Group of automorphisms of the ring ℤA4

The structure of the group of automorphisms of the integer group ring of the group A₄ is studied in terms of a semidirect product. We show that the Zassenhaus conjecture on the structure of automorphisms of integer group rings of finite groups for the group Aut ?A₄ holds.     

On the structure of Δ 1 4 -sets of reals

Assuming that an inaccessible cardinal exists, we construct a ZFC-model where every ₁ ⁴ -set is measurable but there exists a ₁ ⁴ -set without the property of Baire. By a result of Shelah, an inaccessible cardinal is necessary for this result.The author is partially supported by the Basic Research Foundation of the Israel Academy of Sciences and by the Swiss National Funds.     

The analysis of the number of fixed points in the key extending algorithm of RC4

The probabilities of the state transitions of the initial value So in the S table of RC4 are described by a kind of bistochastic matrices, and then a computational formula for such bistochastic matrices is given, by which the mathematical expectation of the number of fixed points in the key extending algorithm of RC4 is obtained. As a result, a statistical weakness of the key extending algorithm of RC4 is presented.     

The Geometry of the Lie Algebra of the Orthogonal Group O(ℝ4)

In the six-dimensional space of bivectors, a Lie product similar to the standard vector product in is introduced. The Lie algebra constructed is proved to be isomorphic to the Lie algebra of the orthogonal group , and the isomorphism is a canonical isometry between and the space of antisymmetric operators in . Bibliography: 2 titles.     

Graphlike Manifolds with the Type of the 1—skeleton of a 4—simplex

ＧｒａｐｈｌｉｋｅＭａｎｉｆｏｌｄｓｗｉｔｈｔｈｅＴｙｐｅｏｆｔｈｅ１－ｓｋｅｌｅｔｏｎｏｆａ４－ｓｉｍｐｌｅｘＧｕｏＴｕｏｙｉｎｇ（ＨｕａｚｈｏｎｇＮａｒｍａｌＵｎｉｖｅｒｓｄｙ，Ｗｕｈａｎ，Ｃｈｉｎａ）（郭驼英）ｈＴｈｅｃｏｎｃｅｐｔｏｆｇｒａｐ...     

White Noise Approach to the Construction of Φ4 4 Quantum Fields

In this paper by Sobolev imbedding theorem and characterization theorem of generalized operators the existence of ₄ ⁴ quantum fields as generalized operators is obtained with space cut-off and a rigorous mathematical interpretation of renormalization procedure is given under white noise theory.     

Willmore Surfaces of ?4 and the Whitney Sphere

We make a contribution to the study of Willmore surfaces infour-dimensional Euclidean space ⁴ by making useof the identification of ⁴ with two-dimensionalcomplex Euclidean space ². We prove that theWhitney sphere is the only Willmore Lagrangian surface of genus zero in⁴ and establish some existence and uniquenessresults about Willmore Lagrangian tori in ^{4 2}.     

On the 2- and 4-dissections of the Rogers–Ramanujan functions

Basil Gordon showed that if the two Rogers–Ramanujan functions are expanded as series, in each case half the coefficients are almost always even. In order to do this, he gave formulae modulo 2 for the 2-dissections of each of the Rogers–Ramanujan functions. In this paper we give the exact 2- and 4-dissections. We then show how our 2-dissections lead to Gordon’s formulae, we go on to give examples of what he calls “linear zero congruences modulo 2” , and finally we give a simple proof of Gordon’s main result that \(g(2n+1)\) and \(h(2n)\) are almost always even.     

Geometry of plane sections of the infinite regular skew polyhedron {4, 6 | 4}

The asymptotic behavior of open plane sections of triply periodic surfaces is dictated, for an open dense set of plane directions, by an integer second homology class of the three-torus. The dependence of this homology class on the direction can have a rather rich structure, leading in special cases to a fractal. In this paper we present in detail the results for the skew polyhedron {4, 6 | 4} and in particular we show that in this case a fractal arises and that such a fractal can be generated through an elementary algorithm, which in turn allows us to verify for this case a conjecture of Novikov that such fractals have zero measure.      

Symmetry algebra of the AdS4×ℂℙ3 superstring

By direct calculation in the classical theory, we derive the central extension of the off-shell symmetry algebra for a string propagating in AdS ₄ ×?? ³ . It turns out to be the same as in the case of the AdS ₅ ×S ⁵ string. We consider the choice of the κ-symmetry gauge in detail and also explain how this gauge can be chosen without breaking the bosonic symmetries.     

On the Small Time Asymptotics of the Dynamical Φ_1~4Model

In this paper,we establish a small time large deviation principle (small time asymptotics)f_√or the dynamicalΦ_1~4model,which not only involves study of the space-time white noise with intensity■,but also the investigation of the effect of the small (withε) nonlinear drift.     

The K°-relation on the Congruence Lattice of a Regular Semigroup with an Inverse Transversal

Let S be a regular semigroup with an inverse transversal S° and C(S) the congruence lattice of S. A relation K° on C(S) is introduced as follows: if ρ, θ∈ C(S), then we say that ρ and θ are K°-related if Ker ρ° = Ker θ° , where ρ° = ρ|S°. Expressions for the least and the greatest congruences in the same K°-class as ρ are provided. A number of equivalent conditions for K° being a congruence are given.     

On the primality of 2h·3n+1

We consider the primality test of Williams and Zarnke for rational integers of the form 2h·3ⁿ+1. We give an algebraic proof of the test, and we resolve a sign ambiguity. We also show that the conditions of the original test can be relaxed, especially if h is divisible by a power of 2.