matrix R=diag(b,b) and the four-element digit set 𝒟={00,10,01,−1−1}. We show that μR,𝒟 is a spectral measure, i.e. there exists a discrete set Λ⊆ℝ2 such that the collection of exponential functions {e−2πi〈λ,x〉:λ∈Λ} forms an orthonormal basis for L2(μ), if and only if b=2k for some k∈ℕ. A

In this note we prove that the Fourier–Mukai transform Φ𝒰 of the universal family of the moduli space ℳℙ2(4,1,3) is not fully faithful.

Let X be an elliptic surface over P1 with κ(X)=1, and M=M(c2) be the moduli scheme of rank-two stable sheaves E on X with (c1(E),c2(E))=(0,c2) in Pic(X)×ℤ. We look into defining equations of M at its singularity E, partly because if M admits only canonical singularities, then the Kodaira dimension κ(M) can be calculated. We show the following: (A) E is at worst canonical singularity of M if the restriction

This paper presents a new non-local expanding flow for convex closed curves in the Euclidean plane which increases both the perimeter of the evolving curves and the enclosed area. But the flow expands the evolving curves to a finite circle smoothly if they do not develop singularity during the evolving process. In addition, it is shown that an additional assumption about the initial curve will ensure

We explore the tan-concavity of the Lagrangian phase operator for the study of the deformed Hermitian Yang–Mills (dHYM) metrics. This new property compensates for the lack of concavity of the Lagrangian phase operator as long as the metric is almost calibrated. As an application, we introduce the tangent Lagrangian phase flow (TLPF) on the space of almost calibrated (1,1)-forms that fits into the GIT

The aim of this paper is to generalize the m-Segre invariant for vector bundles to coherent systems. Let X be a non-singular irreducible complex projective curve of genus g≥0 and G(α;n,d,k) be the moduli space of α-stable coherent systems of type (n,d,k) on X. For any pair of integers (m,t) with 0

We define homogeneous principal Higgs and co-Higgs bundles over irreducible Hermitian symmetric spaces of compact type. We provide a classification for each type of object up to isomorphism, which in each case can be interpreted as defining a moduli space.

We investigate the Pin−(2)-monopole invariants of symplectic 4-manifolds and Kähler surfaces with real structures. We prove a nonvanishing theorem for real symplectic 4-manifolds which is an analogue of Taubes’ nonvanishing theorem of the Seiberg–Witten invariants for symplectic 4-manifolds. Furthermore, the Kobayashi–Hitchin type correspondence for real Kähler surfaces is given.

We prove that the log canonical ring of a projective log canonical pair with Kodaira dimension two is finitely generated.

The purpose of this paper is to explore the geometry of a smooth CR manifold of hypersurface type and its relationship to the higher regularity properties of the complex Green operator on (0,q)-forms in the L2-Sobolev space W0,qk(M) for a fixed k∈ℕ and 1≤q≤n−2.

We define generalized notions of biunitary elements in planar algebras and show that objects arising in quantum information theory such as Hadamard matrices, quantum Latin squares and unitary error bases are all given by biunitary elements in the spin planar algebra. We show that there are natural subfactor planar algebras associated with biunitary elements.

Let M=G/H be an (n+1)-dimensional homogeneous manifold and Jk(n,M)=:Jk be the manifold of k-jets of hypersurfaces of M. The Lie group G acts naturally on each Jk. A G-invariant partial differential equation of order k for hypersurfaces of M (i.e., with n independent variables and 1 dependent one) is defined as a G-invariant hypersurface ℰ⊂Jk. We describe a general method for constructing such invariant

Assume that Φ:𝕄n(ℂ)→𝕄n(ℂ) is a superoperator which preserves hermiticity. We give an algorithm determining whether Φ preserves semipositivity (we call Φpositive in this case). Our approach to the problem has a model-theoretic nature, namely, we apply techniques of quantifier elimination theory for real numbers. An approach based on these techniques seems to be the only one that allows to decide whether

We determine the largest rate of exponential decay at infinity for non-trivial solutions to the Dirac equation 𝒟nψ+𝕍ψ=0in ℝn, being 𝒟n the massless Dirac operator in dimension n≥2 and 𝕍 a (possibly non-Hermitian) matrix-valued perturbation such that |𝕍(x)|∼|x|−𝜖 at infinity, for −∞<𝜖<1. Also, we show that our results are sharp for n∈{2,3}, providing explicit examples of solutions that have the

A quadruple of Lie groups (G,L,K,H), where G is a compact semisimple Lie group, H⊂K⊂L are closed subgroups of G, and the related Casimir constants satisfy certain appropriate conditions, is called a basic quadruple. A basic quadruple is called Einstein if the Killing form metrics on the coset spaces G/H, G/K and G/L are all Einstein. In this paper, we first give a complete classification of the Einstein

Let (M,𝜃) be a compact, connected, strictly pseudo-convex CR manifold. In this paper, we give some properties of the CR Yamabe Operator L𝜃. We present an upper bound for the Second CR Yamabe Invariant, when the First CR Yamabe Invariant is negative, and the existence of a minimizer for the Second CR Yamabe Invariant, under some conditions.

