The eccentricity of a vertex $v$ is the maximum distance between $v$ and anyother vertex. A vertex with maximum eccentricity is called a peripheral vertex.The peripheral Wiener index $ PW(G)$ of a graph $G$ is defined as the sum ofthe distances between all pairs of peripheral vertices of $G.$ In this paper, weinitiate the study of the peripheral Wiener index and we investigate its basicproperti...

We investigate the problem of using a Riemannian sum with random subintervals to approximate the iterated Itô integral ∫ w dw—or, equivalently, solving the corresponding stochastic differential equation by Euler’s method with variable step sizes. In the past this task has been used as a counterexample to illustrate that variable step sizes must be used with extreme caution in stochastic numeric...

A key challenge in game design is achieving balance between the strategies available to the players. Traditionally this has been done through playtesting, with its difficult requirements of time, labor, and interpretation of results. To make it quicker and easier to balance games, we propose a game-theoretic approach that automatically balances strategies based on a mathematical model of the ga...

Let G be the chemical graph of a molecule. The matrix D = [dij ] is called the detour matrix of G, if dij is the length of longest path between atoms i and j. The sum of all entries above the main diagonal of D is called the detour index of G. In this paper, a new algorithm for computing the detour index of molecular graphs is presented. We apply our algorithm on copper and silver nanoclusters ...

This paper describes a method for the automatic evaluation of the Links– Gould two-variable polynomial link invariant (LG) for any link, given only a braid presentation. This method is currently feasible for the evaluation of LG for links for which we have a braid presentation of string index at most 5. Data are presented for the invariant, for all prime knots of up to 10 crossings and various ...

This article describes a Bayesian hierarchical model for factor analysis of spatially correlated multivariate data. The Ž rst level speciŽ es, for each area on a map, the distribution of a vector of manifest variables conditional on an underlying latent factor; at the second level, the areaspeciŽ c latent factors have a joint distribution that incorporates spatial correlation. The framework all...

In this paper, a new method for estimating the linear regression coefficients approximation is presented based on Z-numbers. In this model, observations are real numbers, regression coefficients and dependent variables (y) have values ​​for Z-numbers. To estimate the coefficients of this model, we first convert the linear regression model based on Z-numbers into two fuzzy linear regression mode...

The VSIDS (variable state independent decaying sum) decision heuristic invented in the context of the CDCL (conflict-driven clause learning) SAT solver Chaff, is considered crucial for achieving high efficiency of modern SAT solvers on application benchmarks. This paper proposes ACIDS (average conflict-index decision score), a variant of VSIDS. The ACIDS heuristics is compared to the original i...

In this paper, we compute ABC index, Randic connectivity index, Sum connectivity index, GA index, Harmonic index, General Randic index of Triglyceride. AMS subject classification: