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The problem of a multiple player dice tournament is discussed and solved in the paper. A die has a finite number of faces with real numbers written on each. Finite dice sets are proposed which have the following property, defined by Schütte for tournaments: for an arbitrary subset of k dice there is at least one die that beats each of the k with a probability greater than ½. It is shown that the proposed dice set realizes the Paley tournament, that is known to have the Schütte property (for a given k) if the number of vertices is large enough. The proof is based on Dirichlet's theorem, stating that the sum of quadratic nonresidues is strictly larger than the sum of quadratic residues. [ABSTRACT FROM AUTHOR]

Let G be a connected graph with vertex set V(G). The degree Kirchhoff index of G is defined as S'(G) = Σ {u,υ}⊆V(G) d(u)d(υ)R(u,υ), where d(u) is the degree of vertex u, and R(u,υ) denotes the resistance distance between vertices u and υ. In this paper we obtain some upper and lower bounds for the degree Kirchhoff index of graphs. We also obtain some bounds for the Nordhaus-Gaddum-type result for the degree Kirchhoff index. [ABSTRACT FROM AUTHOR]

Let R be a *-prime ring with characteristic different from two and U ≠ 0 be a square closed *-Lie ideal of R. An additive mapping F : R → R is called an generalized derivation if there exits a derivation d : R → R such that F(xy) = F(x)y+xd(y). In the present paper, it is shown that U ⊆ Z if R is a *-prime ring which admits a generalized derivation satisfying several conditions that are associated with a derivation commuting with *. [ABSTRACT FROM AUTHOR]

In this paper we investigate the boundedness of the Gerber-Shiu expected discounted penalty function applied in insurance mathematics. We give a necessary and sufficient condition for its boundedness. This condition is essentially the boundedness of the conditional expectation given the ruin occurs at the first claim. It assures that the integral equation satisfied by the Gerber- Shiu function has a unique bounded solution and it is exactly the Gerber-Shiu function. By the help of the proven necessary and sufficient condition we can also simplify the theorem concerning the necessary and sufficient condition for the limit property. We do not assume independence between the inter-claim time and the claim size but the results can be applied to the usually investigated independent case as well. We present examples to show the applicability of the condition. [ABSTRACT FROM AUTHOR]

In this paper we provide sharp bounds for the Jensen divergence generated by different classes of functions including functions of bounded variation, absolutely continuous, Lipschitz continuous, convex functions and differentiable functions whose derivatives enjoy various properties as mentioned above. The bounds are expressed in terms of known and simpler divergence measures that are of importance in various applications such as the analysis of diversity as between and within populations and to cluster analysis. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some new estimations of Iyengar-type inequality in which quasi-convex(quasi-concave) functions are involved. These estimations are improvements of some recently obtained estimations. Some error estimations for the trapezoidal formula are given. Applications for special means are also provided. [ABSTRACT FROM AUTHOR]

The total irregularity of a graph G is defined as irrt(G) = ½ Σu,υ∊V(G) ǀdG(u)- dG(υ)ǀ, where dG(u) denotes the degree of a vertex u ∊ V(G). In this paper we give (sharp) upper bounds on the total irregularity of graphs under several graph operations including join, lexicographic product, Cartesian product, strong product, direct product, corona product, disjunction and symmetric difference. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of solutions for boundary value problems of fractional differential equations of order q ∊ (0, 1] with four-point integral boundary conditions. Existence and uniqueness results are obtained by using well known fixed point theorems. Some illustrative examples are also discussed. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the quasilinearization for Riemann-Liouville fractional differential equations with two point boundary condition. By establishing a new comparison principle we get a monotone sequence which converges quadratically to the unique solution of the fractional differential equations. [ABSTRACT FROM AUTHOR]

Let G be a nontrivial connected graph. The radius r(G) of G is the minimum eccentricity among eccentricities of all vertices in G. The Randić index of G is defined as r(G) = ... and the Harmonic index is defined as H(G) = ... where dG(x) is the degree of the vertex x in G. In 1988, Fajtlowicz conjectured that for any connected graph G, R(G) ⩾ r(G)-1. This conjecture remains still open so far. More recently, Deng et al. proved that this conjecture is true for connected graphs with cyclomatic number no more than 4 by means of Harmonic index. In this short paper, we use a class of composite graphs to construct infinite classes of connected graphs, with cyclomatic number greater than 4, for which the above conjecture holds. In particular, for any given positive odd number k ⩾ 7, we construct a connected graph with cyclomatic number k such that the above conjecture holds for this graph. [ABSTRACT FROM AUTHOR]

In this paper, we study the asymptotic behavior of eventually positive (negative) and oscillatory solutions to the following nonhomogeneous second order delay differential equation ... where p and f are suitable real functions. [ABSTRACT FROM AUTHOR]

As a tool to characterize instantaneous codes, Foldes and Singhi determined the maximum number of certain subsets of the set of the first n natural numbers in 2006. This motivated Czédli in 2009 to determine the maximum number of the analogous subsets of a rectangular grid. He called these subsets islands. The present paper summarizes recent results on this topic. [ABSTRACT FROM AUTHOR]

In this paper, we prove some strong and Δ-convergence theorems for two finite families of nonexpansive maps on a hyperbolic space. Our iterative scheme is independent and simpler than the Ishikawa type iteration process. Our results refine and generalize several recent and comparable results in uniformly convex Banach spaces as well as CAT(0) spaces. [ABSTRACT FROM AUTHOR]

Abstract. In this paper, we generalize some results related to the congruence subgroups of modular group Γ, given in [7] and [6] by Kiming, Schütt, and Verrill, to the extended modular group Π. [ABSTRACT FROM AUTHOR]

This paper is concerned with higher integrability for gradients of weak solutions to quasilinear parabolic systems of Hörmander's vector fields. We establish Lp estimates for gradients of weak solutions by deriving a parabolic Caccioppli inequality and using the reverse Hölder inequality in parabolic cylinders, and then obtain Lp estimates for gradients of weak solutions to homogeneous parabolic system. At last higher integrability of gradients in Morrey space with p ⩾ 2 is proved. [ABSTRACT FROM AUTHOR]

Let R be a commutative ring and let M be a finitely generated R-module. Let's denote the cozero-divisor graph of R by ... (R). In this paper, we introduce a certain subgraph ... R(M) of ... (R), called cozero-divisor graph relative to M, and obtain some related results. [ABSTRACT FROM AUTHOR]

In this paper, we use a modification of Krasnoselskii's fixed point theorem introduced by Burton (see [6] Theorem 3) to establish new results on the existence and positivity of solutions for the totally nonlinear neutral periodic differential equation of the form d/dtx(t)= -a(t)x³ (t) + d/dt Q (t, x (g(t))) + G (t, x³) (t), x³(g(t))), x(t + T)=x(t). We invert this equation to construct a sum of a completely continuous map and a large contraction which is suitable for the application of a modification of Krasnoselskii's theorem. [ABSTRACT FROM AUTHOR]

In this paper, the Diophantine equation B1k + B2k + ... Bn+1k = Bn+1l + Bn+2l + ... + Bn+rlfor the positive integer unknowns n ⩾ 2, k, l and r is studied in certain cases, where Bn denotes the nth term of the balancing sequence. [ABSTRACT FROM AUTHOR]

Let (R, *) be a 2-torsion free *-prime ring with involution * and center Z(R), U a nonzero square closed *-Lie ideal of R. An additive mapping F : R→R is called a generalized derivation if there exits a derivation d : R→R such that F(xy)=F(x)y+xd(y). In the present paper, we prove that U ⊆ Z(R) if any one of following conditions holds: 1) [F (u), u] = 0, 2) [d(u), F(v) = 0, 3) d(u)oF(v) = 0; 4) [d(u), F(v)] = ±[u,v], 5) d(u)oF(v) = ±uov, 6) d(u)F(v)±uv ϵ Z(R), for all u, v ϵ U. Furthermore, an example is given to demonstrate that the *-primeness hypothesis is not superfluous. [ABSTRACT FROM AUTHOR]

