Total dominating set, connected vertex cover and Steiner tree are well-known graph problems. Despite the fact that they are NP-complete to optimize, it is easy (even trivial) to find solutions, regardless of their size. In this paper, we study a variant of these problems by adding conflicts, that are pairs of vertices that cannot be both in a solution. This new constraint leads to situations where it is NP-complete to decide if there exists a solution avoiding conflicts. This paper proposes NP-completeness proofs of the existence of a solution for different restricted classes of graphs and conflicts, improving recent results. We also propose polynomial time constructions in several restricted cases and we introduce a new parameter, the stretch, to capture the locality of the conflicts.
Generalized differential transform method (GDTM) is a powerful method to solve the fractional differential equations. In this paper, a new fractional model for systems with single degree of freedom (SDOF) is presented, by using the GDTM. The advantage of this method compared with some other numerical methods has been
shown. The analysis of new approximations, damping and acceleration of systems are also described. Finally, by reducing damping and analysis of the errors, in one of the fractional cases, we have shown that in addition to having a suitable solution for the
displacement close to the exact one, the system enjoys acceleration once crossing the equilibrium point.
One feature of the famous Sharkovsky’s theorem is that it can be proved using digraphs of a special type (the so–called Markov graphs). The most general definition assigns a Markov graph to every continuous map from the topological graph to itself. We show that this definition is too broad, i.e. every finite digraph can be viewed as a Markov graph of some one–dimensional dynamical system on a tree. We therefore consider discrete analogues of Markov graphs for vertex maps on combinatorial trees and characterize all maps on trees whose discrete Markov graphs are of the following types: complete, complete bipartite, the disjoint union of cycles, with every arc being a loop.
In this paper we introduce the notions of interval-valued fuzzy bi-ideal, interval-valued anti fuzzy bi-ideal and interval-valued intuitionistic fuzzy bi-ideal in ternary semirings and some of the basic properties of these ideals are investigated. We also introduce normal interval-valued intuitionistic fuzzy ideals in ternary semirings.
The modified Kudryashov method is powerful, efficient and can be used as an alternative to establish new solutions of different type of fractional differential equations applied in mathematical physics. In this article, we’ve constructed new traveling wave solutions including symmetrical Fibonacci function solutions, hyperbolic function solutions and rational solutions of the space-time fractional Cahn Hillihard equation
D_t^α u − γD_x^α u − 6u(D_x^α u)^2 − (3u^2 − 1)D_x^α (D_x^α u) + D_x^α(D_x^α(D_x^α(D_x^α u))) = 0
and the space-time fractional symmetric regularized long wave (SRLW) equation
D_t^α(D_t^α u) + D_x^α(D_x^α u) + uD_t^α(D_x^α u) + D_x^α u D_t^α u + D_t^α(D_t^α(D_x^α(D_x^α u))) = 0
via modified Kudryashov method. In addition, some of the solutions are described in the figures with the help of Mathematica.
In this paper, we study the existence of positive solutions of a three-point integral boundary value problem (BVP) for the following second-order diff erential equation
u''(t) + \lambda a(t)f(u(t)) = 0; 0 < t < 1;
u'(0) = 0; u(1) = \alpha\int\limits_0^{\eta}{u(s)ds},
where \lambda > 0 is a parameter, 0 <\eta < 1, 0 <\alpha < 1/{\eta}.
. By using the properties of the Green's function and Krasnoselskii's fixed point theorem on cones, the eigenvalue intervals of the nonlinear boundary value problem are considered, some sufficient conditions for the existence of at least one positive solutions are established.
In this note we make some remarks on the classical Laguerre’s
theorem and extend it and some other old results of Walsh
and Gauss-Lucas to the so called trace series
associated with transcendental elements of the completion
of the algebraic closure of Q in C, with respect to the spectral
norm:
In this paper we obtain an extension of the concept of Hutchinson measure (which is the unique fi xed point of a contraction on the set of normalized Borel measures on a compact metric space) related to an iterated function system. Our extension means that we consider vector measures (instead of normalized Borel measures) and, also, an uncountable iterated function system instead of a fi nite one, as in the case of Hutchinson measure.
The aim of this paper is to introduce the Cesaro-Orlicz double
difference sequence space Ces_M^{(2)}(△, p). We study some topological properties of this space and give some inclusion relations
Recently, the author established a general inequality for doubly warped products in arbitrary Riemannian manifolds [14]. In the present paper, we obtain a similar inequality for doubly warped products isometrically immersed in S-space forms. As applications, we derive certain obstructions to the existence of minimal isometric immersions of doubly warped product integral submanifolds in
S-space forms.
MARIA MIHAILOVA, ION MIERLUS-MAZILU, EMILIYA VELIKOVA
This article presents the definition of projection plane,
its importance for the geometry constructions used in civil engineering and comparative analysis of three opportunities for creating a three dimensional basis, used in drawing such a plane. First method consists of transforming affine and orthonormal coordinates and its application in GeoGebra is presented. Second method, using combination of spherical and polar coordinates in space, is introduced. The third suggested method is an application of descriptive geometry for transforming 2D to 3D and a new method of forming a plane of projection, which will be used later in the reviewed example below. The example shows how GeoGebra software can be used in technical drawing used in civil engineering.
Using Lotker’s interlacing theorem on the Laplacian eigenvalues
of a graph in [5] and Wang and Belardo’s interlacing theorem on the
signless Laplacian eigenvalues of a graph in [6], we in this note obtain spectral conditions for some Hamiltonian properties of graphs
Let M be a module over a commutative ring R and U a nonempty
proper subset of M. In this paper, a generalization of the total graph
T(Γ(M)), denoted by T(Γ_U (M)) is presented, where U is a multiplicative prime subset of M. It is the graph with all elements of M as vertices, and for two distinct elements m, n ∈ M, the vertices m and n are adjacent if and only if m + n ∈ U. The main purpose of this paper is to extend the definitions and properties given in [1] and [10] to a more general case.
Numerous results on self-reciprocal polynomials over finite fields
have been studied. In this paper we generalize some of these to a-self reciprocal polynomials defined in [4]. We consider some properties of the divisibility of a-reciprocal polynomials and characterize the parity of the number of irreducible factors for a-self reciprocal polynomials over finite fields of odd characteristic.
In this paper, we try to study a special class of frame wavelets in Banach spaces whose Fourier transforms are supported by frame wavelet sets. Our results generalize the various results of [2] to Banach spaces other than Hilbert spaces using the Feichtinger and Grochenig theory.
In this paper we investigate the existence and stability of quadratic-mean almost periodic mild solutions to stochastic delay functional differential equations driven by fractional Brownian motion with Hurst parameter H > 1/2 , under some suitable assumptions,
by means of semigroup of operators and fixed point method.