Volume 14, Issue 1

For all integers g ≥ 6 we prove the existence of a metric graph G with w41=1$w_4^1 = 1$ such that G has Clifford index 2 and there is no tropical modification G ′ of G such that there exists a finite harmonic morphism of degree 2 from G ′ to a metric graph of genus 1. Those examples show that not all dimension theorems on the space classifying special linear systems for curves have immediate translation to the theory of divisors on metric graphs.

We proved the existence of multivalent solutions with the infinite number of branches for the Riemann-Hilbert problem in the general settings of finitely connected domains bounded by mutually disjoint Jordan curves, measurable coefficients and measurable boundary data. The theorem is formulated in terms of harmonic measure and principal asymptotic values. It is also given the corresponding reinforced criterion for domains with rectifiable boundaries stated in terms of the natural parameter and nontangential limits. Furthermore, it is shown that the dimension of the spaces of these solutions is infinite.

Let G be a graph on n ≥ 3 vertices. A graph G is almost distance-hereditary if each connected induced subgraph H of G has the property d H ( x , y ) ≤ d G ( x , y ) + 1 for any pair of vertices x, y ∈ V ( H ). Adopting the terminology introduced by Broersma et al. and Čada, a graph G is called 1-heavy if at least one of the end vertices of each induced subgraph of G isomorphic to K 1,3 (a claw) has degree at least n /2, and is called claw-heavy if each claw of G has a pair of end vertices with degree sum at least n . In this paper we prove the following two theorems: (1) Every 2-connected, claw-heavy and almost distance-hereditary graph is Hamiltonian. (2) Every 3-connected, 1-heavy and almost distance-hereditary graph is Hamiltonian. The first result improves a previous theorem of Feng and Guo [J.-F. Feng and Y.-B. Guo, Hamiltonian cycle in almost distance-hereditary graphs with degree condition restricted to claws, Optimazation 57 (2008), no. 1, 135–141]. For the second result, its connectedness condition is sharp since Feng and Guo constructed a 2-connected 1-heavy graph which is almost distance-hereditary but not Hamiltonian.

We build up a multiplicative basis for a locally adequate concordant semigroup algebra by constructing Rukolaĭne idempotents. This allows us to decompose the locally adequate concordant semigroup algebra into a direct product of primitive abundant 0-J*$0{\rm{ - }}{\cal J}*$-simple semigroup algebras. We also deduce a direct sum decomposition of this semigroup algebra in terms of the ℛ*${\cal R}*$-classes of the semigroup obtained from the above multiplicative basis. Finally, for some special cases, we provide a description of the projective indecomposable modules and determine the representation type.

We obtain the global weighted Morrey-type regularity of the solution of the regular oblique derivative problem for linear uniformly parabolic operators with VMO coefficients. We show that if the right-hand side of the parabolic equation belongs to certain generalized weighted Morrey space M p,ϕ ( Q, w ), than the strong solution belongs to the generalized weighted Sobolev- Morrey space W˙2,1p,φ(Q,ω)$\dot W_{2,1}^{p,\varphi }\left( {Q,\omega } \right)$.

Some convergent sequences of the lower bounds of the minimum eigenvalue for the Hadamard product of a nonsingular M -matrix B and the inverse of a nonsingular M -matrix A are given by using Brauer’s theorem. It is proved that these sequences are monotone increasing, and numerical examples are given to show that these sequences could reach the true value of the minimum eigenvalue in some cases. These results in this paper improve some known results.

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 study the relation between the deficiencies concerning a meromorphic function f ( z ), its derivative f ′( z ) and differential-difference monomials f ( z ) m f ( z + c ) f ′( z ), f ( z + c ) n f ′( z ), f ( z ) m f ( z + c ). The main results of this paper are listed as follows: Let f ( z ) be a meromorphic function of finite order satisfying lim supr→+∞T(r, f)T(r, f′)<+∞,$$\mathop {\lim \,{\rm sup}}\limits_{r \to + \infty } {{T(r,\,f)} \over {T(r,\,f')}}{\rm{ &#x003C; }} + \infty ,$$ and c be a non-zero complex constant, then δ (∞, f ( z ) m f ( z + c ) f ′( z ))≥ δ (∞, f ′) and δ (∞, f ( z + c ) n f ′( z ))≥ δ (∞, f ′). We also investigate the value distribution of some differential-difference polynomials taking small function a ( z ) with respect to f ( z ).

Let A i ∈ B ( H ), ( i = 1, 2, ..., n ), and T=[0⋯0A1⋮⋰A200⋰⋰⋮An0⋯0] $ T = \left[ {\matrix{ 0 & \cdots & 0 & {A_1 } \cr \vdots & {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} & {A_2 } & 0 \cr 0 & {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} & {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} & \vdots \cr {A_n } & 0 & \cdots & 0 \cr } } \right] $ . In this paper, we present some upper bounds and lower bounds for w ( T ). At the end of this paper we drive a new bound for the zeros of polynomials.

