A selfsimilar manifold is a Riemannian (M,g) endowed with homothetic vector field ξ. We characterize global manifolds and describe the structure of local manifolds. prove that any potential conical or Euclidean space. radiant Hessian (M,∇,g,ξ) such ∇ξ=λId, where λ constant. locally isomorphic to product

In this article, we first obtain an embedding result for the Sobolev spaces with variable-order, and then consider following Schrödinger–Kirchhoff type equations a+b∫Ω×Ω|ξ(x)−ξ(y)|p|x−y|N+ps(x,y)dxdyp−1(−Δ)ps(·)ξ+λV(x)|ξ|p−2ξ=f(x,ξ),x∈Ω,ξ=0,x∈∂Ω, where Ω is a bounded Lipschitz domain in RN, 1<p<+∞, a,b>0 are constants, s(·):RN×RN→(0,1) continuous symmetric function N>s(x,y)p all (x,...

We establish a local existence result for Dirac-Klein-Gordon equations in three space dimensions, employing a null form estimate and a fixed point argument. 0. Introduction and Main Results. In the present work, we like to study the Cauchy problem for the Dirac-Klein-Gordon equations. The unknown quantities are a spinor field ψ : R × R 7→ C and a scalar field φ : R × R 7→ R. The evolution equat...

We consider a pseudodifferential operator defined as follows: Hαφ = ℱ−1[(〈ξ〉α − prα)ℱφ], where 〈ξ〉α (max{|ξ|p, pr})α, and study the Markov process associated with this operator. also analyze first passage time problem Hα for r < 0.

Five Ξ−p→ΛΛ two-body capture events in 12C and 14N emulsion nuclei, which a pair of single-Λ hypernuclei is formed identified by their weak decay, have been observed (K−,K+) exposures at KEK J-PARC. Applying Ξ−-nucleus optical potential methodology to study atomic nuclear transitions, we confirm that these occur from Coulomb assisted 1pΞ− states. Long-range ΞN shell-model correlations are found...

Abstract The Ξ-nuclear potential is investigated in the quark mean-field (QMF) model based on recent results Ξ − + 14 N ( C mathvariant=...

1. (f̂ + g)(ξ) = f̂(ξ) + ĝ(ξ). 2. For any α ∈ C, (α̂f)(ξ) = αf̂(ξ). 3. Let f̄ denote the complex conjugate of f . Then ˆ̄ f(ξ) = f̂(ξ). 4. For λ ∈ R \ {0}, denote fλ(x) = λf(λx). Then f̂λ(ξ) = f̂( ξ λ ). 5. For y ∈ R let (τyf)(t) = f(t− y). Then τ̂yf(ξ) = f̂(ξ)e−2πiξy. 6. |f̂(ξ)| ≤ ‖f‖L1(R). Definition 1.3. The Schwartz space, S(R), is the space of C∞ functions that are rapidly decreasing, in the sense that

The paper the title refers to is that in Proceedings of the Edinburgh Mathematical Society, 40 (1997), 367-374. Taking it as an excuse we intend to realize a twofold purpose: 1o to atomize that important result showing by the way connections which are out of favour, 2o to rectify a tiny piece of history. The objective 1o is going to be achieved by adopting means adequate to goals; it is of grea...

We classify the paracontact Riemannian manifolds that their Riemannian curvature satisfies in the certain condition and we show that this classification is hold for the special cases semi-symmetric and locally symmetric spaces. Finally we study paracontact Riemannian manifolds satisfying R(X, ξ).S = 0, where S is the Ricci tensor.