In this paper, we study the two following minimization problems: S0(q, φ) = inf u∈H2 0 (Ω),‖u+φ‖q=1 ∫ Ω | u|2 and Sθ (q, φ) = inf u∈H2 θ (Ω),‖u+φ‖q=1 ∫ Ω | u|2. We prove that for a class of maps φ, we have Sθ (q, φ) < S0(q, φ) and for another class, we have Sθ (q, φ) = S0(q, φ). c © 2005 Elsevier Ltd. All rights reserved.

Let p be a prime and let φ ∈ Zp[x1, x2, . . . , xp] be a symmetric polynomial, where Zp is the field of p elements. A sequence T in Zp of length p is called a φ-zero sequence if φ(T ) = 0; a sequence in Zp is called a φ-zero free sequence if it does not contain any φ-zero subsequence. Define g(φ, Zp) to be the smallest integer l such that every sequence in Zp of length l contains a φ-zero seque...

and Applied Analysis 3 In the sequel, let q > 1 4p and . . . , φ, ψ, φ, ψ, . . . the unique prime period-two solution of 1.1 with φ < ψ. Define f ∈ C φ, ψ × φ, ψ , φ, ψ by f ( x, y ) p y qx y 2.2 for any x, y ∈ φ, ψ and g ∈ C φ, ψ , φ, ψ by y∗ g ( y ) p y − y2 qy 2.3 for any y ∈ φ, ψ . Then

Let n > 2 be a positive integer and let φ denote Euler’s totient function. Define φ(n) = φ(n) and φ(n) = φ(φ(n)) for all integers k ≥ 2. Define the arithmetic function S by S(n) = φ(n) + φ(n) + · · ·+ φ(n) + 1, where φ(n) = 2. We say n is a perfect totient number if S(n) = n. We give a list of known perfect totient numbers, and we give sufficient conditions for the existence of further perfect ...

Let W a be an affine Weyl group. In 1987 Jian Yi Shi gave characterization of the elements w∈W in terms Φ + -tuples (k(w,α)) α∈Φ called vectors. Using these coefficients, formula is provided to compute standard length . this note we express twisted function coefficients.

We study the way isospin symmetry violation can be generated within the Hidden Local Symmetry (HLS) Model. We show that isospin symmetry breaking effects on pseudoscalar mesons naturally induces correspondingly effects within the physics of vector mesons, through kaon loops. In this way, one recovers all features traditionally expected from ρ−ω mixing and one finds support for the Orsay phase m...

ion Rules Abst1: Variable instantiations with essential ground terms of complexity r (using a modified version of our work [SMT’2013]) Abst2: φ := (l ∨ φrest), (¬l ∨ Crest) ∈ CNF (F ) =⇒ φ φ[Crest / l ] Abst3: φ := (¬φ(t) ∨ φrest), t := pg =⇒ φ φ[(∀x . x = t ∨ (t, x)d ∈ tcR → φ(x)) / φ(t)]

Radiative φ decays give us an excellent opportunity to study scalar and pseudoscalar mesons below 1 GeV. In this paper, results from different experiments are reviewed and compared.

Using Fourier analysis, we study local limit theorems in weak-convergence problems. Among many applications, we discuss random matrix theory, some probabilistic models in number theory, the winding number of complex brownian motion and the classical situation of the central limit theorem, and a conjecture concerning the distribution of values of the Riemann zeta function on the critical line.