In this article, the issue of the best uniform approximation of circular arcs with parametrically defined polynomial curves is considered. The best uniform approximation of degree 2 to a circular arc is given in explicit form. The approximation is constructed so that the error function is the Chebyshev polynomial of degree 4; the error function equioscillates five times; the approximation order is four. For θ = π /4 arcs (quarter of a circle), the uniform error is 5.5 × 10 −3 . The numerical examples demonstrate the efficiency and simplicity of the approximation method as well as satisfy the properties of the best uniform approximation and yield the highest possible accuracy.

Let f be an arithmetic function and S = { x 1 , … , x n } be a set of n distinct positive integers. By ( f ( x i , x j )) (resp. ( f [ x i , x j ])) we denote the n × n matrix having f evaluated at the greatest common divisor ( x i , x j ) (resp. the least common multiple [ x i , x j ]) of x , and x j as its ( i , j )-entry, respectively. The set S is said to be gcd closed if ( x i , x j ) ∈ S for 1 ≤ i , j ≤ n . In this paper, we give formulas for the determinants of the matrices ( f ( x i , x j )) and ( f [ x i , x j ]) if S consists of multiple coprime gcd-closed sets (i.e., S equals the union of S 1 , …, S k with k ≥ 1 being an integer and S 1 , …, S k being gcd-closed sets such that (lcm( S i ), lcm( S j )) = 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.

This paper is devoted to Hermite interpolation with Chebyshev-Lobatto and Chebyshev-Radau nodal points. The aim of this piece of work is to establish the rate of convergence for some types of smooth functions. Although the rate of convergence is similar to that of Lagrange interpolation, taking into account the asymptotic constants that we obtain, the use of this method is justified and it is very suitable when we dispose of the appropriate information.

The aim of this paper is to introduce the concept of a new nonlinear multi-valued mapping so called weakly ( α, ψ, ξ )-contractive mapping and prove fixed point results for such mappings in metric spaces. Our results unify, generalize and complement various results from the literature. We give some examples which support our main results while previous results in literature are not applicable. Also, we analyze the existence of fixed points for mappings satisfying a general contractive inequality of integral type. Many fixed point results for multi-valued mappings in metric spaces endowed with an arbitrary binary relation and metric spaces endowed with graph are given here to illustrate the results in this paper.

In this paper we introduce a property and use this property to prove some common fixed point theorems in b -metric space. We also give some fixed point results on b -metric spaces endowed with an arbitrary binary relation which can be regarded as consequences of our main results. As applications, we applying our result to prove the existence of a common solution for the following system of integral equations: x (t) = ∫abK1 (t,r,x(r)) dr,x (t) = ∫abK2 (t,r,x(r)) dr,     $$\matrix {x (t) = \int \limits_a^b {{K_1}} (t, r, x(r))dr, & & x(t) = \int \limits_a^b {{K_2}}(t, r, x(r))dr,} $$ where a, b ∈ ℝ with a < b, x ∈ C [ a, b ] (the set of continuous real functions defined on [ a, b ] ⊆ ℝ) and K 1 , K 2 : [ a, b ] × [ a, b ] × ℝ → ℝ are given mappings. Finally, an example is also given in order to illustrate the effectiveness of such result.

In this paper, we consider the Z-eigenpair of a tensor. A lower bound and an upper bound for the Z-spectral radius of a weakly symmetric nonnegative irreducible tensor are presented. Furthermore, upper bounds of Z-spectral radius of nonnegative tensors and general tensors are given. The proposed bounds improve some existing ones. Numerical examples are reported to show the effectiveness of the proposed bounds.

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.

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 give a refinement of Jensen’s integral inequality and its generalization for linear functionals. We also present some applications in Information Theory.

New iterative codes for identifying 𝓗 -tensor are obtained. As an application, some sufficient conditions of the positive definiteness for an even-order real symmetric tensor, i.e., an even-degree homogeneous polynomial form are given. Advantages of results obtained are illustrated by numerical examples.

In this paper, the α waybelow relation, which is determined by O 2 -convergence, is characterized by the order on a poset, and a sufficient and necessary condition for O 2 -convergence to be topological is obtained.

In this paper, we have presented and studied two types of the Mittag-Leffler-Hyers-Ulam stability of a fractional integral equation. We prove that the fractional order delay integral equation is Mittag-Leffler-Hyers-Ulam stable on a compact interval with respect to the Chebyshev and Bielecki norms by two notions.

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.

In this paper, we present some basic properties concerning the derivation algebra Der ( T ), the quasiderivation algebra QDer ( T ) and the generalized derivation algebra GDer ( T ) of a Lie triple system T , with the relationship Der ( T ) ⊆ QDer ( T ) ⊆ GDer ( T ) ⊆ End ( T ). Furthermore, we completely determine those Lie triple systems T with condition QDer ( T ) = End ( T ). We also show that the quasiderivations of T can be embedded as derivations in a larger Lie triple system.

