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The correspondence between a vertex and its neighbors has an essential role in the structure of a graph. Type-2 soft sets are also based on the correspondence of primary parameters and underlying parameters. In this study, we present an application of type-2 soft sets in graph theory. We introduce vertex-neighbors based type-2 soft sets over X (set of all vertices of a graph) and E (set of all edges of a graph). Moreover, we introduce some type-2 soft operations in graphs by presenting several examples to demonstrate these new concepts. Finally, we describe an application of type-2 soft graphs in communication networks and present procedure as an algorithm. [ABSTRACT FROM AUTHOR]

The performance of device-to-device (D2D) communication in a cellular network depends on the resource sharing between D2D links and cellular users. Existing researches on resource sharing mainly focus on power control between the D2D users and cellular users that operate in the same frequency band. However, the D2D outage probability performance is hampered by the cellular interference to D2D links. Therefore, the D2D users may not achieve satisfactory SINR performance when D2D users and cellular users are geographically located in a small area; as a result, the outage probability performance would be significantly degraded. In this paper, we provide a novel resource sharing strategy to mitigate the interference from cellular users to D2D receivers by utilizing the low energy characteristics of signals in the guard band and analyze the D2D outage probability performance mathematically. Both the mathematical analysis and numerical results show that the proposed resource sharing strategy provides 1.2 dB SNR gain in D2D outage probability performance while guaranteeing the cellular throughputs. [ABSTRACT FROM AUTHOR]

We introduce the notion of an ordered quasi-ideal of an ordered semiring and show that ordered quasi-ideals and ordered bi-ideals coincide in regular ordered semirings. Then we give characterizations of regular ordered semirings, regular ordered duo-semirings, and left (right) regular ordered semirings by their ordered quasi-ideals. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to study the motion of two associated ruled surfaces in Euclidean 3-space E3. In particular, the motion of Bishop Frenet offsets of ruled surfaces is investigated. Additionally, the characteristic properties for such ruled surfaces are given. Finally, an application is presented and plotted using computer aided geometric design. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to study the motion of two associated ruled surfaces in Euclidean 3-space E3. In particular, the motion of Bishop Frenet offsets of ruled surfaces is investigated. Additionally, the characteristic properties for such ruled surfaces are given. Finally, an application is presented and plotted using computer aided geometric design. [ABSTRACT FROM AUTHOR]

Given a pseudoresiduated lattice M and a lattice L, we introduce and characterize the fuzzy versions of different n-fold implicative (resp., obstinate, Boolean, normal, and extended involutive) filters of M. Moreover, we study some relationships between these different types of fuzzy n-fold filters. [ABSTRACT FROM AUTHOR]

We study lightlike hypersurfaces M of an indefinite generalized Sasakian space form M-(f1,f2,f3), with indefinite trans-Sasakian structure of type (α,β), subject to the condition that the structure vector field of M- is tangent to M. First we study the general theory for lightlike hypersurfaces of indefinite trans-Sasakian manifold of type (α,β). Next we prove several characterization theorems for lightlike hypersurfaces of an indefinite generalized Sasakian space form. [ABSTRACT FROM AUTHOR]

The aimof this work is to introduce an extension for q-standard notations. The q-Apostol type polynomials and study some of their properties. Besides, some relations between the mentioned polynomials and some other known polynomials are obtained. [ABSTRACT FROM AUTHOR]

Motivated by the concept of complete pairs, which was introduced by Krein and Langer, we present the concepts of an almost complete pair of matrices and a complete triple of matrices. It is proved that an almost complete pair of matrices can be extended to a complete triple. An application of the result to differential equations is also given. [ABSTRACT FROM AUTHOR]

A function : ℝ ℝ is said to be a Fibonacci function if f(x + 2) = f(x + 1) + f(x) for all x ∈ ℝ. In 2012, some properties on the Fibonacci functions were presented. In this paper, for any positive integer k, a function f : ℝ ℝ is said to be a Fibonacci function with period k if f(x + 2k) = f(x+k) + f(x) for all x ∈ ℝ we present some properties on the Fibonacci functions with period k. [ABSTRACT FROM AUTHOR]

We investigate the zero distribution of q-shift difference polynomials of meromorphic functions with zero order and obtain some results that extend previous results of K. Liu et al. [ABSTRACT FROM AUTHOR]