In this paper, we study strong convergence of an iteration process for a finite family of asymptotically quasi-nonexpansive mappings in convex metric spaces. We prove some strong convergence theorems for this iterative algorithm. Our results improve and extend the corresponding results of Kettapun et al. [2]. [ABSTRACT FROM AUTHOR]

In this paper, we study modules with the properties (CRE) and (CREE), which are adapted Zöschinger's modules with the properties (E) and (EE). It is shown that: (1) a module M has the propery (CREE) if and only if every submodule of M has the propery (CRE); (2) a ring R is Rad-supplemented if and only if every left R-module has the propery (CRE); (3) over a commutative Von Neumann regular ring a module M has the propery (CRE) if and only if M is cofinitely injective. [ABSTRACT FROM AUTHOR]

In this paper, we extend two curious divisibility properties for the general second order linear recurrence {Un(p,q)}. We also give new recursive identities for the general second linear recurrences {Un(p,q)} and {Vn(p,q)}. These results generalize the results given by E. Kılıç, "A matrix approach for generalizing two curious divisibility properties", Miskolc Math. Notes, vol. 13., No. 2, pp. 389-396, 2012. [ABSTRACT FROM AUTHOR]

In this paper we prove two theorems on absolute generalized Hausdorff summability of orthogonal series. These theorems give some sufficient conditions in terms of coefficients of an orthogonal series under which it is absolute generalized Hausdorff summable. In addition, it is verified that several known results are corollaries of the new results. [ABSTRACT FROM AUTHOR]

In this paper we gave some results of the two Diophantine equations x²±2apb = y4, x, y ϵ ϵ, gcd (x, y) = 1, a, b ϵ ℤ, a⩾0, b⩾0, where p is an odd prime. [ABSTRACT FROM AUTHOR]

In this paper, we establish some new inequalities for class of SX (h, I) convex functions which are super-multiplicative or super-additive and nonnegative. And we also give some applications for special means. [ABSTRACT FROM AUTHOR]

The paper deals with the geometric concept of mechanical systems of N particles. The systems are modelled on the Cartesian product R×XN and its first jet prolongation J1(R×XN) = R × TXN , where X is a 3-dimensional Riemannian manifold with a metric G. The kinetic energy T of the system of N-particles is interpreted by means of the weighted quadratic form ̄Qg associated with the weighted metric tensor g which arises from the original metric tensor G and the system of N particles m1....mN. A requirement for the kinetic energy of the system of N particles to be constant is regarded as a nonholonomic, so-called isokinetic constraint and it is defined as a fibered submanifold T of the jet space R × TXN endowed with a certain distribution C called canonical distribution, which has the meaning of generalized admissible displacements of the system of particles subject to the isokinetic constraint. Vector generators of the canonical distribution are found. [ABSTRACT FROM AUTHOR]

In this paper, we consider a conformal mapping between two nearly quasi-Einstein manifolds Vn and ̄Vn. We find some properties of this transformation from Vn to ̄Vn and some theorems are proved. [ABSTRACT FROM AUTHOR]

We will consider the definition of the degree r of geodesic mobility of a Riemannian manifold and will prove that the well-known results on the geodesic mobility are essentially local. In the last section of our paper, we will prove that the geodesic mobility of an n-dimensional closed, simply-connected Riemannian manifold with positive constant sectional curvature satisfies the identity r = (n + 1)(n + 2)/2, n ≥ 2. [ABSTRACT FROM AUTHOR]

This paper deals with the properties of a special differential operator with respect to the general decomposition of tensor fields on manifolds with affine connection. It is shown that properties of a special differential operator are transferred to the components of a given decomposition. [ABSTRACT FROM AUTHOR]

