A discussion of an extended class of higher-derivative classical theories of gravity is presented. A procedure is given for exhibiting the new propagating degrees of freedom, at the full non-linear level, by transforming the higher-derivative action to a canonical second-order form. For general fourth-order theories, described by actions which are general functions of the scalar curvature, the ...

The accumulation point of the period-tripling bifurcation cascade in complex quadratic map was discovered by Golberg, Sinai, and Khanin (Russ.Math.Surv. 38:1, 1983, 187), and independently by Cvitanović and Myrheim (Phys.Lett. A94:8, 1983, 329). As we argue, in the extended parameter space of smooth maps, not necessary satisfying the Cauchy – Riemann equations, the scaling properties associated...

The N-extended supersymmetric self-dual Poincaré supergravity equations provide a natural local description of supermanifolds possessing hyperkähler structure. These equations admit an economical formulation in chiral superspace. A reformulation in harmonic superspace encodes self-dual supervielbeins and superconnections in a graded skew-symmetric supermatrix superfield prepotential satisfying ...

We study the logarithmic and ratio asymptotic of linear forms constructed from a Nikishin system which satisfy orthogonality conditions with respect to a system of measures generated from another Nikishin system. This construction combines type I and type II multiple orthogonal polynomials. The logarithmic asymptotic of the linear forms is expressed in terms of the extremal solution of an assoc...

At the end of the 19th century Liouville and Riemann introduced the notion of a fractional-order derivative, and in the latter half of the 20th century the concept of the so-called Grünewald-Letnikov fractional-order discrete difference has been put forward. In the paper a predictive controller for MIMO fractional-order discrete-time systems is proposed, and then the concept is extended to nonl...

We describe a new deterministic algorithm for the problem of constructing k-th power nonresidues in nite elds GF(p n), where p is prime and k is a prime divisor of p n ?1. We prove under the assumption of the Extended Riemann Hypothesis (ERH), that for xed n and p ! 1, our algorithm runs in polynomial time. Unlike previous algorithms for this problem, this polynomial time bound holds even if k ...

Abstract. We consider a problem of P. Erdős, A. M. Odlyzko and A. Sárkőzy about the representation of residue classes modulom by products of two not too large primes. While it seems that even the Extended Riemann Hypothesis is not powerful enough to achieve the expected results, here we obtain some unconditional results “on average” over moduli m and residue classes modulo m and somewhat strong...

Hitchin’s twistor treatment of Schlesinger’s equations is extended to the general isomonodromic deformation problem. It is shown that a generic linear system of ordinary differential equations with gauge group SL(n,C) on a Riemann surface X can be obtained by embedding X in a twistor space Z on which sl(n,C) acts. When a certain obstruction vanishes, the isomonodromic deformations are given by ...

A higher dimensional analogue of the dispersionless KP hierarchy is introduced. In addition to the two-dimensional “phase space” variables (k, x) of the dispersionless KP hierarchy, this hierarchy has extra spatial dimensions compactified to a two (or any even) dimensional torus. Integrability of this hierarchy and the existence of an infinite dimensional of “additional symmetries” are ensured ...

By (extended) Wiener–Ikehara theory, the prime-pair conjectures are equivalent to simple pole-type boundary behavior of corresponding Dirichlet series. Under a weak Riemann-type hypothesis, the boundary behavior of weighted sums of the Dirichlet series can be expressed in terms of the behavior of certain double sums Σ 2k(s). The latter involve the complex zeros of ζ(s) and depend in an essentia...