In this paper, we give some equivalent conditions to have an inclusion between two generalized Orlicz spaces. One of these conditions does not depend on generalized Young functions. The obtained results improve the famous ones on Lebesgue spaces.

Some norm inequalities are presented for non- selfadjoint differential operators. First, the resolvent of the introduced non-selfadjoint differential operator using m-sectorial operators in the Hilbert space \(H=L_{2}(\Omega )\) is established. As application of this new result, the resolvent of the considered operator in the Hilbert space \(H^{\ell }=L_{2}(\Omega )^{\ell }\) is obtained utilizing

This paper systematically investigates the Lie symmetry analysis of a class of 3-dimensional non-linear 2-Hessian equations \(u_{xx}u_{yy}+u_{xx}u_{yy}+u_{yy}u_{zz}=u_{xy}^2+u_{yz}^2+u_{xz}^2+f\), where f is an arbitrary smooth function f of the variables (x, y, z). In fact, the preliminary group classification of the 2-Hessian equation was carried out. That means, we find one-dimensional Lie symmetry

In this paper, under m-Bakry–Émery (or \(\infty \)-Bakry–Émery) pseudohermitian Ricci curvature condition, we derive subgradient estimate for positive solutions of \(\Delta _{H,\phi } u(x)=-\lambda u(x)\) on a weighted complete noncompact pseudohermitian manifold which satisfies the sub-Laplacian comparison property.

Let H be a Hilbert \(C^*\)-module, and let \(H_M\) be the indefinite inner space induced by a self-adjointable and invertible operator M on H. Given weighted projections P and Q on \(H_M\), let \(S_{\lambda ,k}=(PQ)^k-\lambda (QP)^k\) for a pair \((k, \lambda )\), where k is a natural number and \(\lambda \) is a complex number. It is proved that \(PQ-QP\) is weighted Moore–Penrose invertible if and

In this paper, we study nonlinear matrix equations $$\begin{aligned} X^p=A+\sum \limits _{i=1}^m M_i^T(X\#B)M_i \end{aligned}$$ and $$\begin{aligned} X^p=A+\sum \limits _{i=1}^j M_i^T(X\#B)M_i+\sum \limits _{i=j+1}^m M_i^T(X^{-1}\#B)M_i, \end{aligned}$$ where p, m, j are positive integers, \(1\le j\le m\), A, B are \(n\times n\) positive definite matrices and \(M_i(i=1,2,3,\ldots ,m)\) are \(n\times

An ideal I of a commutative ring is called a \(z^{\circ }\)-ideal if for every \(a\in I\), \(P_a\subseteq I\), where \(P_a\) denotes the intersection of all minimal prime ideals of the ring that contain a. In this article, we study the sum of \(z^\circ \)-ideals in two classes of subrings of C(X); namely, the intermediate rings and subrings of the form \(I+{\mathbb {R}}\), where I is an ideal in C(X)

We give, in this paper, a characterization of the independent representation in law for a sum of dependent Bernoulli random variables. This characterization is related to the stability property of the probability-generating function of this sum, which is a polynomial with positive coefficients. As an application, we give a Hoeffding inequality for a sum of dependent Bernoulli random variables when

Let \({\mathcal {A}}\) be a factor von Neumann algebra with dim\({\mathcal {A}}\ge 2\). We prove that a map \(\phi : {\mathcal {A}}\rightarrow {\mathcal {A}}\) satisfies \(\phi ([A, B]_{\diamond })=[\phi (A), B]_{\diamond }+[A, \phi (B)]_{\diamond }\) for all \(A, B\in {\mathcal {A}}\) if and only if \(\phi \) is an additive \(*\)-derivation, where \([A, B]_{\diamond }=AB^{*}-BA^{*}\).

The paper studies partially observed optimal control problems of general McKean–Vlasov differential equations, in which the coefficients depend on the state of the solution process as well as of its law and the control variable. By applying Girsanov’s theorem with a standard variational technique, we establish a stochastic maximum principle on the assumption that the control domain is convex. As an

In this article, we continue studying of \( \mathcal {H}_Y \)-ideals. We introduce notions fixed \( \mathcal {H}_Y \)-ideals, free \( \mathcal {H}_Y \)-ideals and relative \( \mathcal {H}_Y \)-ideals as extensions of fixed z-ideal, free z-ideals and relative z-ideals, respectively. It has been shown that large amounts of the results of the papers in the literature about these topics are special cases

