We shall present new oscillation criteria of second order nonlinear difference equations with a non-positive neutral term of the form \(\Delta(a(t)(\Delta(x(t)-p(t)x(t-k)))^{\gamma})+q(t)x^{\beta}(t+1-m)=0,\) with positive coefficients. Examples are given to illustrate the main results.

In this work we develop the weighted square integral estimates for the second derivatives of weak subsolution of forth order Laplace equation. It is natural generalization of inequalities develop for the Superharmonic functions in [1].

With the extensive application of ontology in the fields of information retrieval and artificial intelligence, the ontology-based conceptual similarity calculation becomes a hot topic in ontology research. The essence of ontology learning is to obtain the ontology function through the learning of ontology samples, so as to map the vertices in each ontology graph into real numbers, and finally determine the similarity between corresponding concepts by the difference between real numbers. The essence of ontology mapping is to calculate concepts from different ontologies. In this paper, we introduce new ontology similarity computing in view of stochastic primal dual coordinate method, and two experiments show the effectiveness of our proposed ontology algorithm.

The aim of this paper is to present new sixth order iterative methods for solving non-linear equations. The derivation of these methods is purely based on variational iteration technique. Our methods are verified by means of various test examples and numerical results show that our developed methods are more effective with respect to the previously well known methods.

In this paper, dynamics of a two-dimensional Fitzhugh-Nagumo model is discussed. The discrete-time model is obtained with the implementation of forward Euler’s scheme. We present the parametric conditions for local asymptotic stability of steady-states. It is shown that the two-dimensional discrete-time model undergoes period-doubling bifurcation and Neimark-Sacker bifurcation at its positive steady-state. Furthermore, in order to illustrate theoretical discussion some interesting numerical examples are presented.

Let \(D\) be a connected digraph of order \(n\); \((n \geq 3)\) and let \(B(D)=\{B_1,B_2,\ldots,B_N\}\) be a set of blocks of \(D\). The block digraph \(Q=\mathbb{B}(D)\) has vertex set \(V(Q)=B(D)\) and arc set \(A(Q)=B_iB_j\) and \(B_i,B_j \in V(Q),\) \(B_i,B_j\) have a cut-vertex of \(D\) in common and every vertex of \(B_j\) is reachable from every other vertex of \(B_i\) We study the properties of \(\mathbb{B}(D)\) and present the characterization of digraphs whose \(\mathbb{B}(D)\) are planar; outerplanar; maximal outerplanar; minimally nonouterplanar; Eulerian; and Hamiltonian.

In this paper, the notions of fuzzy zero-divisors and fuzzy integral domains are illustrated. Some fundamental properties of fuzzy integral domains are proved. Moreover, the notions of fuzzy regular element and fuzzy regular sequences are defined. It is shown that any permutation (resp. any positive integral power) of a fuzzy regular sequence is again a fuzzy regular sequence. At the end, fuzzy regular sequences of two fuzzy submodules are related with the help of fuzzy short exact sequences.

In 1965, L.A Zadeh inaugurated the idea of fuzzy set theory by extrapolating classical set theory. Later, Atanassov popularized it as an intuitionistic fuzzy set (IFS) more precisely than the fuzzy logic theory in 1983. IFS is highly fruitful in expounding uncertain situations which we face in decision making. In this paper, we have reexamined the idea of IFS and suggested the applications in decision making methods. Moreover, this theory helps us find the solution of one-shot decision (OSD) problems we mostly face in trade and economics, and the behavior of the decision person and assists them to get the best answer.

A line graph has many useful applications in physical chemistry. Topological indices are numerical parameters associated to a structure and, in combination, determine properties of the concerned material. In this paper, we compute the closed form of Zagreb polynomilas of all generalized class of carbon nanocones and compute important degree-based topological indices.

Unsteady free convection flow of Casson fluid over an unbounded upright plate subject to time dependent velocity \(U_{o}f(t)\) with constant wall temperature has been carried out. By introducing dimensionless variables, the general solutions are obtained by Laplace transform method. The solution corresponding to Newtonian fluid for \(\gamma \rightarrow \infty\) is obtained as a limiting case. Exact solutions corresponding to (i) \(f(t)=f H(t)\), (ii) \(f(t)=f t^{a}\), \(a > 0 \) (iii) \( f(t)=f H(t)cos(\omega t)\) are also discussed as special cases of our general solutions. Expressions for shear stress in terms of skin friction and the rate of heat transfer in the form of Nusselt number are also presented. Velocity and temperature profiles for different parameters are discussed graphically.Free convection; Time depending velocity; Exact solutions; Casson fluid; Vertical plate.