In this paper, we study existence, dependence, and optimal control results concerning solutions to a class of hemivariational inequalities for stationary Navier–Stokes equations but without making use of the theory of pseudo-monotone operators. To do so, we consider a classical assumption, due to Rauch, which constrains us to make a slight change on the definition of a solution. The Rauch assumption

In this paper, we study a nonlinear inverse problem for a third-order partial differential equation with integral conditions. This inverse problem is formulated as an auxiliary inverse problem which, in turn, is reduced to the operator equation in a specified Banach space using the method of spectral analysis. Finally, the existence and uniqueness of this operator equation is proved by applying the

This article has been retracted. Please see the retraction notice for more detail: https://doi.org/10.1007/s41980-019-00232-4.

In this paper, we introduce the irreducible \(\alpha \)-Nekrasov matrices and irreducible \(\alpha \)-S-Nekrasov matrices as the extended irreducible Nekrasov matrices and we analyze the relationships among the involved matrices and irreducible H-matrices.

The Cauchy problem for general elliptic equations of second order is considered. In a previous paper (Berntsson et al. in Inverse Probl Sci Eng 26(7):1062–1078, 2018), it was suggested that the alternating iterative algorithm suggested by Kozlov and Maz’ya can be convergent, even for large wavenumbers \(k^2\), in the Helmholtz equation, if the Neumann boundary conditions are replaced by Robin conditions

Throughout this article, we fix a group G and a commutative ring \(\Bbbk \). This is an exposition on 2-equivalences between a 2-category of small \(\Bbbk \)-categories with pseudo G-actions and a 2-category of G-graded small \(\Bbbk \)-categories, which generalizes (Asashiba in Appl Categor Sturct 25(8):3278–3296, 2017). This article is a translation of some parts of Ch. 4 and 5 in the book (Asashiba

Let \({\mathcal {A}}\) and \({\mathcal {B}}\) be two factors with dim\({\mathcal {A}}>4\). In this article, it is proved that a bijective map \(\Phi : {\mathcal {A}}\rightarrow {\mathcal {B}}\) satisfies \(\Phi ([A\bullet B, C])=[\Phi (A)\bullet \Phi (B), \Phi (C)]\) for all \(A, B, C\in {\mathcal {A}}\) if and only if \(\Phi \) is a linear \(*\)-isomorphism, or a conjugate linear \(*\)-isomorphism

Let \({\mathcal {R}}\) be a semiprime ring with center \(Z({\mathcal {R}})\) and with extended centroid C and let \(\sigma : {\mathcal {R}} \rightarrow {\mathcal {R}}\) be an automorphism. Assume that \(\tau : {\mathcal {R}} \rightarrow {\mathcal {R}} \) is an anti-homomorphism, such that the image of \(\tau \) has small centralizer. It is proved that the following are equivalent: (1) \(x^{\sigma }x^{\tau

We study the load-balanced capacitated vehicle routing problem (LBCVRP): the problem is to design a collection of tours for a fixed fleet of vehicles with capacity Q to distribute a supply from a single depot between a number of predefined clients, in a way that the total traveling cost is a minimum, and the vehicle loads are balanced. The unbalanced loads cause the decrease of distribution quality

In this paper, we present a modified SP iteration with the inertial technical term for three quasi-nonexpansive multivalued mappings in a Hilbert space. We then obtain weak convergence theorem under suitable conditions. The strong convergence theorems are given using CQ and shrinking projection methods with our modified iteration. Finally, we test some numerical experiments to illustrate that our inertial

For a non-empty set X denote the full transformation semigroup on X by T(X) and suppose that \(\sigma \) is an equivalence relation on X. For every \(f\in T(X)\), the kernel of f is defined to be \(\ker f =\{(x, y)\in X\times X\mid f(x) = f(y)\}\). Evidently, \(E(X, \sigma )=\{f\in T(X) \mid \sigma \subseteq \ker f\}\) is a subsemigroup of T(X). Also, the subset \(RE(X, \sigma )\) of \(E(X, \sigma

We introduce and study the notions of restricted projective, injective and flat complexes of modules. It is shown in the paper that a complex C of modules is restricted projective if and only if for each \(m\in \mathbb {Z}\) the module \(C^{m}\) is restricted projective. A similar result for restricted injective complexes is also given. As an application, we characterize the complex of strongly torsion-free

Based on the Schur complements, two upper bounds for the infinity norm of the inverse of doubly strictly diagonally dominant (DSDD) matrices are presented. As applications, an error bound for linear complementarity problems of DB-matrices and a lower bound for the smallest singular value of matrices are given.

