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This paper is concerned with a class of hyperbolic systems of conservation laws admitting delta-waves. The Riemann problem is completely solved. The solutions exhibit four kinds of wave patterns: the first contains a vacuum state bounded by two contact discontinuities; the second involves the overcompressible delta-wave; the third and fourth include a vacuum state bounded by a contact delta-wave and a contact discontinuity. The highlight of this paper is the contact delta-waves. [ABSTRACT FROM AUTHOR]

The uniqueness problems of entire function that share a non-zero finite value have been studied and many results on this topic have been obtained. In this paper we prove a uniqueness theorem for an entire function, which shares polynomials with its higher order derivatives. In particular, the result of the paper is an improvement of the corresponding results of H. Zhong [8] and I. Lahiri and G.K. Ghosh [5]. [ABSTRACT FROM AUTHOR]

Let Ω a bounded domain in Rn with smooth boundary ∂Ω. In this article, in view of our earlier paper [12], let the conditions made on this paper be sufficiently more general than [12]. We investigate the spectral properties of a non-selfadjoint elliptic differential operator (Pu)(x) = -Σni,j=1 (ρ2α(x)aij(x)Q(x)u'xi(x))'xj, acting on Hilbert space H∂ = L²(Ω)∂. Here c|s|² ≤ Σni,j=1 aij(x)sisj (s = (s1,. . ., sn) ∊ Cn, x ∊ Ω), ρ(x) = dist{x, ∂Ω}, aij(x) = aji(x) ∊ C²(Ω), 0 ≤ α < Ω. Fur-thermore, suppose that Q(x) ∊ C²(Ω, End C∂) such that for each x ∊ Ω the matrix function Q(x) has non-zero simple eigenvalues μj (x) ∊ C²(Ω) (1 ∊ j ℹ ∂) lie in the C\ɸ, where ɸ = {z ⅂ C: |arg z| ∊ φ}, φ 2 (0, π). [ABSTRACT FROM AUTHOR]

Since the beginning of research on graph related to ring, many graphs have been constructed by the concept of rings to investigate the relation between graph theory and ring theory. The unity product graph associated with a ring R is a graph which is obtained by setting all unit elements of R as the vertex set and two distinct elements ri and rj are joined by an edge if and only if ri · rj = e. A subset C of the vertex set in a unity product graph is called a perfect code if for all ri 2 C, the unions of their closed neighbourhoods, S1(ri) yield the whole vertex set in such a way that any of two closed neighbourhoods have no common elements. In this paper, we determine different order perfect codes in unity product graphs associated with some commutative rings with identity. We classify the commutative rings with identity in which their associated unity product graphs admit the trivial (order 1) and non-trivial perfect codes. In addition, it is proved that the complement unity product graphs associated with the commutative rings with identity admit only the trivial perfect code. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to study ωe *-continuity via ωe *-open sets. We obtain several characterizations and some fundamental properties of ωe *-continuous functions. Also, we introduce some new functions such as ωe *-irresolute functions, ωe *-open functions and ωe *-closed functions by means of ωe *-open sets. Moreover, we obtain ωe *-open function is independent with ωe*-irresolute function and ωe *-continuous function. Furthermore, we give not only various properties and characterizations but also examples and counterexamples. [ABSTRACT FROM AUTHOR]

In this paper, the mathematical model of the biofiltration of a mixture of n-propanol and toluene is developed based on the gasbiofilm phases. The homotopy perturbation technique is applied to get the approximate analytical expression for the concentration of toluene and n-propanol in non-steady-state conditions for both gasbiofilm interfaces. Our analytical results were validated by direct comparison with numerical simulations generated using the "bvp4c" function in the MATLAB platform. For various parameter values, the comparison was found to be in good agreement. The saturated and unsaturated kinetics also have been investigated analytically. [ABSTRACT FROM AUTHOR]

In this paper, a high-order compact exponential (HOE) scheme is constructed for solving time fractional integro-differential convection-diffusion equations with initial singularity. For spatial discretization, the convection and diffusion terms are approximated by a compact exponential difference formula. For temporal discretization, we use the L1 formula and trapezoidal PI rule with nonuniform meshes to approximate the Caputo derivative and the Riemann-Liouville integral, respectively. For this fully discrete implicit scheme, the local truncation error is obtained. The stability and convergence of the proposed scheme are analyzed based on the discrete fractional Gronwall inequality and the energy method. Numerical experiences are carried out to confirm our theoretical results. [ABSTRACT FROM AUTHOR]

