Embeddings of variable Hajlasz-Sobolev spaces into holder spaces of variable order

Pointwise estimates in variable exponent Sobolev spaces on quasi-metric measure spaces are investigated. Based on such estimates, Sobolev embeddings into Holder spaces with variable order are obtained. This extends some known results to the variable exponent setting. (C) 2008 Elsevier Inc. All rights reserved.INTAS [06-1000017-8792]info:eu-repo/semantics/publishedVersio

Fractional integrals and hypersingular integrals in variable order Holder spaces on homogeneous spaces

We consider non-standard Holder spaces H(lambda(.))(X) of functions f on a metric measure space (X, d, mu), whose Holder exponent lambda(x) is variable, depending on x is an element of X. We establish theorems on mapping properties of potential operators of variable order alpha(x), from such a variable exponent Holder space with the exponent lambda(x) to another one with a "better" exponent lambda(x) + alpha(x), and similar mapping properties of hypersingular integrals of variable order alpha(x) from such a space into the space with the "worse" exponent lambda(x) - alpha(x) in the case alpha(x) 0. We admit variable complex valued orders alpha(x), where R alpha(x) may vanish at a set of measure zero. To cover this case, we consider the action of potential operators to weighted generalized Holder spaces with the weight alpha(x).FCT, Portugal [SFRH/BPD/34258/2006

Variations of cosmic rays according to the data of interplanetary probes Zond-3 and Venus-2

Cosmic ray intensity variation measured by Zond 3 and Venus 2 interplanetary probe

Indexes Objectively Reflecting Performance Evaluation of Technical Rubber Goods

AbstractIn order to choose a characteristic index which objectively reflects performance evaluation of technical rubber goods, accelerated thermal-oxidative ageing of rubbers was carried out. It has been demonstrated that as the index accountable for maintaining workability the rate of set at compressing or tension relaxing at pressing of technical rubber goods in a statically deformed state is usually taken. Besides, breaking elongation or tensile strength of technical rubber goods in a free state can be taken as an index, as well. It has been educed that the most sensitive index which reflexes the structural changes in the rubber of the rubber-cord casing (RCC) during the process of ageing is breaking elongation, the value of which is drastically dropping in the initial period of the thermal ageing and monotonously changing thereafter

Weighted Sobolev theorem with variable exponent for spatial and spherical potential operators, II

In [S.G. Samko, B.G. Vakulov, Weighted Sobolev theorem with variable exponent for spatial and spherical potential operators, J. Math. Anal. Appl. 310 (2005) 229-246], Sobolev-type p((.)) -> q((.))-theorems were proved for the Riesz potential operator I-alpha in the weighted Lebesgue generalized spaces L-p(.)(R-n, p) with the variable exponent p(x) and a two-parameter power weight fixed to an arbitrary finite point x(0) and to infinity, under an additional condition relating the weight exponents at x(0) and at infinity. We show in this note that those theorems are valid without this additional condition. Similar theorems for a spherical analogue of the Riesz potential operator in the corresponding weighted spaces L-p(.) (S-n, p) on the unit sphere S-n in Rn+1 are also improved in the same way. (c) 2006 Elsevier Inc. All rights reserved.info:eu-repo/semantics/publishedVersio

Weighted Sobolev theorem with variable exponent for spatial and spherical potential operators

We prove Sobolev-type p((.)) -> q ((.))-theorems for the Riesz potential operator I-alpha in the weighted Lebesgue generalized spaces L-p(.)(R-n, p) with the variable exponent p (x) and a two-parametrical power weight fixed to an arbitrary finite point and to infinity, as well as similar theorems for a spherical analogue of the Riesz potential operator in the corresponding weighted spaces L-p(.)(S-n, p) on the unit sphere S-n in Rn+1. (c) 2005 Elsevier Inc. All rights reserved.info:eu-repo/semantics/publishedVersio

Weighted Sobolev theorem in Lebesgue spaces with variable exponent

For the Riesz potential operator I-alpha there are proved weighted estimates [GRAPHICS] within the framework of weighted Lebesgue spaces L (P(center dot)) (Omega, omega) with variable exponent. In case Omega is a bounded domain, the order alpha = alpha (x) is allowed to be variable as well. The weight functions are radial type functions "fixed" to a finite point and/or to infinity and have a typical feature of Muckenhoupt-Wheeden weights: they may oscillate between two power functions. Conditions on weights are given in terms of their Boyd-type indices. An analogue of such a weighted estimate is also obtained for spherical potential operators on the unit sphere S-n subset of R-n. (c) 2007 Elsevier Inc. All rights reserved.info:eu-repo/semantics/publishedVersio

Effect of thickness on the piezoelectric properties of LiNbO3 films

The results were obtained using the equipment of Research and Education Center and the Center of collective use “Nanotechnology” of Southern Federal University

Study of the electromechanical properties of aligned carbon nanotubes coated with ZnO using atomic force microscopy

The reported study was funded by RFBR according to the research projects No. 18-32-00652 mol_a, No.18-29-11019 mk and by grant of the Southern Federal University (project No. VnGr-07/2017-26)