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Letp3(n) denote the number of 3-component multipartitions ofn. Recently, using a 3-dissection formula for the generating function ofp3(n), Baruah and Ojah proved that forn≥ 0,p3(9n+ 5) ≡ 0 (mod 33) andp3 (9n+ 8) ≡ 0 (mod 34). In this paper, we prove several congruences modulo powers of 3 forp3(n) by using some theta function identities. For example, we prove that forn≥ 0,p3 (243n+ 233) ≡p3 (729n+ 638) ≡ 0 (mod 310).

Using the generalized Erdélyi-Kober fractional integrals, an attempt is made to establish certain new fractional integral inequalities, related to the weighted version of the Chebyshev functional. The results given earlier by Purohit and Raina (2013) and Dahmani et al. (2011) are special cases of results obtained in present paper.

In this paper, we investigate oscillation results for the solutions of impulsive conformable fractional differential equations of the form t k D α p t t k D α x t + r t x t + q t x t = 0 , t ≥ t 0 , t ≠ t k , x t k + = a k x ( t k − ) , t k D α x t k + = b k t k − 1 D α x ( t k − ) , k = 1 , 2 , … . $$\left\{ \begin{array}{l} {t_k}{D^\alpha }\left( {p\left( t \right)\left[ {{t_k}{D^\alpha }x\left( t \right) + r\left( t \right)x\left( t \right)} \right]} \right) + q\left( t \right)x\left( t \right) = 0,\quad t \ge {t_0},\;t \ne {t_k},\\ x\left( {t_k^ + } \right) = {a_k}x(t_k^ - ),\quad {t_k}{D^\alpha }x\left( {t_k^ + } \right) = {b_{k\;{t_{k - 1}}}}{D^\alpha }x(t_k^ - ),\quad \;k = 1,2, \ldots. \end{array} \right.$$ Some new oscillation results are obtained by using the equivalence transformation and the associated Riccati techniques.

In this paper, we introduce some definitions of uncertainty orders for random vectors in a sublinear expectation space. We all know that, under some continuity conditions, each sublinear expectation 𝔼 has a robust representation as the supremum of a family of probability measures. We describe uncertainty orders from two different viewpoints. One is from sublinear operator viewpoint. After giving definitions such as monotonic orders, convex orders and increasing convex orders, we use these uncertainty orders to derive characterizations for maximal distributions, G-normal distributions and G-distributions, which are the most important random vectors in the sublinear expectation space theory. On the other hand, we also establish some uncertainty orders’ characterizations from the viewpoint of probability measures and build some connections with the theory of risk measures.

The purpose of this paper is to introduce the notions of ∈, ∈ ∨q k -fuzzy ideals of a fuzzy ordered semigroup with the ordering being a fuzzy relation. Several characterizations of ∈, ∈ ∨q k -fuzzy left (resp. right) ideals and ∈, ∈ ∨q k -fuzzy interior ideals are derived. The lattice structures of all ∈, ∈ ∨q k -fuzzy (interior) ideals on such fuzzy ordered semigroup are studied and some methods are given to construct an ∈, ∈ ∨q k -fuzzy (interior) ideals from an arbitrary fuzzy subset. Finally, the characterizations of generalized semisimple fuzzy ordered semigroups in terms of ∈, ∈ ∨q k -fuzzy ideals (resp. ∈, ∈ ∨q k -fuzzy interior ideals) are developed.

A two species non-autonomous competitive phytoplankton system with Beddington-DeAngelis functional response and the effect of toxic substances is proposed and studied in this paper. Sufficient conditions which guarantee the extinction of a species and global attractivity of the other one are obtained. The results obtained here generalize the main results of Li and Chen [Extinction in two dimensional nonautonomous Lotka-Volterra systems with the effect of toxic substances, Appl. Math. Comput. 182(2006)684-690]. Numeric simulations are carried out to show the feasibility of our results.

In this paper we present factorization theorems for strong maps between matroids of arbitrary cardinality. Moreover, we present a new way to prove the factorization theorem for strong maps between finite matroids.

In this paper, we consider the existence of a pullback attractor for the random dynamical system generated by stochastic two-compartment Gray-Scott equation for a multiplicative noise with the homogeneous Neumann boundary condition on a bounded domain of space dimension n ≤ 3. We first show that the stochastic Gray-Scott equation generates a random dynamical system by transforming this stochastic equation into a random one. We also show that the existence of a random attractor for the stochastic equation follows from the conjugation relation between systems. Then, we prove pullback asymptotical compactness of solutions through the uniform estimate on the solutions. Finally, we obtain the existence of a pullback attractor.