Let \({{\mathfrak {J}}}\, \) and \({{\mathfrak {J}}}\, ^{'}\) be Jordan rings. In this paper we study the additivity of n-multiplicative isomorphisms from \({{\mathfrak {J}}}\, \) onto \({{\mathfrak {J}}}\, ^{'}\) and of n-multiplicative derivations of \({{\mathfrak {J}}}\, \). Suppose that \({{\mathfrak {J}}}\, \) contains a nontrivial idempotent; we prove that if \({{\mathfrak {J}}}\, \) satisfying

This paper investigates the concomitants of m-dual generalized order statistics (m-DGOS) under the generalized Farlie–Gumbel–Morgenstern-type bivariate distributions as an extension of several recent papers. This study can also be applied to the model of m-generalized order statistics (m-GOS) as a parallel model of m-DGOS. Furthermore, the joint distributions of the concomitants of the m-DGOS and the

A new flow on an open manifold with bounded geometry has been considered. We prove short time existence and uniqueness for the flow. The approach is based on the study of the geometry of the manifold of Riemannian metrics on open manifolds. Moreover, some properties of this flow are investigated.

The nilpotent Filippov algebra of class two plays an essential role in some geometric problems, and the classification of nilpotent Lie algebras of class two is one of the most important issues in Lie algebras. In this paper, we classify 9-dimensional nilpotent 3-ary algebras of class two over an arbitrary field.

In this paper, we define \(C ^*\)-module algebras as a generalization of Hilbert algebras and study their properties. We describe some structures of a \(C ^*\)-module algebra including bounded elements and left (right) module adjointable maps. Furthermore we establish some properties of Hilbert algebras for \(C ^*\)-module algebras.

For every prime power \(q \equiv 7 \; mod \; 16\), there are (q; a, b, c, d)-partitions of GF(q), with odd integers a, b, c, and d, where \(a \equiv \pm 1 \; mod \; 8\) such that \(q=a^2+2(b^2+c^2+d^2)\) and \(d^2=b^2+2ac+2bd\). Many results for the existence of \(4-\{q^2; \; \frac{q(q-1)}{2}; \; q(q-2) \}\) SDS which are simple homogeneous polynomials of parameters a, b, c and d of degree at most

We describe the orbits of a cohomogeneity two Riemannian G-manifold M from topological point of view, under the conditions that G is nonsemisimple and M decomposes as a product of negatively curved Riemannian manifolds.

In this work, we consider a decreasing sequence of groups \(\left( G_{n}\right) _{n\ge 1}\) provided with the structures of Banach manifolds and satisfying some conditions, then we show that the group \(G_{\infty }=\bigcap _{n\ge 1}G_{n}\) equipped with the projective topology is a regular Lie–Fréchet group. We use this result to prove the regularity of some Fréchet–Lie groups.

Let \(G_{2}\) be a group which acts trivially on an abelian group \(G_{1}\). According to the Schreier’s Theorem, each 2-cocycle \(\varepsilon \in Z^{2}(G_{2},G_{1})\) determines a group \(G_{\varepsilon }\) which is a central extension of \(G_{1}\) by \(G_{2}\), and we will denote this group by \(G_{1}\underset{\varepsilon }{\times }G_{2} \) and call it the perturbed direct product of \(G_{1}\) by

In this paper, we propose a viscosity-type and self-adaptive iterative algorithm resulting in strong convergence theorem for finding the common solution of generalized split system of variational inclusion problem. The self-adaptive technique presented in this paper is a way of selecting the stepsizes such that the implementation of our algorithms does not need any prior information about the operator

In the original article published, during the final typesetting stage the equation in the proof of the Theorem 3.5 was published incorrectly.

In this paper, we obtain the following local weighted Lorentz gradient estimates $$\begin{aligned} g^{-1}\left( {\mathcal {M}}_1(\mu ) \right) \in L_{w,{\text {loc}}}^{q,r}(\Omega ) \Longrightarrow |Du| \in L_{w,{\text {loc}}}^{q,r}(\Omega ) \end{aligned}$$ for the weak solutions of a class of non-homogeneous quasilinear elliptic equations with measure data $$\begin{aligned} -\text {div} ~\! \left(

