saac \ewlon, considefed by Albcrt l j lnstein t0 bc thc grcatost physlcist who cver l ived, workcd in both science and tltcokrgy. tle believcd that, tire methuds rut sciencc could and should be uscd to dem0nstrate the cxistence ofGod. Ht: cxprcssed it, this way: "Whcn I wr0te my treatise about, the Isolarl system, I had an eye upon such pr inciples as might work with cOnsidering men for the bel...

2014 Intrinsic defects tend to oscillate relative to the domains in the two-phase region of the orientational transformation. When the solid is treated as a continuous elastic medium, the vibrational frequencies of vacancies and mobile dislocations are found to decrease as (To T)1/3 and | T0 T |1/2, respectively, near the transition point To. From the ultrasonic excitation of the soft mode of d...

In this paper we give a characterization for the uniform exponential stability of evolution families {Φ(t, t0)}t≥t0 on R+ that do not have an exponential growth, using the hypothesis that the pairs of function spaces (L1(X), L∞(X)) and (Lp(X), Lq(X)), (p, q) 6= (1,∞), are admissible to the evolution families.

Abstract We introduce some properties of the new better than used in convex ordering at age t0 (NBUC − t0) and new better than used of second order(2) at age t0 (NBU(2)−t0) classes of life distributions,where the survival probability at age 0 is greater than or equal to the conditional survival probability at specified age t0 > 0. Preservation properties of the two classes under various reliabi...

We study the Aharonov–Bohm conductance oscillations of a constriction with an antidot in the fractional quantum Hall regime using a recently proposed composite-fermion Fermi liquid theory, and also using Wen’s chiral Luttinger liquid theory extended to include mesoscopic effects. The predictions of the composite-fermion Fermi liquid theory are very similar to standard Fermi liquid theory and ar...

Let (R, g(t)), 0 ≤ t ≤ T , n ≥ 3, be a standard solution of the Ricci flow with radially symmetric initial data g0. We will extend a recent existence result of P. Lu and G. Tian and prove that for any t0 ∈ [0, T ) there exists a solution of the corresponding harmonic map flow φt : (R, g(t)) → (R, g(t0)) satisfying ∂φt/∂t = ∆g(t),g(t0)φt of the form φt(r, θ) = (ρ(r, t), θ) in polar coordinates i...

and Applied Analysis 3 Then for each B ∈ B, L problem 1.1 , 2.1 has a unique solution u. If B / 0, then the solution u is damped and oscillatory with decreasing amplitudes and lim t→∞ u t 0. 2.4 Proof. The assertion follows from Theorems 2.3, 2.10 and 3.1 in 19 . Example 2.3. The functions i p t t, p t t ln t 1 , k, ∈ 0,∞ , ii p t t α sin t, α ∈ −1, 1 , iii p t t/ 1 t , k, ∈ 0,∞ , < k satisfy 1...

Recall the setting at the end of the previous lecture: A is an abelian variety over a field F of characteristic zero, with dimension g > 0. Let L be a number field of degree 2g over Q “acting” on A; that is, we have an embedding L ↪→ End(A). The elements of L that actually act on A – i.e., O := L ⋂ End(A) – form an order in L. Since char(F ) = 0, the action of O on T0(A) (a g-dimensional F -vec...

and Applied Analysis 3 delay. In the end, an example is provided to illustrate the effectiveness and the advantages of the results obtained. 2. Preliminaries Let R denote the set of real numbers, R the set of nonnegative real numbers, Z the set of positive integers, and R the n-dimensional real space equipped with the Euclidean norm | · |. Let τ > 0 and PC −τ, 0 ;R {φ : −τ, 0 → Rn|φ t φ t for a...