Abstract. In this work, we present a new approach to the construction of variational integrators. In the general case, the estimation of the action integral in a time interval [qk, qk+1] is used to construct a symplectic map (qk, qk+1) → (qk+1, qk+2). The basic idea here, is that only the partial derivatives of the estimation of the action integral of the Lagrangian are needed in the general th...

This paper considers random Hill’s equations in the limit where the periodic forcing function becomes a Dirac delta function. For this class of equations, the forcing strength qk, the oscillation frequency λk, and the period (∆τ)k are allowed to vary from cycle to cycle. Such equations arise in astrophysical orbital problems in extended mass distributions, in the reheating problem for inflation...

Let £ be a partially ordered linear normed space over the field of real numbers whose positive cone K has nonempty interior K0.1 A functional / in E*, the conjugate space of E, is called positive if f(K)^0 and/5^0. A semi-group V of linear operators on E is called positive if r(A7) QK. It will be assumed that T contains the identity operator. This note is concerned with the properties of positi...

We calculate the large Yukawa coupling corrections to the top and bottom scalar quark pair production in e+e− annihilation within the Minimal Supersymmetric Standard Model. For consistency we also include the corrections to the gauge boson propagator enhanced by large masses. The corrections are significant. In some regions of the parameter space they are larger than 10%. PACS numbers: 11.30.Pb...

double system of exponents with complex-valued coefficients is considered. under some conditions on the coefficients, we prove that if this system forms a basis for the morrey-lebesgue type space on $left[-pi , pi right]$, then it is isomorphic to the classical system of exponents in this space.

A number of recessive autosomal genes cause male infertility. Male mice homozygous for the blind-sterile (bs/bs) and quaking-sterile (qk/qk) gene mutations are sterile, because they either do not produce any spermatozoa or produce only a few abnormal spermatozoa. Mice lacking the cyclic AMP responsive-element modulator gene are sterile due to failure of spermiogenesis. All these mice, however, ...

For 0 ≤ k < ∞, let Ωk be the conical domain in the complex plane C defined by Ωk = {w ∈ C : w = u + iv, u2 > k2((u − 1)2 + v2), u > 0}. Let qk(z) be the Riemann map of U := {z ∈ C : |z| < 1} onto Ωk satisfying qk(0) = 1, q′k(0) > 0. Let P (qk) be the class of analytic functions h(z) subordinate in U to qk(z) and represented by h(z) = 1 + b1z + b2z + · · ·, (z ∈ U). Sharp estimates for |b2 − ub1...

We give a criterion for q-valent analytic functions in the unit disk to belong to Q K , a Möbius-invariant space of functions analytic in the unit disk in the plane for a nonde-creasing function K : [0, ∞) → [0, ∞), and we show by an example that our condition is sharp. As corollaries, classical results on univalent functions, the Bloch space, BMOA, and Q p spaces are obtained. 1. Introduction....

Under mild conditions on the weight function K we characterize lacunary series in the so-called QK spaces.

Let z be a real quadratic irrational. We compare the asymptotic behavior of Dedekind sums S(pk, qk) belonging to convergents pk/qk of the regular continued fraction expansion of z with that of Dedekind sums S(sj/tj) belonging to convergents sj/tj of the negative regular continued fraction expansion of z. Whereas the three main cases of this behavior are closely related, a more detailed study of...