This paper deals with applying the concept of fuzzy sets to Leibniz algebras in order to introduce and to study the descriptions of fuzzy Leibniz subalgebras and fuzzy Leibniz ideals. More concretely, our main goal is to introduce the notion of interval-valued fuzzy Leibniz ideals in Leibniz algebras. Additionally, we present some of their properties. [ABSTRACT FROM AUTHOR]

The Jump graph J(G) of a graph G is the graph whose vertices are edges of G and two vertices of J(G) are adjacent if and only if they are not adjacent in G. Equivalently complement of line graph L(G) is the Jump graph J(G) of G. In this paper, we give characterization for the Jump graph of cycles into Monotonic star decomposition. Also we give characterization for the Jump graph of complete bipartite graphs into even decomposition. [ABSTRACT FROM AUTHOR]

Let f(z), g(z), h(z) be three entire functions of non zero finite order and fn(z) the iterations of f(z) with respect to g(z) and h(z) also T (r, f), T (r, g), T (r, h), T (r, fn) are there respective characteristic functions. In this paper we study comparative growth properties of T(r, fn) with respect to T (r, f), T (r, g) and T (r, h) in terms of generalist order. [ABSTRACT FROM AUTHOR]

This paper uses the resolvent operator technique to investigate second-order non-autonomous neutral integrodifferential equations with impulsive conditions in a Banach space. We study the existence of a mild solution and the system's approximate controllability. The semigroup and resolvent operator theory, graph norm, and Krasnoselskii's fixed point theorem are used to demonstrate the results. Finally, we present our findings with an example. [ABSTRACT FROM AUTHOR]

In this paper, we introduce some new subclasses of analytic functions in the open unit disk U with negative coefficients defined by generalized Alexander integral operator. The aim of the present paper is to determine coefficient inequalities, inclusion relations, neighborhoods, partial sums and integral means properties for functions f belonging to these subclasses. [ABSTRACT FROM AUTHOR]

In this paper, the notion of soft normal int-field over a field has been introduced. We have established a correspondence, called Soft Galois correspondence, between the soft intermediate int-fields of a finite Galois extension and the soft intgroups of the Galois group corresponding to the field extension. We have generalized some results of Galois theory in the environment of soft set theory. [ABSTRACT FROM AUTHOR]

An act As satisfies Condition (PWP) if as = a's for a, a' ∈ As, s ∈ S implies that there exist a" ∈ As and u, v ∈ S such that a = a"u, a' = a"v and us = vs. In this paper we introduce a generalization of Condition (PWP) called Condition (LPWP) and will characterize monoids using this property. It can be seen easily that any right locally cyclic act satisfies Condition (LPWP). [ABSTRACT FROM AUTHOR]

This paper is an attempt to study ordered semigroups which are nil-extensions of simple and π-inverse ordered semigroups. Different characterizations of complete semilattice decomposition of nil-extensions of ordered semigroups have been given here. [ABSTRACT FROM AUTHOR]

In this paper, we proved that each nonlinear non-global semi-Jordan triple higher derivable mapping on a 2-torsion free triangular algebra is an additive higher derivation. As its application, we get the similar conclusion on a nest algebra or a 2-torsion free block upper triangular matrix algebra, respectively. [ABSTRACT FROM AUTHOR]

The notion of factor set in Lie algebras is defined by Moneyhun in 1994. It was developed by Eshrati et al. on n-Lie algebras. In this paper we present an m-factor set notion on Filippov algebras and obtain some results for finite dimensional m-stem Filippov algebras. Moreover, we show that if A and B are two finite dimensional m-stem Filippov algebras or have the same dimensions, then A ∼m B if and only if A≅B. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to introduce a new class of convex functions with respect to non-negative functions h and bifunction n(., .), which is called generalized (p, r, h, n-convex functions. We derive some new integral inequalities for this class of functions. Some special cases are also discussed. The ideas and techniques of this paper may stimulate further research. [ABSTRACT FROM AUTHOR]

In earlier papers the author has developed the theory of Loos symmetric cones, which are Loos symmetric spaces on an open cone in a Banach space, and developed the foundations of a geometric theory based on (modified) Loos axioms for such cones. Such cones present an abstract version of the cone of positive elements in a C*-algebra. In this paper the close connection between Loos symmetric cones and a special class of Jordan algebras called JB-algebras is developed. Recent work of C.-H. Chu is applied to show that every Loos symmetric cone arises as the cone of positive invertible elements of a unital JB-algebra and conversely that this JB-algebra is unique and can be constructed on the Banach space containing the Loos symmetric cone. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the two concepts of betweeness in a metric linear space that arise from the vector space structure and from the metric space structure. We also explore the relation between the mid-points obtained from the algebraic structure and the metric structure in such spaces. We show that a real metric linear space is normable if and only if every algebraic mid-point is a metric mid-point if and only if algebraic betweeness implies metric betweeness. We also show that a real metric linear space is pseudo strictly convex if and only if the metric betweeness implies the algebraic betweeness. As a corollary, it turns out that a real metric linear space is normable with a strictly convex norm if and only if the notions of algebraic mid-points and metric mid-points coincide if and only if the notions of algebraic betweeness and metric betweeness coincide. [ABSTRACT FROM AUTHOR]

