Volume 16, Issue 1

We prove new theorems related to the construction of the shallow water bi-Hamiltonian systems associated to the semi-direct product of Virasoro and affine Kac–Moody Lie algebras. We discuss associated Verma modules, coadjoint orbits, Casimir functions, and bi-Hamiltonian systems.

In this contribution a particular plane steady-state channel flow including evaporation effects is investigated from analytical point of view. The channel is assumed to be horizontal. The motion of two heavy viscous immiscible fluids is governed by a free boundary value problem for a coupled system of Navier-Stokes and Stephan equations. The flow domain is unbounded in two directions and the free interface separating partially both liquids is semi-infinite, i.e. infinite in one direction. The free interface begins in some point Q where the half-line Σ 1 separating the two parts of the channel in front of Q ends. Existence and uniqueness of a suitable solution in weighted HÖLDER spaces can be proved for small data (i.e. small fluxes) of the problem.

In (Lawnik M., Generation of numbers with the distribution close to uniform with the use of chaotic maps, In: Obaidat M.S., Kacprzyk J., Ören T. (Ed.), International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH) (28-30 August 2014, Vienna, Austria), SCITEPRESS, 2014) Lawnik discussed a method of generating pseudo-random numbers from uniform distribution with the use of adequate chaotic transformation. The method enables the “flattening” of continuous distributions to uniform one. In this paper a inverse process to the above-mentioned method is presented, and, in consequence, a new manner of generating pseudo-random numbers from a given continuous distribution. The method utilizes the frequency of the occurrence of successive branches of chaotic transformation in the process of “flattening”. To generate the values from the given distribution one discrete and one continuous value of a random variable are required. The presented method does not directly involve the knowledge of the density function or the cumulative distribution function, which is, undoubtedly, a great advantage in comparison with other well-known methods. The described method was analysed on the example of the standard normal distribution.

In this paper we obtain the solution of the singular Cauchy problem for the Euler-Poisson-Darboux equation when differential Bessel operator acts by each variable.

We introduce and study ternary f -distributive structures, Ternary f -quandles and more generally their higher n -ary analogues. A classification of ternary f -quandles is provided in low dimensions. Moreover, we study extension theory and introduce a cohomology theory for ternary, and more generally n -ary, f -quandles. Furthermore, we give some computational examples.

A parametrization of the fine Simpson moduli spaces of 1-dimensional sheaves supported on plane quartics is given: we describe the gluing of the Brill-Noether loci described by Drézet and Maican, provide a common parameter space for these loci, and show that the Simpson moduli space M = M 4 m ± 1 (ℙ 2 ) is a blow-down of a blow-up of a projective bundle over a smooth moduli space of Kronecker modules. Two different proofs of this statement are given.

We provide an explicit analytical representation for a number of logarithmic integrals in terms of the Lerch transcendent function and other special functions. The integrals in question will be associated with both alternating harmonic numbers and harmonic numbers with positive terms. A few examples of integrals will be given an identity in terms of some special functions including the Riemann zeta function. In general none of these integrals can be solved by any currently available mathematical package.

In this work we obtain easy characterizations for the boundedness of the solutions of the discrete, self–adjoint, second order and linear unidimensional equations with periodic coefficients, including the analysis of the so-called discrete Mathieu equations as particular cases.

Consider the first-order linear differential equation with several retarded arguments x′ (t)+∑ k=1npk(t)x(τ k(t))=0,t≥ t0,$$\begin{array}{} \displaystyle x^{\prime }(t)+\sum\limits_{k=1}^{n}p_{k}(t)x(\tau _{k}(t))=0,\;\;\;t\geq t_{0}, \end{array} $$ where the functions p k , τ k ∈ C ([ t 0 , ∞), ℝ + ), τ k ( t ) < t for t ≥ t 0 and lim t →∞ τ k ( t ) = ∞, for every k = 1, 2, …, n . Oscillation conditions which essentially improve known results in the literature are established. An example illustrating the results is given.

This paper is devoted to study the existence and regularity of mild solutions in some interpolation spaces for a class of functional partial differential equations with nonlocal initial conditions. The linear part is assumed to be a sectorial operator in Banach space X . The fractional power theory and α -norm are used to discuss the problem so that the obtained results can be applied to equations with terms involving spatial derivatives. Moreover, we present an example to illustrate the application of main results.

Recently, Chen and Xia proved that for n ≥ 6, the q -derangement numbers D n ( q ) are log-concave except for the last term when n is even. In this paper, employing a recurrence relation for DnB(q) $\begin{array}{} \displaystyle D^B_n(q) \end{array}$ discovered by Chow, we show that for n ≥ 4, the q -derangement numbers of type B DnB(q) $\begin{array}{} \displaystyle D^B_n(q) \end{array}$ are also log-concave.

In this paper, we attempt to cope with states in a universal algebraic setting, that is, introduce a notion of generalized state map from a pseudo equality algebra X to an arbitrary pseudo equality algebra Y . We give two types of special generalized state maps, namely, generalized states and generalized internal states. Also, we study two types of states, namely, Bosbach states and Rie č an states. Finally, we discuss the relations among generalized state maps, states and internal states (or state operators) on pseudo equality algebras. We verify the results that generalized internal states are the generalization of internal states, and generalized states are the generalization of state-morphisms on pseudo equality algebras. Furthermore, we obtain that generalized states are the generalization of Bosbach states and Rie č an states on linearly ordered and involutive pseudo equality algebras, respectively. Hence we can come to the conclusion that, in a sense, generalized state maps can be viewed as a possible united framework of the states and the internal states, the state-morphisms and the internal state-morphisms on pseudo equality algebras.

An ultraproduct can be a helpful organizing principle in presenting solutions of problems at many levels, as argued by Terence Tao. We apply it here to the solution of a calculus problem: every infinite sequence has a monotone infinite subsequence, and give other applications.

We investigate the group irregularity strength ( s g ( G )) of graphs, i.e. the smallest value of s such that taking any Abelian group 𝓖 of order s , there exists a function f : E ( G ) → 𝓖 such that the sums of edge labels at every vertex are distinct. So far it was not known if s g ( G ) is finite for disconnected graphs. In the paper we present some upper bound for all graphs. Moreover we give the exact values and bounds on s g ( G ) for disconnected graphs without a star as a component.

We prove that a variant of the Courtois-Finiasz-Sendrier signature is strongly existentially unforgeable under chosen message attack in the random oracle model, assuming hardness of the Permuted Goppa Syndrome Decoding Problem (also known as the Niederreiter problem). In addition, we explicitly show that security against key substitution attacks can be arranged by a standard technique of Menezes and Smart, hashing the public key.

In this paper, we study the ordered regular equivalence relations on ordered semihypergroups in detail. To begin with, we introduce the concept of weak pseudoorders on an ordered semihypergroup, and investigate several related properties. In particular, we construct an ordered regular equivalence relation on an ordered semihypergroup by a weak pseudoorder. As an application of the above result, we completely solve the open problem on ordered semihypergroups introduced in [B. Davvaz, P. Corsini and T. Changphas, Relationship between ordered semihypergroups and ordered semigroups by using pseuoorders, European J. Combinatorics 44 (2015), 208–217]. Furthermore, we establish the relationships between ordered regular equivalence relations and weak pseudoorders on an ordered semihypergroup, and give some homomorphism theorems of ordered semihypergroups, which are generalizations of similar results in ordered semigroups.

From the notion of Jacobi type vector fields for a real hypersurface in complex quadric Q m we prove that if the structure vector field is of Jacobi type it is Killing when the real hypersurface is either Hopf or compact. In such cases we classify real hypersurfaces whose structure vector field is of Jacobi type.

Let A be a {0, 1}-matrix and r ( A ) denotes its rank. The complement matrix of A is defined and denoted by A c = J − A , where J is the matrix with each entry being 1. In particular, when A is a square {0, 1}-matrix with each diagonal entry being 0, another kind of complement matrix of A is defined and denoted by A = J − I − A , where I is the identity matrix. We determine the possible values of r ( A ) ± r ( A c ) and r ( A ) ± r ( A ) in the general case and in the symmetric case. Our proof is constructive.

In the paper, we study Lie n superderivations and generalized Lie n superderivations of superalgebras, using the theory of functional identities in superalgebras. We prove that if A = A 0 ⊕ A 1 is a prime superalgebra with deg( A 1 ) ≥ 2 n + 5, n ≥ 2, then any Lie n superderivation of A is the sum of a superderivation and a linear mapping, and any generalized Lie n superderivation of A is the sum of a generalized superderivation and a linear mapping.

