In this work, we refine the results of Sendov and Shan [New representation theorems for completely monotone and Bernstein functions with convexity properties on their measures, J. Theor. Probab. 28 (2015), 1689–1725] on subordinators obtained by the class of Bernstein functions stable by the Mellin-Euler differential operator I−xddx by giving a stochastic interpretation, proving monotonicity properties

In the article, we present a new (p,q)-integral identity for the first-order (p,q)-differentiable functions and establish several new (p,q)-quantum error estimations for various integral inequalities via (α,m)-convexity. We also compare our results with the previously known results and provide two examples to show the superiority of our obtained results.

In this paper, we introduce the concept of the perfect ϕ-type to describe the growth of the maximal molecule of Laplace-Stieltjes transform by using the more general function than the usual. Based on this concept, we investigate the approximation and growth of analytic functions F(s) defined by Laplace-Stieltjes transforms convergent in the half plane and obtain some results about the necessary and

We address the question of identifying non-smooth points in Vℝ(I) the real part of an affine algebraic variety. Two simple algebraic criteria will be formulated and proven. As an application, we investigate the configuration spaces of the planar four-bar linkage and the delta robot and prove that all singularities are CS-singularities.

We mainly consider the limit behaviors of the Riemann solutions to Chaplygin Euler equations for nonisentropic fluids. The formation of delta shock wave and the appearance of vacuum state are found as parameter ε tends to a certain value. Different from the isentropic fluids, the weight of delta shock wave is determined by variance density ρ and internal energy H. Meanwhile, involving the entropy inequality

We characterize skew-symmetric operators on a reproducing kernel Hilbert space in terms of their Berezin symbols. The solution of some operator equations with skew-symmetric operators is studied in terms of Berezin symbols. We also studied essentially unitary operators via Berezin symbols.

In this paper, we present a new refinement of Jensen’s inequality with applications in information theory. The refinement of Jensen’s inequality is obtained based on the general functional in the work of Popescu et al. As the applications in information theory, we provide new tighter bounds for Shannon’s entropy and some f-divergences.

A map is called edge-regular if it is edge-transitive but not arc-transitive. In this paper, we show that a complete graph Kn has an orientable edge-regular embedding if and only if n=pd>3 with p an odd prime such that pd≡3 (mod4). Furthermore, Kpd has pd−34dϕ(pd−12) non-isomorphic orientable edge-regular embeddings.

In this paper, a Cauchy problem for the Laplace equation is considered. We develop a modified Tikhonov regularization method based on Hermite expansion to deal with the ill posed-ness of the problem. The regularization parameter is determined by a discrepancy principle. For various smoothness conditions, the solution process of the method is uniform and the convergence rate can be obtained self-adaptively

A subgroup H of a finite group G is called weakly pronormal in G if there exists a subgroup K of G such that G=HK and H∩K is pronormal in G. In this paper, we investigate the structure of the finite groups in which some subgroups are weakly pronormal. Our results improve and generalize many known results.

We study the modularity of Ramanujan’s function k(τ)=r(τ)r2(2τ), where r(τ) is the Rogers-Ramanujan continued fraction. We first find the modular equation of k(τ) of “an” level, and we obtain some symmetry relations and some congruence relations which are satisfied by the modular equations; these relations are quite useful for reduction of the computation cost for finding the modular equations. We

As an effective and possible method for computing PageRank problem, the inner-outer (IO) iteration has attracted wide interest in the past few years since it was first proposed by Gleich et al. (2010). In this paper, we present a variant of the IO iteration, which is based on multi-step power and multi-step splitting and is denoted by MPMIO. The description and convergence are discussed in detail.

For a finitely generated tensor norm α, we investigate the α-approximation property (α-AP) and the bounded α-approximation property (bounded α-AP) in terms of some approximation properties of operator ideals. We prove that a Banach space X has the λ-bounded αp,q-AP (1≤p,q≤∞,1/p+1/q≥1) if it has the λ-bounded gp-AP. As a consequence, it follows that if a Banach space X has the λ-bounded gp-AP, then

In this paper, we define the entropy number in probabilistic setting and determine the exact order of entropy number of finite-dimensional space in probabilistic setting. Moreover, we also estimate the sharp order of entropy number of univariate Sobolev space in probabilistic setting by discretization method.

The purpose of this paper is to introduce the logarithmic mean of two convex functionals that extends the logarithmic mean of two positive operators. Some inequalities involving this functional mean are discussed as well. The operator versions of the functional theoretical results obtained here are immediately deduced without referring to the theory of operator means.

