A new test for E-infinity fractal-spacetime theory

E-infinity theory is the analytical version of fractal-spacetime theory; the other is simulational fractal-spacetime theory. It is proposed that E-infinity theory can be used to calculate the size – and by implication the threshold energy for their formation – of microscopic black holes. This prospect is of great interest in the context of the Large–Hadron–Collider (LHC) experiment which may or may not produce miniblack holes at energies eight times higher than ever tried before.     

Equivalence of Many-Photon Green's Functions in the Duffin–Kemmer–Petiau and Klein–Gordon–Fock Statistical Quantum Field Theories

Using the functional integral formalism for the statistical generating functional in the statistical (finite temperature) quantum field theory, we prove the equivalence of many-photon Green's functions in the Duffin–Kemmer–Petiau and Klein–Gordon–Fock statistical quantum field theories. As an illustration, we calculate the one-loop polarization operators in both theories and demonstrate their coincidence.     

Applying fuzzy weighted average approach to evaluate office layouts with Feng–Shui consideration

Office layout is an important issue, especially in China and the Asian countries, where the Feng–Shui theory frequently plays a vital role. Yet, in the literature, Feng–Shui theory has seldom been discussed. Another problem is the imprecise or vague satisfaction level of the linguistic expression used in this theory. In this article, the fuzzy set theory is applied to deal with this aspect of the problem. Using an improved and efficient fuzzy weighted average (EFWA) algorithm, which has been shown to be more advantageous than the existing FWA algorithms, an empirical study of an office-layout design problem with the consideration of Feng–Shui is presented to illustrate the EFWA approach. The results and the criteria developed, based on the interpretation of the Form school concept of the Feng–Shui are reported.     

Melting of Two-Dimensional Systems: Dependence of the Type of Transition on the Radius of the Potential

In the framework of the two-dimensional melting theory based on the density functional approach, we use a Monte Carlo computer simulation to study melting of a two-dimensional hard disk system with a rectangular-well attraction potential. We show that depending on the attraction radius, the melting can occur via a single first-order transition as well as continuously in accordance with the Kosterlitz–Thouless–Halperin–Nelson–Young theory.     

Universal (Co) Homology Theories

It is shown that the homology and cohomology theories on separable C*–algebras given by nonstable E–theory are the universal such theories. By specializing to Abelian C*–algebras, we obtain a family of extraordinary Steenrod homology and cohomology theories on pointed compact metric spaces which are the universal such theories in the same way. For each of the extraordinary Steenrod (co)homology theories considered, we describe an –spectrum which represents the theory.     

Corrigendum to “A note on the Loewenstein–Prelec theory of intertemporal choice” [Math. Social Sci. 52 (1) (2006) 99–108]

In a critique of the Loewenstein and Prelec [Loewenstein G., Prelec D., 1992. Anomalies in intertemporal choice: Evidence and an interpretation. The Quarterly Journal of Economics 107, 573–597] theory of intertemporal choice, [al-Nowaihi, A., Dhami, S., 2006. A note on the Loewenstein–Prelec theory of intertemporal choice. Mathematical Social Sciences 52, 99–108] point out four errors. One of the alleged errors was that the elasticity of the value function in prospect theory is decreasing. But it is in fact increasing. We provide a correction and a formal proof. As a corollary, we show that the elasticity of the value function is bounded between zero and one. Nevertheless, all the remaining points in [al-Nowaihi, A., Dhami, S., 2006. A note on the Loewenstein–Prelec theory of intertemporal choice. Mathematical Social Sciences 52, 99–108] remain valid     

The use of the Sherman–Morrison–Woodbury formula to solve cyclic block tri-diagonal and cyclic block penta-diagonal linear systems of equations

The article presents a new theoretical viewpoint of Batista’s algorithms for solving cyclic tri-diagonal (and penta-diagonal) linear systems. The theory is based on the Sherman–Morrison–Woodbury formula.     

Superrigidity for homomorphisms into isometry groups of CAT(−1) spaces

CAT(–1) spaces are generalizations of manifolds with negative curvature. In this paper, we prove three types of rigidity results related to CAT(–1) spaces, namely the rigidity of the isometric actions on CAT(–1) spaces under the commensurability subgroups, the higher rank lattices and certain ergodic cocycles. The main idea for our approach relies on a study of the boundary theory we established for the general CAT(–1) spaces.     