We obtain, by using the Leggett-Williams fixed point theorem, sufficient conditions that ensure the existence of at least three positive solutions to some p-Laplacian boundary value problems on time scales. [ABSTRACT FROM AUTHOR]

This paper deals with the initial boundary value problem for the nonlinear viscoelastic Petrovsky equation utt + Δ²u - Δt0(t - Τ)Δ²u(x,Τ)dΤ-Δut Δutt + |ut|m-1ut = |u|p-1u. Under certain conditions on g and the assumption that m < p, we establish some asymptotic behavior and blow-up results for solutions with positive initial energy. [ABSTRACT FROM AUTHOR]

We utilize q-fractional Caputo initial value problems of order 0 < α ≤ 1 to derive a q-analogue for Gronwall-type inequality. Some particular cases are derived where q-Mittag-Leffler functions and q-exponential type functions are used. An example is given to illustrate the validity of the derived inequality. [ABSTRACT FROM AUTHOR]

This paper gives a unified characterization of Fredholm weighted composition operator on a class of weighted Hardy spaces. [ABSTRACT FROM AUTHOR]

We find necessary and sufficient conditions on weighted sequences ω,i = 1,2,...,n-1, u, and v, for which the operator (Sn-1f)i = Σi k1=1 ω1,k1... Σkn-2 Σkn-1=1 ωn-1,kn-1 Σkn-1j=1 fj, i ≥ 1, is bounded from lp,v to lq,u for 1 < q < p < ∞. [ABSTRACT FROM AUTHOR]

A necessary and sufficient condition is given for a positive measure μ on D to be a K-Carleson measure. We give the predual of Qk spaces in terms of this condition. [ABSTRACT FROM AUTHOR]

We point out some equivalence between the results in (Sedghi et al., 2012) and (Khamsi, 2010).Then, we introduce the notion of a general distance between three arbitrary points and study some of its properties. In the final section, some fixed point results are proposed. [ABSTRACT FROM AUTHOR]

Results on Colombeau product of distributions x-r-1/2+ and x-r-1/2- are derived. They are obtained in Colombeau differential algebra G(R) of generalized functions that contains the space D' (R) of Schwartz distributions as a subspace and has a notion of "association" that is a faithful generalization of the weak equality in D' (R). [ABSTRACT FROM AUTHOR]

Diagonal updating scheme is among the cheapest Newton-like methods for solving system of nonlinear equations. Nevertheless, the method has some shortcomings. In this paper, we proposed an improved matrix-free secant updating scheme via line search strategies, by using the steps of backtracking in the Armijo-type line search as a step length predictor and Wolfe-Like condition as corrector. Our approach aims at improving the overall performance of diagonal secant updating scheme. Under mild assumptions, the global convergence results have been presented. Numerical experiments verify that the proposed approach is very promising. [ABSTRACT FROM AUTHOR]

We study the role of predation dynamics in oscillation of pest population in insect ecology. A two-dimensional pest control model (under the use of insecticides) with time delay in predation is considered in this paper. By the Hopf bifurcation theory, we prove the existence of the stable oscillation of the system. We also consider the economic viability of the control process. First we improve the Pontryagin maximum principle (PMP) where the delay in the system is sufficiently small and control function is linear, and then we apply the improved version of PMP to perform the optimal analysis of the pest control model as a special case. [ABSTRACT FROM AUTHOR]

The notion of generalized derivations of BCC-algebras is introduced, and some related properties are investigated. Also, we consider regular generalized derivations and the D-invariant on ideals of BCC-algebras. We also characterized KerD by generalized derivations. [ABSTRACT FROM AUTHOR]

For n ⩾ 1, let P(n) = F2 [x1, . . . , x n ] be the polynomial algebra in n variables xi, of degree one, over the field F2 of two elements. The mod-2 Steenrod algebra A acts on P(n) according to well-known rules. Let A+P(n) denote the image of the action of the positively graded part of A. A major problem is that of determining a basis for the quotient vector space Q(n) = P(n)/A+P(n). Both P(n) = ⊕ d⩾0Pd (n) and Q(n) are graded where Pd (n) denotes the set of homogeneous polynomials of degree d. A spike of degree d is a monomial of the form x 12λ1 -1 … x n 2λn -1 where λ i ⩾ 0 for each i. In this paper we show that if n ⩾ 2 and d ⩾ 1 can be expressed in the form d = d(λ) = (n - 1)(2λ - 1) with λ ⩾ 2, then dim(Qd(λ) (n)) ⩾ B(n, d(λ)) + {Σ λ q=2 ( n q ), ifλ < n;2n - (n + 1), ifλ ⩾ n}, where B(n, d(λ)) is the number of spikes of degree d(λ). [ABSTRACT FROM AUTHOR]