Consider a parabolic equation which is degenerate on the boundary. By the degeneracy, to assure the well-posedness of the solutions, only a partial boundary condition is generally necessary. When 1 ≤ α < p – 1, the existence of the local BV solution is proved. By choosing some kinds of test functions, the stability of the solutions based on a partial boundary condition is established.

We consider a financial market with memory effects in which wealth processes are driven by mean-field stochastic Volterra equations. In this financial market, the classical dynamic programming method can not be used to study the optimal investment problem, because the solution of mean-field stochastic Volterra equation is not a Markov process. In this paper, a new method through Malliavin calculus introduced in [1], can be used to obtain the optimal investment in a Volterra type financial market. We show a sufficient and necessary condition for the optimal investment in this financial market with memory by mean-field stochastic maximum principle.

In this paper, the author introduces parabolic generalized local Morrey spaces and gets the boundedness of a large class of parabolic rough operators on them. The author also establishes the parabolic local Campanato space estimates for their commutators on parabolic generalized local Morrey spaces. As its special cases, the corresponding results of parabolic sublinear operators with rough kernel and their commutators can be deduced, respectively. At last, parabolic Marcinkiewicz operator which satisfies the conditions of these theorems can be considered as an example.

In the paper, we introduce the notion of annihilators in BL-algebras and investigate some related properties of them. We get that the ideal lattice ( I ( L ), ⊆) is pseudo-complemented, and for any ideal I , its pseudo-complement is the annihilator I ⊥ of I . Also, we define the An ( L ) to be the set of all annihilators of L , then we have that ( An (L); ⋂,∧ An ( L ) ,⊥,{0}, L ) is a Boolean algebra. In addition, we introduce the annihilators of a nonempty subset X of L with respect to an ideal I and study some properties of them. As an application, we show that if I and J are ideals in a BL-algebra L , then JI⊥$J_I^ \bot $ is the relative pseudo-complement of J with respect to I in the ideal lattice ( I ( L ), ⊆). Moreover, we get some properties of the homomorphism image of annihilators, and also give the necessary and sufficient condition of the homomorphism image and the homomorphism pre-image of an annihilator to be an annihilator. Finally, we introduce the notion of α -ideal and give a notation E ( I ). We show that ( E ( I ( L )), ∧ E , ∨ E , E (0) , E ( L ) is a pseudo-complemented lattice, a complete Brouwerian lattice and an algebraic lattice, when L is a BL-chain or a finite product of BL-chains.

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.

Let p be a prime number, and let Q¯~p$\bf{\tilde{\bar {\text Q}}}_p$ be the completion of Q with respect to the pseudovaluation w which extends the p -adic valuation v p . In this paper our goal is to give a characterization of closed subfields of Q¯~p$\bf{\tilde{\bar {\text Q}}}_p$, the completion of Q with respect w , i.e. the spectral extension of the p -adic valuation v p on Q.

We consider a class of tridiagonal operators induced by not necessary pseudoergodic biinfinite sequences. Using only elementary techniques we prove that the numerical range of such operators is contained in the convex hull of the union of the numerical ranges of the operators corresponding to the constant biinfinite sequences; whilst the other inclusion is shown to hold when the constant sequences belong to the subshift generated by the given biinfinite sequence. Applying recent results by S. N. Chandler-Wilde et al. and R. Hagger, which rely on limit operator techniques, we are able to provide more general results although the closure of the numerical range needs to be taken.

The paper deals with the existence of positive ω -periodic solutions for a class of nonlinear delay differential equations. For example, such equations represent the model for the survival of red blood cells in an animal. The sufficient conditions for the exponential stability of positive ω -periodic solution are also considered.

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.

In this paper, we consider the ratios of order statistics in samples from uniform distribution and establish strong and weak laws for these ratios.

In this article we introduce and study the concept of α -almost Artinian modules. We show that each α -almost Artinian module M is almost Artinian (i.e., every proper homomorphic image of M is Artinian), where α ∈ {0,1}. Using this concept we extend some of the basic results of almost Artinian modules to α -almost Artinian modules. Moreover we introduce and study the concept of α -Krull modules. We observe that if M is an α -Krull module then the Krull dimension of M is either α or α + 1.

A random graph evolution based on interactions of N vertices is studied. During the evolution both the preferential attachment rule and the uniform choice of vertices are allowed. The weight of an M -clique means the number of its interactions. The asymptotic behaviour of the weight of a fixed M -clique is studied. Asymptotic theorems for the weight and the degree of a fixed vertex are also presented. Moreover, the limits of the maximal weight and the maximal degree are described. The proofs are based on martingale methods.

