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A graph G is said to be DQS if there is no other non-isomorphic graph with the same signless Laplacian spectrum as G. Let k, ti (1 ≤ i ≤ k), and s be natural numbers. A path-friendship graph, Gs,t1...,tk, is a graph of order n = 2s + t1 + ... + tk+1 which consists of s triangles and k paths of lengths t1,t2 ..., tk sharing a common vertex. In this paper, we show that these graphs are DQS and using this result, we respond to a conjecture in [F. Wen, Q. Huang, X. Huang and F. Liu, The spectral characterization of wind-wheel graphs, Indian J. Pure Appl. Math. [ABSTRACT FROM AUTHOR]

A subset S = V is a dominating set of G if every vertex in V / S has a neighbor in S, and it is a total dominating set if every vertex in V has a neighbor in S. The total domination number of G, t(G), is the minimum cardinality of a total dominating set of G. A vertex v of a graph G is said to ve-dominate every edge incident to v, as well as every edge adjacent to these incident edges. A set S is a vertex-edge dominating set (or simply, a ve-dominating set) if every edge of E is ve-dominated by at least one vertex of S. A total ve-dominating set of G is a ve-dominating set whose induced subgraph has no isolated vertex. The vertex-edge domination number ve(G) is the minimum cardinality of a total ve-dominating set and the total vertex-edge domination number tv e(G) is the minimum cardinality of a total ve-dominating set in G. In this paper, we characterize all trees T with tv e(T) = t(T) or tv e(T) = ve(T), answering two open problems posed in [Boutrig R. and Chellali M., Total vertex-edge domination, Int. J. Comput. Math. 95 (2018), 1820-1828]. Moreover, we show that it is NP-hard to decide whether tv e(G) = ve(G) for a given connected (K4 - e)-free graph G. [ABSTRACT FROM AUTHOR]

In this paper, we show that the continuity requirement assumed in the main result of Vara Prasad and Singh [Meir-Keeler type contraction via rational expression, Acta Math. Univ. Comenianae LXXXIX(1) (2020), 19-25] can be relaxed further. As a by-product we explore some new answers to the open question posed by Rhoades [Contemporary Mathematics 72 (1988), 233-245] regarding the existence of contractive mappings that admit discontinuity at the fixed point. [ABSTRACT FROM AUTHOR]

The paper deals with m by n rectangular arrays whose mn cells are filled with symbols. A section of the array consists of m cells, one from each row and no two from the same column. The paper focuses on the existence of sections that do contain symbols with high multiplicity. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the properties of curves of constant breadth in a 3-dimensional Lie group. Also, we find the condition of general helix as constant breadth curves and construct constant breadth curves which the tangent component of the curve vanishes. [ABSTRACT FROM AUTHOR]

Let (M, g) be a Riemannian manifold and G a nondegenerate g-natural metric on its tangent bundle TM. In this paper we establish a relation between the Jacobi operators of (M, g) and that of (TM,G). In the case of a Riemannian surface (M, g), we compute explicitly the spectrum of some Jacobi operators of (TM,G) and give necessary and sufficient conditions for (TM,G) to be an Osserman manifold. [ABSTRACT FROM AUTHOR]

In this paper it is shown that the Hilbert inequality for double series can be improved by introducing a weight function of the form (Multiple line equation(s) cannot be represented in ASCII text), where n ϵ N. A similar result for the Hilbert integral inequality is also given. As applications, some sharp results of Hardy-Littlewood's theorem and Widder's theorem are obtained. [ABSTRACT FROM AUTHOR]

In this paper, the concepts of distributive, standard and neutral elements introduced in lattices by O. Ore, G. Grätzer and G. Birkhoff, respectively, have been extended to trellises (also called weakly associative lattices) and some of their analogous characterizations are obtained. Also, the concept of a normal trellis is introduced as a generalization of a lattice and it is proved that an element d of a normal trellis L is neutral if and only if for any x, y ϵ L, the elements d, x, y generate a distributive subtrellis of L. [ABSTRACT FROM AUTHOR]

In this paper, we shall establish some strong convergence results for the recently introduced Jungck-Mann iteration process of Singh et al. [18] and the newly introduced Jungck-Ishikawa iteration process in the class of non-selfmappings in an arbitrary Banach space. Our results are generalizations and extensions of those of Berinde [4], Rhoades [13, 14] as well as some other analogous ones in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the relationship between solutions and their derivatives of the differential equation f(κ) + A(z)f = 0, κ ≥ 2, where A(z) is a transcendental meromorphic function with ρρ(A) = ρ > 0 and meromorphic functions of finite iterated p-order. [ABSTRACT FROM AUTHOR]