In this paper, we prove that geodesic mappings of (pseudo-) Riemannian manifolds preserve the class of differentiability (Cr , r ≥ 1). Also, if the Einstein space Vn admits a nontrivial geodesic mapping onto a (pseudo-) Riemannian manifold ̄Vn ∈ C1, then VNn is an Einstein space. If a four-dimensional Einstein space with non-constant curvature globally admits a geodesic mapping onto a (pseudo-) Riemannian manifold ̄V4 ∈ C1, then the mapping is affine and, moreover, if the scalar curvature is non-vanishing, then the mapping is homothetic, i. e. ̄g D const · g. [ABSTRACT FROM AUTHOR]

In this paper we study conformal holomorphically projective mappings between conformal e-Kähler manifolds Kn=(M, g, F) and (̄Kn=(̄M, ̄g, ̄F), i. e. diffeomorphisms f : M → ̄M satisfying f = f1 엯 f2 엯 f3, where f1, f3 are conformal mappings and f2 is a holomorphically projective mapping between e-Kähler manifolds (i. e. Kähler, pseudo-Kähler and hyperbolic Kähler manifolds). Suppose that the initial condition f* ̄g = k · g is satisfied at a point x0 ∈ M and that at this point the Weyl conformal tensor satisfies a certain inequality. We prove that the mapping f is then necessarily conformal. [ABSTRACT FROM AUTHOR]

In this paper we study the mobility degree of (pseudo-) Riemannian spaces with respect to concircular mappings. We assume that the smoothness class of differentiability is C2. [ABSTRACT FROM AUTHOR]

The aim of this paper is to give a survey of recent developments in global variational geometry, and in particular, to complete the results on the construction of classes (terms) in the variational sequences related to higher-order variational problems on fibred spaces. Explicit description of the first order variational sequences is given as an example. [ABSTRACT FROM AUTHOR]

This paper covers several topics that involve symmetries of differential equations: from the connection between Lie symmetries and Jacobi last multiplier with a detour to the inverse problem of calculus of variations, to the importance of maximal group of Noether symmetries on the road from classical to quantum mechanics. [ABSTRACT FROM AUTHOR]

In this paper, we revisit the existence, background independence and uniqueness of closed, open and open-closed bosonic- and topological string field theory, using the machinery of homotopy algebra. In the theory of classical open- and closed strings, the space of inequivalent open string field theories is isomorphic to the space of classical closed string backgrounds. We then discuss obstructions of these moduli spaces at the quantum level. For the quantum theory of closed strings, uniqueness on a given background follows from the decomposition theorem for loop homotopy algebras. We also address the question of background independence of closed string field theory. [ABSTRACT FROM AUTHOR]

In this paper, we establish some sharp estimates for certain vector-valued multilinear integral operators. The operators include Littlewood-Paley operators, Marcinkiewicz operators and the Bochner-Riesz operator. As an application, we obtain the (Lp, Lq)-norm inequality for the vector-valued multilinear operators. [ABSTRACT FROM AUTHOR]

In this paper we consider cone metric type spaces which are introduced as a generalization of symmetric and metric spaces by Khamsi and Hussain in 2010. Then we prove several common fixed point for weakly compatible mappings in cone metric type spaces. All results are proved in the settings of a solid cone, without the assumption of continuity of the mappings. [ABSTRACT FROM AUTHOR]

In this paper, we use the notion of ideal to obtain two more general concepts and call them as I-A-statistical convergence and ideal A-summability. We also use the the concept of I-A-statistical convergence to prove a Korovkin type approximation theorem for double sequences of positive linear operators and present an interesting example to show that our Korovkin theorem is stronger than those proved earlier. [ABSTRACT FROM AUTHOR]

In this paper, we present a fixed point theorem for a new type of contractive mappings. Our main result extends and unifies some well-known results in the literature. [ABSTRACT FROM AUTHOR]

Let R be a prime ring. By a generalized derivation we mean an additive mapping g : R → R such that g(xy) = g(x)y + xd(y) for all x, y ∈ R where d is a derivation of R. In the present paper our main goal is to generalize some results concerning derivations of prime rings to generalized derivations of prime rings. [ABSTRACT FROM AUTHOR]

In this paper we present some existence, uniqueness and Hyers-Ulam stability results for the coupled fixed point of a pair of contractive type operators on complete metric spaces. The approach is based on a Perov type fixed point theorem for contractions. Some applications to integral equations and to boundary value problems are also given. [ABSTRACT FROM AUTHOR]