In this paper, we present an analysis for the stability of a differential equation with state-dependent delay. We establish existence and uniqueness of solutions of differential equation with delay term τ(u(t))=a+bu(t)c+bu(t).$\tau (u(t)) = \frac{{a + bu(t)}}{{c + bu(t)}}.$ Moreover, we put the some restrictions for the positivity of delay term τ ( u ( t )) Based on the boundedness of delay term, we obtain stability criterion in terms of the parameters of the equation.

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 this paper, we present a family of three-point with eight-order convergence methods for finding the simple roots of nonlinear equations by suitable approximations and weight function based on Maheshwari’s method. Per iteration this method requires three evaluations of the function and one evaluation of its first derivative. These class of methods have the efficiency index equal to 814≈1.682${8^{{\textstyle{1 \over 4}}}} \approx 1.682$. We describe the analysis of the proposed methods along with numerical experiments including comparison with the existing methods. Moreover, the attraction basins of the proposed methods are shown with some comparisons to the other existing methods.

In this paper, we find the formula of general solution for a generalized impulsive differential equations of fractional-order q ∈ (2, 3).

Let X be a completely regular Hausdorff space, E and F be Banach spaces. Let C b ( X , E ) be the space of all E -valued bounded, continuous functions on X , equipped with the strict topology β . We develop the Riemman-Stieltjes-type Integral representation theory of ( β , || · || F ) -continuous operators T : C b ( X , E ) → F with respect to the representing Borel operator measures. For X being a k -space, we characterize strongly bounded ( β , || · || F )-continuous operators T : C b ( X , E ) → F . As an application, we study ( β , || · || F )-continuous weakly compact and unconditionally converging operators T : C b ( X , E ) → F . In particular, we establish the relationship between these operators and the corresponding Borel operator measures given by the Riesz representation theorem. We obtain that if X is a k -spaceand E is reflexive, then ( C b ( X , E ), β ) has the V property of Pełczynski.

In this paper, we investigate oscillation results for the solutions of impulsive conformable fractional differential equations of the form tkDαpttkDαxt+rtxt+qtxt=0,t≥t0,t≠tk,xtk+=akx(tk−),tkDαxtk+=bktk−1Dαx(tk−),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.

The present paper focuses on the dynamics of doubly stochastic quadratic operators (d.s.q.o) on a finite-dimensional simplex. We prove that if a d.s.q.o. has no periodic points then the trajectory of any initial point inside the simplex is convergent. We show that if d.s.q.o. is not a permutation then it has no periodic points on the interior of the two dimensional (2D) simplex. We also show that this property fails in higher dimensions. In addition, the paper also discusses the dynamics classifications of extreme points of d.s.q.o. on two dimensional simplex. As such, we provide some examples of d.s.q.o. which has a property that the trajectory of any initial point tends to the center of the simplex. We also provide and example of d.s.q.o. that has infinitely many fixed points and has infinitely many invariant curves. We therefore came-up with a number of evidences. Finally, we classify the dynamics of extreme points of d.s.q.o. on 2D simplex.

By using the critical point method, some new criteria are obtained for the existence and multiplicity of homoclinic solutions to a 2 n th-order nonlinear difference equation. The proof is based on the Mountain Pass Lemma in combination with periodic approximations. Our results extend and improve some known ones.

The notion of L -fuzzy extended ideals is introduced in a Boolean ring, and their essential properties are investigated. We also build the relation between an L -fuzzy ideal and the class of its L -fuzzy extended ideals. By defining an operator “⇝” between two arbitrary L -fuzzy ideals in terms of L -fuzzy extended ideals, the result that “the family of all L -fuzzy ideals in a Boolean ring is a complete Heyting algebra” is immediately obtained. Furthermore, the lattice structures of L -fuzzy extended ideals of an L -fuzzy ideal, L -fuzzy extended ideals relative to an L -fuzzy subset, L -fuzzy stable ideals relative to an L -fuzzy subset and their connections are studied in this paper.

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 we investigate some extensions of sufficient conditions for meromorphic multivalent functions in the open unit disk to be meromorphic multivalent starlike and convex of order α . Our results unify and extend some starlikeness and convexity conditions for meromorphic multivalent functions obtained by Xu et al. [2], and some interesting special cases are given.