Let P(z) be a polynomial of degree n which have no zeros in |z| < k, k ≥ 1. Then it was proved by Govil [8] that max |z|=1 P (s) (z) ≤ ns 1 + k s (max |z|=1|P(z)| − min |z|=k|P(z)|) . As a generalization and Lγ analogue of the above inequality was recently given by Zireh [16] who under the same hypothesis proved, for γ > 0 ||P(s)(z) + βmns 1 + Λk,s ||γ ≤ ns ||Λk,s+ z||q ||P(z)||γ, where |β| ≤ 1, ns = n(n − 1)· · ·(n − s + 1), m = min|z|=k |P(z)| and Λk,s = C(n, s)(|a0| − m)k s+1 + |as|k 2s C(n, s)(|a0| − m) + |as|k s+1. In this paper, we shall present an interesting generalization and refinement of this result which include some previous results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the notion of quasi-ideals in gamma semirings on weak nearness approximation spaces and explain some of the concepts and definitions. Also, it is given an example related to the subject. The features described in this study will contribute greatly to the theoretical development of the nearness semirings theory. [ABSTRACT FROM AUTHOR]

This paper presents the concept of an operation on a new class of topological spaces δPS-open subsets in topological spaces. The new set was called a %-open set and its properties were studied. Here we also defined the relationship between already existing open sets such as preopen sets, δ-preopen sets and γ-open sets. [ABSTRACT FROM AUTHOR]

In this paper, we study the transfer of notion of feebly nil-clean (i.e., a ring in which every element is a sum of a nilpotent element and the difference of two orthogonal idempotents) to the bi-amalgamated algebras along ideals. We also find the necessary and sufficient conditions for the feebly nil-clean property to the amalgamated rings. [ABSTRACT FROM AUTHOR]

In this paper, the reproducing kernel Hilbert space method (RKHSM) is applied for solving the non linear system of ordinary differential equations of the dynamics of tuberculosis due to smoking model. The exact solution of the system has been obtained in terms of a convergent series. The results in the figure show that the proposed method is effective for solving such non linear system of ordinary differential equations as compare to numerical methods. [ABSTRACT FROM AUTHOR]

In this paper, we define the general class Hp (λ, α, γ) of analytic and p-valent functions with negative coefficients. We investigate various important properties and characteristies of this class. Also, modified Hadamard products for functions in this class are obtained. Finally, a family of integral operators is considered [ABSTRACT FROM AUTHOR]

In this paper, we obtain the coefficient bounds and closure properties for a class of analytic functions defined using q-differential operator which are closely related to the classes of α-spiralike and convex α-spiral functions. Also we investigate convolution properties and necessary and sufficient conditions for functions in the defined class. [ABSTRACT FROM AUTHOR]

If p(z) is a polynomial of degree n having no zero in |z| < k, k ≥ 1, and ||p||r = ( 1/2π ∫ 2π0|p(eiθ) | r dθ)1/r, 0 < r < ∞ then Govil and Rahman in [16] proved ||p||r ≤ n/|| k+ z||r ||p||r, r ≥ 1. In this paper, by involving certain co-efficients of the polynomial, we not only prove an integral inequality which improves as well as generalizes the above inequality, but also gives a number of interesting consequences as special cases [ABSTRACT FROM AUTHOR]

Let L be a lattice. For a natural number n, we associate a simple graph, denoted by ΓnL, with Ln\ {0} as the vertex set and two distinct vertices X and Y being adjacent if and only if there exists an n×n lower triangular matrix A over L such that AXT = YT or AYT = XT, where for a matrix B, BT is the matrix transpose of B. In this paper, we study some basic properties of ΓnL. Also, we investigate the genus number of the generalized Cayley graph ΓnL. [ABSTRACT FROM AUTHOR]

In this paper, we study the pseudo-slant submanifolds of conformal Kenmotsu manifolds. Some results on submanifolds of conformal Kenmotsu manifolds with parallel canonical structures are obtained. Finally we discuss integrability of the distributions embeded in the definition of pseudo-slant submanifolds of conformal Kenmotsu manifolds. [ABSTRACT FROM AUTHOR]