By the work of Abu Muriefah, Al-Rashed, Dujella and the author, the problem of the existence of D(z)-quadruples in the ring ℤ[√-2] has been solved, except for the cases z = 24a + 2 + (12b + 6) √-2,z = 24a + 5 + (12b + 6) √-2, z = 48a = 44 + (24b + 12) √-2. In this paper, we present some new formulas for D(z)-quadruples in these remaining cases, involving some congruence conditions modulo 11 on integers a and b. We show the existence of D(z)-quadruple for significant proportion of the remaining three cases. [ABSTRACT FROM AUTHOR]

In this paper, the existence of solutions of some minimization problems for noncyclic mappings in G—metric spaces is studied. Our results can be considered as an extension of Abkar and Gabeleh's result [Global Optimal Solutions of Noncyclic Mappings in Metric Spaces, J. Optim. Theory. Appl. 153 (2011), 298-305] to the case of G群metric spaces. [ABSTRACT FROM AUTHOR]

Let {X, Xn, n ≥ 1} be a sequence of identically distributed random variables and {ai,n, 1 ⩽ i ⩽ n} be a triangular array of constants. In this short paper, we establish a general almost sure convergence theorem for the weighted sum Sn = ... ai,nXi. Our results improves the works of Sung [14]. Furthermore, almost sure convergence theorems of Sn for negatively associated random variables, martingale difference sequence and ρ-mixing sequence are obtained. [ABSTRACT FROM AUTHOR]

Let n×n complex matrices P and Q be nontrivial generalized reflection matrices, i.e., P* = P = P-1 ≠ In, Q* = Q = Q-1 ≠ In. A complex matrix A with order n is said to be a (P, Q) generalized anti-reflexive matrix, if PAQ = -A. We in this paper mainly investigate the (P, Q) generalized anti-reflexive maximal and minimal rank solutions to the system of matrix equation AX = B. We present necessary and sufficient conditions for the existence of the maximal and minimal rank solutions, with (P, Q) generalized anti-reflexive, of the system. Expressions of such solutions to this system are also given when the solvability conditions are satisfied. In addition, in correspondence with the minimal rank solution set to the system, the explicit expression of the nearest matrix to a given matrix in the Frobenius norm has been provided. [ABSTRACT FROM AUTHOR]

In this paper, we give a recurrence relation for the Tribonacci numbers with indices in aritmetics progression, {Trn+s} for 0 ⩽ s < n. We find sums of {Trn} for arbitrary integer r via matrix methods. [ABSTRACT FROM AUTHOR]

In this paper, the perturbation method and Padé transformation are used to provide an approximate solution of elliptic integrals of the second kind and of complete integrals of the first kind. Besides, we used the obtained results to calculate an analytic expression for the period of a simple pendulum. The method has an acceptable accuracy for high values of the initial amplitude, compared to the relative error < 1:7% for initial angles θ ⩽ 70°. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a class of 2nth-order regular differential operator with eigenparameter-dependent boundary conditions and transmission conditions at an interior discontinuous point. By constructing a new linear operator A associated with the problem, we prove that the operator A is self-adjoint in a suitable Hilbert space H, and the eigenvalues of the problem coincide with those of A. In terms of basic solutions of differential equation, we show that the eigenvalues of this problem coincide with the zeros of the entire function det Φ(1, λ), and obtain that the operator A has only point spectrum. [ABSTRACT FROM AUTHOR]

In this paper we introduce the Mittag-Leffler operators, which includes the modified Szász-Mirakjan operators. We obtain the transformation properties and compute the rate of convergence by using modulus of continuity. Furthermore we give the A-statistical approximation theorem for these operators. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a generalization of the Stancu- Schurer operators based on q-integers and get a Bohman-Korovkin type approximation theorem of these operators. We also compute the rate of convergence by using the first modulus of smoothness and give some numerical result of operators based on Matlab algorithms. [ABSTRACT FROM AUTHOR]