The aim of this paper is to investigate the effectiveness and cost-effectiveness of leptospirosis control measures, preventive vaccination and treatment of infective humans that may curtail the disease transmission. For this, a mathematical model for the transmission dynamics of the disease that includes preventive, vaccination, treatment of infective vectors and humans control measures are considered. Firstly, the constant control parameters’ case is analyzed, also calculate the basic reproduction number and investigate the existence and stability of equilibria. The threshold condition for disease-free equilibrium is found to be locally asymptotically stable and can only be achieved when the basic reproduction number is less than unity. The model is found to exhibit the existence of multiple endemic equilibria. Furthermore, to assess the relative impact of each of the constant control parameters measures the sensitivity index of the basic reproductive number to the model’s parameters are calculated. In the time-dependent constant control case, Pontryagin’s Maximum Principle is used to derive necessary conditions for the optimal control of the disease. The cost-effectiveness analysis is carried out by first of all using ANOVA to check on the mean costs. Then followed by Incremental Cost-Effectiveness Ratio (ICER) for all the possible combinations of the disease control measures. Our results revealed that the most cost-effective strategy for the control of leptospirosis is the combination of the vaccination and treatment of infective livestocks. Though the combinations of all control measures is also effective, however, this strategy is not cost-effective and so too costly. Therefore, more efforts from policy makers on vaccination and treatment of infectives livestocks regime would go a long way to combat the disease epidemic.

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.

In this paper, we study the relation between a fuzzy measure and a fuzzy metric which is induced by the fuzzy measure. We also discuss some basic properties of the constructed fuzzy metric space. In particular, we show that the nonatom of fuzzy measure space can be characterized in the constructed fuzzy metric space.

We study a twisted generalization of Lie superalgebras, called Hom-Lie superalgebras. It is obtained by twisting the graded Jacobi identity by an even linear map. We give a complete classification of the complex multiplicative Hom-Lie superalgebras of low dimensions.

The purpose of this paper is to study W (2, 2) Lie conformal algebra, which has a free ℂ[∂]-basis { L, M } such that [LλL]=(∂+2λ)L,[LλM]=(∂+2λ)M,[MλM]=0$\begin{equation}[{L_\lambda }L] = (\partial + 2\lambda )L,[{L_\lambda }M] = (\partial + 2\lambda )M,[{M_\lambda }M] = 0]\end{equation}$ . In this paper, we study conformal derivations, central extensions and conformal modules for this Lie conformal algebra. Also, we compute the cohomology of this Lie conformal algebra with coefficients in its modules. In particular, we determine its cohomology with trivial coefficients both for the basic and reduced complexes.

As a generalization of the Sierpiński-like graphs, the subdivided-line graph Г( G ) of a simple connected graph G is defined to be the line graph of the barycentric subdivision of G . In this paper we obtain a closed-form formula for the enumeration of spanning trees in Г( G ), employing the theory of electrical networks. We present bounds for the largest and second smallest Laplacian eigenvalues of Г( G ) in terms of the maximum degree, the number of edges, and the first Zagreb index of G . In addition, we establish upper and lower bounds for the Laplacian Estrada index of Г( G ) based on the vertex degrees of G . These bounds are also connected with the number of spanning trees in Г( G ).

In this paper, we study the the parabolic Marcinkiewicz integral MΩ,hρ1,ρ2${\cal M}_{\Omega, h}^{{\rho _{1,}}{\rho _2}}$ on product domains R n × R m ( n , m ≥ 2). L p 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.

The method of brackets is a method of integration based upon a small number of heuristic rules. Some of these have been made rigorous. An example of an integral involving the Bessel function is used to motivate a new evaluation rule.

Many algorithms for globally solving sum of affine ratios problem (SAR) are based on equivalent problem and branch-and-bound framework. Since the exhaustiveness of branching rule leads to a significant increase in the computational burden for solving the equivalent problem. In this study, a new range reduction method for outcome space of the denominator is presented for globally solving the sum of affine ratios problem (SAR). The proposed range reduction method offers a possibility to delete a large part of the outcome space region of the denominators in which the global optimal solution of the equivalent problem does not exist, and which can be seen as an accelerating device for global optimization of the (SAR). Several numerical examples are presented to demonstrate the advantages of the proposed algorithm using new range reduction method in terms of both computational efficiency and solution quality.

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.

It is well known that SOR iterative methods are convergent for linear systems, whose coefficient matrices are strictly or irreducibly diagonally dominant matrices and strong H -matrices (whose comparison matrices are nonsingular M -matrices). However, the same can not be true in case of those iterative methods for linear systems with weak H -matrices (whose comparison matrices are singular M -matrices). This paper proposes some necessary and sufficient conditions such that SOR iterative methods are convergent for linear systems with weak H -matrices. Furthermore, some numerical examples are given to demonstrate the convergence results obtained in this paper.

We develop the existence theory for sequential fractional differential equations involving Liouville-Caputo fractional derivative equipped with anti-periodic type (non-separated) and nonlocal integral boundary conditions. Several existence criteria depending on the nonlinearity involved in the problems are presented by means of a variety of tools of the fixed point theory. The applicability of the results is shown with the aid of examples. Our results are not only new in the given configuration but also yield some new special cases for specific choices of parameters involved in the problems.