For \(n\ge 2\), an additive map f between two rings A and B is called an n-Jordan homomorphism, or an n-homomorphism if \(f(a^n)=f(a)^n\), for all \(a\in A\), or \(f(a_1a_2\cdots a_n)=f(a_1)f(a_2)\cdots f(a_n)\), for all \(a_1,a_2,\ldots ,a_n\in A\), respectively. In particular, if \(n=2\) then f is simply called a Jordan homomorphism or a homomorphism, respectively. The notion of n-Jordan homomorphism

In this paper, we find a sharp upper and lower bound for the metric dimension of a geometric manifold with boundary. We also determine the cases in which the bounds hold with equality

In this paper, the consensus tracking of second-order multi-agent systems with pure delay is studied by two kinds of delayed exponential matrices and iterative learning control technique. Theoretical analysis is easier with the help of delay exponential matrices, and it is simpler to design the control strategies. Further, sufficient conditions are put forward via delay exponential matrices, which

Given a metric continuum X and a positive integer n, \(F_{n}(X)\) denotes the hyperspace of all nonempty subsets of X with at most n points endowed with the Hausdorff metric. For any \(K\in F_{n}(X)\), we define \(F_{n}(K,X)\) as the collection of elements of \(F_{n}(X)\) containing K and we consider \(F_{n}^K(X)\) as the quotient space obtained from \(F_{n}(X)\) by shrinking \(F_{n}(K,X)\) to one

This paper considers wavelet estimations for a multivariate density function based on strongly mixing data. We first construct a linear wavelet estimator and provide a convergence rate over \(L^{p} (1\le p<\infty )\) risk in Besov space \(B^{s}_{r,q}(\mathbb {R}^{d})\). However, this estimator depends on the smoothness of density function, which means that the estimator is not adaptive. A nonlinear

In this paper, the generalized Erlang(n) risk model with two-sided jumps and a constant dividend barrier is considered. We assume that the downward jump sizes follow an arbitrary distribution and the upward jump sizes follow the mixed Erlang distribution. An integro-differential equation with boundary conditions for the expected discounted penalty function is derived and the solution is provided. The

Let \(\mathcal {A}\) and \(\mathcal {B}\) be two factor von Neumann algebras. In this paper, we proved that a bijective mapping \(\varPhi :\mathcal {A}\rightarrow \mathcal {B}\) satisfies \(\varPhi (a\circ b-ba^{*})=\varPhi (a)\circ \varPhi (b)-\varPhi (b)\varPhi (a)^{*}\) (where \(\circ \) is the special Jordan product on \(\mathcal {A}\) and \(\mathcal {B},\) respectively), for all elements \(a,b\in

In this paper, we introduce and study a torsion-theoretic generalization of the weakly-flat module using the concept of \(\tau \)-closed submodule for an idempotent radical \(\tau \). We introduce a new class of modules called weakly-\(\tau \)-flat. We study these modules, generalizing several results both on extending modules and flat modules. We study generalizations and characterizations of IF ring

The quon algebra is an approach to particle statistics introduced by Greenberg to provide a theory in which the Pauli exclusion principle and Bose statistics are violated by a small amount. We generalize these models by introducing a deformation of the quon algebra generated by a collection of operators \(\mathtt {a}_i\), \(i \in {\mathbb {N}}^*\) the set of positive integers, on an infinite dimensional

In this paper, motivating the range of operators, we propose an appropriate representation space to introduce synthesis and analysis operators of controlled g-frames and discuss the properties of these operators. Especially, we show that the operator obtained by the composition of the synthesis and analysis operators of two controlled g-Bessel sequence is a trace class operator. Also, we define the

In this paper, we present some basic properties concerning the quasiderivation algebra \(\mathrm{QDer}(A)\) and the quasicentroid algebra \(\mathrm{QC}(A)\) of a Novikov algebra A. Furthermore, we determine the dimension of Novikov algebras A with condition \(\mathrm{QDer}(A)=\mathrm{End}(A)\). We also show that the quasiderivations of A can be embedded as derivations in a larger Novikov algebra.