In this paper, we study the geometry of an A-metric space of Subba Rao [15], by introducing the concepts of metric betweenness and its properties t1, t2, B-linearity and D-linearity. It is proved that there do not exist equilateral triangles in any Ametric space (A, A, d), where A is any representable autometrized algebra satisfying (R) and(S). It is also proved that any A-metric space is Ptolemaic. [ABSTRACT FROM AUTHOR]

In this paper, we study the semirings which satisfy the identities x n ≈ x, (2n − 1)x ≈ x, (x + y) n−1 ≈ x n−1 + y n−1 and (xy) n−1 ≈ x n−1 y n−1 . We give the characterizations of the binary relations L · ∧ D +, L · ∧ L +, L · ∧ R + and L + ∧ D ·, and obtain the sufficient and necessary conditions which make these binary relations be congruences. Finally, we show that the classes of semirings which can be determined by the above congruences are indeed varieties of semirings. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to obtain inclusion relations between various subclasses of harmonic univalent mappings by applying a convolution operator involving generalized Wright functions. To be more precise, we investigate such connections with Goodman-Rønning-type harmonic univalent functions, k-uniformly harmonic convex functions and k-uniformly harmonic starlike functions in the open unit disc U. Some of our results generalize and correct the results of Maharana and Sahoo [11]. [ABSTRACT FROM AUTHOR]

In this paper, we introduced a reproducing kernel space which is a particular class of Hilbert space. We discuss various properties of the reproducing kernel. In particular, our aim is to construct kernel in reproducing kernel Hilbert space of the specific function space (Sobolev space) with the improved inner product and norm. Also, we derive the reproducing kernel for periodic boundary conditions. [ABSTRACT FROM AUTHOR]

Aim of this paper is to introduce extended hyperbolic function by using a modified extension of beta function [12] and to establish new properties like integral representation, Mellin transform and many more. Furthermore, we apply Prabhakar fractional integral operator, Caputo-Fabrizio operator and Atangana-Baleanu operator on it. Other than this, we present a graphical representation of the extended hyperbolic function with different values of α also a graphical comparison between Caputo-Fabrizio operator and Atangana-Baleanu operator of hyperbolic function for different values of r. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of three parameters-fuzzy sets. We define three parameters fuzzy ideals in non associative algebraic structures namely Abel Grassman groupoids (AG-groupoids). We explored several properties of an intraregular AG-groupoid using three parameters-fuzzy AG-subgroupoids and three parameters-fuzzy right ideals. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the notion of quadratic exponential invertible graphs whose vertex set is reduced residue system mod n and there will be an edge between x and y such that x2α ≡ y2α (mod n) for some positive integer α. The proposed graph is completely characterized for each positive integer n and also, we find the class of integers in which quadratic exponential invertible graphs are isomorphic to each other. Moreover, the class of those integers is investigated in which the proposed graph is a complete graph. [ABSTRACT FROM AUTHOR]

In this paper, we apply two approximate analytical methods called parameter perturbation method (PPM) and variational iteration method (VIM) to solve the equation of beam deformation with two fixed end and under uniform distributed load. The presented results in this paper reveal that these two methods are very effective and can be easily extended to other nonlinear systems. Hence, they can be found widely applicable in engineering and other sciences. [ABSTRACT FROM AUTHOR]

In this paper, maximal prefix codes with constant average length are investigated. This class of codes is a generalized class of thin codes. Some basic properties of the class of codes are given in this paper. This class of codes is shown to be closed under two operations "product of languages" and "composition of codes". Finite maximal prefix codes over binary alphabets with constant average length n = 3 are completely determined (the cases n = 1 and 2 are trivial). There are infinitely many such codes which can be classified into 9 series. [ABSTRACT FROM AUTHOR]

In this paper, the notions of the generation and the fundamental of an ordered hypersemigroup are introduced. We obtain the maximal hyperideal generation and the minimal hyperideal generation with relative to the same fundamental of a hyperideal generation. Furthermore, we give the construction of C(S), and find out the least strong congruence on an (ordered) hypersemigroup. As an application of the least strong congruence on an ordered hypersemigroup, we give the description of a contained or anti-contained ordered hypersemigroup. Finally, we give some examples to describe the definitions and properties mentioned in this paper. [ABSTRACT FROM AUTHOR]

Quaternionic numerical range is not always convex, and so it is natural to characterize those matrices with convex quaternionic numerical range. In this paper, we present a necessary and sufficient condition in terms of matrix entries for the quaternionic numerical range of a 2 × 2 matrix to be convex. As a consequence, all 2 × 2 matrices with convex quaternionic numerical range are essentially Hermitian, skew-Hermitian, or real matrices up to real translation and unitary similarity. [ABSTRACT FROM AUTHOR]

