Schwinger-Dyson operator of Yang-Mills matrix models with ghosts and derivations of the graded shuffle algebra

We consider large-N multi-matrix models whose action closely mimics that of Yang-Mills theory, including gauge-fixing and ghost terms. We show that the factorized Schwinger-Dyson loop equations, expressed in terms of the generating series of gluon and ghost correlations G(xi), are quadratic equations S^i G = G xi^i G in concatenation of correlations. The Schwinger-Dyson operator S^i is built from the left annihilation operator, which does not satisfy the Leibnitz rule with respect to concatenation. So the loop equations are not differential equations. We show that left annihilation is a derivation of the graded shuffle product of gluon and ghost correlations. The shuffle product is the point-wise product of Wilson loops, expressed in terms of correlations. So in the limit where concatenation is approximated by shuffle products, the loop equations become differential equations. Remarkably, the Schwinger-Dyson operator as a whole is also a derivation of the graded shuffle product. This allows us to turn the loop equations into linear equations for the shuffle reciprocal, which might serve as a starting point for an approximation scheme.Comment: 13 pages, added discussion & references, title changed, minor corrections, published versio

Interplay between antioxidant activity, health and disease

The article discusses the relationship between oxidative stress (OS) and pathological conditions, the possibilities and benefits of estimating OS considering the integral antioxidant activity (AOA) as an OS criterion, and using a simple accessible hybrid potentiometric method (HPM) with a mediator system for AOA monitoring. The results of AOA of blood serum in healthy volunteers and patients with various diseases are presented. Preliminary reference values are found. The lower levels of AOA of blood serum in patients with different diseases in comparison with the control group are observed. The potential mechanisms of changes in the AOA levels and it’s clinical significance are discussed from the position of biointerfaces interplay. With AOA equal or greater than 1.40 mmol-eq l–1 the person is healthy, the range from 0.95 to 1.40 mmol-eq l–1 indicates that the patient is at risk and needs to undergo a further medical examination. When AOA blood serum is below 0.95 mmol-eq l–1, detailed diagnostics and relevant treatment are required. The findings allow suggesting that the approach determine antioxidant/oxidant activity of biological fluids holds considerable promise for monitoring OS; it opens up new opportunities in expanding the use of analytical chemistry in medicine. © 2019 by the authors

Random Energy Model with complex replica number, complex temperatures and classification of the string's phases

The results by E. Gardner and B.Derrida have been enlarged for the complex temperatures and complex numbers of replicas. The phase structure is found. There is a connection with string models and their phase structure is analyzed from the REM's point of view.Comment: 11 pages,revte

Disposable potentiometric sensory system for skin antioxidant activity evaluation

The skin is a natural barrier between the external and internal environment. Its protective functions and the relationship of its state with the state of health of the organism as a whole are very important. It is known that oxidant stress (OS) is a common indicator of health status. This paper describes a new sensory system for monitoring OS of the skin using antioxidant activity (AOA) as its criteria. The contact hybrid potentiometric method (CHPM) and new electrochemical measuring scheme were used. A new sensory system, including disposable modified screen-printed carbon and silver electrodes covered by membrane impregnated by mediator, was developed. Its informative ability was demonstrated in the evaluation of the impact of fasting, consumption of food and food enriched by vitamins (antioxidants) on skin AOA. This device consisting of a sensory system and potentiometric analyzer can be used in on-site and in situ formats. © 2019 by the authors. Licensee MDPI, Basel, Switzerland

Influence of Rb, Cs and Ba on Superconductivity of Magnesium Diboride

Magnesium diboride has been thermally treated in the presence of Rb, Cs, and Ba. Magnetic susceptibility shows onsets of superconductivity in the resulting samples at 52K (Rb), 58K (Cs) and 45K (Ba). Room-temperature 11B NMR indicates to cubic symmetry of the electric field gradient at boron site for the samples reacted with Rb and Cs, in contrast to the axial symmetry in the initial MgB2 and in the sample treated with Ba.Comment: 3 pages (twocolumn), 2 figure

Two Phase Description Logic Reasoning for Efficient Information Retrieval

Description Logics are used more and more frequently for knowledge representation, creating an increasing demand for efficient automated DL reasoning. However, the existing implementations are inefficient in the presence of large amounts of data. This paper summarizes the results in transforming DL axioms to a set of function-free clauses of first-order logic which can be used for efficient, query oriented data reasoning. The described method has been implemented in a module of the DLog reasoner openly available on SourceForge to download