Let p be a prime not dividing the integer n. By an Ihara result, we mean existence of a cokernel torsion-free injection from a full lattice in the space of p-old modular forms into a full lattice in the space of all modular forms of level pn. In this paper, we will prove an Ihara result in the number field case, for Siegel modular forms. The case of elliptic modular forms is discussed in Ihara (Discrete

The zero forcing number of a graph is the minimum size of a zero forcing set. This parameter bounds the path cover number which is the minimum number of vertex-disjoint-induced paths that cover all the vertices of graph. In this paper, we investigate these two parameters and present an infinite number of graphs with the large difference between these two parameters and an infinite number of graphs

Suppose that L is a nonempty language over A, \(k\in \mathbb {N}^0\) and \(m\in \mathbb {N}\). If L satisfies \((LA^k)^mL\)\(\cap A^+(LA^k)^{m-1}LA^+=\emptyset \), then L is a code and is called a (k, m)-comma code. If L is a (k, m)-comma code, then it is known that L is an infix code when \(m=1\) and L is a bifix code when \(m\ge 1\). In this paper, we extend the study and find that the class of (k

A new definition of connectedness of an object in a category with respect to a closure operator is given. It is shown that many of the classical results about connectedness of topological spaces, under mild conditions, hold in an arbitrary category. In particular it is shown that the image of a connected object is connected; that the union and the product of connected objects are connected. Several

The purpose of this paper is to introduce several finite sets of orthogonal polynomials in two variables, and investigate some general properties of them such as recurrence relations, generating functions, differential equations, and Rodrigues type representations.

This paper concerns with a new three-operator splitting algorithm for solving a class of variational inclusions. The main advantage of the proposed algorithm is that it can be easily implemented without the prior knowledge of Lipschitz constant, strongly monotone constant and cocoercive constant of component operators. A reason explained for this is that the algorithm uses a sequence of stepsizes which

In this paper, we introduced relatively star-C-Hurewicz property in topological spaces following the approach of Bonanzinga and Pansera (Acta Math Hungar 117(3):231–243, 2007) and Guido and Kočinac (Quest Answ Gen Topol 19:107–114, 2001). A subspace A of a topological space X is said to have relatively star-C-Hurewicz property in X (in short, RSCH) or relatively star-C-Hurewicz subspace of X if for

In this paper, we determine all of finite groups whose order and the largest of their irreducible character degrees are the same as \({\textit{PGL}}( 2 , p^{2} ) \) for all odd prime numbers p. As a consequence, we show that the groups \({\textit{PGL}}( 2 , p^{2} ) \) are uniquely determined by the structure of their complex group algebras.

In this paper, we consider the Yamabe flow on Lie groups with left invariant metrics in particular case on the higher dimensional classical Heisenberg nilpotent Lie groups and the higher dimensional quaternion Lie groups. We construct a explicit solution of the Yamabe flow on each group. Then we investigate the some properties on these Lie groups under the Yamabe flow. At the end of paper, we study

In this paper, some new upper bounds on the spectral radius of Hadamard product of nonnegative tensors are given. To show their sharpness, the comparisons among these bounds, including the existing one by Sun et al. (Linear Multilinear Algebra 66:1199–1214, 2018), are performed. We also present some lower bounds on the minimum eigenvalue of Fan product of irreducible strong \({{\mathcal {M}}}\)-tensors

Let \({\mathbb {F}}\) be a field of algebraically closed and L be a finite dimensional Lie algebra over field \( {\mathbb {F}}\) . \(L'=[L,L]\) denotes the derived subalgebra of L. Following the analogy with group theory, we define the subalgebra D(L) of L to be the intersection of the normalizer of the derived subalgebras of all subalgebras of L. In a Lie algebra L, this is an ideal of L, allowing

This paper is concerned with the following Klein–Gordon equation with sublinear nonlinearity coupled with Born–Infeld theory: $$\begin{aligned} \left\{ \begin{array}{ll} \displaystyle -\Delta u+ V(x)u-(2\omega +\phi )\phi u=f(x,u), &{}\quad x\in {\mathbb {R}}^{3},\\ \Delta \phi +\beta \Delta _{4}\phi =4\pi (\omega +\phi )u^{2},&{}\quad x\in {\mathbb {R}}^{3}. \end{array} \right. \end{aligned}$$ Under

In this paper, we show that if an entire function \(f(z_1,z_2)\) of two (or more) complex variables verifies \(\left| f(z_1,z_2) \right| \le K(\left| P(z_1,z_2) \right| )\), where \(P(z_1,z_2)\) is a polynomial that is not a power in \({{\mathbb {C}}}[[z_1,z_2]]\), and K is any positive-valued real function, then \(f(z_1,z_2)\) can be written as a holomorphic function of P.

In this note, we introduce and study some generalizations of Reiter’s condition \((P_p)\) and their modifications in the context of Orlicz spaces. We use these conditions to study amenability of hypergroups. We end this paper with a result for polynomial hypergroups.

