Motivated by a discrete-time process intended to measure the speed of the spread of contagion in a graph,the burning number b(G)of a graph G,is defined as the smallest integer k for which there are vertices x1,…xk su...Motivated by a discrete-time process intended to measure the speed of the spread of contagion in a graph,the burning number b(G)of a graph G,is defined as the smallest integer k for which there are vertices x1,…xk such that for every vertex u of G,there exists i∈{1,…k}with dG(u,xi)≤k−i,and dG(xi,xj)≥j−i for any 1≤i<j≤k.The graph burning problem has been shown to be NP-complete even for some acyclic graphs with maximum degree three.In this paper,we determine the burning numbers of all short barbells and long barbells,respectively.展开更多
This article studies effects of heat generation/absorption and chemical reaction on the unsteady magnetohydrodynamic(MHD)Casson fluid flow past over exponentially accelerated vertical plate embedded in porous medium.I...This article studies effects of heat generation/absorption and chemical reaction on the unsteady magnetohydrodynamic(MHD)Casson fluid flow past over exponentially accelerated vertical plate embedded in porous medium.It is assumed that the bounding plate has ramped temperature with ramped surface concentration and isothermal temperature with ramped surface concentration.This phenomenon is modeled in the form of system of partial differential equations with initial and boundary conditions.The goveming dimensionless equations are solved using Laplace transfom technique and expressions for velocity,temperature and concentration profiles are obtained.Expressions for skin friction,Nusselt number and Sherwood number are also derived and represented in tabular form.Effect of pertinent parameters on velocity,temperature and concentration profiles are presented through graphically.展开更多
A stochastic approximation (SA)algorithm with new adaptive step sizes for solving unconstrained minimization problems in noisy environment is proposed.New adaptive step size scheme uses ordered statistics of fixed num...A stochastic approximation (SA)algorithm with new adaptive step sizes for solving unconstrained minimization problems in noisy environment is proposed.New adaptive step size scheme uses ordered statistics of fixed number of previous noisy function values as a criterion for accepting good and rejecting bad steps.The scheine allows the algorithm to move in bigger steps and avoid steps proportional to 1/k when it is expected that larger steps will improve the performance.An algorithin with the new adaptive scheme is defined for a general descent direction.The ahnost sure convergence is established.The performance of new algorithm is tested on a set of standard test problems and compared with relevant algorithms.Numerical results support theoretical expectations and verify efficiency of the algorithm regardless of chosen search direction and noise level.Numerical results on probleins arising in machine learning are also presented.Linear regression problem is considered using real data set.The results suggest that the proposed algorithln shows proinise.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11971158,12371345,11971196).
文摘Motivated by a discrete-time process intended to measure the speed of the spread of contagion in a graph,the burning number b(G)of a graph G,is defined as the smallest integer k for which there are vertices x1,…xk such that for every vertex u of G,there exists i∈{1,…k}with dG(u,xi)≤k−i,and dG(xi,xj)≥j−i for any 1≤i<j≤k.The graph burning problem has been shown to be NP-complete even for some acyclic graphs with maximum degree three.In this paper,we determine the burning numbers of all short barbells and long barbells,respectively.
文摘This article studies effects of heat generation/absorption and chemical reaction on the unsteady magnetohydrodynamic(MHD)Casson fluid flow past over exponentially accelerated vertical plate embedded in porous medium.It is assumed that the bounding plate has ramped temperature with ramped surface concentration and isothermal temperature with ramped surface concentration.This phenomenon is modeled in the form of system of partial differential equations with initial and boundary conditions.The goveming dimensionless equations are solved using Laplace transfom technique and expressions for velocity,temperature and concentration profiles are obtained.Expressions for skin friction,Nusselt number and Sherwood number are also derived and represented in tabular form.Effect of pertinent parameters on velocity,temperature and concentration profiles are presented through graphically.
文摘A stochastic approximation (SA)algorithm with new adaptive step sizes for solving unconstrained minimization problems in noisy environment is proposed.New adaptive step size scheme uses ordered statistics of fixed number of previous noisy function values as a criterion for accepting good and rejecting bad steps.The scheine allows the algorithm to move in bigger steps and avoid steps proportional to 1/k when it is expected that larger steps will improve the performance.An algorithin with the new adaptive scheme is defined for a general descent direction.The ahnost sure convergence is established.The performance of new algorithm is tested on a set of standard test problems and compared with relevant algorithms.Numerical results support theoretical expectations and verify efficiency of the algorithm regardless of chosen search direction and noise level.Numerical results on probleins arising in machine learning are also presented.Linear regression problem is considered using real data set.The results suggest that the proposed algorithln shows proinise.
