The sigma model approach to the closed bosonic string on the affine-metric manifold is considered. The two-loop metric counterterms for the nonlinear twodimensional sigma model with affine-metric target manifold are calculated. The correlation of the metric and affine connection is considered as the result of the conformal invariance condition for the nonlinear sigma model. The examples of the ...

The close form of some integrals involving recently developed generalized k-Struve functions is obtained. The outcome of these integrations is expressed in terms of generalized Wright functions. Several special cases are deduced which lead to some known results.

Explicit closed forms are derived for the probability density function of the stable distribution Sα(β, γ, μ), α ∈ (1, 2]. Consequent asymptotic expansions are given. The expressions involve the Srivastava-Daoust generalized Kampé de Fériet hypergeometric S-function, the Fox-Wright generalized hypergeometric Ψ-function, and the Gauss hypergeometric function 2F1. 2000 Mathematics subject classif...

for all a, b ∈ E and 0 ≤ t ≤ 1. Equivalently, f is affine if the map T :E → F , defined by Tx = fx− f(0), is linear. An isometry need not be affine. To see this, let E be the real line R, let F be the plane with the norm ‖x‖ = max(|x1|, |x2|), and let φ:R → R be any function such that |φ(s)−φ(t)| ≤ |s−t| for all s, t ∈ R, for example, φ(t) = |t| or φ(t) = sin t. Setting f(s) = (s, φ(s)) we get ...

In this paper, we consider minimization of a real-valued function f over R and study the choice of the affine normal of the level set hypersurfaces of f as a direction for minimization. The affine normal vector arises in affine differential geometry when answering the question of what hypersurfaces are invariant under unimodular affine transformations. It can be computed at points of a hypersur...

In this paper we investigate aspects of rigidity and flexibility for conformal iterated function systems. For the case in which the systems are not essentially affine we show that two such systems are conformal equivalent if and only if in each of their Lyapunov spectra there exists at least one level set such that the corresponding Gibbs measures coincide. We then proceed by comparing this res...

We examine the affine Wigner distribution from a quantization perspective with an emphasis on underlying group structure. One of our main results expresses scalogram as (affine) convolution distributions. strive to unite literature distributions and we provide connection Mellin transform in rigorous manner. Moreover, present ambiguity function show how this can be used illuminate properties dis...

Let $$\mathbb {K}$$ be an uncountable field of characteristic zero and let f a function from {K}^n$$ to . We show that if the restriction every affine plane $$L\subset \mathbb is regular, then regular function.

We consider a two-stage adaptive linear optimization problem under right hand side uncertainty with a min–max objective and give a sharp characterization of the power and limitations of affine policies (where the second stage solution is an affine function of the right hand side uncertainty). In particular, we show that the worst-case cost of an optimal affine policy can be (m1/2−δ) times the w...