Let p 3( n ) denote the number of 3-component multipartitions of n . Recently, using a 3-dissection formula for the generating function of p 3( n ), Baruah and Ojah proved that for n ≥ 0, p 3(9 n + 5) ≡ 0 (mod 3 3 ) and p 3 (9 n + 8) ≡ 0 (mod 3 4 ). In this paper, we prove several congruences modulo powers of 3 for p 3( n ) by using some theta function identities. For example, we prove that for n ≥ 0, p 3 (243 n + 233) ≡ p 3 (729 n + 638) ≡ 0 (mod 3 10 ).

In this paper, we give a new bound for the largest singular value of nonnegative rectangular tensors when m = n , which is tighter than the bound provided by Yang and Yang in “Singular values of nonnegative rectangular tensors”, Front. Math. China, 2011, 6, 363-378.

We first prove that the convolution of a normalized right half-plane mapping with another subclass of normalized right half-plane mappings with the dilatation −z(a+z)/(1+az)$ - z(a + z)/(1 + az)$ is CHD (convex in the horizontal direction) provided a=1$a = 1$ or −1≤a≤0$ - 1 \le a \le 0$. Secondly, we give a simply method to prove the convolution of two special subclasses of harmonic univalent mappings in the right half-plane is CHD which was proved by Kumar et al. [1, Theorem 2.2]. In addition, we derive the convolution of harmonic univalent mappings involving the generalized harmonic right half-plane mappings is CHD. Finally, we present two examples of harmonic mappings to illuminate our main results.

In this paper, we introduce GP-po-flatness property of S -posets over a pomonoid S , which lies strictly between principal weak po-flatness and po-torsion freeness. Furthermore, we investigate the homological classification problems of pomonoids by using this new property. Finally, we consider direct products of GP-po-flat S -posets. As an application, characterizations of pomonoids over which direct products of nonempty families of principally weakly po-flat S -posets are principally weakly po-flat are obtained, and some results of Khosravi, R. in a certain extent are generalized.

We introduce a new subgroup embedding property of finite groups called CSQ -normality of subgroups. Using this subgroup property, we determine the structure of finite groups with some CSQ -normal subgroups of Sylow subgroups. As an application of our results, some recent results are generalized.

The homogeneous balance of undetermined coefficients method is firstly proposed to solve such nonlinear partial differential equations (PDEs), the balance numbers of which are not positive integers. The proposed method can also be used to derive more general bilinear equation of nonlinear PDEs. The Eckhaus equation, the KdV equation and the generalized Boussinesq equation are chosen to illustrate the validity of our method. The proposed method is also a standard and computable method, which can be generalized to deal with some types of nonlinear PDEs.

In this study, we characterize all families of saturated numerical semigroups with multiplicity four. We also present some results about invariants of these semigroups.

In this work we show that the Bruhat rank of a symmetric (0,1)-matrix of order n with a staircase pattern, total support, and containing I n , is at most 2. Several other related questions are also discussed. Some illustrative examples are presented.

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, geometric properties of spacelike curves on a timelike surface in Lorentz-Minkowski 3-space are investigated by applying the singularity theory of smooth functions from the contact viewpoint.

An S -type upper bound for the largest singular value of a nonnegative rectangular tensor is given by breaking N = {1, 2, … n } into disjoint subsets S and its complement. It is shown that the new upper bound is smaller than that provided by Yang and Yang (2011). Numerical examples are given to verify the theoretical results.

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.

In this article, we study the uniqueness problem of meromorphic functions in m -punctured complex plane Ω and obtain that there exist two sets S 1 , S 2 with ♯S 1 = 2 and ♯S 2 = 9, such that any two admissible meromorphic functions f and g in Ω must be identical if f, g share S 1 , S 2 I M in Ω .

In the 1960s Professor Hu Guoding proposed a method of measuring information based on the idea that connotation and denotation of a concept satisfies inverse ratio rule. According to this information measure, firstly we put forward the information quantity for information systems and decision systems; then, we discuss the updating mechanism of information quantity for decision systems; finally, we give an attribute reduction algorithm for decision tables with dynamically varying attribute values.

The main goal of this paper is to investigate very true MTL-algebras and prove the completeness of the very true MTL-logic. In this paper, the concept of very true operators on MTL-algebras is introduced and some related properties are investigated. Also, conditions for an MTL-algebra to be an MV-algebra and a Gödel algebra are given via this operator. Moreover, very true filters on very true MTL-algebras are studied. In particular, subdirectly irreducible very true MTL-algebras are characterized and an analogous of representation theorem for very true MTL-algebras is proved. Then, the left and right stabilizers of very true MTL-algebras are introduced and some related properties are given. As applications of stabilizer of very true MTL-algebras, we produce a basis for a topology on very true MTL-algebras and show that the generated topology by this basis is Baire, connected, locally connected and separable. Finally, the corresponding logic very true MTL-logic is constructed and the soundness and completeness of this logic are proved based on very true MTL-algebras.

