Hardening rules for finite deformation micropolar plasticity: Restrictions imposed by the second law of thermodynamics and the postulate of Il'iushin

Received April 9, 2001 / Published online August 16, 2001     

Generalized strain and stress tensors associated by duality

Received April 23, 2001 / Published online August 16, 2001     

An interesting triangle

A peculiar triangle and its properties, which can become the basis for a number of challenging constructions, are discussed.     

Some Information Theoretic Ideas Useful in Statistical Inference

In this paper we discuss four information theoretic ideas and present their implications to statistical inference: (1) Fisher information and divergence generating functions, (2) information optimum unbiased estimators, (3) information content of various statistics, (4) characterizations based on Fisher information. This paper was written while the first author was visiting the University of Cyprus, Department of Mathematics and Statistics.     

Space-time symmetries and the gravitational-neutrino field equations in general relativity

We consider a neutrino field with geodesic rays in interaction with a gravitational field admitting a Killing vector field n^μ. It is found that for solutions of the Einstein-Weyl field equations the neutrino field ξ^A and the neutrino flux vector l^μ are restricted by the equations: $\text{L}{}_{\mathrm{n}}\text{ξ}{}^{\mathrm{<mtext>A\; =\; ?</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{is}\text{ξ}{}^{\mathrm{A}}$ and $\text{L}{}_{\mathrm{n}}\text{l}{}^{\mathrm{\mu }}\text{= 0}$, whereas s is a real constant. In the case of pure radiation neutrino fields these equations become: $\text{L}\text{ξ}{}^{\mathrm{A}}\text{=}\text{case1}\text{2}\text{(p ? is)ξ}{}^{\mathrm{A}}$, $\text{L}{}_{\mathrm{n}}\text{l}{}^{\mathrm{\mu }}\text{= pl}{}^{\mathrm{\mu }}$, where p and s are in general real functions of the coordinates.     

Higgs production cross-section in a Standard Model with four generations at the LHC

We present theoretical predictions for the Higgs boson production cross-section via gluon fusion at the LHC in a Standard Model with four generations. We include QCD corrections through NLO retaining the full dependence on the quark masses, and the NNLO corrections in the heavy quark effective theory approximation. We also include electroweak corrections through three loops. Electroweak and bottom-quark contributions are suppressed in comparison to the Standard Model with three generations.     

Exploring Repunits

This article describes a discovery activity which is organized and developed at two different levels of treatment corresponding to the different degree of mathematical maturity of students. Using an 8-digit calculator, students at the first level (7-9th graders) explore patterns which lead them to discover the properties of repunits and their relationships to many mathematical curiosities. At the second level (10-12th graders) students may be interested in further extension exploring why these patterns emerge and offering algebraic justification.     

On the isometries of ideal polyhedra

Résumé  On montre que siX est un polyèdre idéal complet fini satisfaisant la condition CAT(−1) locale, alors toute isométrie deX homotope à l’identité est l’identité, pourvu queπ ₁(X) ne soit pas élémentaire. On montre aussi que le groupe des isométies deX est fini.      

A Generalization of the Poincaré--Bendixson Theorem for Compact 3-manifolds

It is shown that compressible cylindrical ends in compact foliated 3-manifolds spiral onto toral leaves.Mathematics Subject Classification (2000).57R30, 57M99.     

The synthesis of novel polycyclic heterocyclic ring systems via photocyclization. 9. Phenanthro[9′,10′:4,5]thieno[2,3-c]quinoline,benzo[f]phenanthro[9′,10′:4,5]thieno[2,3-c]quinoline,and benzo[h]-phenanthro[9′,10′:4,5]thieno[2,3-c]quinoline

The synthesis of three novel polycyclic heterocyclic ring systems are reported via photocyclization. The specific final products in these ring systems are: phenanthro[9′,10′:4,5]thieno[2,3-c]quinoline ( 13 ), benzo[h]-phenanthro[9′,10′:4,5]thieno[2,3-c]quinoline ( 14 ), and benzo[f]phenanthro[9′,10′:4,5]thieno[2,3-c]quinoline ( 15 ).