Some basic concepts for functions defined on subsets of the unit sphere, such as s-directional derivative, s-gradient and s-Gateaux s-Frechet differentiability etc, are introduced investigated. These different from usual ones Euclidean spaces, however, results obtained here very similar. Then, applications, we provide some criterions s-convexity spheres which improvements or refinements known r...

In acoustic seismic-reeection experiments, because of the lack of low frequencies in the usual seismic sources, the reeection of the energy back to the surface is associated to the short wavelengths of the slowness (the reeectivityy parameters), while the long wavelengths of the slowness (the propagatorr parameters) are associated to the kinematics of the arrival times of this energy. Such a de...

Abstract Infinitesimal symmetries of a partial differential equation (PDE) can be defined algebraically as the solutions linearisation (Frechet derivative) holding on space to PDE, and they are well-known comprise linear having structure Lie algebra. Solutions adjoint PDE called adjoint-symmetries. Their algebraic for general systems is studied herein. This motivated by correspondence between v...

We provide a new analysis framework for the adversarial multi-armed bandit problem. Using the notion of convex smoothing, we define a novel family of algorithms with minimax optimal regret guarantees. First, we show that regularization via the Tsallis entropy, which includes EXP3 as a special case, matches the O( √ NT ) minimax regret with a smaller constant factor. Second, we show that a wide ...

The initial value problem for the KdV equation @tu+ u@xu + @ 3 xu = 0; u(x; 0) = (x) establishes a nonlinear map K from H(R) to C([ T; T ];H(R)). It has been known for many years that this map K is continuous [2] , [17] and is proved recently being Lipschitz continuous [23]. In this paper it is shown that the nonlinear map K is in nitely many times Frechet di erentiable from H(R) to C([ T; T ];...

Frechet distance is one of the most fundamental measures used to compute dissimilarity between two sequences of points (e.g., between two signatures recorded by an electronic pen). It is often referred to as the “dog-leash” distance. This is because it corresponds to the minimal length of a “leash” so that a dog and its owner can traverse their respective sequences from beginning to end, while ...

We initiate a study of non-commutative Choquet boundary for spaces unbounded operators. define the notion local representations operator systems in locally C⁎-algebras and prove that provide an intrinsic invariant particular class systems. An appropriate analog purity completely positive maps on is used to characterize Frechet C⁎-algebras.

This article introduces a new family of Generalized Exponentiated Exponential distribution. Using the T-R{Y} framework, T-Exponentiated Exponential{Y} distributions named Exponential{Frechet} is proposed. Some general properties such as hazard rate function, quantile non-central moment, mode, mean absolute deviations and Shannon’s entropy are discussed. A continuous univariate probability distr...

(Thus the subgradients of / correspond to the nonvertical supporting hyperplanes to the convex set consisting of all the points of E®R lying above the graph of /.) The set of subgradients of / at x is denoted by dfix). If d/(x) is not empty, / is said to be subdifferentiable at x. If/actually had a gradient x* = V/(x) at x in the sense of Gateaux (or Frechet), one would in particular have d/(x)...