By using the bifurcation method, we study the existence of an S-shaped connected component in the set of positive solutions for discrete second-order Neumann boundary value problem. By figuring the shape of unbounded connected component of positive solutions, we show that the Neumann boundary value problem has three positive solutions suggesting suitable conditions on the weight function and nonlinearity

For a partially ordered set (A,≤), let GA be the simple, undirected graph with vertex set A such that two vertices a≠b∈A are adjacent if either a≤b or b≤a. We call GA the partial order graph or comparability graph of A. Furthermore, we say that a graph G is a partial order graph if there exists a partially ordered set A such that G=GA. For a class C of simple, undirected graphs and n, m≥1, we define

In this paper, we develop the elementary theory of inverse semigroups to the cases of type B semigroups. The main aim of this paper is to study proper type B semigroups. We introduce first the concept of a left admissible triple. After obtaining some basic properties of left admissible triple, we give the definition of a Q-semigroup and get a structure theorem of Q-semigroup. In particular, we introduce

In this paper, the blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients are investigated under Neumann boundary conditions. By constructing some suitable auxiliary functions and using differential inequality techniques, we show some sufficient conditions to ensure that the solution u(x,t) blows up at a finite time under appropriate measure sense. Furthermore, an

The paper deals with a quasilinear Dirichlet problem involving a competing (p,q)-Laplacian and a convection term. Due to the lack of ellipticity, monotonicity and variational structure, the known methods to find a weak solution are not applicable. We develop an approximation procedure permitting to establish the existence of solutions in a generalized sense. If in place of competing (p,q)-Laplacian

In 2006, Hubert, Mauduit and Sárközy extended the notion of binary sequences to n-dimensional binary lattices and introduced the measures of pseudorandomness of binary lattices. In 2011, Gyarmati, Mauduit and Sárközy extended the notions of family complexity, collision and avalanche effect from binary sequences to binary lattices. In this paper, we construct pseudorandom binary lattices by using cyclotomic

A connected even [2,2s]-factor of a graph G is a connected factor with all vertices of degree i(i=2,4,…,2s), where s≥1 is an integer. In this paper, we show that a k+1s+2-tough k-tree has a connected even [2,2s]-factor and thereby generalize the result that a k+13-tough k-tree is Hamiltonian in [Hajo Broersma, Liming Xiong, and Kiyoshi Yoshimoto, Toughness and hamiltonicity in k-trees, Discrete Math

In this paper, the authors present some inequalities of the generalized trigonometric and hyperbolic functions which occur in the solutions of some linear differential equations and physics. By these results, some well-known classical inequalities for them are improved, such as Wilker inequality, Huygens inequality, Lazarević inequality and Cusa-Huygens inequality.

A triangular matroid is a rank-3 matroid whose ground set consists of the points of an n3-configuration and whose bases are the point triples corresponding to non-triangles within the configuration. Raney previously enumerated the n3-configurations which induce triangular matroids for 7≤n≤15. In this work, the enumeration is extended to configurations having up to 18 points. Several examples of such

We investigate the abelian sandpile group on modified wheels Wˆn by using a variant of the dollar game as described in [N. L. Biggs, Chip-Firing and the critical group of a graph, J. Algebr. Comb. 9 (1999), 25–45]. The complete structure of the sandpile group on a class of graphs is given in this paper. In particular, it is shown that the sandpile group on Wˆn is a direct product of two cyclic subgroups

In this paper, we discuss the monotonicity of the first nonzero eigenvalue of the Laplace operator and the p-Laplace operator under a forced mean curvature flow (MCF). By imposing conditions associated with the mean curvature of the initial hypersurface and the coefficient function of the forcing term of a forced MCF, and some special pinching conditions on the second fundamental form of the initial

The concept of the domination number plays an important role in both theory and applications of digraphs. Let D=(V,A) be a digraph. A vertex subset T⊆V(D) is called a dominating set of D, if there is a vertex t∈T such that tv∈A(D) for every vertex v∈V(D)\T. The dominating number of D is the cardinality of a smallest dominating set of D, denoted by γ(D). In this paper, the domination number of round

In this paper, we study the Hyers-Ulam-Rassias stability of (m,n)-Jordan derivations. As applications, we characterize (m,n)-Jordan derivations on C⁎-algebras and some non-self-adjoint operator algebras.

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In this paper, we prove that the topological spaces of nonzero weighted composition operators acting on some Hilbert spaces of analytic functions on the unit open ball are simply connected.