In this paper, we introduce a practical strategy to select an adaptive time step size suitable for the parareal algorithm designed to parallelize a numerical scheme for solving stiff initial value problems. For the adaptive time step size, a technique to detect stiffness of a given system is first considered since the step size will be chosen according to the extent of stiffness. Finally, the stiffness detection technique is applied to an initial prediction step of the parareal algorithm, and select an adaptive step size to each time interval according to the stiffness. Several numerical experiments demonstrate the efficiency of the proposed method.

The paper is dealing with stability problems for a nonlinear system on the Lie group SO (3) × R 3 × R 3 . The approximate analytic solutions of the considered system via Optimal Homotopy Asymptotic Method are presented, too.

In this work, we introduce the notions of ( s , p , α )-quasi-contractions and ( s , p )-weak contractions and deduce some fixed point results concerning such contractions, in the setting of b -metric-like spaces. Our results extend and generalize some recent known results in literature to more general metric spaces. Moreover, some examples and applications support the results.

In this paper, some algebraic and combinatorial characterizations of the spanning simplicial complex Δ s (𝓙 n , m ) of the Jahangir’s graph 𝓙 n , m are explored. We show that Δ s (𝓙 n , m ) is pure, present the formula for f -vectors associated to it and hence deduce a recipe for computing the Hilbert series of the Face ring k [ Δ s (𝓙 n , m )]. Finally, we show that the face ring of Δ s (𝓙 n , m ) is Cohen-Macaulay and give some open scopes of the current work.

We show that the greedy algorithm provided in this paper works for interval greedoids with positive weights under some conditions, and also characterize an exchangeable system to be an interval greedoid with the assistance of the greedy algorithm.

Here we study the existence of a solution and also the behavior of the existing solution of the abstract nonlinear differential equation of second order that, in particular, is the nonlinear hyperbolic equation with nonlinear main parts, and in the special case, is the equation of the type of equation of traffic flow.

In this paper we provide some new sufficient conditions that ensure the existence of the solution of a weak vector equilibrium problem in Hausdorff topological vector spaces ordered by a cone. Further, we introduce a dual problem and we provide conditions that assure the solution set of the original problem and its dual coincide. We show that many known problems from the literature can be treated in our primal-dual model. We provide several coercivity conditions in order to obtain the existence of the solution of the primal-dual problems without compactness assumption. We apply the obtained results to perturbed vector equilibrium problems.

An operator T acting on a Banach space X satisfies the property ( UW Π ) if σ a ( T )∖ σ SF+− $\begin{array}{} \sigma_{SF_{+}^{-}} \end{array} $( T ) = Π ( T ), where σ a ( T ) is the approximate point spectrum of T , σ SF+− $\begin{array}{} \sigma_{SF_{+}^{-}} \end{array} $( T ) is the upper semi-Weyl spectrum of T and Π ( T ) the set of all poles of T . In this paper we introduce and study two new spectral properties, namely ( V Π ) and ( V Π a ), in connection with Browder type theorems introduced in [1], [2], [3] and [4]. Among other results, we have that T satisfies property ( V Π ) if and only if T satisfies property ( UW Π ) and σ ( T ) = σ a ( T ).

A set in the complex plane which involves n parameters in [0, 1] is given to localize all eigenvalues different from 1 for stochastic matrices. As an application of this set, an upper bound for the moduli of the subdominant eigenvalues of a stochastic matrix is obtained. Lastly, we fix n parameters in [0, 1] to give a new set including all eigenvalues different from 1, which is tighter than those provided by Shen et al. (Linear Algebra Appl. 447 (2014) 74-87) and Li et al. (Linear and Multilinear Algebra 63(11) (2015) 2159-2170) for estimating the moduli of subdominant eigenvalues.

The Golomb-Welch conjecture states that there is no perfect r -error correcting Lee code of word length n over ℤ for n ≥ 3 and r ≥ 2. This problem has received great attention due to its importance in applications in several areas beyond mathematics and computer sciences. Many results on this subject have been achieved, however the conjecture is only solved for some particular values of n and r , namely: 3 ≤ n ≤ 5 and r ≥ 2; n = 6 and r = 2. Here we give an important contribution for the case n = 7 and r = 2, establishing cardinality restrictions on codeword sets.

Let T be the singular integral operator with variable kernel defined by Tf(x)=p.v.∫RnΩ(x,x−y)|x−y|nf(y)dy$$\begin{array}{} \displaystyle Tf(x)= p.v. \int\limits_{\mathbb{R}^{n}}\frac{{\it\Omega}(x,x-y)}{|x-y|^{n}}f(y)\text{d}y \end{array} $$ and D γ (0 ≤ γ ≤ 1) be the fractional differentiation operator. Let T ∗ and T ♯ be the adjoint of T and the pseudo-adjoint of T , respectively. The aim of this paper is to establish some boundedness for TD γ − D γ T and ( T ∗ − T ♯ ) D γ on the homogeneous Morrey-Herz-type Hardy spaces with variable exponents HMK˙p(⋅),λα(⋅),q$\begin{array}{} HM\dot{K}^{\alpha(\cdot),q}_{p(\cdot),\lambda} \end{array} $ via the convolution operator T m , j and Calderón-Zygmund operator, and then establish their boundedness on these spaces. The boundedness on HMK˙p(⋅),λα(⋅),q$\begin{array}{} HM\dot{K}^{\alpha(\cdot),q}_{p(\cdot),\lambda} \end{array} $(ℝ n ) is shown to hold for TD γ − D γ T and ( T ∗ − T ♯ ) D γ . Moreover, the authors also establish various norm characterizations for the product T 1 T 2 and the pseudo-product T 1 ∘ T 2 .

This paper is an introduction to disoriented knot theory, which is a generalization of the oriented knot and link diagrams and an exposition of new ideas and constructions, including the basic definitions and concepts such as disoriented knot, disoriented crossing and Reidemesiter moves for disoriented diagrams, numerical invariants such as the linking number and the complete writhe, the polynomial invariants such as the bracket polynomial, the Jones polynomial for the disoriented knots and links.

The restricted triangulation existence problem on a given graph decides whether there exists a triangulation on the graph’s vertex set that is restricted with respect to its edge set. Let G = C ( n , S ) be a circulant graph on n vertices with jump value set S . We consider the restricted triangulation existence problem for G . We determine necessary and sufficient conditions on S for which G admitting a restricted triangulation. We characterize a set of jump values S ( n ) that has the smallest cardinality with C ( n , S ( n )) admits a restricted triangulation. We present the measure of non-triangulability of K n − G for a given G .

Let Σ be a linear system on a connected Lie group G and assume that the reachable set 𝓐 from the identity element e ∈ G is open. In this paper, we give an algebraic condition to warrant the boundedness of the existent control set with a nonempty interior containing e . We concentrate the search for the class of decomposable groups which includes any solvable group and also every compact semisimple group.

In this paper, we obtain Chen’s inequalities for submanifolds in ( κ , μ )-contact space form endowed with a semi-symmetric metric connection.

This work presents a novel combining method called ‘orthogonalizing ORing ◯ ∨ $\bigcirc\!\!\!\!\!\!\vee $’ which enables the building of the union of two conjunctions whereby the result consists of disjointed conjunctions. The advantage of this novel technique is that the results are already presented in an orthogonal form which has a significant advantage for further calculations as the Boolean Differential Calculus. By orthogonalizing ORing two calculation steps - building the disjunction and the subsequent orthogonalization of two conjunctions - are performed in one step. Postulates, axioms and rules for this linking technique are also defined which have to be considered getting correct results. Additionally, a novel equation, based on orthogonalizing ORing, is set up for orthogonalization of every Boolean function of disjunctive form. Thus, disjointed Sum of Products can be easily calculated in a mathematical way by this equation.

In this paper we propose a new parametric linearizing approach for globally solving quadratically inequality constrained quadratic programs. By utilizing this approach, we can derive the parametric linear programs relaxation problem of the investigated problem. To accelerate the computational speed of the proposed algorithm, an interval deleting rule is used to reduce the investigated box. The proposed algorithm is convergent to the global optima of the initial problem by subsequently partitioning the initial box and solving a sequence of parametric linear programs relaxation problems. Finally, compared with some existing algorithms, numerical results show higher computational efficiency of the proposed algorithm.

