We consider stochastic algorithms derived from methods for solving deterministic optimization problems, especially comparison-based approximation with a constant step-size. develop methodology proving geometric convergence of the parameter sequence {θn}n⩾0 such algorithms. employ ordinary differential equation (ODE) method, which relates algorithm to its mean ODE, along Lyapunov-like function Ψ...

Let Ψ(t, k) denote the set of pairs (v, λ) for which there exists a graphical t-(v, k, λ) design. Most results on graphical designs have gone to show the finiteness of Ψ(t, k) when t and k satisfy certain conditions. The exact determination of Ψ(t, k) for specified t and k is a hard problem and only Ψ(2, 3), Ψ(2, 4), Ψ(3, 4), Ψ(4, 5), and Ψ(5, 6) have been determined. In this paper, we determin...

J/ψ, a charmonium bound state made of charm and an anti-charm quark, was discovered in the 1970s confirmed quark model. Because mass quarks is significantly above quantum chromodynamics (QCD) scale ΛQCD, charmonia are considered excellent probes to test perturbative (pQCD) calculations. In recent decades, they have been studied extensively at different high-energy colliders. However, their prod...

We argue that the critical behaviour near the point of " gradient catastrophe " of the solution to the Cauchy problem for the focusing nonlinear Schrödinger equation ii ψ t + 2 2 ψ xx + |ψ| 2 ψ = 0 with analytic initial data of the form ψ(x, 0;) = A(x) e i S(x) is approximately described by a particular solution to the Painlevé-I equation.

Let G be a reductive group over a finite field F = Fq. Fix a non-trivial additive character ψ : F → Q × l . In [3] we introduced certain γ-functions γG,ρ,ψ on the set Irr(G) of irreducible representations of the finite group G = G(F ). As usual every function γG,ρ,ψ on Irr(G) gives rise to an AdG-equivariant function ΦG,ρ,ψ on G. The purpose of this paper is to construct an irreducible perverse...

A generalized cusp C is diffeomorphic to [0,∞) times a closed Euclidean manifold. Geometrically C is the quotient of a properly convex domain by a lattice, Γ, in one of a family of affine groups G(ψ), parameterized by a point ψ in the (dual closed) Weyl chamber for SL(n+1,R), and Γ determines the cusp up to equivalence. These affine groups correspond to certain fibered geometries, each of which...

Recently, many scientists have studied a wide range of strategies for solving characteristic types symmetric differential equations, including fractional equations (FDEs). In our manuscript, we obtained sufficient conditions to prove the existence and uniqueness solutions (EUS) FDEs in sense ψ-Caputo derivative (ψ-CFD) second-order 1<α<2. We know that ψ-CFD is generalization previously fa...

and Applied Analysis 3 Theorem3. Letφ, ψ∈H∞(T) orφ,ψ ∈ H(T), the following statements are equivalent: (1.1) U φ and U ψ commute; (1.2) U φ and U ψ essentially commute; (1.3) φ(zk)ψ(z) = φ(z)ψ(z); (1.4) there exist scalars α andβ, not both zero, such that αφ+ βψ = 0. Nowwe start to study the commutativity of two kth-order slant Toeplitz operators with harmonic symbols. Proposition4. Letφ(z)=∑n p...