A ring R is called weakly SG-hereditary if every ideal of R is SG-projective. In this note, we prove that a local domain R is a Noetherian Warfield domain if and only if it is weakly SG-hereditary. Furthermore, we prove that any countably generated submodule of any free module over a Noetherian local Warfield domain is SG-projective.

In this paper, we propose a new customized proximal point algorithm for linearly constrained convex optimization problem, and further extend the proposed method to separable convex optimization problem. Unlike the existing customized proximal point algorithms, the proposed algorithms do not involve relaxation step, but still ensure the convergence. We obtain the particular iteration schemes and the

This paper presents a novel numerical strategy based on combination of an adaptive semismooth Newton (ASN) method and the Lavrentiev regularization technique for the solution of elliptic optimal control problems with state constraints. Using the global convergence proof for a nonmonotone semismooth Newton method, we will exploit an adaptive nonmonotone line search method such that the nonmonotonicity

A path cover of a graph G is a spanning subgraph of G consisting of vertex disjoint paths; a minimum path cover of G is a path cover of G consisting of minimum number of paths; a path cover number of G, denoted by p(G), is the number of paths in a minimum path cover of G, i.e., \(p(G)=\min \{|{\mathcal {P}}|:\)\({\mathcal {P}}\) is a path cover of \(G\}.\) A graph G is quasi-claw-free if for any two

In this paper, we study the numerical radius parallelism for bounded linear operators on a Hilbert space \(\big ({\mathscr {H}}, \langle \cdot ,\cdot \rangle \big )\). More precisely, we consider bounded linear operators T and S which satisfy \(\omega (T + \lambda S) = \omega (T)+\omega (S)\) for some complex unit \(\lambda \), and is denoted by \(T \parallel _{\omega } S\). We show that \(T \parallel

It is shown that two Levi–Tanaka and infinitesimal CR automorphism algebras, associated with a totally nondegenerate model of CR dimension one are isomorphic. As a result, the model surfaces are maximally homogeneous and standard. This gives an affirmative answer in CR dimension one to a certain question formulated by Beloshapka.

Let R be a standard graded algebra over an infinite field \(\mathbb {K}\) and M a finitely generated \({\mathbb Z}\)-graded R-module. Let \(I_1,\ldots I_m\) be graded ideals of R. The functions \(r(M/I_1^{a_1}\ldots I_m^{a_m}M)\) and \(r(I_1^{a_1}\ldots I_m^{a_m}M)\) are investigated and their asymptotical behaviours are given. Here, \(r(\bullet )\) stands for the reduction number of a finitely generated

An independent double Roman dominating function (IDRDF) on a graph \(G=(V,E)\) is a function \(f{:}V(G)\rightarrow \{0,1,2,3\}\) having the property that if \(f(v)=0\), then the vertex v has at least two neighbors assigned 2 under f or one neighbor w assigned 3 under f, and if \(f(v)=1\), then there exists \(w\in N(v)\) with \(f(w)\ge 2\), such that the set of vertices with positive weight is independent

This paper concerns with a class of fractional integro-differential equations in the space of continuous functions which defined on interval \( \left[ 0,a\right] \) and take values in a Banach space E. Using a generalized Darbo fixed-point theorem associated with measure of noncompactness, the existence of solutions has been established. Also an example which shows that the main result is applicable

In this paper, we give some sufficient conditions for the algebraic dependence of three meromorphic mappings from Kähler manifold into \({\mathbb {P}}^n({\mathbb {C}})\) sharing hyperplanes in subgeneral position, where all zeros with multiplicities more than certain values do not need to be counted.

Let \(P_t(\mu )\) be the matrix power mean of a compactly supported probability measure \(\mu \) on the set of positive definite matrices \(\mathbb {P}_n\). We present an inequality involving the matrix power mean \(P_t(\mu )\) and its adjoint \(P_{-t}(\mu )\). Our result gives in particular a comparison of the quasi arithmetic mean \(\sharp _{\omega ,t}\) and its adjoint \(\sharp _{\omega ,-t}\).

This paper is concerned with bistable wave fronts in a class of nonlocal reaction diffusion model for a single species with stage structure and distributed maturation delay. By choosing the strong and weak kernel functions to transform system with delays to a two- or three-dimensional system without any delays, the existence of traveling wave fronts is established by abstract results. Then we prove