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 M 3 be a three-dimensional almost Kenmotsu manifold satisfying ▽ ξ h = 0. In this paper, we prove that the curvature tensor of M 3 is harmonic if and only if M 3 is locally isometric to either the hyperbolic space ℍ 3 (-1) or the Riemannian product ℍ 2 (−4) × ℝ. This generalizes a recent result obtained by [Wang Y., Three-dimensional locally symmetric almost Kenmotsu manifolds, Ann. Polon. Math., 2016, 116, 79-86] and [Cho J.T., Local symmetry on almost Kenmotsu three-manifolds, Hokkaido Math. J., 2016, 45, 435-442].

This paper addresses the problem of robust fault-tolerant control design scheme for a class of Takagi-Sugeno fuzzy systems subject to interval time-varying delay and external disturbances. First, by using improved delay partitioning approach, a novel n-steps iterative learning fault estimation observer under H ∞ constraint is constructed to achieve estimation of actuator fault. Then, based on the online estimation information, a fuzzy dynamic output feedback fault-tolerant controller considered interval time delay is designed to compensate for the impact of actuator faults, while guaranteing that the closed-loop system is asymptotically stable with the prescribed H ∞ performance. Moreover, all the obtained less conservative sufficient conditions for the existence of fault estimation observer and fault-tolerant controller are formulated in terms of linear matrix inequalities. Finally, the numerical examples and simulation results are presented to show the effectiveness and merits of the proposed methods.

Some new bounds for the minimum eigenvalue of M -matrices are obtained. These inequalities improve existing results, and the estimating formulas are easier to calculate since they only depend on the entries of matrices. Finally, some examples are also given to show that the bounds are better than some previous results.

In this paper, we continue the study of s -topological and irresolute-topological groups. We define semi-quotient mappings which are stronger than semi-continuous mappings, and then consider semi-quotient spaces and groups. It is proved that for some classes of irresolute-topological groups ( G , *, τ ) the semi-quotient space G/H is regular. Semi-isomorphisms of s -topological groups are also discussed.

In this paper, we study the boundedness of fractional multilinear integral operators with rough kernels TΩ,αA1,A2,…,Ak,$T_{\Omega ,\alpha }^{{A_1},{A_2}, \ldots ,{A_k}},$ which is a generalization of the higher-order commutator of the rough fractional integral on the generalized weighted Morrey spaces M p,ϕ ( w ). We find the sufficient conditions on the pair ( ϕ 1 , ϕ 2 ) with w ∈ A p,q which ensures the boundedness of the operators TΩ,αA1,A2,…,Ak,$T_{\Omega ,\alpha }^{{A_1},{A_2}, \ldots ,{A_k}},$ from Mp,φ1wptoMp,φ2wq${M_{p,{\varphi _1}}}\left( {{w^p}} \right)\,{\rm{to}}\,{M_{p,{\varphi _2}}}\left( {{w^q}} \right)$ for 1 < p < q < ∞. In all cases the conditions for the boundedness of the operator TΩ,αA1,A2,…,Ak,$T_{\Omega ,\alpha }^{{A_1},{A_2}, \ldots ,{A_k}},$ are given in terms of Zygmund-type integral inequalities on ( ϕ 1 , ϕ 2 ) and w , which do not assume any assumption on monotonicity of ϕ 1 ( x,r ) , ϕ 2 ( x, r ) in r .

We study a parameterized family of singular functions which appears in a paper by H. Okamoto and M. Wunsch (2007). Various properties are revisited from the viewpoint of fractal geometry and probabilistic techniques. Hausdorff dimensions are calculated for several sets related to these functions, and new properties close to fractal analysis and strong negations are explored.

We present sufficient conditions for the existence of solutions of Fredholm integral inclusion equations using new sort of contractions, named as multivalued almost F -contractions and multivalued almost F -contraction pairs under ı-distance, defined in b -metric spaces. We give its relevance to fixed point results in orbitally complete b -metric spaces. To rationalize the notions and outcome, we illustrate the appropriate examples.

In this paper a class of general type α -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 define the arrowhead-Fibonacci numbers by using the arrowhead matrix of the characteristic polynomial of the k -step Fibonacci sequence and then we give some of their properties. Also, we study the arrowhead-Fibonacci sequence modulo m and we obtain the cyclic groups from the generating matrix of the arrowhead-Fibonacci numbers when read modulo m . Then we derive the relationships between the orders of the cyclic groups obtained and the periods of the arrowhead-Fibonacci sequence modulo m .

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.

In this paper, we study a kind of fractional differential system with impulsive effect and find the formula of general solution for the impulsive fractional-order system by analysis of the limit case (as impulse tends to zero). The obtained result shows that the deviation caused by impulses for fractional-order system is undetermined. An example is also provided to illustrate the result.

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.

In this paper we consider some elastic spacelike and timelike curves in the Lorentz-Minkowski plane and obtain the respective vectorial equations of their position vectors in explicit analytical form. We study in more details the generalized Sturmian spirals in the Lorentz-Minkowski plane which simultaneously are elastics in this space.