In this paper, we characterize peudo-sequence-covering π-images of locally separable metric spaces by means of fcs-covers and point-star networks. We also investigate pseudo-sequence-covering π-s-images of locally separable metric spaces. [ABSTRACT FROM AUTHOR]

In this paper some results on the structure of finite-dimensional Lie algebras are obtained by means of the concept of maximal abelian dimension. More concretely, a sufficient condition is given for the solvability in finite-dimensional Lie algebras by using maximal abelian dimensions. Besides, a necessary condition for the nilpotency is also stated for such Lie algebras. Finally, the maximal abelian dimension is applied to characterize the n-dimensional nilpotent Lie algebras with maximal abelian dimension equal to their codimension. [ABSTRACT FROM AUTHOR]

In this paper we are concerned with the solutions of the differential equation f‴ + f f″ + g(f′) = 0 on [0,∞), satisfying the boundary conditions f(0) =α f′(0) =β⩾ 0, f′(∞) = λ, and where g is a given continuous function. This general boundary value problem includes the Falkner-Skan case, and can be applied, for example, to free or mixed convection in porous medium, or flow adjacent to stretching walls in the context of boundary layer approximation. Under some assumptions on the function g, we prove existence and uniqueness of a concave or a convex solution. We also give some results about nonexistence and asymptotic behaviour of the solution. [ABSTRACT FROM AUTHOR]

In purely infinite factors, P. de la Harpe proved that a normal subgroup of the unitary group which contains a non-trivial self-adjoint unitary contains all self-adjoint unitaries of the factor. Also he proved the same result in finite continuous factors. In a previous work the author proved a similar result in some types of unital AF-algebras. In this paper we extend the result of de la Harpe, concerning the purely infinite factors to a main example of purely infinite C*-algebras called the Cuntz algebras Ҩn(2 ⩽ n⩽ 1) and we prove that U(Ҩn) is normally generated by some non-trivial involution. In particular, in the Cuntz algebra Ҩ∞ we prove that U(Ҩ∞) is normally generated by self-adjoint unitary of odd type. [ABSTRACT FROM AUTHOR]

In this paper the structure of the class of all reciprocal bases of N is investigated from metric and topological point of view. For this purpose the method of dyadic values of infinite subsets of N will be applied. [ABSTRACT FROM AUTHOR]

We derive the precise limit of SHS in the high activation energy scaling suggested by B. J. Matkowsky and G. I. Sivashinsky in 1978 and by A. Bayliss, B. J. Matkowsky and A. P. Aldushin in 2002. In the time-increasing case the limit turns out to be the Stefan problem for supercooled water with spatially inhomogeneous coefficients. Although the present paper leaves open mathematical questions concerning the convergence, our precise form of the limit problem suggests a strikingly simple explanation for the numerically observed pulsating waves. [ABSTRACT FROM AUTHOR]

In this paper we have introduced 1-parameter Lorentzian spherical motion. In addition to that we have given the relations between the absolute, relative and sliding velocities of these motions. Furthermore, the relations between fixed and moving pole curves in the Lorentzian spherical motions have also been obtained. [ABSTRACT FROM AUTHOR]

In this paper we prove the existence of a universal, i.e. independent of the initial data, bound for global positive solutions of a diffusion equation with a mixed local-nonlocal reaction term. Such results are already known in some cases of local or nonlocal reaction terms. [ABSTRACT FROM AUTHOR]

In this paper we show that in a regular additively inverse semiring (S,+,·) with 1 satisfying the conditions (A) a(a + a') = a + a'; (B) a(b + b') = (b + b')a and (C) a + a(b + b') = a, for all a, b ∈ S, the sum of two principal left ideals is again a principal left ideal. Also, we decompose S as a direct sum of two mutually inverse ideals. [ABSTRACT FROM AUTHOR]

This paper introduces a closed-form expression for the second-order recurrence relation an = c1an-1 + c2a n-2, in which c1 and c2 are fixed constants and the value of two arbitrary terms an-p and an-q are known where p and q are positive integers and p > q. This expression is (Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed.) [ABSTRACT FROM AUTHOR]