Dynamical differential equations compatible with rational qKZ equations

For the Lie algebra $gl_N$ we introduce a system of differential operators called the dynamical operators. We prove that the dynamical differential operators commute with the $gl_N$ rational quantized Knizhnik-Zamolodchikov difference operators. We describe the transformations of the dynamical operators under the natural action of the $gl_N$ Weyl group.Comment: 7 pages, AmsLaTe

Automatic reduction of four-loop bubbles

We give technical details about the computational strategy employed in a recently completed investigation of the four-loop QCD free energy. In particular, the reduction step from generic vacuum bubbles to master integrals is described from a practical viewpoint, for fully massive as well as QED-type integrals.Comment: 5 pages. Talk presented at RADCOR/Loops and Legs 2002, Kloster Banz, German

Fractional Derivative as Fractional Power of Derivative

Definitions of fractional derivatives as fractional powers of derivative operators are suggested. The Taylor series and Fourier series are used to define fractional power of self-adjoint derivative operator. The Fourier integrals and Weyl quantization procedure are applied to derive the definition of fractional derivative operator. Fractional generalization of concept of stability is considered.Comment: 20 pages, LaTe

Results of the study of the vestibular apparatus and the functions of the perception of space in cosmonauts (pre- and post-flight observations)

The effect of the set of space flight factors caused a change in the activity of the vestibular apparatus and the spatial perception function. More significant and longer shifts were observed during expeditions of great duration. The detected disorders (increase in reactivity of the otolithic apparatus, decrease in sensitivity of the cupula receptor, deterioration in the perception accuracy, etc.) had a definite tendency to be restored. The primary damage to the otolithic reflex (changes were found in practically all the subjects) is probably caused by the specific effect of zero gravitation, and apparently, may be one of the trigger mechanisms for discrepancy in the activity of the sensory systems, disorders in the correcting function of the cerebellum, and central vestibular formations

Results of the investigation of the otolith function in manned space flights

The effects of conditions of long term and short term space flights on the otolith function of cosmonauts were investigated via pre and post examinations. The results show that after long term flight, the intensity of the otolith reflex increased and asymmetry occurred in the indicators of the otolith function. Large changes in terms of expression and duration in the indicators of the otolith function after long term flight as compared with short term flight were also noted

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

Dynamics of the Chain of Oscillators with Long-Range Interaction: From Synchronization to Chaos

We consider a chain of nonlinear oscillators with long-range interaction of the type 1/l^{1+alpha}, where l is a distance between oscillators and 0< alpha <2. In the continues limit the system's dynamics is described by the Ginzburg-Landau equation with complex coefficients. Such a system has a new parameter alpha that is responsible for the complexity of the medium and that strongly influences possible regimes of the dynamics. We study different spatial-temporal patterns of the dynamics depending on alpha and show transitions from synchronization of the motion to broad-spectrum oscillations and to chaos.Comment: 22 pages, 10 figure

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

Fractional Dynamics from Einstein Gravity, General Solutions, and Black Holes

We study the fractional gravity for spacetimes with non-integer dimensions. Our constructions are based on a geometric formalism with the fractional Caputo derivative and integral calculus adapted to nonolonomic distributions. This allows us to define a fractional spacetime geometry with fundamental geometric/physical objects and a generalized tensor calculus all being similar to respective integer dimension constructions. Such models of fractional gravity mimic the Einstein gravity theory and various Lagrange-Finsler and Hamilton-Cartan generalizations in nonholonomic variables. The approach suggests a number of new implications for gravity and matter field theories with singular, stochastic, kinetic, fractal, memory etc processes. We prove that the fractional gravitational field equations can be integrated in very general forms following the anholonomic deformation method for constructing exact solutions. Finally, we study some examples of fractional black hole solutions, fractional ellipsoid gravitational configurations and imbedding of such objects in fractional solitonic backgrounds.Comment: latex2e, 11pt, 40 pages with table of conten