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.     

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.     

Immunity in the ABM-DSGE Framework for Preventing and Controlling Epidemics—Validation of Results

The COVID-19 pandemic has raised many questions on how to manage an epidemiological and economic crisis around the world. Since the beginning of the COVID-19 pandemic, scientists and policy makers have been asking how effective lockdowns are in preventing and controlling the spread of the virus. In the absence of vaccines, the regulators lacked any plausible alternatives. Nevertheless, after the introduction of vaccinations, to what extent the conclusions of these analyses are still valid should be considered. In this paper, we present a study on the effect of vaccinations within the dynamic stochastic general equilibrium model with an agent-based epidemic component. Thus, we validated the results regarding the need to use lockdowns as an efficient tool for preventing and controlling epidemics that were obtained in November 2020.     

Machine Learning Algorithms for Prediction of the Quality of Transmission in Optical Networks

Increasing demand in the backbone Dense Wavelength Division (DWDM) Multiplexing network traffic prompts an introduction of new solutions that allow increasing the transmission speed without significant increase of the service cost. In order to achieve this objective simpler and faster, DWDM network reconfiguration procedures are needed. A key problem that is intrinsically related to network reconfiguration is that of the quality of transmission assessment. Thus, in this contribution a Machine Learning (ML) based method for an assessment of the quality of transmission is proposed. The proposed ML methods use a database, which was created only on the basis of information that is available to a DWDM network operator via the DWDM network control plane. Several types of ML classifiers are proposed and their performance is tested and compared for two real DWDM network topologies. The results obtained are promising and motivate further research.     

Real-World Data Difficulty Estimation with the Use of Entropy

In the era of the Internet of Things and big data, we are faced with the management of a flood of information. The complexity and amount of data presented to the decision-maker are enormous, and existing methods often fail to derive nonredundant information quickly. Thus, the selection of the most satisfactory set of solutions is often a struggle. This article investigates the possibilities of using the entropy measure as an indicator of data difficulty. To do so, we focus on real-world data covering various fields related to markets (the real estate market and financial markets), sports data, fake news data, and more. The problem is twofold: First, since we deal with unprocessed, inconsistent data, it is necessary to perform additional preprocessing. Therefore, the second step of our research is using the entropy-based measure to capture the nonredundant, noncorrelated core information from the data. Research is conducted using well-known algorithms from the classification domain to investigate the quality of solutions derived based on initial preprocessing and the information indicated by the entropy measure. Eventually, the best 25% (in the sense of entropy measure) attributes are selected to perform the whole classification procedure once again, and the results are compared.