In this paper, we study a generalized convex vector equilibrium problem with cone and set constraints in real Banach spaces. We provide some basic characterizations on generalized convexity for the first- and second-order directional derivatives. We obtain Kuhn–Tucker second-order necessary and sufficient optimality conditions for efficiency to such problem under suitable assumptions on the generalized

Let \(G=(V,E)\) be a simple graph. A set \(M\subseteq E\) is a matching if no two edges in M have a common vertex. The matching number, denoted \(\beta (G)\) (or \(\beta \)), is the maximum size of a matching in G. A double Roman dominating function (DRDF) on a graph G is a function f: \(V\longrightarrow \{0,1,2,3\}\) satisfying the conditions that for every vertex u of weight \(f(u)\in \left\{ 0,1\right\}

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

Localization operators have a relatively recent development in pure and applied mathematics. Motivated by Wong’s approach, we will study in this paper the time–frequency analysis associated with the hypergeometric Wigner transform related to the Cherednik operators in the case of the root system \(BC_{d}\).

Related to earlier work on existence results of best proximity points (pairs) for cyclic (noncyclic) condensing operators of integral type in the setting of reflexive Busemann convex spaces, in this paper, we introduce another class of cyclic (noncyclic) condensing operators and study the existence of best proximity points (pairs) as well as coupled best proximity points (pairs) in such spaces. Then

In this paper, we investigate CSS-quasinormality of maximal subgroups of Sylow subgroups of some Fitting subgroup and obtain a sufficient condition about the supersolvablity of finite groups, such that some known results about c-normality and SS-quasinormality are generalized and unified.

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

Let X be a Banach space, C be a nonempty closed convex set and \(\sigma _C\) be the support function of the set C. In this work, we give some necessary and sufficient conditions for the set C to satisfy \(\mathrm {int}(\mathrm {dom}\sigma _C)\ne \emptyset \), which enable us to study the Frechet and Gateaux differentiability of support function on the set C.

The main aim of this paper is studying the family \(W_b(E,F)\) of b-weakly compact operators between two Banach lattices. For an order dense sublattice G of a vector lattice E, if \(T:G\rightarrow F\) is a b-weakly compact operator between two Banach lattices, then \(T\in W_b(E,F)\) whenever the norm of E is order continuous and \(T:E\rightarrow F\) is a positive operator. We also investigate the relationship

A subgroup H of a finite group G is said to be weakly \(\mathcal {H}C\)-embedded in G if there exists a normal subgroup T of G such that \(H^G = HT\) and \(H^g \cap N_T(H) \le H\) for all \(g \in G\), where \(H^G\) is the normal closure of H in G. In this paper, we investigate the structure of the finite group G under the assumption that P a Sylow p-subgroup of G, where p is a prime dividing the order

We introduce the notion of additive units (addits) of a pointed inclusion system of Hilbert modules over the \(C^*\)-algebra of all compact operators acting on a Hilbert space G. By a pointed inclusion system, we mean an inclusion system with a fixed normalised reference unit. We prove that if G is a Hilbert space of finite dimension, then there is a bijection between the set of addits of a pointed

Based on the matrix unfolding technique of a tensor, three easily checkable sufficient conditions for the M-positive definiteness of fourth-order partially symmetric tensors are given. Numerical examples show that the proposed results are efficient.

This paper deals with parabolic equations with nonlocal Dirichlet boundary conditions. Critical exponent and simultaneous blow-up criteria are studied for blow-up solutions. Moreover, we determine uniform blow-up profiles and blow-up set to all kinds of simultaneous blow-up solutions. It is interesting that large weighted functions could provide sufficient help to the occurring of blow-up of solutions