We consider a partial action (X, α) with enveloping action (T, β). In this work we extend α to a partial action on the ring (P(X), Δ ,∩) and find its enveloping action (E, β). Finally, we introduce the concept of partial action of finite type to investigate the relationship between (E, β) and (P(T),β). [ABSTRACT FROM AUTHOR]

The notion of symmetric left bi-derivation of a BCI-algebra X is introduced, and related properties are investigated. Some results on componentwise regular and d-regular symmetric left bi-derivations are obtained. Finally, characterizations of a p-semisimple BCI-algebra are explored, and it is proved that, in a p-semisimple BCI-algebra, F is a symmetric left bi-derivation if and only if it is a symmetric bi-derivation. [ABSTRACT FROM AUTHOR]

Let N be a near ring. An additive mapping f : N → N is said to be a right generalized (resp., left generalized) derivation with associated derivation d on N if f(xy) = f(x)y + xd(y) (resp., f(xy) = d(x)y + xf(y)) for all x, y ϵ N. A mapping f : N → N is said to be a generalized derivation with associated derivation d on N if f is both a right generalized and a left generalized derivation with associated derivation d on N. The purpose of the present paper is to prove some theorems in the setting of a semi group ideal of a 3-prime near ring admitting a generalized derivation, thereby extending some known results on derivations. [ABSTRACT FROM AUTHOR]

Thefirst main idea of this paper is to develop thematrix sequences that represent Padovan and Perrin numbers. Then, by taking into account matrix properties of these new matrix sequences, some behaviours of Padovan and Perrin numbers will be investigated. Moreover, some important relationships between Padovan and Perrin matrix sequences will be presented. [ABSTRACT FROM AUTHOR]

Some comparison theorems for the spectral radius of double splittings of different matrices under suitable conditions are presented, which are superior to the corresponding results in the recent paper by Miao and Zheng (2009). Some comparison theorems between the spectral radius of single and double splittings of matrices are established and are applied to the Jacobi and Gauss-Seidel double SOR method. [ABSTRACT FROM AUTHOR]

We use a nonlinear transformation method to develop equivalent equations of motion of nonlinear homogeneous oscillatory systems with linear and nonlinear odd damping terms. We illustrate the applicability of our approach by using the equations of motion that arise in many engineering problems and compare their amplitude-time curves with those obtained by the numerical integration solutions of the original equations of motion. [ABSTRACT FROM AUTHOR]

We consider some integral operators defined by analytic functions in the open unit disk and derive new univalence criteria for these operators, using Kudriasov condition for a function to be univalent. [ABSTRACT FROM AUTHOR]

New fixed-point theorems on metric spaces are established, and analogous results on partial metric spaces are deduced. This work can be considered as a continuation of the paper Samet et al. (2013). [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to establish a Hörmander multiplier theorem for Herz-type Hardy spaces associated with the Dunkl transform. [ABSTRACT FROM AUTHOR]

We study Jensen's inequality for generalized Peng's g-expectations and give four equivalent conditions on Jensen's inequality for generalized Peng's g-expectations without the assumption that the generator g is continuous with respect to t. This result includes and extends some existing results. Furthermore, we give some applications of Jensen's inequality for generalized Peng's g-expectations. [ABSTRACT FROM AUTHOR]

We extend the second Noether theoremto variational problems on time scales. As corollarieswe obtain the classical second Noether theorem, the second Noether theorem for the h-calculus and the second Noether theorem for the q-calculus. [ABSTRACT FROM AUTHOR]

The r-Bell numbers are generalized using the concept of the Hankel contour. Some properties parallel to those of the ordinary Bell numbers are established. Moreover, an asymptotic approximation for r-Bell numbers with real arguments is obtained. [ABSTRACT FROM AUTHOR]

