We give an elementary proof of optimality conditions for linear programming. The proof is direct, built on a straightforward classical perturbation of the constraints, and does not require either the use of Farkas’ lemma or the use of the simplex method.

recent studies show significant reduction of postural stability in transtibial amputees (ttas) especially when a perturbation is applied. however, no record has been seen on the consequences of such perturbation on the stump-socket interface pressure (ssip). our objective was to investigate whether such perturbation impose excessive pressures on the stump. we were also interested on the type of...

abstract background: several studies have examined the reflex response of ankle musculature to sudden inversion in noninjured and injured subjects. to date, there have been no studies to determine the effect of versatile degrees & conditions of perturbation on the ankle musculature latency. the purpose of this study was to measure and determine whether there was a difference in ankle musculatur...

singular perturbation problems have been studied by many mathematicians. since the approximate solutions of these problems are as the sum of internal solution (boundary layer area) and external ones, the formation or non-formation of boundary layers should be specified. this paper, investigates this issue for a singular perturbation problem including a first order differential equation with gen...

In this issue of Neuron, Lee et al. (2016) assessed the brain-wide effects of stimulating the direct and indirect pathway by optogenetic activation of D1 and D2 striatal neurons. This work demonstrates the exquisite power of combining cell-type-specific perturbation methods with focal and whole-brain measurements of brain activity.

In this paper, the homotopy perturbation method (HPM) is considered for finding approximate solutions of two-dimensional viscous flow. This technique provides a sequence of functions which converges to the exact solution of the problem. The HPM does not need a small parameters in the equations, but; the perturbation method depends on small parameter assumption and the obtained results. In most ...

the present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. the proposed scheme is based on laplace transform and new homotopy perturbation methods. the fractional derivatives are considered in caputo sense. to illustrate the ability and reliability of the method some examples are provided. the results ob...

In this paper we examine fluctuation and frequency of the governing equation ofoscillator with odd and even nonlinearities without damping and we present a new efficientmodification of the He’s homotopy perturbation method for this equation. We applied standard andmodified homotopy perturbation method and compare them with the numerical solution (NS), also weapplied He’s Energy balance method (...

The standard approach for identifying gene networks is based on experimental perturbations of gene regulatory systems such as gene knock-out experiments, followed by a genome-wide profiling of differential gene expressions. However, this approach is significantly limited in that it is not possible to perturb more than one or two genes simultaneously to discover complex gene interactions or to d...