Volume 2 (2018)

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

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 $n$; $(n\ge 3)$ and let $B(D)=\{B_1,B_2,\dots ,B_N\}$ be a set of blocks of $D$. The block digraph $Q=\mathbb{B}(D)$ has vertex set $V(Q)=B(D)$ and arc set $A(Q)=B_i{B}_j$ 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.

In this paper we have presented a new method to compute the determinant of a $5\times 5$ matrix.

In this paper, some inequalities related to Čebyšev’s functional are proved.

For any graph $G=(V,E)$, lict graph $\eta (G)$ of a graph $G$ is the graph whose vertex set is the union of the set of edges and the set of cut-vertices of $G$ in which two vertices are adjacent if and only if the corresponding edges are adjacent or the corresponding members of $G$ are incident. A secure lict dominating set of a graph $\eta (G)$ , is a dominating set $F\subseteq V(\eta (G))$ with the property that for each $v_1\in (V(\eta (G))-F)$, there exists $v_2\in F$ adjacent to $v_1$ such that $(F-\{v_2\})\cup \{v_1\}$ is a dominating set of $\eta (G)$. The secure lict dominating number ${\gamma }_{se}(\eta (G))$ of $G$ is a minimum cardinality of a secure lict dominating set of $G$. In this paper many bounds on ${\gamma }_{se}(\eta (G))$ are obtained and its exact values for some standard graphs are found in terms of parameters of $G$. Also its relationship with other domination parameters is investigated.