In this paper, we present the concepts of generalized derivative, directional generalized derivative, subdifferential and conjugate for n-dimensional fuzzy-number-valued functions and discuss the characterizations of generalized derivative and directional generalized derivative by, respectively, using the derivative and directional derivative of crisp functions that are determined by the fuzzy mapping

New families of uniformities are introduced on UC(X,Y), the class of uniformly continuous mappings between X and Y, where (X,U) and (Y,V) are uniform spaces. Admissibility and splittingness are introduced and investigated for such uniformities. Net theory is developed to provide characterizations of admissibility and splittingness of these spaces. It is shown that the point-entourage uniform space

In this paper, we develop a technique which enables us to obtain several results from the theory of Γ-semigroups as logical implications of their semigroup theoretical analogues.

In this paper, we study the strong nil-cleanness of certain classes of semigroup rings. For a completely 0-simple semigroup M=ℳ0(G;I,Λ;P), we show that the contracted semigroup ring R0[M] is strongly nil-clean if and only if either |I|=1 or |Λ|=1, and R[G] is strongly nil-clean; as a corollary, we characterize the strong nil-cleanness of locally inverse semigroup rings. Moreover, let S=[Y;Sα,φα,β]

In Applied Mathematics Letters 74 (2017), 147–153, the Hyers-Ulam stability of the one-dimensional time-independent Schrödinger equation was investigated when the relevant system has a potential well of finite depth. As a continuous work, we prove in this paper a type of Hyers-Ulam stability of the one-dimensional time-independent Schrödinger equation with a rectangular potential barrier of V0 in height

We present a more general homological characterization of the direct summand theorem (DST). Specifically, we state two new conjectures: the socle-parameter conjecture (SPC) in its weak and strong forms. We give a proof for the weak form by showing that it is equivalent to the DST. Furthermore, we prove the SPC in its strong form for the case when the multiplicity of the parameters is smaller than or

In this paper, some new integral curves are defined in three-dimensional Euclidean space by using a new frame of a polynomial spatial curve. The Frenet vectors, curvature and torsion of these curves are obtained by means of new frame and curvatures. We give the characterizations and properties of these integral curves under which conditions they are general helix. Also, the relationships between these

In this paper, we give a boundedness criterion for the potential operator ℐα in the local generalized Morrey space LMp,φ{t0}(Γ) and the generalized Morrey space Mp,φ(Γ) defined on Carleson curves Γ, respectively. For the operator ℐα, we establish necessary and sufficient conditions for the strong and weak Spanne-type boundedness on LMp,φ{t0}(Γ) and the strong and weak Adams-type boundedness on Mp,φ(Γ)

A novel method with two variations is proposed with which the number of positive and negative zeros of a polynomial with real coefficients and degree n can be restricted with significantly better determinacy than that provided by the Descartes rule of signs. The method also allows the isolation of the zeros of the polynomial quite successfully, and the determined root bounds are significantly narrower

In this article, the error term of the mean value theorem for binary Egyptian fractions is studied. An error term of prime number theorem type is obtained unconditionally. Under Riemann hypothesis, a power saving can be obtained. The mean value in short interval is also considered.

In this paper, we consider the Cauchy problem for a second-order nonlinear equation with mixed fractional derivatives related to the fractional Khokhlov-Zabolotskaya equation. We prove the nonexistence of a classical local in time solution. The obtained instantaneous blow-up result is proved via the nonlinear capacity method.

In this manuscript, we first consider the diffusive competition and cooperation system subject to Neumann boundary conditions without delay terms and get the conclusion that the unique positive constant equilibrium is locally asymptotically stable. Then, we study the diffusive delayed competition and cooperation system subject to Neumann boundary conditions, and the existence of Hopf bifurcation at

In this article, meromorphic exact solutions for the (2 + 1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff (gCBS) equation are obtained by using the complex method. With the applications of our results, traveling wave exact solutions of the breaking soliton equation are achieved. The dynamic behaviors of exact solutions of the (2 + 1)-dimensional gCBS equation are shown by some graphs. In

In this paper, we investigate the problem for optimal control of a viscous generalized θ-type dispersive equation (VG θ-type DE) with weak dissipation. First, we prove the existence and uniqueness of weak solution to the equation. Then, we present the optimal control of a VG θ-type DE with weak dissipation under boundary condition and prove the existence of optimal solution to the problem.

