Whitehead test modules

A (right -) module is said to be a Whitehead test module for projectivity (shortly: a p-test module) provided for each module , implies is projective. Dually, i-test modules are defined. For example, is a p-test abelian group iff each Whitehead group is free. Our first main result says that if is a right hereditary non-right perfect ring, then the existence of p-test modules is independent of ZFC + GCH. On the other hand, for any ring , there is a proper class of i-test modules. Dually, there is a proper class of p-test modules over any right perfect ring.

A non-semisimple ring is said to be fully saturated (-saturated) provided that all non-projective (-generated non-projective) modules are i-test. We show that classification of saturated rings can be reduced to the indecomposable ones. Indecomposable 1-saturated rings fall into two classes: type I, where all simple modules are isomorphic, and type II, the others. Our second main result gives a complete characterization of rings of type II as certain generalized upper triangular matrix rings, . The four parameters involved here are skew-fields and , and natural numbers . For rings of type I, we have several partial results: e.g. using a generalization of Bongartz Lemma, we show that it is consistent that each fully saturated ring of type I is a full matrix ring over a local quasi-Frobenius ring. In several recent papers, our results have been applied to Tilting Theory and to the Theory of -modules.

     

Infinite products of finite simple groups

We classify the sequences of finite simple nonabelian groups such that has uncountable cofinality.

     

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.     

STAR inner tracking upgrade—a performance study

Anisotropic flow measurements have demonstrated development of partonic collectivity in 200 GeV Au+Au collisions at RHIC. To understand the partonic EOS, thermalization must be addressed. Collective motion of heavy-flavor (c, b) quarks can be used to indicate the degree of thermalization of the light-flavor quarks (u, d, s). Measurement of heavy-flavor quark collectivity requires direct reconstruction of heavy-flavor hadrons in the low p _T region. Measurement of open charm spectra to high p _T can be used to investigate heavy-quark energy loss and medium properties. The Heavy Flavor Tracker (HFT), a proposed upgrade to the STAR experiment at midrapidity, will measure v ₂ of open-charm hadrons to very low p _T by reconstructing their displaced decay vertices. The innermost part of the HFT is the PIXEL detector (made of two low mass monolithic active pixel sensor layers), which delivers a high precision position measurement close to the collision vertex. The Intermediate Silicon Tracker (IST), a 1-layer strip detector, is essential to improve hit identification in the PIXEL detector when running at full RHIC-II luminosity. Using a full GEANT simulation, open charm measurement capabilities of STAR with the HFT will be shown. Its performance in a broad p _T range will be demonstrated on v ₂ (p _T>0.5 GeV/c) and R _CP (p _T<10 GeV/c) measurements of D⁰ meson. Results of reconstruction of Λ_C baryon in heavy-ion collisions are presented.     

Fluorescence Properties of Selected Benzo[c]phenanthridines

The fluorescence properties of selected benzo[c]phenanthridines (BPs) were examined. The effect of structure, pH and solvent on the fluorescence properties has been investigated. It was found out that the presence of charged iminium nitrogen significantly decreased the fluorescence of the compounds. The fluorescence (intensity as well as emission spectra shape) of the investigated compounds was significantly dependent on pH as well as used solvent. The utilization in epigenetic modification mechanisms studies as demethylase probe and as possible pH indicator was suggested.     

用连续记录的方法测量高Tc超导材料的转变温度

本文介绍了用连续测量和记录的方法，准确测量高Ｔｃ超导材料的转变温度和实验装置。     

Structural aspects of antibody-antigen interaction revealed through small random peptide libraries

Summary Two small random peptide libraries, one composed of 4550 dodecapeptides and one of 8000 tripeptides, were synthesized in newly developed credit-card format miniPEPSCAN cards (miniPEPSCAN libraries). Each peptide was synthesized in a discrete well (455 peptides/card). The two miniPEPSCAN libraries were screened with three different monoclonal antibodies (Mabs). Two other random peptide libraries, expressed on the wall of bacteria (recombinant libraries) and composed of 10⁷ hexa- and octapeptides, were screened with the same three Mabs. The aim of this study was to compare the amino acid sequence of peptides selected from small and large pools of random peptides and, in this way, investigate the potential of small random peptide libraries. The screening of the two miniPEPSCAN libraries resulted in the identification of a surprisingly large number of antibody-binding peptides, while the screening of the large recombinant libraries, using the same Mabs, resulted in the identification of only a small number of peptides. The large number of peptides derived from the small random peptide libraries allowed the determination of consensus sequences. These consensus sequences could be related to small linear and nonlinear parts of the respective epitopes. The small number of peptides derived from the large random peptide libraries could only be related to linear epitopes that were previously mapped using small libraries of overlapping peptides covering the antigenic protein. Thus, with respect to the cost and speed of identifying peptides that resemble linear and nonlinear parts of epitopes, small diversity libraries based on synthetic peptides appear to be superior to large diversity libraries based on expression systems.Abbreviations ABTS 2,2-azino-di-3-ethylbenzthiazoline sulfonate - EGF epidermal growth factor - Mab monoclonal antibody - OD_ccd optical density obtained using CCD camera - RAMPO rabbit-antimouse peroxidase - SDS sodium dodecylsulfate - TGEV transmissible gastroenteritis virus