A quantale is a complete lattice equipped with an associative binary multiplication distributing over arbitrary joins. We define the notions of right (left, two) sided derivation and idempotent derivation and investigate the properties of them. It’s well known that quantic nucleus and quantic conucleus play important roles in a quantale. In this paper, the relationships between derivation and quantic nucleus (conucleus) are studied via introducing the concept of pre-derivation.

WOS: 000393617200001, In this paper a class of general type alpha-admissible contraction mappings on quasi-b-metric-like spaces are defined. Existence and uniqueness of fixed points for this class of mappings is discussed and the results are applied to Ulam stability problems. Various consequences of the main results are obtained and illustrative examples are presented.

In this paper, we investigate the value distribution of meromorphic solutions of homogeneous and non-homogeneous complex linear differential-difference equations, and obtain the results on the relations between the order of the solutions and the convergence exponents of the zeros, poles, a-points and small function value points of the solutions, which show the relations in the case of non-homogeneous equations are sharper than the ones in the case of homogeneous equations.

Let f be an arithmetic function and S = {x 1, …, xn } be a set of n distinct positive integers. By (f(xi , xj )) (resp. (f[xi , xj ])) we denote the n × n matrix having f evaluated at the greatest common divisor (xi , xj ) (resp. the least common multiple [xi , xj ]) of x, and xj as its (i, j)-entry, respectively. The set S is said to be gcd closed if (xi , xj ) ∈ S for 1 ≤ i, j ≤ n. In this paper, we give formulas for the determinants of the matrices (f(xi , xj )) and (f[xi , xj ]) if S consists of multiple coprime gcd-closed sets (i.e., S equals the union of S 1, …, Sk with k ≥ 1 being an integer and S 1, …, Sk being gcd-closed sets such that (lcm(Si ), lcm(Sj )) = 1 for all 1 ≤ i ≠ j ≤ k). This extends the Bourque-Ligh, Hong’s and the Hong-Loewy formulas obtained in 1993, 2002 and 2011, respectively. It also generalizes the famous Smith’s determinant.

In this paper, we introduce two different contractive conditions and prove some new fixed point theorems for cyclic (ψ,ϕ,φ) α -contractive mappings and α-(κ,φ)g -contractive mappings in complete metric-like spaces via altering distance functions. Our results generalize and extend some existing results. Moreover, some examples are given to support the obtained results.

In this paper, the classical Lie theory is applied to study the Benjamin-Bona-Mahony (BBM) and modified Benjamin-Bona-Mahony equations (MBBM) to obtain their symmetries, invariant solutions, symmetry reductions and differential invariants. By observation of the the adjoint representation of Mentioned symmetry groups on their Lie algebras, we find the primary classification (optimal system) of their group-invariant solutions which provides new exact solutions to BBM and MBBM equations. Finally, conservation laws of the BBM and MBBM equations are presented. Some aspects of their symmetry properties are given too.

A graph X is said to be End-regular (End-orthodox) if its endomorphism monoid End(X) is a regular (orthodox) semigroup. In this paper, we determine the End-regular and the End-orthodox generalized lexicographic products of bipartite graphs.

In this paper, we introduce the new fully degenerate poly-Bernoulli numbers and polynomials and inverstigate some properties of these polynomials and numbers. From our properties, we derive some identities for the fully degenerate poly-Bernoulli numbers and polynomials.

In this paper, the stability of the adaptive fading extended Kalman filter with the matrix forgetting factor when applied to the state estimation problem with noise terms in the non–linear discrete–time stochastic systems has been analysed. The analysis is conducted in a similar manner to the standard extended Kalman filter’s stability analysis based on stochastic framework. The theoretical results show that under certain conditions on the initial estimation error and the noise terms, the estimation error remains bounded and the state estimation is stable.The importance of the theoretical results and the contribution to estimation performance of the adaptation method are demonstrated interactively with the standard extended Kalman filter in the simulation part.

In this paper, we firstly introduce a special congruence relation U(μ, t) induced by a fuzzy ideal μ in a semigroup S. Then we define the lower and upper approximations based on a fuzzy ideal in semigroups. We can establish rough semigroups, rough ideals, rough prime ideals, rough fuzzy semigroups, rough fuzzy ideals and rough fuzzy prime ideals according to the definitions of rough sets and rough fuzzy sets. Furthermore, we shall consider the relationships among semigroups and rough semigroups, fuzzy semigroups and rough fuzzy semigroups, and some relative properties are also discussed.