In this paper, a compact finite difference scheme is constructed and investigated for the fourth-order time-fractional integro-differential equation with singular kernels. In temporal direction, the Caputo derivative is treated by L1 discrete formula and the Riemann-Liouville fractional integral is discretized by trapezoidal PI rule respectively. In spatial direction, the fourth order derivative is approximating by high-order accuracy compact difference method. The detailed analysis shows that the proposed scheme is unconditionally stable and convergent with the convergence order O(N-min{rσ,2-α} + M-4). N,M denote the numbers of grids in temporal direction and in spatial direction, α ∊ (0, 1) is the fractional order of the Caputo derivative and -4 is a regularity parameter. At last, some numerical results are also given to confirm our theoretical statement. [ABSTRACT FROM AUTHOR]

The reciprocal product degree distance RDD*(G), which is a weight version of the Harary index defined for a connected graph G as vertex-degree-weighted sum of the reciprocal distances, that is RDD*(G) = 1/2 Su,v∊V(G)dG(u)dG(v)/dG(u,v), where dG(u) denotes the degree of a vertex u in G and dG(u, v) denotes the distance between two vertices u and v in G. In this paper, we obtain an upper bound for reciprocal product degree distance of F-sum of graphs which is defined by Eliasi [4]. [ABSTRACT FROM AUTHOR]

In this paper, by using the principal of subordination, we obtain sharp bounds for certain class of non-Bazilevič functions involving linear operator. [ABSTRACT FROM AUTHOR]

Let S(p) be the class of meromorphic univalent functions f in the unit disk D with a simple pole at p ∊ (0, 1), CO(p,α) be the subclass of S(p) such that C \ f(D) is a convex domain of order α. In this paper, some characterizations of functions in CO(p, α) are given and the Livingston conjecture of f ∊ CO(p, α) is considered. [ABSTRACT FROM AUTHOR]

A right near-ring (N,+, ·) is called Boolean - zero square or BZS if, for all n ∊ N either n² = n or n² = 0. BZS near-rings generalize Boolean, zero square, and Malone trivial near-rings. This paper initiates a study of the structure of BZS nearrings; in particular, it is shown that non-Boolean BZS near-rings with additive groups of prime order must be zero-symmetric Malone trivial near-rings. This leads to results giving both the number of multiplications and the number of isomorphism classes of non-Boolean BZS near-rings with additive groups of prime order. Such near-rings are also shown to have trivial centers provided they have a non-zero multiplication. Examples are given to illustrate and delimit the theory. [ABSTRACT FROM AUTHOR]

In this paper, we show that the results obtained in [7]: On a system of general mixed variational inequalities are incorrect. Also we suggest and analyze new approximation schemes 4.1 for solving the (SGMVID) which were introduced by M.A. Noor in [7]. [ABSTRACT FROM AUTHOR]

Let A be a nilpotent Filippov (n-Lie) algebra of dimension d and put s(A) = (d−1n) + n − 1 − dim M (A), where M(A) denotes the multiplier of A. The aim of this paper is to classify all nilpotent n-Lie algebras A for which s(A) = 4 or 5. [ABSTRACT FROM AUTHOR]

Let G(V, E) be a graph with vertex set V and edge set E. A map of f from the union of a vertex set and edge sets to {1, 2, . . ., k} such that for each different edge uv and u' v' have different weights is called an irregular total edge k-graph labeling G(V, E). The weight of the edge uv is the sum of the edge label uv, the vertex label u, and the vertex label v. The smallest k so that the graph G(V, E) can be labeled with the edge irregular total k labeling is called the total edge irregularity strength of G(V, E) and is denoted by tes(G). Book graphs Bd(G) have d copies of graph G with a common edge, and the common edge is the same fixed one in all copies of G. We modify the book graphs by replacing G with a wheel graph or a complete graph to obtain wheel book graphs or complete book graphs, respectively. In this paper, we determine the total edge irregularity strength of modified book graphs: wheel book graphs and complete book graphs. [ABSTRACT FROM AUTHOR]

Gröbner-Hofreiter-type integrals were evaluated by the use of applicable contour integrals and Cauchy’s residue theorem. In this paper, we obtain the solutions of Gröbner-Hofreiter-type integrals and other associated integrals with suitable convergence conditions by using hypergeometric approach. Some applications of GröbnerHofreiter-type integrals are also obtained in the form of Weber-Anger-type functions. [ABSTRACT FROM AUTHOR]