We study parafermion vertex algebras N−3/2(𝔰𝔩(2)) and N−3/2(𝔰𝔩(3)). Using the isomorphism between N−3/2(𝔰𝔩(3)) and the logarithmic vertex algebra 𝒲0(2)A2 from [D. Adamović, A realization of certain modules for the N=4 superconformal algebra and the affine Lie algebra A2(1), Transform. Groups21(2) (2016) 299–327], we show that these parafermion vertex algebras are infinite direct sums of irreducible

Let π:𝒳→Δ be a holomorphic family of compact complex manifolds over an open disk in ℂ. If the fiber π−1(t) for each nonzero t in an uncountable subset B of Δ is Moishezon and the reference fiber X0 satisfies the local deformation invariance for Hodge number of type (0,1) or admits a strongly Gauduchon metric introduced by D. Popovici, then X0 is still Moishezon. We also obtain a bimeromorphic embedding

This paper proposes an alternative estimation method for cointegration, which allows for variation in the leads and lags in the cointegration relation. The method is more powerful than a standard method. Illustrations to annual inflation rates for Japan and the USA and to seasonal cointegration for quarterly consumption and income in Japan shows its ease of use and empirical merits.

Hierarchical B-splines that allow local refinement have become a promising tool for developing adaptive isogeometric methods. Unfortunately, similar to tensor-product B-splines, the computational cost required for assembling the system matrices in isogeometric analysis with hierarchical B-splines is also high, particularly if the spline degree is increased. To address this issue, we propose an efficient

In this work, a matrix Riemann–Hilbert problem of a mixed Chen–Lee–Liu derivative nonlinear Schrödinger (CLL-NLS in brief) equation on the half-line is established by the unified transformation approach. The solution satisfying an initial–boundary value data of the CLL-NLS equation is reconstructed by solving the matrix Riemann–Hilbert problem. Especially, the spectral functions are not independent

The order statistics (OSs) arise in both practical and theoretical aspects including goodness-of-fit tests, characterizations of probability distributions and some estimation approaches such as the L-moments method. Most of these instances are connected with moments of OSs. The records and k-record statistics, also called kth record values in the literature, are other important topics related to the

This article presents an error analysis of the symmetric linear/bilinear partially penalized immersed finite element (PPIFE) methods for interface problems of Helmholtz equations. Under the assumption that the exact solution possesses a usual piecewise H2 regularity, the optimal error bounds for the PPIFE solutions are derived in an energy norm and the usual L2 norm. A numerical example is conducted

In reliability analysis of the stress–strength models, it is generally assumed that an individual only has one type of strength. However, in some situation, an individual, which has several types of independent or dependent strengths, is subjected several types of independent stresses in the working environment. Hence, we define a new multi-state stress–strength model for multi-state system consisting

Inspired by Stein’s lemma, we derive two expressions for the joint moments of elliptical distributions. We use two different methods to derive E[X12f(X)] for any measurable function f satisfying some regularity conditions. Then, by making use of this result, we obtain new formulae for expectations of product of normally distributed random variables, and also present simplified expressions of E[X12f(X)]

In this paper, we propose two complementary variants of the projected Levenberg–Marquardt (LM) algorithm for solving convex constrained nonlinear equations. Since the orthogonal projection onto the feasible set may be computationally expensive, we first propose a local LM algorithm in which inexact projections are allowed. The feasible inexact projections used in our algorithm can be easily obtained

Let S n be a symmetric simple random walk on the integer lattice Z d . For a Bernstein function ϕ we consider a random walk S n ϕ which is subordinated to S n . Under a certain assumption on the behaviour of ϕ at zero we establish global estimates for the transition probabilities of the random walk S n ϕ . The main tools that we apply are a parabolic Harnack inequality and appropriate bounds for the

