The zeroth-order general Randić index of a simple connected graph G is defined as \(R_{\alpha}^{0}(G)=\sum_{u\in V(G)} \big(d(u)\big)^{\alpha}\), where \(d(u)\) is the degree of \(u\) and \(\alpha\not\in \{0,1\}\) is a real number. A \(k\)-polygonal cactus is a connected graph in which every edge lies in exactly one cycle of length \(k\). In this paper, we present the extremal \(k\)-polygonal cactus with \(n\) cycles for \(k\geq3\) with respect to the zeroth-order general Randić index.

The aim of this paper is to present a viscosity approximation method for asymptotically nonexpansive mappings in Banach spaces. The strong convergence of the viscosity rules is proved with some assumptions. This paper extend and improve results presented in [1, 2, 3, 4].

Chemical reaction network theory is an area of applied mathematics that attempts to model the behavior of real world chemical systems. Since its foundation in the 1960s, it has attracted a growing research community, mainly due to its applications in biochemistry and theoretical chemistry. It has also attracted interest from pure mathematicians due to the interesting problems that arise from the mathematical structures involved. In this report, we compute newly defined topological indices, namely, Arithmetic-Geometric index (\(AG_{1}\) index), \(SK\) index, \(SK_{1}\) index, and \(SK_{2}\) index of the Honey Comb Derived Networks. We also compute sum connectivity index and modified Randić index. Moreover we give geometric comparison of our results.

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.