Sharp Hardy type inequalities with weights depending on bessel function

© Nasibullin R.G. 2017.We prove exact Hardy type inequalities with the weights depending on a Bessel function. We obtain one-dimensional Lp-inequalities and provide an example of extending these inequalities for the case of convex domains with a finite inner radius. The proved statements are generalization for the case of arbitrary p ≥ 2 of the corresponding inequality proved by F.G. Avkhadiev and K.-J. Wirths for p = 2

Generalizations of hardy-type inequalities in the form of Dubinskii

Hardy-type inequalities with power and logarithmic singularities are considered. New one-dimensional inequalities and their multidimensional analogs are proved. © 2014 Pleiades Publishing, Ltd

Avkhadiev–Becker Type Univalence Conditions for Biharmonic Mappings

© 2018, Pleiades Publishing, Ltd. In this paper we consider complex-valued biharmonic functions that are locally univalent. We construct families of biharmonic univalent mappings of the unite disc similar to Avkhadiev- Becker type conditions for analytic functions. Also, we investigate the case where biharmonic functions are defined on the exterior of the unit disc. In this case we obtain three analogs of Avkhadiev–Becker type conditions of univalence

Assessment of the state of synergies between the structural and functional characteristics of the kidneys and liver during external use of a seaweed product Laminaria algae

The authors conducted studies to study the relationship between the functional activity of the kidneys, the detoxification activity of the liver and the structural features of the parenchymatous tissue of these organs under normal conditions and with external use of the laminar algae product “Lamidan”. The work was performed on 164 white outbred Wistar rats weighing 180-200 g. The work was carried out in accordance with current standards for working with laboratory animals. The results of many years of research have shown that normally the indicators of detoxification activity of the liver and functional activity of the kidneys practically do not change, and they correspond to the structural organization of the parenchymatous tissue of these organs, corresponding to the descriptions given in well-known manuals on the activities of these organs. The use of "Lamidan" activates the detoxification function of the liver by 28 % and the functional activity of the kidneys by 28.5 %, i.e. changes are unidirectional and proportionate. In the parenchyma of both organs, changes in the structural organization are recorded, characteristic of an increase in functional activity. Thus, there is a strictly interrelated set of stereotypical changes in the indices of the two organs under study, reflecting between the organs interrelations of functional systems

Study of the effect of external use of a brown algae product on the structural-functional continuum

The authors, in a study on 25 outbred Wistar white rats weighing 180-200 g, determined the effect of Lamidana (a product from sea brown algae) on the structural-functional continuum, that is, the correlation of the functional activity of the liver parenchyma and its structural characteristics. Methods. The detoxifying function of the liver was studied by the duration of sleep of animals due to the action of anesthesia - intraperitoneal administration of sodium thiopental (estimate the rate of metabolism of thiopental, carried out by the cytochrome-P-450-dependent monooxygenase system of hepatocytes). The structural and functional state of the liver parenchyma was assessed according to the study of histological preparations. The results of the studies showed that under the influence of the external application of "Lamidin" in the test rats, the liver1s detoxification function is enhanced (significantly significant decrease in the duration of sleep of animals). At the same time, structural signs of increased functional activity of hepatocytes are determined in the parenchyma. Conclusions. The authors believe that "Lamidan", due to the peculiarities of its chemical composition, enhances the metabolic and functional activity of hepatocytes but does not damage the correlative relationships between the structure and function of hepatocytes

Influence of millimeter electromagnetic waves on the functional capabilities of the lower limb muscles in athletes - volleyball players

The authors, when observing 22 athletes - volleyball players of different volleyball specialization, assessed the effect of millimeter electromagnetic waves (EMW) on the functional state of the muscular system of the lower extremities. The electromagnetic effect was carried out using the "Complex SP 80" apparatus (frequencies 3900 - 4120 kHz were used). Electrodes were applied to the muscles of the thigh and lower leg, sinusoidal discharges were applied for 10 seconds during the strength training period. The results of observations showed that under the influence of EME, the height of the jump increases by 7%, due to the increase in the energy of the jump and its intensity. The release of the activity of the knee joint is also noted. The authors believe that under the influence of EME, the transmission of regulatory impulses in neuromuscular contact improves, which contributes to the synchronization and strength of contractions of the muscle fiber bundles. Also, under the influence of EMW, blood microcirculation in the muscle improves

Sharp Hardy type inequalities with weights depending on bessel function

© Nasibullin R.G. 2017. We prove exact Hardy type inequalities with the weights depending on a Bessel function. We obtain one-dimensional L p -inequalities and provide an example of extending these inequalities for the case of convex domains with a finite inner radius. The proved statements are generalization for the case of arbitrary p ≥ 2 of the corresponding inequality proved by F.G. Avkhadiev and K.-J. Wirths for p = 2

Hardy type inequalities for fractional integrals and derivatives of Riemann–Liouville

© 2017, Pleiades Publishing, Ltd. We prove new Hardy type inequalities for Riemann–Liouville fractional integrals and derivatives in the case when the weight function have power and logarithmic singularities

Features of the reaction of the kidney function of healthy rats to the intake of boric hydrocarbonate sodium mineral waters of varying quantitative macro- and micro-composition

The purpose of the work is a comparative assessment of the effect of boron hydrocarbonate sodium mineral waters with a varying quantitative and qualitative composition of macroelements and with different amounts of a bioactive element on the state of the urinary system of rats. Materials and methods. The work was performed on 81 white rats of the Wistar line of auto bred breeding, weighing 180-200 g. The rats were divided into four groups: group 1 - 21 intact rats served as controls; group 2 - 20 rats treated intragastrically with a soft probe MW "Polyana Ploskivskaya" at a dose of 1% of body weight daily, a course of 7 days; group 3 - 20 rats treated with MW "Polyana Kupel" according to the above method; group 4 - 20 rats treated with MW "Svalyava" according to the above process. Before removing the animals from the experiment, daily urine was collected from them; blood was also taken from the tail vein for biochemical studies. At autopsy, pieces of kidneys were taken for histological and histoenzymological studies (the activity of succinate dehydrogenase and lactate dehydrogenase was determined). Results. The histological studies showed no pathological changes in the kidneys were observed with the use of the studied boron MW. Still, there were structural changes, as well as an increase in the activity of redox enzymes. Changes in kidney function were unidirectional with using any of the investigated MW. Still, they had quantitative differences, which are less related to the amount of boron (in the form of orthoboric acid) in 1 liter of MW and more dependent on the osmolarity of the MW, the qualitative composition of macronutrients, and their ratio. Conclusion. We believe that osmolarity, as an integrated indicator of the state of the macronutrient component of MW, can be used to assess its effect on the structural and functional characteristics of the kidneys

Hardy type inequalities with weights dependent on the bessel functions

© 2016, Pleiades Publishing, Ltd.We obtain a new sharp Hardy type inequality with an additional term. Using the Bessel functions we prove one dimensional inequality and their multidimensional analogs in domains with a finite inradius. The weight functions depend on the Bessel functions and Lamb’ s constants