We work in the smooth category. Let $N$ be a closed connected orientable 4-manifold with torsion free $H_1$, where $H_q := H_q(N; {\mathbb Z} )$. Our main result is a readily calculable classification of embeddings $N \to {\mathbb R}^7$ up to isotopy, with an indeterminacy. Such a classification was only known before for $H_1=0$ by our earlier work from 2008. Our classification is complete when $H_2=0$

We first establish a family of sharp Caffarelli–Kohn–Nirenberg type inequalities (shortly, sharp CKN inequalities) on the Euclidean spaces and then extend them to the setting of Cartan–Hadamard manifolds with the same best constant. The quantitative version of these inequalities also is proved by adding a non-negative remainder term in terms of the sectional curvature of manifolds. We next prove several

We consider the inverse problem of determining the shape of a general nonlinear term appearing in a semilinear hyperbolic equation on a Riemannian manifold with boundary ( M , g ) of dimension n = 2 , 3 . We prove results of unique recovery of the nonlinear term F ( t , x , u ) , appearing in the equation ∂ t 2 u − Δ g u + F ( t , x , u ) = 0 on ( 0 , T ) × M with T > 0 , from partial knowledge of

Concordance invariants of knots are derived from the instanton homology groups with local coefficients, as introduced in earlier work of the authors. These concordance invariants include a 1‐parameter family of homomorphisms f r , from the knot concordance group to R . Prima facie, these concordance invariants have the potential to provide independent bounds on the genus and number of double points

This paper is concerned with the global attractivity of the positive steady state for a time-delayed viral infection model when R0>1. Our study solves the open problem left in a recent work of Yang and Wei (2020) by Lyapunov functional method.

This paper deals with the study of combined effects of logarithmic and critical nonlinearities for the following class of fractional p-Kirchhoff equations: M([u]s,pp)(−Δ)psu=λ|u|q−2uln|u|2+|u|ps∗−2uinΩ,u=0inRN∖Ω,where Ω⊂RN is a bounded domain with Lipschitz boundary, N>sp with s∈(0,1), p≥2, ps∗=Np∕(N−ps) is the fractional critical Sobolev exponent, and λ is a positive parameter. The main result establishes

We present a HIV virus-to-cell model with reactivation of latent infection, Beddington–DeAngelis functional response, distributed and discrete time delays. The basic reproduction number R0 is defined, and the global kinetic of the model is studied by characteristic equation and constructing suitable Lyapunov functions. We show that if R0<1 the infection-free equilibrium is globally asymptotically stable

In this paper, we establish a new blow-up criterion of the strong solution to the quantum hydrodynamic model. This blow-up criterion is different from the one established in our former paper(Wang and Guo, 2020). This blow-up criterion only depends on the gradient of the velocity, the first order time derivative of the square root of the density.

For positive integers s,t,u,v, we define a bipartite graph ΓR(XsYt,XuYv) where each partite set is a copy of R3, and a vertex (a1,a2,a3) in the first partite set is adjacent to a vertex [x1,x2,x3] in the second partite set if and only if a2+x2=a1sx1tanda3+x3=a1ux1v.In this paper, we classify all such graphs according to girth.

The aim of this paper is to compute the commutativity degree in polygroup’s theory, more exactly for the polygroup PG and for extension of polygroups by polygroups, obtaining boundaries for them. Also, we have analyzed the nilpotencitiy of 𝒜[𝒝], meaning the extension of polygroups 𝒜 and 𝒝.

This manuscript involves a class of first-order controllability results for nonlocal non-autonomous neutral differential systems with non-instantaneous impulses in the space 𝕉n. Sufficient conditions guaranteeing the controllability of mild solutions are set up. Concept of evolution family and Rothe’s fixed point theorem are employed to achieve the required results. A model is investigated to delineate

We show that any Weyl group orbit of weights for the Tannakian group of semisimple holonomic 𝒟-modules on an abelian variety is realized by a Lagrangian cycle on the cotangent bundle. As applications we discuss a weak solution to the Schottky problem in genus five, an obstruction for the existence of summands of subvarieties on abelian varieties, and a criterion for the simplicity of the arising Lie

The main result of this paper is to give that if b∈Lip⁡(ℝn), hj∈BMO⁡(ℝn), j=1,…,k, k∈ℤ+ and w∈Ap, 1

Brownfield has become one of the critical issues in modern cities. Over the past few decades, a considerable number of papers on brownfield research have been published. This study reviewed 773 documents themed with “brownfield” in the Web of Science core database between 1980 and 2020 and used the CiteSpace software to sort out the spatial and temporal distribution, knowledge groups, subject structures