We study properties of Linear Genetic Programming (LGP) through several regression and classification benchmarks. In each problem, we decompose the results into bias and variance components, and explore the effect of varying certain key parameters on the overall error and its decomposed contributions. These parameters are the maximum program size, the initial population, and the function set used. We confirm and quantify several insights into the practical usage of GP, most notably that (a) the variance between runs is primarily due to initialization rather than the selection of training samples, (b) parameters can be reasonably optimized to obtain gains in efficacy, and (c) functions detrimental to evolvability are easily eliminated, while functions well-suited to the problem can greatly improve performance—therefore, larger and more diverse function sets are always preferable.

A major drawback of orthogonal frequency division multiplexing (OFDM) signals is the high value of peak to average power ratio (PAPR). Partial transmit sequences (PTS) is a popular PAPR reduction method with good PAPR reduction performance, but its search complexity is high. In this paper, in order to reduce PTS search complexity we propose a new technique based on biogeography-based optimization (BBO). More specifically, we present a new Generalized Oppositional Biogeography Based Optimization (GOBBO) algorithm which is enhanced with Oppositional Based Learning (OBL) techniques. We apply both the original BBO and the new Generalized Oppositional BBO (GOBBO) to the PTS problem. The GOBBO-PTS method is compared with other PTS schemes for PAPR reduction found in the literature. The simulation results show that GOBBO and BBO are in general highly efficient in producing significant PAPR reduction and reducing the PTS search complexity.

In this study, a vibration problem of Euler-Bernoulli beam manufactured with Functionally Graded Material (FGM), which is modelled by fourth-order partial differential equations with variable coefficients, is examined by using the Adomian Decomposition Method (ADM).The method is one of the useful and powerful methods which can be easily applied to linear and nonlinear initial and boundary value problems. As to functionally graded materials, they are composites mixed by two or more materials at a certain rate. This mixture at a certain rate is expressed with an exponential function in order to try to minimize singularities from transition between different surfaces of materials as much as possible. According to the structure of the ADM in terms of initial conditions of the problem, a Fourier series expansion method is used along with the ADM for the solution of simply supported functionally graded Euler-Bernoulli beams. Finally, by choosing an appropriate mixture rate for the material, the results are shown in figures and compared with those of a standard (homogeneous) Euler-Bernoulli beam.

Necessary and sufficiently conditions are derived for the decomposition of a second order linear time- varying system into two cascade connected commutative first order linear time-varying subsystems. The explicit formulas describing these subsystems are presented. It is shown that a very small class of systems satisfies the stated conditions. The results are well verified by simulations. It is also shown that its cascade synthesis is less sensitive to numerical errors than the direct simulation of the system itself.

In this paper, we study differential equations arising from the generating functions of the generalized Bell polynomials.We give explicit identities for the generalized Bell polynomials. Finally, we investigate the zeros of the generalized Bell polynomials by using numerical simulations.

In this paper, we present differential equation for the generating function of the p , q -Touchard polynomials. An application to ordered partitions of a set is investigated.

In this paper, we present some theorems on weighted approximation by two dimensional nonlinear singular integral operators in the following form: Tλ (f;x,y)=∬ R2Kλ (t− x,s− y,f(t,s))dsdt,(x,y)∈ R2,λ ∈ Λ ,$${T_\lambda }(f;x,y) = \iint\limits_{{\mathbb{R}^2}}K_\lambda {(t - x,s - y,f(t,s))dsdt,\;(x,y) \in {\mathbb{R}^2},\lambda \in \Lambda ,}$$ where Λ is a set of non-negative numbers with accumulation point λ0.

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.

Elastica and inextensible flows of curves play an important role in practical applications. In this paper, we construct a new characterization of inextensible flows by using elastica in space. The inextensible flow is completely determined for any space-like curve in de Sitter space S13$\mathbb{S}_{1}^{3}$. Finally, we give some characterizations for curvatures of a space-like curve in de Sitter space S13$\mathbb{S}_{1}^{3}$.

In this article we modify an iteration process to prove strong convergence and Δ— convergence theorems for a finite family of nonexpansive multivalued mappings in hyperbolic spaces. The results presented here extend some existing results in the literature.

In this study, we present an epidemic model that characterizes the behavior of a financial network of globally operating stock markets. Since the long time series have a global memory effect, we represent our model by using the fractional calculus. This model operates on a network, where vertices are the stock markets and edges are constructed by the correlation distances. Thereafter, we find an analytical solution to commensurate system and use the well-known differential transform method to obtain the solution of incommensurate system of fractional differential equations. Our findings are confirmed and complemented by the data set of the relevant stock markets between 2006 and 2016. Rather than the hypothetical values, we use the Hurst Exponent of each time series to approximate the fraction size and graph theoretical concepts to obtain the variables.

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 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.