In this paper, we obtained new generalizations of Steffensen’s inequality for n-convex functions by using extension of Montgomery identity via Taylor’s formula. Since 1-convex functions are nondecreasing functions, new inequalities generalize Stefensen’s inequality. Related Ostrowski type inequalities are also provided. Bounds for the reminders in new identities are given by using the Chebyshev and Grüss type inequalities.

We show that if a vector field X has the C 1 robustly barycenter property then it does not have singularities and it is Axiom A without cycles. Moreover, if a generic C 1 -vector field has the barycenter property then it does not have singularities and it is Axiom A without cycles. Moreover, we apply the results to the divergence free vector fields. It is an extension of the results of the barycenter property for generic diffeomorphisms and volume preserving diffeomorphisms [1].

Let V be a smooth variety. A hypersurface arrangement 𝓜 in V is a union of smooth hypersurfaces, which locally looks like a union of hyperplanes. We say 𝓜 is free if all these local models can be chosen to be free hyperplane arrangements. In this paper, we use Saito’s criterion to study the freeness of hypersurface arrangements consisting of hyperplanes and spheres, and construct the bases for the derivation modules explicitly.

The Witt algebra 𝔚 d of rank d (≥ 1) is the derivation algebra of Laurent polynomial algebras in d commuting variables. In this paper, all biderivations of 𝔚 d without anti-symmetric condition are determined. As an applications, commutative post-Lie algebra structures on 𝔚 d are obtained. Our conclusions recover and generalize results in the related papers on low rank or anti-symmetric cases.

We give criteria for the spectra of some nuclear operators in subspaces of quotients of L p -spaces to be central-symmetric, as well as for the spectra of linear operators in Banach spaces to be Z d -symmetric in the sense of B. Mityagin. Also, we present a short proof of a corresponding Mityagin’s theorem.

This paper is devoted to pose several interpolation problems on the open unit disk 𝔻 of the complex plane in a recursive and linear way. We look for interpolating sequences ( z n ) in 𝔻 so that given a bounded sequence ( a n ) and a suitable sequence ( w n ), there is a bounded analytic function f on 𝔻 such that f ( z 1 ) = w 1 and f ( z n +1 ) = a n f ( z n ) + w n +1 . We add a recursion for the derivative of the type: f ′( z 1 ) = w1′$\begin{array}{} w_1' \end{array} $ and f ′( z n +1 ) = an′$\begin{array}{} a_n' \end{array} $ [(1 − | z n | 2 )/(1 − | z n +1 | 2 )] f ′( z n ) + wn+1′,$\begin{array}{} w_{n+1}', \end{array} $ where (an′$\begin{array}{} a_n' \end{array} $) is bounded and (wn′$\begin{array}{} w_n' \end{array} $) is an appropriate sequence, and we also look for zero-sequences verifying the recursion for f ′. The conditions on these interpolating sequences involve the Blaschke product with zeros at their points, one of them being the uniform separation condition.

We define a new algebraic structure for singular knots and links. It extends the notion of a bikei (or involutory biquandle) from regular knots and links to singular knots and links. We call this structure a singbikei. This structure results from the generalized Reidemeister moves representing singular isotopy. We give several examples on singbikei and we use singbikei to distinguish several singular knots and links.

In this paper, we study linear codes over ring R k = 𝔽 p m [ u 1 , u 2 ,⋯, u k ]/〈ui2$\begin{array}{} u^{2}_{i} \end{array} $ = u i , u i u j = u j u i 〉 where k ≥ 1 and 1 ≤ i , j ≤ k . We define a Gray map from RkntoFpm2kn$\begin{array}{} R_{k}^n\,\,\text{to}\,\,{\mathbb F}_{p^m}^{2^kn} \end{array} $ and give the generator polynomials of constacyclic codes over R k . We also study the MacWilliams identities of linear codes over R k .

In this paper, we consider positively weak measure expansive homeomorphisms and flows with the shadowing property on a compact metric space X . Moreover, we prove that if a homeomorphism (or flow) has a positively weak expansive measure and the shadowing property on its nonwandering set, then its topological entropy is positive.

The paper belongs to the qualitative theory of half-linear equations which are located between linear and non-linear equations and, at the same time, between ordinary and partial differential equations. We analyse the oscillation and non-oscillation of second-order half-linear differential equations whose coefficients are given by the products of functions having mean values and power functions. We prove that the studied very general equations are conditionally oscillatory. In addition, we find the critical oscillation constant.

In this paper, we give some characterizations of 𝓠-regular semigroups and show that the class of 𝓠-regular semigroups is closed under the direct product and homomorphic images. Furthermore, we characterize the 𝓠-subdirect products of this class of semigroups and study the E -unitary 𝓠-regular covers for 𝓠-regular semigroups, in particular for those whose maximum group homomorphic image is a given group. As an application of these results, we claim that the similar results on V -regular semigroups also hold.

In this paper, we use the analysis method and the properties of trigonometric sums to study the computational problem of one kind power mean of the hybrid Gauss sums. After establishing some relevant lemmas, we give an exact computational formula for it. As an application of our result, we give an exact formula for the number of solutions of one kind diagonal congruence equation mod p , where p be an odd prime.

Sum of ratios problem occurs frequently in various areas of engineering practice and management science, but most solution methods for this kind of problem are often designed for determining local solutions . In this paper, we develop a reduced space branch and bound algorithm for globally solving sum of convex-concave ratios problem. By introducing some auxiliary variables, the initial problem is converted into an equivalent problem where the objective function is linear. Then the convex relaxation problem of the equivalent problem is established by relaxing auxiliary variables only in the outcome space. By integrating some acceleration and reduction techniques into branch and bound scheme, the presented global optimization algorithm is developed for solving these kind of problems. Convergence and optimality of the algorithm are presented and numerical examples taken from some recent literature and MINLPLib are carried out to validate the performance of the proposed algorithm.

In this paper, by making use of the generating function methods and Padé approximation techniques, we establish some new recurrence formulas for the Hermite polynomials and their squares. These results presented here are the corresponding extensions of some known formulas.

In this paper, we propose a relaxed block splitting preconditioner for a class of complex symmetric indefinite linear systems to accelerate the convergence rate of the Krylov subspace iteration method and the relaxed preconditioner is much closer to the original block two-by-two coefficient matrix. We study the spectral properties and the eigenvector distributions of the corresponding preconditioned matrix. In addition, the degree of the minimal polynomial of the preconditioned matrix is also derived. Finally, some numerical experiments are presented to illustrate the effectiveness of the relaxed splitting preconditioner.

In this paper, we introduce the concepts of f -prime ideals, f -semiprime ideals and f -prime radicals in ordered semigroups. Furthermore, some results on f -prime radicals and f -primary decomposition of an ideal in an ordered semigroup are obtained.

In this paper, the existence of positive solutions for systems of semipositone singular fractional differential equations with a parameter and integral boundary conditions is investigated. By using fixed point theorem in cone, sufficient conditions which guarantee the existence of positive solutions are obtained. An example is given to illustrate the results.

We characterize disjointness of supercyclic operators which map a holomorphic function to a partial sum of the Taylor expansion. In particular, we show that disjoint hypercyclicity equals disjoint supercyclicity for families of Taylor-type operators. Moreover, we give a sufficient condition to yield the disjoint supercyclicity for families of Taylor-type operators.

Considering the fact that the development of low carbon economy calls for the low carbon technology sharing between interested enterprises, this paper study a stochastic differential game of low carbon technology sharing in collaborative innovation system of superior enterprises and inferior enterprises. In the paper, we consider the random interference factors that include the uncertain external environment and the internal understanding limitations of decision maker. In the model, superior enterprises and inferior enterprises are separated entities, and they play Stacklberg master-slave game, Nash non-cooperative game, and cooperative game, respectively. We discuss the feedback equilibrium strategies of superior enterprises and inferior enterprises, and it is found that some random interference factors in sharing system can make the variance of improvement degree of low carbon technology level in the cooperation game higher than the variance in the Stackelberg game, and the result of Stackelberg game is similar to the result of Nash game. Additionally, a government subsidy incentive and a special subsidy that inferior enterprises give to superior enterprises are proposed.