On M. G. Krein's papers in the theory of spaces with an indefinite metric

This is a survey of the papers by M. G. Krein (and his disciples) devoted to the theory of operators in spaces with an indefinite metric and its applications.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, Nos. 1–2, pp. 5–17, January–February, 1994.     

The WDVV Equations in Pure Seiberg–Witten Theory

We review the relationship between pure four-dimensional Seiberg–Witten theory and the periodic Toda chain. We discuss the definition of the prepotential and give two proofs that it satisfies the generalized Witten–Dijkgraaf–Verlinde–Verlinde equations. A number of steps in the definitions and proofs that is missing in the literature is supplied.Mathematics Subject Classifications (2000) 14H10, 14H20, 14H40, 14H70, 14D45.     

Formal and precise derivation of the Green functions for a simple potential

In formal scattering theory, the Green functions are obtained as solutions of a distributional equation. In this paper, we use the Sturm–Liouville theory to compute the Green functions within a rigorous mathematical theory. We shall show that both the Sturm–Liouville theory and the formal treatment yield the same Green functions. We shall also show how the analyticity of the Green functions as functions of the energy keeps track of the so-called “incoming” and “outgoing” boundary conditions.     

Theory of self-adjoint extensions of symmetric operators. entire operators and boundary-value problems

This is a brief survey of M. G. Krein's contribution to the theory of self-adjoint extensions of Hermitian operators and to the theory of boundary-value problems for differential equations. The further development of these results is also considered.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, Nos. 1–2, pp. 55–62, January–February, 1994.     

Exponential Sums and Coding Theory: A Review

This article is a survey of several recent applications of methods from analytic number theory to research in coding theory, including results on Kloosterman codes, binary Goppa codes, and prime phase shift sequences. The mathematical methods focus on exponential sums, in particular Kloosterman sums. The interrelationships with the Weil–Carlitz–Uchiyama bound, results on Hecke operators, theorems of Bombieri and Deligne and the Eichler–Selberg trace formula are reviewed.     

Concerning the static-geometric analogy and the complex equations of Timoshenko-type shell theory

The static-geometric analogy of the classical Kirchhoff-Love shell theory, established by Gol'denveizer, is extended to the theory (Timoshenko type) in which transverse shear strains are taken into account [1, 2, 7, 8]. The construction of the complex equations of this theory is discussed.Franko L'vov State University; L'vov Polytechnic Institute. Translated from Mekhanika Polimerov, No. 5, pp. 942–945, September–October, 1969.     

Coverings and Integrability of the Gauss–Mainardi–Codazzi Equations

Using the covering theory approach (zero-curvature representations with the gauge group SL), we insert the spectral parameter into the Gauss–Mainardi–Codazzi equations in Chebyshev and geodesic coordinates. For each choice, four integrable systems are obtained.     

On M. G. Krein's work in the theory of linear periodic Hamiltonian systems

We present basic ideas of the theory of linear periodic Hamiltonian systems.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, Nos. 1–2, pp. 128–144, January–February, 1994.     

Yang–Mills Theory over Compact Symplectic Manifolds

In this paper, Yang–Mills theory over a compactKähler manifold is naturally extended to a compactsymplectic manifold. The relation betweenthe Yang–Mills equation and symplecticstructure is explicitly clarified, and the moduli spaceof Yang–Mills connections over a compactsymplectic manifold is constructed. Furthermore, theabsolute minima of the Yang–Mills functional arecharacterized, and finite dimensionality ofthe moduli space of the minimizers of the Yang–Millsfunctional is shown.     

Foliations

The survey is based on works on the theory of foliations reviewed in RZhMatematika during 1970–1979. The basic topics are the classification of foliations, characteristic classes, the qualitative theory of foliations (holonomy, growth of leaves, etc.), and special classes of foliations (compact foliations, Riemannian foliations, etc.).Translated from Itogi Nauki i Tekhniki, Seriya Algebra, Topologiya, Geometriya, Vol. 18, pp. 151–213, 1981.