This paper focuses on finite-order meromorphic solutions of nonlinear difference equation fn(z)+q(z)eQ(z)Δcf(z)=p(z), where p,q,Q are polynomials, n≥2 is an integer, and Δcf is the forward difference of f. A relationship between the growth and zero distribution of these solutions is obtained. Using this relationship, we obtain the form of these solutions of the aforementioned equation. Some examples

In this paper, an equivalent quasinorm for the Lipschitz space of noncommutative martingales is presented. As an application, we obtain the duality theorem between the noncommutative martingale Hardy space hpc(ℳ) (resp. hpr(ℳ)) and the Lipschitz space λβc(ℳ) (resp. λβr(ℳ)) for 0

In this paper, we show that if λ1,λ2,λ3 are non-zero real numbers, and at least one of the numbers λ1,λ2,λ3 is irrational, then the integer parts of λ1n12+λ2n23+λ3n34 are prime infinitely often for integers n1,n2,n3. This gives an improvement of an earlier result.

We describe a standard form for the elements in the universal field of fractions of free associative algebras (over a commutative field). It is a special version of the normal form provided by Cohn and Reutenauer and enables the use of linear algebra techniques for the construction of minimal linear representations (in standard form) for the sum and the product of two elements (given in a standard

The paper deals with the existence of solutions for (p,Q) coupled elliptic systems in the Heisenberg group, with critical exponential growth at infinity and singular behavior at the origin. We derive existence of nonnegative solutions with both components nontrivial and different, that is solving an actual system, which does not reduce into an equation. The main features and novelties of the paper

In this paper, we decorate leaves and edges of planar rooted forests simultaneously and use a part of them to construct free nonunitary Rota-Baxter family algebras. As a corollary, we obtain the construction of free nonunitary Rota-Baxter algebras.

The aim of this paper is to investigate a class of nonlinear stochastic reaction-diffusion systems involving fractional Laplacian in a bounded domain. First, the existence and uniqueness of weak solutions are proved by using Galërkin’s method. Second, the existence of optimal controls for the corresponding stochastic optimal control problem is obtained. Finally, several examples are provided to demonstrate

In this paper, by using the ideal theory in residuated lattices, we construct the prime and maximal spectra (Zariski topology), proving that the prime and maximal spectra are compact topological spaces, and in the case of De Morgan residuated lattices they become compact T0 topological spaces. At the same time, we define and study the reticulation functor between De Morgan residuated lattices and bounded

In this short note, we provide a brief proof for a recent determinantal formula involving a particular family of banded matrices.

In this paper, firstly, we study the structural form of reflective integral for a given system. Then the sufficient conditions are obtained to ensure there exists the reflective integral with these structured form for such system. Secondly, we discuss the necessary conditions for the equivalence of such systems and a general three-dimensional differential system. And then, we apply the obtained results

This paper focuses on the existence and the multiplicity of classical radially symmetric solutions of the mean curvature problem: −div∇v1+|∇v|2=f(x,v,∇v)inΩ,a0v+a1∂v∂ν=0on∂Ω,with Ω an open ball in ℝN, in the presence of one or more couples of sub- and super-solutions, satisfying or not satisfying the standard ordering condition. The novel assumptions introduced on the function f allow us to complement

This paper derives elliptic gradient estimates for positive solutions to a nonlinear parabolic equation defined on a complete weighted Riemannian manifold. Applications of these estimates yield Liouville-type theorem, parabolic Harnack inequalities and bounds on weighted heat kernel on the lower boundedness assumption for Bakry-Émery curvature tensor.

This study focuses on finding super edge-magic total (SEMT) labeling and deficiency of imbalanced fork and disjoint union of imbalanced fork with star, bistar and path; in addition, the SEMT strength for Imbalanced Fork is investigated.

This paper deals with the existence of mild solutions for a class of non-local stochastic integro-differential equations driven by a fractional Brownian motion with Hurst parameter H∈12,1. Discussions are based on resolvent operators in the sense of Grimmer, stochastic analysis theory and fixed-point criteria. As a final point, an example is given to illustrate the effectiveness of the obtained theory

The aim of this paper is to establish some fixed point results for surrounding quasi-contractions in non-triangular metric spaces. Also, we prove the Banach principle of contraction in non-triangular metric spaces. As applications of our theorems, we deduce certain well-known results in b-metric spaces as corollaries.

In 2006, Schuster introduced the radial Blaschke-Minkowski homomorphisms. In this article, associating with the star duality of star bodies and dual quermassintegrals, we establish Brunn-Minkowski inequalities and monotonic inequality for the radial Blaschke-Minkowski homomorphisms. In addition, we consider its Shephard-type problems and give a positive form and a negative answer, respectively.