This paper investigates the dynamic behavior analysis on the prey-predator model with ratio-dependent Monod-Haldane response function under the homogeneous Dirichlet boundary conditions, which is used to simulate a class of biological system. Firstly, the sufficient and necessary conditions on existence and non-existence of coexistence states of this model are discussed by comparison principle and fixed point index theory. Secondly, taking a as a main bifurcation parameter, the structure of global bifurcation curve on positive solutions is established by using global bifurcation theorem and properties of principal eigenvalue. Finally, the stability of coexistence states is obtained by the eigenvalue perturbation theory; the multiplicity of coexistence states is investigated when a satisfies some condition by the fixed point index theory.

In this paper, we investigate some properties of points on quantales. It is proved that the two sided prime elements are in one to one correspondence with points. By using points of quantales, we give the concepts of p-spatial quantales, and some equivalent characterizations for P-spatial quantales are obtained. It is shown that two sided quantale Q is a spatial quantale if and only if Q is a P-spatial quantale. Based on a quantale Q, we introduce the definition of diameters. We also prove that the induced topology by diameter coincides with the topology of the point spaces.

Let S be a pomonoid. In this paper, we introduce some new types of epimorphisms with certain purity conditions, and obtain equivalent descriptions of various flatness properties of S -posets, such as strong flatness, Conditions (E), (E′), (P), (P w ), (WP), (WP) w , (PWP) and (PWP) w . Thereby, we present other equivalent conditions in the Stenström-Govorov-Lazard theorem for S -posets. Furthermore, we prove that these new epimorphisms are closed under directed colimits. Meantime, this implies that by a new approach we can show that most of flatness properties of S -posets can be transferred to their directed colimit. Finally, we prove that every class of S -posets having a flatness property is closed under directed colimits.

A simple graph G = ( V , E ) admits an H -covering, if every edge in E ( G ) belongs to a subgraph of G isomorphic to H . A graph G admitting an H -covering is called an ( a , d )- H -antimagic if there exists a bijective function f : V ( G ) ∪ E ( G ) → {1, 2, …, | V ( G )| + | E ( G )|} such that for all subgraphs H ′ isomorphic to H the sums ∑ v ∈ V ( H ′) f ( v ) + ∑ e ∈ E ( H ′) f ( e ) form an arithmetic sequence { a , a + d , …, a + ( t − 1) d }, where a > 0 and d ≥ 0 are integers and t is the number of all subgraphs of G isomorphic to H . Moreover, if the vertices are labeled with numbers 1, 2, …, | V ( G )| the graph is called super. In this paper we deal with super cycle-antimagicness of subdivided graphs. We also prove that the subdivided wheel admits an ( a , d )-cycle-antimagic labeling for some d .

The main purpose of this paper is to use the mathematical induction and the properties of Lucas polynomials to study the power sum problem of Lucas polynomials. In the end, we obtain an interesting divisible property.

This paper is concerned with a compressible shear thickening fluid-particle interaction model for the evolution of particles dispersed in a viscous non-Newtonian fluid. Taking the influence of non-Newtonian gravitational potential into consideration, the existence and uniqueness of strong solutions are established.

The class of generalized P-reducible manifolds (briefly GP-reducible manifolds) was first introduced by Tayebi and his collaborates [1]. This class of Finsler manifolds contains the classes of P-reducible manifolds, C-reducible manifolds and Landsberg manifolds. We prove that every compact GP-reducible manifold with positive or negative character is a Randers manifold. The norm of Cartan torsion plays an important role for studying immersion theory in Finsler geometry. We find the relation between the norm of Cartan torsion, mean Cartan torsion, Landsberg and mean Landsberg curvatures of the class of GP-reducible manifolds. Finally, we prove that every GP-reducible manifold admitting a concurrent vector field reduces to a weakly Landsberg manifold.

In 2003 Bartoszyński and Halbeisen published the results on various equivalences of Kuratowski and Banach theorem from 1929 concerning some aspect of measure theory. They showed that the existence of the so called BK-matrix related to Banach and Kuratowski theorem is equivalent to the existence of a K-Lusin set of cardinality continuum. On the other hand, in 1965 Efimov introduced the strong sequences method and using this method proved some well-known theorems in dyadic spaces. The goal of this paper is to show that the existence of such a K-Lusin set is equivalent to the existence of strong sequences of the same cardinality. Some applications of this results are also shown.

In this paper, we consider the square function (Sf)(x)=(∫ 0∞ |(f⊗ Φ t)(x)|2dtt)1/2$$\begin{array}{} \displaystyle (\mathcal{S}f)(x)=\left( \int\limits_{0}^{\infty }|(f\otimes {\it\Phi}_{t})\left( x\right) |^{2}\frac{dt}{t}\right) ^{1/2} \end{array} $$ associated with the Bessel differential operator Bt=d2dt2+(2α +1)tddt,$\begin{array}{} B_{t}=\frac{d^{2}}{dt^{2}}+\frac{(2\alpha+1)}{t}\frac{d}{dt}, \end{array} $ α > −1/2, t > 0 on the half-line ℝ + = [0, ∞). The aim of this paper is to obtain the boundedness of this function in L p , α , p > 1. Firstly, we proved L 2, α -boundedness by means of the Bessel-Plancherel theorem. Then, its weak-type (1, 1) and L p , α , p > 1 boundedness are proved by taking into account vector-valued functions.

In paper we prove that: a space of Borel functions B ( X ) on a set of reals X , with pointwise topology, to be countably selective sequentially separable if and only if X has the property S 1 ( B Γ , B Γ ); there exists a consistent example of sequentially separable selectively separable space which is not selective sequentially separable. This is an answer to the question of A. Bella, M. Bonanzinga and M. Matveev; there is a consistent example of a compact T 2 sequentially separable space which is not selective sequentially separable. This is an answer to the question of A. Bella and C. Costantini; min{𝔟, 𝔮} = { κ : 2 κ is not selective sequentially separable}. This is a partial answer to the question of A. Bella, M. Bonanzinga and M. Matveev.

This article is motivated by a problem posed by David A. Singer in 1999 and by the classical Euler elastic curves. We study spacelike and timelike curves in the Lorentz-Minkowski plane 𝕃 2 whose curvature is expressed in terms of the Lorentzian pseudodistance to fixed geodesics. In this way, we get a complete description of all the elastic curves in 𝕃 2 and provide the Lorentzian versions of catenaries and grim-reaper curves. We show several uniqueness results for them in terms of their geometric linear momentum. In addition, we are able to get arc-length parametrizations of all the aforementioned curves and they are depicted graphically.

In this paper, we study the asymptotic property of underlying operator corresponding to the M/G/1 queueing model with single working vacation, where both service times in a regular busy period and in a working vacation period are function. We obtain that all points on the imaginary axis except zero belong to the resolvent set of the operator and zero is an eigenvalue of both the operator and its adjoint operator with geometric multiplicity one. Therefore, we deduce that the time-dependent solution of the queueing model strongly converges to its steady-state solution. We also study the asymptotic behavior of the time-dependent queueing system’s indices for the model.

In this paper we study a class of semilinear evolution equations with nonlocal initial conditions and give some new results on the existence of asymptotically periodic mild solutions. As one would expect, the results presented here would generalize and improve some results in this area.

In this paper we study the entire solutions to a certain type of difference-differential equations. We also give an affirmative answer to the conjecture of Zhang et al. In addition, our results improve and complement earlier ones due to Yang-Laine, Latreuch, Liu-Lü et al. and references therein.

A subset D of vertices of a graph G is a dominating set if for each u ∈ V ( G ) ∖ D , u is adjacent to some vertex v ∈ D . The domination number , γ ( G ) of G , is the minimum cardinality of a dominating set of G . For an even integer n ≥ 2 and 1 ≤ Δ ≤ ⌊log 2 n ⌋, a Knödel graph W Δ , n is a Δ -regular bipartite graph of even order n , with vertices ( i , j ), for i = 1, 2 and 0 ≤ j ≤ n /2 − 1, where for every j , 0 ≤ j ≤ n /2 − 1, there is an edge between vertex (1, j ) and every vertex (2, ( j +2 k − 1) mod (n/2)), for k = 0, 1, ⋯, Δ − 1. In this paper, we determine the domination number in 4-regular Knödel graphs W 4, n .

In this paper, we introduce the concept of S p -pseudo almost periodicity on time scales and present some basic properties of it, including the translation invariance, uniqueness of decomposition, completeness and composition theorem. Moreover, we prove the seemingly simple but nontrivial result that pseudo almost periodicity implies Stepanov-like pseudo almost periodicity. As an application of the abstract results, we present some existence and uniqueness results on the pseudo almost periodic solutions of dynamic equations with delay.