Let be a simple graph. Graph polynomials are a well-developed area useful for analyzing properties of graphs. We consider domination polynomial, matching polynomial, and edge cover polynomial of G. Graphs which their polynomials have few roots can sometimes give surprising information about the structure of the graph. This paper is primarily a survey of graphs whose domination polynomial, matching polynomial, and edge cover polynomial have few distinct roots. In addition, some new unpublished results and questions are concluded. [ABSTRACT FROM AUTHOR]

We provide a sufficient condition for the existence of a cycle C in a connected graph G which is edge-disjoint from two connected subgraphs H1 and H2 of G such that G -- E(C) is connected. [ABSTRACT FROM AUTHOR]

We show a new method to construct constant slope surfaces with quaternions. Moreover, we give some results and illustrate an interesting shape of constant slope surfaces by using Mathematica [ABSTRACT FROM AUTHOR]

This short note deals with Morita equivalence of (arbitrary) semigroups. We give a necessary and sufficient condition for a Morita context containing two semigroups S and T to induce an equivalence between the category of closed right S-acts and the category of closed right T-acts. [ABSTRACT FROM AUTHOR]

We define GCR-lightlike submanifolds of indefinite cosymplectic manifolds and give an example. Then, we study mixed geodesic GCR-lightlike submanifolds of indefinite cosymplectic manifolds and obtain some characterization theorems for a GCR-lightlike submanifold to be a GCR-lightlike product. [ABSTRACT FROM AUTHOR]

By using the theory of means, various refinements of Huygens' trigonometric and hyperbolic inequalities will be proved. New Huygens' type inequalities will be provided, too. [ABSTRACT FROM AUTHOR]

This paper deals with anisotropic obstacle problem for the A-harmonic equation Σi=1 n Di(ai(x,Du(x))) = 0. An integrability result is given under suitable assumptions, which show higher integrability of the boundary datum, and the obstacle force solutions u have higher integrability as well. [ABSTRACT FROM AUTHOR]

We continue to adopt notations and methods used in the papers illustrated by Yang (2009, 2010) to investigate the monotonicity properties of the ratio of mixed two-parameter homogeneous means. As consequences of our results, the monotonicity properties of four ratios of mixed Stolarsky means are presented, which generalize certain known results, and some known and new inequalities of ratios of means are established. [ABSTRACT FROM AUTHOR]

Recently, some interesting and new identities are introduced in the work of Kim et al. (2012). From these identities, we derive some new and interesting integral formulae for Bernoulli and Genocchi polynomials. [ABSTRACT FROM AUTHOR]

Let T be a time scale such that a < b; a, b ∈ 핋. We will show the existence and uniqueness of solutions for the second-order boundary value problem yΔΔ(t) = f(t, y(t), yΔ(t)), t ∈ [a, b]핋, y(a) = A, y(b) = B, by matching a solution of the first equation satisfying boundary conditions on [a, c]핋 with a solution of the first equation satisfying boundary conditions on [c, b]핋, where c ∈ (a, b)핋. [ABSTRACT FROM AUTHOR]

Seiffert has defined two well-known trigonometric means denoted by Ρ and Τ. In a similar way it was defined by Carlson the logarithmic mean L as a hyperbolic mean. Neuman and Sándor completed the list of such means by another hyperbolic mean M. There are more known inequalities between the means Ρ, Τ, and L and some power means Ap. We add to these inequalities two new results obtaining the following nice chain of inequalities A0 < L < A1/2 < Ρ < A1 < M < A3/2 < Τ < A2, where the power means are evenly spaced with respect to their order. [ABSTRACT FROM AUTHOR]

We show geometrical properties of a submanifold of a (LCS)n-manifold. The properties of the induced structures on such a submanifold are also studied. [ABSTRACT FROM AUTHOR]

In this paper, for the difference of famous means discussed by Taneja in 2005, we study the Schurgeometric convexity in (0,∞) × (0,∞) of the difference between them. Moreover some inequalities related to the difference of those means are obtained. [ABSTRACT FROM AUTHOR]

Using Buşneag's model, the notion of pseudovaluations (valuations) on a WFI algebra is introduced, and a pseudometric is induced by a pseudovaluation on WFI algebras. Given a valuation with additional condition, we show that the binary operation in WFI algebras is uniformly continuous. [ABSTRACT FROM AUTHOR]

We give some interesting identities on the Bernoulli numbers and polynomials, on the Genocchi numbers and polynomials by using symmetric properties of the Bernoulli and Genocchi polynomials. [ABSTRACT FROM AUTHOR]