This paper is devoted to the study of fractional differential equations with Riemann-Liouville fractional derivatives and infinite delay in Banach spaces. The weighted delay is developed to deal with the case of non-zero initial value, which leads to the unboundedness of the solutions. Existence and uniqueness results are obtained based on the theory of measure of non-compactness, Schaude’s and Banach’s fixed point theorems. As auxiliary results, a fractional Gronwall type inequality is proved, and the comparison property of fractional integral is discussed.

Operation principle of the engineering systems occupies an important role in the reliability theory. In most of the studies, the reliability function of the system is obtained analytically according to the structure of the system. Also in such studies the mean operating time of the system is calculated. However, the reliability function of some systems, such as repairable system, cannot be easily obtained analytically. In this case, forming Laplace-Stieltjes transform of the system can provide a solution to the problem. In this paper, we have designed a system which consists of two components that can be repairable with the aging property. Firstly, the Laplace-Stieltjes transform of the system is formed. Later, the mean operating time of the system is calculated by means of Laplace-Stieltjes transform. The system’s repair policy is evaluated depending on the geometric process. This property provides the aging of the system. We also provide special systems with different marginal lifetime distributions to illustrate the theoretical results in this study.

This paper suggests several models that describe the symmetry and asymmetry structure of each subdimension for the multiway square contingency table with ordered categories. A classical three-way categorical example is examined to illustrate the model results. These models analyze the subsymmetric and asymetric structure of the table.

In this paper, we study the the parabolic Marcinkiewicz integral M Ω , h ρ 1 , ρ 2 ${\cal M}_{\Omega, h}^{{\rho _{1,}}{\rho _2}}$ on product domains R n × R m (n, m ≥ 2). Lp estimates of such operators are obtained under weak conditions on the kernels. These estimates allow us to use an extrapolation argument to obtain some new and improved results on parabolic Marcinkiewicz integral operators.

In this paper, we study multiplication lattice modules. We establish a new multiplication over elements of a multiplication lattice module.With this multiplication, we characterize idempotent element, prime element, weakly prime element and almost prime element in multiplication lattice modules.

In this paper, we use the mean value theorem of Dirichlet L-functions, the properties of Gauss sums and Dedekind sums to study the hybrid mean value problem involving Dedekind sums and the two-term exponential sums, and give an interesting identity and asymptotic formula for it.

In a polynomial ring over a perfect field, the symbolic powers of a prime ideal can be described via differential operators: a classical result by Zariski and Nagata says that the n-th symbolic power of a given prime ideal consists of the elements that vanish up to order n on the corresponding variety. However, this description fails in mixed characteristic. In this paper, we use p-derivations, a notion due to Buium and Joyal, to define a new kind of differential powers in mixed characteristic, and prove that this new object does coincide with the symbolic powers of prime ideals. This seems to be the first application of p-derivations to commutative algebra.

In this paper, the necessary and sufficient conditions are found for the boundedness of the Riesz potential I α {I_{\alpha}} in the local Morrey–Lorentz spaces M p , q ; λ loc ⁢ ( ℝ n ) {M_{p,q;{\lambda}}^{\mathrm{loc}}({\mathbb{R}^{n}})} . This result is applied to the boundedness of particular operators such as the fractional maximal operator, fractional Marcinkiewicz operator and fractional powers of some analytic semigroups on the local Morrey–Lorentz spaces M p , q ; λ loc ⁢ ( ℝ n ) {M_{p,q;{\lambda}}^{\mathrm{loc}}({\mathbb{R}^{n}})} .

The Banach algebras of Harmonic Analysis are usually far from being Arens regular and often turn out to be as irregular as possible. This utmost irregularity has been studied by means of two notions: strong Arens irregularity, in the sense of Dales and Lau, and extreme non-Arens regularity, in the sense of Granirer. Lau and Losert proved in 1988 that the convolution algebra L 1 ⁢ ( G ) {L^{1}(G)} is strongly Arens irregular for any infinite locally compact group. In the present paper, we prove that L 1 ⁢ ( G ) {L^{1}(G)} is extremely non-Arens regular for any infinite locally compact group. We actually prove the stronger result that for any non-discrete locally compact group G, there is a linear isometry from L ∞ ⁢ ( G ) {L^{\infty}(G)} into the quotient space L ∞ ⁢ ( G ) / ℱ ⁢ ( G ) {L^{\infty}(G)/\mathcal{F}(G)} , with ℱ ⁢ ( G ) {\mathcal{F}(G)} being any closed subspace of L ∞ ⁢ ( G ) {L^{\infty}(G)} made of continuous bounded functions. This, together with the known fact that ℓ ∞ ⁢ ( G ) / 𝒲 ⁢ 𝒜 ⁢ 𝒫 ⁢ ( G ) {\ell^{\infty}(G)/\mathscr{W\!A\!P}(G)} always contains a linearly isometric copy of ℓ ∞ ⁢ ( G ) {\ell^{\infty}(G)} , proves that L 1 ⁢ ( G ) {L^{1}(G)} is extremely non-Arens regular for every infinite locally compact group.

