Abstract. The DSM (dynamical systems method) version of the Newton’s method is for solving operator equation F (u) = f in Banach spaces is discussed. If F is a global homeomorphism of a Banach space X onto X, that is continuously Fréchet differentiable, and the DSM version of the Newton’s method is u̇ = −[F ′(u)]−1(F (u)− f), u(0) = u0, then it is proved that u(t) exists for all t ≥ 0 and is uni...

Quadratic functions are often used in regression to infer the existence of an extremum in a relationship although tests of the location of the extremum are rarely performed. We investigate the construction of the following confidence intervals: Delta, Fieller, estimated first derivative, bootstrapping, Bayesian and likelihood ratio. We propose interpretations for the unbounded intervals that ma...

in this article, a numerical approximation to the solution of the newell-whitehead equation (nwe) and cauchy problem of ill-posed non-linear diffusion equation have been studied. the presented scheme is obtained by using the derivative of the cubic b-spline quasi-interpolation (bsqi) to approximate the spatial derivative of the dependent variable and first order forward difference to approximat...

The notions of N = 1 Neveu-Schwarz vertex operator superal-gebra over a Grassmann algebra and with odd formal variables and of N = 1 Neveu-Schwarz vertex operator superalgebra over a Grass-mann algebra and without odd formal variables are introduced, and we show that the respective categories of such objects are isomorphic. The weak supercommutativity and weak associativity properties for an N ...

We discuss the axioms for vertex algebras and their modules, using formal calculus. Following certain standard treatments, we take the Jacobi identity as our main axiom and we recall weak commutativity and weak associativity. We derive a third, companion property that we call “weak skew-associativity.” This third property in some sense completes an S3-symmetry of the axioms, which is related to...

We give an account of the construction of exterior differential systems based on the notion of tableaux over Lie algebras as developed in [33]. The definition of a tableau over a Lie algebra is revisited and extended in the light of the formalism of the Spencer cohomology; the question of involutiveness for the associated systems and their prolongations is addressed; examples are discussed.

The existence and regularity of Young measure-valued solutions and weak solutions to non-Newtonian flows are considered. Galerkin approximation and an L2 compactness theorem are main ingredients for the proof of the existence of Young measurevalued solutions. Under a certain convexity condition for the energy, we prove that Young measure-valued solutions are weak solutions. Also, for the limite...

In this paper we will provide a new operatorial counterpart of the path-integral formalism of classical mechanics developed in recent years. We call it new because the Jacobi fields and forms will be realized via finite dimensional matrices. As a byproduct of this we will prove that all the operations of the Cartan calculus, such as the exterior derivative, the interior contraction with a vecto...

In In this paper, we introduce two convergent Monte Carlo algorithms for optimizing complex stochastic systems. The first algorithm, which is applicable to to regenerative processes, operates by estimating finite differences. The second method is of Robbins-Monro type and is applicable to to Markov chains. The algorithm is driven by derivative estimates obtained via a likelihood ratio argument. 1.

This work is concerned with the development and validation of two accurate, precise and specific spectrophotometric and chromatographic methods for analysis of Phenylepherine (PE), Lidocaine (LC) and Thiomersal (TM) in their ternary mixture and in Chromoderm® solution. The developed spectrophotometric method is the mean centering of ratio spectra (MCR) spectrophotometric method that depends on ...