Based on the Frobenius series method, stresses analysis of the functionally graded rotating thick cylindrical pressure vessels (FGRTCPV) are examined. The vessel is considered in both plane stress and plane strain conditions. All of the cylindrical shell properties except the Poisson ratio are considered exponential function along the radial direction. The governing Navier equation for this pro...

We study how certain invariants of numerical semigroups relate to the number second kind gaps. Furthermore, given two fixed non-negative integers F and k, we provide an algorithm compute all whose Frobenius is which have exactly k

Keywords: Frobenius integrable decompositions Partial differential equations Differential polynomials Bäcklund transformations Ordinary differential equations Nonlinearity a b s t r a c t Frobenius integrable decompositions are presented for a kind of ninth-order partial differential equations of specific polynomial type. Two classes of such partial differential equations possessing Frobenius i...

In this work, we give parametrizations of telescopic numerical semigroups with multiplicity ten and embedding dimension three.
 We also express some its invariants in terms generators these such as the Frobenius number, genus Sylvester number.

We study co-Frobenius and more generally Quasi-co-Frobenius corings over arbitrary baserings and over PF baserings in particular. We generalize some results about (Quasi-) co-Frobenius coalgebras to the case of non-commutative base rings and give several new characterisations for co-Frobenius and Quasi-co-Frobenius corings, some of them are new even in the coalgebra situation. We construct Mori...

We begin with personal notes describing the atmosphere of ”Bogoliubov renormalization group” birth. Then we expose the history of RG discovery in the QFT and of the RG method devising in the mid-fifties. The third part is devoted to proliferation of RG ideas into diverse parts of theoretical physics. We conclude with discussing the perspective of RG method further development and its applicatio...

INTRODUCTION The Cohomological Field Theory was propose by Kontsevich and Manin [5] for description of Gromov-Witten Classes. They prove that Cohomological Field Theory is equivalent to Formal Frobenius manifold. Formal Frobenius manifold is defined by a formal series F , satisfying to associative equations. In points of convergence the series F defines a Frobenius algebras. The set of these po...

We will discuss knapsack problems that arise in certain computational number theory settings. A common theme is that the search space for the standard real relaxation is large; in a sense this translates to a poor choice of variables. Lattice reduction methods have been developed in the past few years to improve handling of such problems. We show explicitly how they may be applied to computatio...

Class field theory relates abelian extensions of a given number field K to certain generalized ideal class groups ofK. The fundamental tool for doing this is Frobenius elements, and the Artin map obtained from them. Recall from lecture 24 that if L/K is an abelian extension (i.e., a Galois extension with abelian Galois group), and p is a prime of OK unramified in OL, then we defined Fr(p) ∈ Gal...

We will discuss knapsack problems that arise in certain computa− tional number theory settings. A common theme is that the search space for the standard real relaxation is large; in a sense this trans− lates to a poor choice of variables. Lattice reduction methods have been developed in the past few years to improve handling of such problems. We show explicitly how they may be applied to comput...