In the present paper, we investigate the existence, uniqueness and continuous dependence of mild solutions of an impulsive neutral integro-differential equations with nonlocal condition in Banach spaces. We use Banach contraction principle and the theory of fractional power of operators to obtain our results.

A general construction of the free algebra over a poset in varieties finitely generated is given in [8]. In this paper, we apply this to the varieties of Łukasiewicz-Moisil algebras, giving a detailed description of the free algebra over a finite poset (X, ≤) , Freen((X, ≤)). As a consequence of this description, the cardinality of Freen((X, ≤)). is computed for special posets.

An extended generalization of recent result of Kikina and Kikina (2011) has been established through the notions of weak compatibility and the property E.A., under an implicit-type relation and restricted orbital completeness of the space. The result of this paper also extends and generalizes that of Imdad and Ali (2007).

This paper is concerned with the existence of at least one solution of the nonlinear 2k-th order BVP. We use the Mountain Pass Lemma to get an existence result for the problem, whose linear part depends on several parameters.

The purpose of this paper is to prove the following result. Let X be a complex Hilbert space, let L(X) be an algebra of all bounded linear operators on X and let A(X) ⊂ L(X) be a standard operator algebra, which is closed under the adjoint operation. Suppose there exists a linear mapping D : A(X) → L(X) satisfying the relation 2D(AA*A) = D(AA*)A + AA*D(A) + D(A)A*A + AD(A*A) for all A ∈ A(X). In this case, D is of the form D(A) = [A,B] for all A ∈ A(X) and some fixed B ∈ L(X), which means that D is a derivation.

In this paper, we consider the problem of the existence of conformal metrics with prescribed scalar curvature on the standard sphere S n, n ≥ 3. We give new existence and multiplicity results based on a new Euler-Hopf formula type. Our argument also has the advantage of extending well known results due to Y. Li [16].

Introduction It is interesting that using the properties of quaternionic regular functions in the sense of Fueter, one can obtain the significant results in complex analysis (see, e.g. [1], [3]). There are many amazing relations between quaternionic functions and some objects of complex analysis. This paper is devoted to show one of them, namely that there is a correspondence between quaternionic regular functions in the sense of Fueter and fundamental 2-forms on a 4-dimensional almost Kahler manifold.

In this paper, we study radical transversal lightlike submanifolds and screen slant radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds giving some non-trivial examples of these submanifolds. Integrability conditions of distributions D and RadTM on radical transversal lightlike submanifolds and screen slant radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds, have been obtained. We also study totally contact umbilical radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds.

In this paper, we consider Willett’s and Rozanova’s generalizations of Opial’s inequality and extend them to inequalities in several independent variables. Also, we present some new Opial-type inequalities in several independent variables.

In this paper we prove some composition results for strongly summing and dominated operators. As an application we give necessary and sufficient conditions for a multilinear tensor product of multilinear operators to be strongly summing or dominated. Moreover, we show the failure of some possible n-linear versions of Grothendieck’s composition theorem in the case n ≥ 2 and give a new example of a 1-dominated, hence strongly 1-summing bilinear operator which is not weakly compact.

In the four-dimensional pseudo-Euclidean space with neutral metric there are three types of rotational surfaces with two-dimensional axis - rotational surfaces of elliptic, hyperbolic or parabolic type. A surface whose mean curvature vector field is lightlike is said to be quasi-minimal. In this paper we classify all quasi-minimal rotational surfaces of elliptic, hyperbolic and parabolic type, respectively., 16 pages

In this short note we present a new general definition of local fractional derivative, that depends on an unknown kernel. For some appropriate choices of the kernel we obtain some known cases. We establish a relation between this new concept and ordinary differentiation. Using such formula, most of the fundamental properties of the fractional derivative can be derived directly., This is a preprint of a paper whose final and definite form is published in 'Open Mathematics'

It is known that one can associate a Kontsevich-type formality morphism to every Drinfeld associator. In the present paper, we show that this morphism may be extended to a Kontsevich–Shoikhet formality morphism of cochains and chains, by describing the action of the Grothendieck–Teichmüller group on such objects (up to homotopy).

