Blaschke-Süss type theorems for closed plane curves

A C¹-class of plane closed curves is considered, which contains all ovals and rosettes. This class is divided into some subclasses for which greatest lower bounds of numbers of antipodal and arc-antipodal sets are determined.     

Trading by Quantum Rules: Quantum Anthropic Principle

This is a short review of the background and recent development in quantum game theory and its possible application in economics and finance. The intersection of science and society is discussed and Quantum Anthropic Principle is put forward. The review is addressed to nonspecialists.     

A reanalysis of branching fractions of charmed mesonsD 0,D + andD s +

We combine highly complementary information on branching fractions of charmed mesonsD ⁰,D ⁺ andD _s ⁺ coming from two experiments both yielding doublecharm samples. The NA 32 experiment provided exclusive branching fractions for channels with at least two charged decay products while a recent Mark III paper provides results on inclusive charm decay properties. The knowledge of channels withK ⁰'s in the former is used to recalculate the charged multiplicity distribution in the latter. We obtain 〈n _ch〉=2.25±0.08 forD ⁰, 〈n _ch〉=1.96±0.08 forD ⁺ and 〈n _ch〉=2.41±0.38 forD _s ⁺ . In turn the knowledge of the charged multiplicity improves the overall normalization of exclusive branching fractions. This reanalysis yields model-independent results for charmed mesons. In particular we obtain branching fractions for 16D _s ⁺ decay channels including $$BF(D_s^ + \to \phi \pi ^ + ) = \left( {4.4\begin{array}{*{20}c} { + 2.3} \\ { - 1.8} \\ \end{array} } \right)\% .$$ .     

The new method of fabrication of submicron structures by optical lithography with mask shifting and mask rotation

This paper presents the methods of fabricating narrow parallel submicrometric stripes in silicon dioxide and a resist layer. The experiments were conducted by two techniques: double patterning lithography and double exposure lithography. In addition to the above mentioned processes, mask translation was applied. For all conducted experiments, chrome masks and a 405 nm line of the high pressure mercury lamp of an MA-56 Mask Aligner System were used. The main aim of the performed tests was to establish the utility and the possible applications of the methods used.     

The plasticity of the Cu(H2O) 6 2+ Jahn-Teller complex affected by lattice strains and cooperative interactions

The EPR spectra evolution of Cs₂Zn_1?x Cu_x(ZrF₆)₂ · 6H₂O (x=0.01, 0.6, 0.8, and 1.0) in the temperature range 4.2–330 K and the x-ray structure analysis of the compound with x=1.0 in the range 150–327 K show that the Jahn-Teller (JT) complex Cu(H₂O)₆ coordination sphere undergoes a plastic deformation. The observed effect is due to the combined influence of small lattice strains existing in the paraphase and a new one appearing as a result of a ferroelastic phase transition and increasing with decreasing temperature below T _c . It is proved that both cooperative interactions between JT complexes and ferroelastic strain stabilize a certain JT configuration. The problem of instability of a JT configuration compressed at T ～ 265 K is discussed.     

Boundary G/G Theory and Topological Poisson–Lie Sigma Model

We study a boundary version of the gauged WZW model with a Poisson–Lie group G as the target. The Poisson–Lie structure of G is used to define the Wess–Zumino term of the action on surfaces with boundary. We clarify the relation of the model to the topological Poisson sigma model with the dual Poisson–Lie group G ^* as the target and show that the phase space of the theory on a strip is essentially the Heisenberg double of G introduced by Semenov–Tian–Shansky.     

SU(2) Chern-Simons theory at genus zero

We present a detailed study of the Schrödinger picture space of states in theSU(2) Chern-Simons topological gauge theory in the simplest geometry. The space coincides with that of the solutions of the chiral Ward identities for the WZW model. We prove that its dimension is given by E. Verlinde's formulae.     

GeneralizedG-theory

A generalization of theG-theory defined by A. Heilet al. is presented.     

Cauchy boundary andb-incompleteness of space-time

It is shown that if a space-time (M, g) is time-orientable and its Levi-Civita connection [in the bundle of orthonormal frames over (M, g)] is reducible to anO(3) structure, one can naturally select a nonvanishing timelike vector field and a Riemann metricg ⁺ onM. The Cauchy boundary of the Riemann space (M, g ⁺) consists of endpoints ofb-incomplete curves in (M, g); we call it theCauchy singular boundary. We use the space-time of a cosmic string with a conic singularity to test our method. The Cauchy singular boundary of this space-time is explicitly constructed. It turns out to consist of what should be expected.