Strict RA semigroups are common generalizations of ample semigroups and inverse semigroups. The aim of this paper is to study algebras of strict RA semigroups. It is proved that any algebra of strict RA semigroups with finite idempotents has a generalized matrix representation whose degree is equal to the number of non-zero regular 𝓓-classes. In particular, it is proved that any algebra of finite right ample semigroups has a generalized upper triangular matrix representation whose degree is equal to the number of non-zero regular 𝓓-classes. As its application, we determine when an algebra of strict RA semigroups (right ample monoids) is semiprimitive. Moreover, we prove that an algebra of strict RA semigroups (right ample monoids) is left self-injective iff it is right self-injective, iff it is Frobenius, and iff the semigroup is a finite inverse semigroup.

In this paper we investigate the stochastic retarded reaction-diffusion equations with multiplicative white noise on unbounded domain ℝ n ( n ≥ 2). We first transform the retarded reaction-diffusion equations into the deterministic reaction-diffusion equations with random parameter by Ornstein-Uhlenbeck process. Next, we show the original equations generate the random dynamical systems, and prove the existence of random attractors by conjugation relation between two random dynamical systems. In this process, we use the cut-off technique to obtain the pullback asymptotic compactness.

In this paper some sufficient conditions are obtained to guarantee the existence of nontrivial 4 T + 2 periodic solutions of asymptotically linear delay difference equations. The approach used is based on Morse theory.

The limit point 𝓧 of an approximating rank-R sequence of a tensor Ƶ can be obtained by fitting a decomposition ( S , T , U ) ⋅ 𝓖 to Ƶ . The decomposition of the limit point 𝓧 = ( S , T , U ) ⋅ 𝓖 with 𝓖 = blockdiag (𝓖 1 , … , 𝓖 m ) can be seen as a three order generalization of the real Jordan canonical form. The main aim of this paper is to study under what conditions we can turn 𝓖 j into canonical form if some of the upper triangular entries of the last three slices of 𝓖 j are zeros. In addition, we show how to turn 𝓖 j into canonical form under these conditions.

The aim of this paper is to study the lattice of subvarieties of the ai-semiring variety defined by the additional identities xp+1≈xandzxyz≈(zxzyz)pzyxz(zxzyz)p,$$\begin{array}{} \displaystyle x^{p+1}\approx x\,\,\mbox{and}\,\,zxyz\approx(zxzyz)^{p}zyxz(zxzyz)^{p}, \end{array} $$ where p is a prime. It is shown that this lattice is a distributive lattice of order 179. Also, each member of this lattice is finitely based and finitely generated.

This paper mainly deals with the abstract-valued Orlicz spaces of range-varying type. Using notions of Banach space net and continuous modular net etc., we give definitions of L ϱ θ (⋅) ( I , X θ (⋅) ) and L+ϱθ(⋅)$\begin{array}{} L_{+}^{\varrho_{\theta(\cdot)}} \end{array} $( I , X θ (⋅) ), and discuss their geometrical properties as well as the representation of L+ϱθ(⋅)$\begin{array}{} L_{+}^{\varrho_{\theta(\cdot)}} \end{array} $( I , X θ (⋅) ) * . We also investigate some functionals and operators on L ϱ θ (⋅) ( I , X θ (⋅) ), giving expression for the subdifferential of the convex functional generated by another continuous modular net. After making some investigations on the Bochner-Sobolev spaces W 1, ϱ θ (⋅) ( I , X θ (⋅) ) and Wper1,ϱθ(⋅)$\begin{array}{} W_{\textrm{per}}^{1,\varrho_{\theta(\cdot)}} \end{array} $( I , X θ (⋅) ), and the intersection space Wper1,ϱθ(⋅)$\begin{array}{} W_{\textrm{per}}^{1,\varrho_{\theta(\cdot)}} \end{array} $( I , X θ (⋅) ) ∩ L φ ϑ (⋅) ( I , V ϑ (⋅) ), a second order differential inclusion together with an anisotropic nonlinear elliptic equation with nonstandard growth are also taken into account.

The main purpose of this paper is to study the computational problem of one kind hybrid power mean involving two-term exponential sums and quartic Gauss sums using the analytic method and the properties of the classical Gauss sums, and to prove some interesting fourth-order linear recurrence formulae for this problem. As an application of our result, we can also obtain an exact computational formula for one kind congruence equation mod p , an odd prime.

Dedekind sums were introduced by Dedekind to study the transformation properties of Dedekind η function under the action of SL 2 (ℤ). In this paper, we study properties of generalized Dedekind sums s i , j ( p , q ). We prove an asymptotic expansion of a function on ℚ defined in terms of generalized Dedekind sums by using its modular property. We also prove an equidistribution property of generalized Dedekind sums.

Stochastic Automata Networks (SANs) have a large amount of applications in modelling queueing systems and communication systems. To find the steady state probability distribution of the SANs, it often needs to solve linear systems which involve their generator matrices. However, some classical iterative methods such as the Jacobi and the Gauss-Seidel are inefficient due to the huge size of the generator matrices. In this paper, the multipreconditioned GMRES (MPGMRES) is considered by using two or more preconditioners simultaneously. Meanwhile, a selective version of the MPGMRES is presented to overcome the rapid increase of the storage requirements and make it practical. Numerical results on two models of SANs are reported to illustrate the effectiveness of these proposed methods.

In this paper we study an inverse time problem for the nonhomogeneous heat equation under the conformable derivative which is a severely ill-posed problem. Using the quasi-boundary value method with two regularization parameters (one related to the error in a measurement process and the other is related to the regularity of the solution) we regularize this problem and obtain a Hölder-type estimation error for the whole time interval. Numerical results are presented to illustrate the accuracy and efficiency of the method.

On a general hyperring, there is a fundamental relation, denoted γ * , such that the quotient set is a classical ring. In a previous paper, the authors defined the relation ε m on general hyperrings, proving that its transitive closure ε m∗ $\begin{array}{} \displaystyle \varepsilon^{*}_{m} \end{array}$ is a strongly regular equivalence relation smaller than the γ * -relation on some classes of hyperrings, such that the associated quotient structure modulo ε m∗ $\begin{array}{} \displaystyle \varepsilon^{*}_{m} \end{array}$ is an ordinary ring. Thus, on such hyperrings, ε m∗ $\begin{array}{} \displaystyle \varepsilon^{*}_{m} \end{array}$ is a fundamental relation. In this paper, we discuss the transitivity conditions of the ε m -relation on hyperrings and m -idempotent hyperrings.

The problem of structures learning in Bayesian networks is to discover a directed acyclic graph that in some sense is the best representation of the given database. Score-based learning algorithm is one of the important structure learning methods used to construct the Bayesian networks. These algorithms are implemented by using some heuristic search strategies to maximize the score of each candidate Bayesian network. In this paper, a bi-velocity discrete particle swarm optimization with mutation operator algorithm is proposed to learn Bayesian networks. The mutation strategy in proposed algorithm can efficiently prevent premature convergence and enhance the exploration capability of the population. We test the proposed algorithm on databases sampled from three well-known benchmark networks, and compare with other algorithms. The experimental results demonstrate the superiority of the proposed algorithm in learning Bayesian networks.

This paper studies the prediction based on a composite target function that allows to simultaneously predict the actual and the mean values of the unobserved regressand in the generalized linear model. The best linear unbiased prediction (BLUP) of the target function is derived. Studies show that our BLUP has better properties than some other predictions. Simulations confirm its better finite sample performance.

In this paper we develop Windschitl’s approximation formula for the gamma function by giving two asymptotic expansions using a little known power series. In particular, for n ∈ ℕ with n ≥ 4, we have Γ x+1=2π xxexxsinh⁡ 1xx/2exp∑ k=3n− 1anx2n− 1+Rnx$$\begin{array}{} \displaystyle {\it \Gamma} \left( x+1\right) =\sqrt{2\pi x}\left( \tfrac{x}{e}\right) ^{x}\left( x\sinh \tfrac{1}{x}\right) ^{x/2}\exp \left( \sum_{k=3}^{n-1} {\frac{a_{n}}{x^{2n-1}}}+R_{n}\left( x\right) \right) \end{array}$$ with Rnx≤ B2n2n2n− 11x2n− 1$$\begin{array}{} \displaystyle \left\vert R_{n}\left( x\right) \right\vert \leq \frac{\left\vert B_{2n}\right\vert }{2n\left( 2n-1\right) }\frac{1}{x^{2n-1}} \end{array}$$ for all x > 0, where a n has a closed-form expression, B 2 n is the Bernoulli number. Moreover, we present some approximation formulas for the gamma function related to Windschitl’s approximation, which have higher accuracy.

In this paper, we introduce the notion of state maps from a semihoop H 1 to another semihoop H 2 , which is a generalization of internal states (or state operators) on a semihoop H . Also we give a type of special state maps from a semihoop H 1 to H 1 , which is called internal state maps (or IS-maps). Then we give some examples and basic properties of (internal) state maps on semihoops. Moreover, we discuss the relations between state maps and internal states on other algebras. Then we introduce several kinds of filters by state maps on semihoops, called SM-filters, state filters and dual state filters, respectively, and discuss the relations among them. Furthermore we introduce and study the notion of prime SM-filters on semihoops. Finally, using SM-filter, we characterize two kinds of state semihoops.

In this paper, we first introduce the notion of 𝓜𝓝-convergence in posets as an unified form of O -convergence and O 2 -convergence. Then, by studying the fundamental properties of 𝓜𝓝-topology which is determined by 𝓜𝓝-convergence according to the standard topological approach, an equivalent characterization to the 𝓜𝓝-convergence being topological is established. Finally, the lim-inf 𝓜 -convergence in posets is further investigated, and a sufficient and necessary condition for lim-inf 𝓜 -convergence to be topological is obtained.

In this paper we develop and analyze the local discontinuous Galerkin (LDG) finite element method for solving the general Lax equation. The local discontinuous Galerkin method has the flexibility for arbitrary h and p adaptivity, and allows for hanging nodes. By choosing the numerical fluxes carefully we prove stability and give an error estimate. Finally some numerical examples are computed to show the convergence order and excellent numerical performance of proposed method.

In this paper, by using the notion of upsets in residuated lattices and defining the operator D a ( X ), for an upset X of a residuated lattice L we construct a new topology denoted by τ a and ( L , τ a ) becomes a topological space. We obtain some of the topological aspects of these structures such as connectivity and compactness. We study the properties of upsets in residuated lattices and we establish the relationship between them and filters. O. Zahiri and R. A. Borzooei studied upsets in the case of BL-algebras, their results become particular cases of our theory, many of them work in residuated lattices and for that we offer complete proofs. Moreover, we investigate some properties of the quotient topology on residuated lattices and some classes of semitopological residuated lattices. We give the relationship between two types of quotient topologies τ a / F and τa−$\begin{array}{} \displaystyle \mathop {{\tau _a}}\limits^ - \end{array}$. Finally, we study the uniform topology τΛ¯$\begin{array}{} \displaystyle {\tau _{\bar \Lambda }} \end{array}$ and we obtain some conditions under which (L/J,τΛ¯)$\begin{array}{} \displaystyle (L/J,{\tau _{\bar \Lambda }}) \end{array}$ is a Hausdorff space, a discrete space or a regular space ralative to the uniform topology. We discuss briefly the applications of our results on classes of residuated lattices such as divisible residuated lattices, MV-algebras and involutive residuated lattices and we find that any of this subclasses of residuated lattices with respect to these topologies form semitopological algebras.

This paper deals with optimality conditions and duality theory for vector optimization involving non-convex set-valued maps. Firstly, under the assumption of nearly cone-subconvexlike property for set-valued maps, the necessary and sufficient optimality conditions in terms of limit sets are derived for local weak minimizers of a set-valued constraint optimization problem. Then, applications to Mond-Weir type and Wolfe type dual problems are presented.

We obtain an new boundary Schwarz inequality, for analytic functions mapping the unit disk to itself. The result contains and improves a number of known estimates.

The main purpose of this paper is to study the initial layer problem and the infinite Prandtl number limit of Rayleigh-Bénard convection with an ill prepared initial data. We use the asymptotic expansion methods of singular perturbation theory and the two-time-scale approach to obtain an exact approximating solution and the convergence rates O(ε32)$O(\varepsilon^{\frac{3}{2}})$ and O ( ε 2 ).

We consider the Toeplitz matrices whose elements are the coefficients of Bazilevič functions and obtain upper bounds for the first four determinants of these Toeplitz matrices. The results presented here are new and noble and the only prior compatible results are the recent publications by Thomas and Halim [1] for the classes of starlike and close-to-convex functions and Radhika et al. [2] for the class of functions with bounded boundary rotation.

A space ( X , τ ) is called epi-mildly normal if there exists a coarser topology τ ′ on X such that ( X , τ ′) is Hausdorff ( T 2 ) mildly normal. We investigate this property and present some examples to illustrate the relationships between epi-mild normality and other weaker kinds of normality.

In this paper, we consider the nonlinear fourth order boundary value problem of the form u(4)(x)−λu(x)=f(x,u(x))−h(x),x∈(0,1),u(0)=u(1)=u′(0)=u′(1)=0,$$ \begin{array}\text \left\{ \begin{aligned} &u^{(4)}(x)-\lambda u(x)=f(x, u(x))-h(x), \ \ x\in (0,1),\\ &u(0)=u(1)=u'(0)=u'(1)=0,\\ \end{aligned}\right. \end{array} $$ which models a statically elastic beam with both end-points cantilevered or fixed. We show the existence of at least one or two solutions depending on the sign of λ − λ 1 , where λ 1 is the first eigenvalue of the corresponding linear eigenvalue problem and λ is a parameter. The proof of the main result is based upon the method of lower and upper solutions and global bifurcation techniques.

In this paper, by the Orlicz-Minkowski combinations of convex bodies, we define the general Orlicz difference bodies and study their properties. Furthermore, we obtain the extreme values of the general Orlicz difference bodies and their polars.

In this paper, we provide explicit generators for the Picard groups of cyclic Brauer-Severi varieties defined over the base field. In particular,we provide such generators for all Brauer-Severi surfaces. To produce these generators we use the theory of twists of smooth plane curves.

In this paper we study a particular parametric family of differential equations, the so-called Linear Polyanin-Zaitsev Vector Field , which has been introduced in a general case in [1] as a correction of a family presented in [2]. Linear Polyanin-Zaitsev Vector Field is transformed into a Liénard equation and, in particular, we obtain the Van Der Pol equation. We present some algebraic and qualitative results to illustrate some interactions between algebra and the qualitative theory of differential equations in this parametric family.

In this paper, we introduce the weak group inverse (called as the WG inverse in the present paper) for square complex matrices of an arbitrary index, and give some of its characterizations and properties. Furthermore, we introduce two orders: one is a pre-order and the other is a partial order, and derive several characterizations of the two orders. The paper ends with a characterization of the core EP order using WG inverses.

In this paper we study the growth of solutions of second order differential equation f ′′ + A ( z ) f ′ + B ( z ) f = 0. Under certain hypotheses, the non-trivial solution of this equation is of infinite order.

In this paper we will define and discuss semi-Hurewicz type covering properties in ditopological texture spaces. We consider the behaviour of semi-Hurewicz and co-semi-Hurewicz selection properties under direlation and difunction between ditopological texture spaces.

In this paper, chaos and bifurcation are explored for the controlled chaotic system, which is put forward based on the hybrid strategy in an unusual chaotic system. Behavior of the controlled system with variable parameter is researched in detain. Moreover, the normal form theory is used to analyze the direction and stability of bifurcating periodic solution.

The concept of a k -translatable groupoid is explored in depth. Some properties of idempotent k -translatable groupoids, left cancellative k -translatable groupoids and left unitary k -translatablegroupoids are proved. Necessary and sufficient conditions are found for a left cancellative k -translatable groupoid to be a semigroup. Any such semigroup is proved to be left unitary and a union disjoint copies of cyclic groups of the same order. Methods of constructing k -translatable semigroups that are not left cancellative are given.

The concept of minimal resolving partition and resolving set plays a pivotal role in diverse areas such as robot navigation, networking, optimization, mastermind games and coin weighing. It is hard to compute exact values of partition dimension for a graphic metric space, ( G , d G ) and networks. In this article, we give the sharp upper bounds and lower bounds for the partition dimension of generalized Möbius ladders, M m , n , for all n ≥3 and m ≥2.

In this paper, we obtain uniqueness theorems of L-functions from the extended Selberg class, which generalize and complement some recent results due to Li, Wu-Hu, and Yuan-Li-Yi.

In this paper, we present an effective algorithm for globally solving quadratic programs with quadratic constraints, which has wide application in engineering design, engineering optimization, route optimization, etc. By utilizing new parametric linearization technique, we can derive the parametric linear programming relaxation problem of the quadratic programs with quadratic constraints. To improve the computational speed of the proposed algorithm, some interval reduction operations are used to compress the investigated interval. By subsequently partitioning the initial box and solving a sequence of parametric linear programming relaxation problems the proposed algorithm is convergent to the global optimal solution of the initial problem. Finally, compared with some known algorithms, numerical experimental results demonstrate that the proposed algorithm has higher computational efficiency.

A super edge-magic total (SEMT) labeling of a graph ℘( V , E ) is a one-one map ϒ from V (℘)∪ E (℘) onto {1, 2, … ,| V (℘)∪ E (℘) |} such that ∃ a constant “a” satisfying ϒ( υ ) + ϒ( υν ) + ϒ( ν ) = a , for each edge υν ∈ E (℘), moreover all vertices must receive the smallest labels. The super edge-magic total (SEMT) strength , sm (℘), of a graph ℘ is the minimum of all magic constants a (ϒ), where the minimum runs over all the SEMT labelings of ℘. This minimum is defined only if the graph has at least one such SEMT labeling. Furthermore, the super edge-magic total (SEMT) deficiency for a graph ℘, signified as μs(℘)$\mu_{s}(\wp)$ is the least non-negative integer n so that ℘∪ nK 1 has a SEMT labeling or +∞ if such n does not exist. In this paper, we will formulate the results on SEMT labeling and deficiency of fork, H -tree and disjoint union of fork with star, bistar and path. Moreover, we will evaluate the SEMT strength for trees.

S -quantales are characterized as injective objects in the category of S -posets with respect to certain class of homomorphisms that are order-preserving mappings. This paper is devoted to exhibitions of categorical structures on S -quantales.

Extending works of Ono and Boylan to the half-integral weight case, we relate the algebraicity of Fourier coefficients of half-integral weight mock modular forms to the vanishing of Fourier coefficients of their shadows.

In the present work, we construct a Dunkl generalization of the modified Szász-Mirakjan operators of integral form defined by Pǎltanea [1]. We study the approximation properties of these operators including weighted Korovkin theorem, the rate of convergence in terms of the modulus of continuity, second order modulus of continuity via Steklov-mean, the degree of approximation for Lipschitz class of functions and the weighted space. Furthermore, we obtain the rate of convergence of the considered operators with the aid of the unified Ditzian-Totik modulus of smoothness and for functions having derivatives of bounded variation.

In this paper, we consider the definition of “useful” Csiszár divergence and “useful” Zipf-Mandelbrot law associated with the real utility distribution to give the results for majorizatioQn inequalities by using monotonic sequences. We obtain the equivalent statements between continuous convex functions and Green functions via majorization inequalities, “useful” Csiszár functional and “useful” Zipf-Mandelbrot law. By considering “useful” Csiszár divergence in the integral case, we give the results for integral majorization inequality. Towards the end, some applications are given.

In this paper, we discussed a infinitely distributed delayed viral infection model with nonlinear immune response and general incidence rate. We proved the existence and uniqueness of the equilibria. By using the Lyapunov functional and LaSalle invariance principle, we obtained the conditions of global stabilities of the infection-free equilibrium, the immune-exhausted equilibrium and the endemic equilibrium. Numerical simulations are given to verify the analytical results.

Due to resource limitation, nonlinear impulsive control tactics related to integrated pest management have been proposed in a generalized pest-natural enemy model, which allows us to address the effects of nonlinear pulse control on the dynamics and successful pest control. The threshold conditions for the existence and global stability of pest-free periodic solution are provided by Floquet theorem and analytic methods. The existence of a nontrivial periodic solution is confirmed by showing the existence of nontrivial fixed point of the stroboscopic mapping determined by time snapshot, which equals to the common impulsive period. In order to address the applications of generalized results and to reveal how the nonlinear impulses affect the successful pest control, as an example the model with Holling II functional response function is investigated carefully. The main results reveal that the pest free periodic solution and a stable interior positive periodic solution can coexist for a wide range of parameters, which indicates that the local stability does not imply the global stability of the pest free periodic solution when nonlinear impulsive control is considered, and consequently the resource limitation (i.e. nonlinear control) may result in difficulties for successful pest control.

The authors explore the boundary value problems of a discrete generalized beam equation. Using the critical point theory, some sufficient conditions for the existence of the solutions are obtained. Several consequences of the main results are also presented. Examples are given to illustrate the theorems.

In this paper, we study the existence and uniqueness of common fixed point of six self-mappings in Menger spaces by using the common limit range property (denoted by ( CLR ST )) of two pairs. Our results improve, extend, complement and generalize several existing results in the literature. Also, some examples are provided to illustrate the usability of our results.

We consider a 2 n th-order nonlinear difference equation containing both many advances and retardations with p -Laplacian. Using the critical point theory, we obtain some new explicit criteria for the existence and multiplicity of periodic and subharmonic solutions. Our results generalize and improve some known related ones.

A free-form Sudoku puzzle is a square arrangement of m × m cells such that the cells are partitioned into m subsets (called blocks) of equal cardinality. The goal of the puzzle is to place integers 1, . . , m in the cells such that the numbers in every row, column and block are distinct. Represent each cell by a vertex and add edges between two vertices exactly when the corresponding cells, according to the rules, must contain different numbers. This yields the associated free-form Sudoku graph. This article studies the eigenvalues of free-form Sudoku graphs, most notably integrality. Further, we analyze the evolution of eigenvalues and eigenspaces of such graphs when the associated puzzle is subjected to a ‘blow up’ operation, which scales the cell grid including its block partition.

(Fuzzy) convergence spaces are extensions of (fuzzy) topological spaces. ⊤-convergence spaces are one of important fuzzy convergence spaces. In this paper, we present an extending dual Fischer diagonal condition, and making use of this we discuss a regularity of ⊤-convergence spaces.

We study the initial boundary value problem of a compressible non-Newtonian fluid. The system describes the motion of the compressible viscous isentropic gas flow driven by the non-Newtonian self-gravitational force. The existence of strong solutions are derived in one dimensional bounded intervals by constructing a semi-discrete Galerkin scheme. Moreover, the uniqueness of solutions are also investigated. The main point of the study is that the viscosity term and potential term are fully nonlinear, and the initial vacuum is allowed.

In this paper sharp results on operator Young’s inequality are obtained. We first obtain sharp multiplicative refinements and reverses for the operator Young’s inequality. Secondly, we give an additive result, which improves a well-known inequality due to Tominaga. We also provide some estimates for the difference A 1/2 ( A −1/2 BA −1/2 ) v A 1/2 -{(1- v ) A + vB } for v ∉[ 0,1].

Let A be the adjacency matrix of a graph G and suppose U ( t ) = exp( itA ). We say that we have perfect state transfer in G from the vertex u to the vertex v at time t if there is a scalar γ of unit modulus such that U ( t ) e u = γ e v . It is known that perfect state transfer is rare. So C.Godsil gave a relaxation of this definition: we say that we have pretty good state transfer from u to v if there exists a complex number γ of unit modulus and, for each positive real ϵ there is a time t such that ‖ U ( t ) e u – γ e v ‖ < ϵ . In this paper, the quantum state transfer on 1-sum of star graphs F k , l is explored. We show that there is no perfect state transfer on F k , l , but there is pretty good state transfer on F k , l if and only if k = l .

Chaotic meta-Fibonacci sequences which are generated by intriguing examples of nonlinear recurrences still keep their mystery although substantial progress has been made in terms of well-behaved solutions of nested recurrences. In this study, a recent generalization of Hofstadter’s famous Q -sequence is studied beyond the known methods of generational approaches in order to propose a generalized conjecture regarding the existence of infinitely many different solutions for all corresponding recurrences of this generalization.

This article deals with univariate binary approximating subdivision schemes and their generalization to non-tensor product bivariate subdivision schemes. The two algorithms are presented with one tension and two integer parameters which generate families of univariate and bivariate schemes. The tension parameter controls the shape of the limit curve and surface while integer parameters identify the members of the family. It is demonstrated that the proposed schemes preserve monotonicity of initial data. Moreover, continuity, polynomial reproduction and generation of the schemes are also discussed. Comparison with existing schemes is also given.

We introduce and study a new kind of nonlocal boundary value problems of multi-term fractional differential equations. The existence and uniqueness results for the given problem are obtained by applying standard fixed point theorems. We also construct some examples for demonstrating the application of the main results.

Homoclinic and heteroclinic solutions to a standard hepatitis C virus (HCV) evolution model described by T. C. Reluga, H. Dahari and A. S. Perelson, ( SIAM J. Appl. Math ., 69 (2009), pp. 999–1023) are considered in this paper. Inverse balancing and generalized differential techniques enable derivation of necessary and sufficient existence conditions for homoclinic/heteroclinic solutions in the considered system. It is shown that homoclinic/heteroclinic solutions do appear when the considered system describes biologically significant evolution. Furthermore, it is demonstrated that the hepatitis C virus evolution model is structurally stable in the topological sense and does maintain homoclinic/heteroclinic solutions as diffusive coupling coefficients tend to zero. Computational experiments are used to illustrate the dynamics of such solutions in the hepatitis C evolution model.

In this paper we introduce and investigate the regularity properties of one-sided multilinear fractional maximal operators, both in continuous case and in discrete case. In the continuous setting, we prove that the one-sided multilinear fractional maximal operatorsMβ +andMβ − $\mathfrak{M}_\beta^{+}\; \text{and}\, \mathfrak{M}_\beta^{-}$map W 1, p 1 (ℝ)×· · ·× W 1, pm (ℝ) into W 1, q (ℝ) with 1 < p 1 , … , p m < ∞, 1 ≤ q < ∞ and 1/q=∑ i=1m1/pi− β $1/q= \sum_{i=1}^m1/p_i-\beta$, boundedly and continuously. In the discrete setting, we show that the discrete one-sided multilinear fractional maximal operators are bounded and continuous from ℓ 1 (ℤ)×· · ·× ℓ 1 (ℤ) to BV(ℤ). Here BV(ℤ) denotes the set of functions of bounded variation defined on ℤ. Our main results represent significant and natural extensions of what was known previously.

For every positive integer n ,we introduce and discuss an isotone Galois connection between the sets of paths of lengths n in a simple graph and the closure operators on the (vertex set of the) graph. We consider certain sets of paths in a particular graph on the digital line Z and study the closure operators associated, in the Galois connection discussed, with these sets of paths. We also focus on the closure operators on the digital plane Z 2 associated with a special product of the sets of paths considered and show that these closure operators may be used as background structures on the plane for the study of digital images.

Gravitational Search Algorithm (GSA) is a metaheuristic for solving unimodal problems. In this paper, a K-means based GSA (KGSA) for multimodal optimization is proposed. This algorithm incorporates K-means and a new elitism strategy called “loop in loop” into the GSA. First in KGSA, the members of the initial population are clustered by K-means. Afterwards, new population is created and divided in different niches (or clusters) to expand the search space. The “loop in loop” technique guides the members of each niche to the optimum direction according to their clusters. This means that lighter members move faster towards the optimum direction of each cluster than the heavier members. For evaluations, KGSA is benchmarked on well-known functions and is compared with some of the state-of-the-art algorithms. Experiments show that KGSA provides better results than the other algorithms in finding local and global optima of constrained and unconstrained multimodal functions.

The aim of this paper is to deal with the boundedness of the θ -type Calderón-Zygmund operators and their commutators on Herz spaces with two variable exponents p (⋅), q (⋅). It is proved that the θ -type Calderón-Zygmund operators are bounded on the homogeneous Herz space with variable exponents K˙ p(⋅ )α ,q(⋅ )(Rn).$\begin{array}{} \displaystyle \dot{K}^{\alpha,q(\cdot)}_{p(\cdot)}(\mathbb{R}^{n}). \end{array}$ Furthermore, the boundedness of the corresponding commutators generated by BMO function and Lipschitz function is also obtained respectively.

Given a real function f on an interval [ a , b ] satisfying mild regularity conditions, we determine the number of zeros of f by evaluating a certain integral. The integrand depends on f , f ′ and f ″. In particular, by approximating the integral with the trapezoidal rule on a fine enough grid, we can compute the number of zeros of f by evaluating finitely many values of f , f ′ and f ″. A variant of the integral even allows to determine the number of the zeros broken down by their multiplicity.

In this paper, we introduce a rough set in a universal set based on cores of successor classes with respect to level in a closed unit interval under a fuzzy relation, and some interesting properties are investigated. Based on this point, we propose a rough completely prime ideal in a semigroup structure under a compatible preorder fuzzy relation, including the rough semigroup and rough ideal. Then we provide sufficient conditions for them. Finally, the relationships between rough completely prime ideals (rough semigroups and rough ideals) and their homomorphic images are verified.

This paper presents a methodology to quantify computationally the uncertainty in a class of differential equations often met in Mathematical Physics, namely random non-autonomous second-order linear differential equations, via adaptive generalized Polynomial Chaos (gPC) and the stochastic Galerkin projection technique. Unlike the random Fröbenius method, which can only deal with particular random linear differential equations and needs the random inputs (coefficients and forcing term) to be analytic, adaptive gPC allows approximating the expectation and covariance of the solution stochastic process to general random second-order linear differential equations. The random inputs are allowed to functionally depend on random variables that may be independent or dependent, both absolutely continuous or discrete with infinitely many point masses. These hypotheses include a wide variety of particular differential equations, which might not be solvable via the random Fröbenius method, in which the random input coefficients may be expressed via a Karhunen-Loève expansion.

It is shown that the strongly noncanonical fourth order operator Ly=r3(t)r2(t)r1(t)y′(t)′′′$$\begin{array}{} \displaystyle \mathcal {L}\,y=\left(r_3(t)\left(r_2(t)\left(r_1(t)y'(t)\right)'\right)'\right)' \end{array}$$ can be written in essentially unique canonical form as Ly=q4(t)q3(t)q2(t)q1(t)q0(t)y(t)′′′′.$$\begin{array}{} \displaystyle \mathcal {L}\,y = q_4(t)\left(q_3(t)\left(q_2(t)\left(q_1(t)\left(q_0(t)y(t)\right)'\right)'\right)'\right)'. \end{array}$$ The canonical representation essentially simplifies examination of the fourth order strongly noncanonical equations r3(t)r2(t)r1(t)y′(t)′′′+p(t)y(τ (t))=0.$$\begin{array}{} \displaystyle \left(r_3(t)\left(r_2(t)\left(r_1(t)y'(t)\right)'\right)'\right)'+p(t)y(\tau(t))=0. \end{array}$$

The implantation of Remote Electronic Voting (REV) systems to Electoral Processes is happening at a slower pace than anticipated. One of the relevant factors explaining that reality is the lack of studies about the Cryptographic Schemes and Primitives applied to the existing REV solutions. In this paper, the authors review the main cryptographic schemes applied to date, as well as the most relevant Post Quantum research in the field. The aim is twofold: contribute to clarify the strengths and weaknesses of each scheme as well as expose the remaining challenges, as a necessary step towards a broader introduction of REV solutions in binding elections.

Decimation-based sequence generators are a class of non-linear cryptographic generators designed to be used in hardware implementations. An inherent characteristic of such generators is that their output sequences are interleaved sequences. This profitable characteristic can be used in the cryptanalysis of those generators. In this work, emphasis is on the most representative decimation-based generator, the shrinking generator, which has been cryptanalyzed just by solving linear equation systems. Compared with previous cryptanalysis, computational complexity and intercepted sequence requirements are dramatically reduced. Although irregularly decimated generators have been conceived and designed as non-linear sequence generators, in practice they can be easily analyzed in terms of simple linear structures.

Random Decentering Algorithm (RDA) on a undirected unweighted graph is defined and tested over several concrete scale-free networks. RDA introduces ancillary nodes to the given network following basic principles of minimal cost, density preservation, centrality reduction and randomness. First simulations over scale-free networks show that RDA gives a significant decreasing of both betweenness centrality and closeness centrality and hence topological protection of network is improved. On the other hand, the procedure is performed without significant change of the density of connections of the given network. Thus ancillae are not distinguible from real nodes (in a straightforward way) and hence network is obfuscated to potential adversaries by our manipulation.