The main purpose of this paper is to introduce a class of new extended forms of the beta function, Gauss hypergeometric function and Appell-Lauricella hypergeometric functions by means of the modified Bessel function of the third kind. Some typical generating relations for these extended hypergeometric functions are obtained by defining the extension of the Riemann-Liouville fractional derivative operator. Their connections with elementary functions and Fox’s H-function are also presented The research of J.J. Nieto has been partially supported by the Ministerio de Economía y Competitividad of Spain under grants MTM2016–75140–P, MTM2013–43014–P, Xunta de Galicia, Grants GRC2015-004 and R2016-022, and co- nanced by the European Community fund FEDER SI

Very recently bounds for the L q spectra of inhomogeneous self-similar measures satisfying the Inhomogeneous Open Set Condition (IOSC), being the appropriate version of the standard Open Set Condition (OSC), were obtained. However, if the IOSC is not satisfied, then almost nothing is known for such measures. In the paper we study the L q spectra and Renyi dimension of generalized inhomogeneous self-similar measures, for which we allow an infinite number of contracting similarities and probabilities depending on positions. As an application of the results, we provide a systematic approach to obtaining non-trivial bounds for the L q spectra and Renyi dimension of inhomogeneous self-similar measures not satisfying the IOSC and of homogeneous ones not satisfying the OSC. We also provide some non-trivial bounds without any separation conditions.

In this paper we give a new proof of the André–Oort conjecture under the generalised Riemann hypothesis. In fact, we generalise the strategy pioneered by Edixhoven, and implemented by Klingler and Yafaev, to all special subvarieties. Thus, we remove ergodic theory from the proof of Klingler, Ullmo and Yafaev and replace it with tools from algebraic geometry. Our key ingredient is a lower bound for the degrees of strongly special subvarieties coming from Prasad’s volume formula for S-arithmetic quotients of semisimple groups.

In this paper, we give some new characterizations of orthodox semigroups in terms of the set of inverses of idempotents. As a generalization, a new class of regular semigroups, namely Vn-semigroups, is introduced. Also, we give a characterization of Vn-semigroups and investigate some properties of Vn-semigroups. Furthermore, we show that the class of Vn-semigroups is closed under direct products and homomorphic images. However, regular subsemigroups of Vn-semigroups (n ≥ 2) are not necessarily Vn-semigroups in general. Therefore, the class of Vn-semigroups (n ≥ 2) does not form an e-variety. Finally, we obtain that a E-solid semigroup S is a V2-semigroup if and only if S is orthodox.

In this paper, we introduce a new concept of (α, φ)g-contractive type mappings and establish coupled coincidence and coupled common fixed point theorems for such mappings in partially ordered G-metric spaces. The results on fixed point theorems are generalizations of some existing results.We also give some examples to illustrate the usability of the obtained results.

The theory of Schur complement plays an important role in many fields, such as matrix theory and control theory. In this paper, applying the properties of Schur complement, some new estimates of diagonally dominant degree on the Schur complement of I(II)-block strictly diagonally dominant matrices and I(II)-block strictly doubly diagonally dominant matrices are obtained, which improve some relative results in Liu [Linear Algebra Appl. 435(2011) 3085-3100]. As an application, we present several new eigenvalue inclusion regions for the Schur complement of matrices. Finally, we give a numerical example to illustrate the advantages of our derived results.

In this paper, we establish certain spaces of generalized functions for a class of ɛs 2,1 transforms. We give the definition and derive certain properties of the extended ɛs 2,1 transform in a context of Boehmian spaces. The extended ɛs 2,1 transform is therefore well defined, linear and consistent with the classical ɛs 2,1 transforms. Certain results are also established in some detail.

Relating to the crucial problem of branch switching, the calculation of codimension 2 bifurcation points is one of the major issues in numerical bifurcation analysis. In this paper, we focus on the double Hopf points for delay differential equations and analyze in detail the corresponding eigenspace, which enable us to obtain the finite dimensional defining system of equations of such points, instead of an infinite dimensional one that happens naturally for delay systems. We show that the double Hopf point, together with the corresponding eigenvalues, eigenvectors and the critical values of the bifurcation parameters, is a regular solution of the finite dimensional defining system of equations, and thus can be obtained numerically through applying the classical iterative methods. We show our theoretical findings by a numerical example.

We establish in this paper some Jensen’s type inequalities for functions defined by power series with nonnegative coefficients. Applications for functions of selfadjoint operators on complex Hilbert spaces are provided as well.

In this paper, the boundedness properties for some Toeplitz type operators associated to the Riesz potential and general integral operators from Lebesgue spaces to Orlicz spaces are proved. The general integral operators include singular integral operator with general kernel, Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator.