Abstract:
The aim of the research work was to develop cyst-targeted alginates microspheres of diloxanide furoate (DF) for the effective treatment of amoebiasis. Calcium alginates microspheres of DF were prepared using emulsification method using calcium chloride as a cross-linking agent. Alginate is a natural polysaccharide found in brown algae. Alginates are widely used in the food and pharmaceutical industries and have been employed as a matrix for the entrapment of drugs, macromolecules and biological cells. Alginate microspheres produced by the emulsification method using calcium chloride. Formulations were characterized for particle size and shape, surface morphology, entrapment efficiency, and in vitro drug release in simulated gastrointestinal fluids. XRD and differential scanning calorimetery were used to confirm successful entrapment of DF into the alginates microspheres. All the microsphere formulations showed good % drug entrapment (73.82 1.99). Calcium alginate retarded the release of DF at low pH (1.2 and 4.5) and released microspheres slowly at pH 7.4 in the colon without colonic enzymes.

Abstract:
The limit -Bernstein operator , , emerges naturally as a modification of the Szász-Mirakyan operator related to the Euler distribution. The latter is used in the -boson theory to describe the energy distribution in a -analogue of the coherent state. Lately, the limit -Bernstein operator has been widely under scrutiny, and it has been shown that is a positive shape-preserving linear operator on with . Its approximation properties, probabilistic interpretation, eigenstructure, and impact on the smoothness of a function have been examined. In this paper, the functional-analytic properties of are studied. Our main result states that there exists an infinite-dimensional subspace of such that the restriction is an isomorphic embedding. Also we show that each such subspace contains an isomorphic copy of the Banach space .

Abstract:
Предметом исследования послужили диалектные (севернорусские) мелкие слова , производные от форм глаголов быть, бывать (бы, бывает, будет), которые мы рассматриваем в составе синтаксических конструкций в связи с категорией модальности.

Abstract:
The limit -Bernstein operator , , emerges naturally as a modification of the Szász-Mirakyan operator related to the Euler distribution. The latter is used in the -boson theory to describe the energy distribution in a -analogue of the coherent state. Lately, the limit -Bernstein operator has been widely under scrutiny, and it has been shown that is a positive shape-preserving linear operator on with . Its approximation properties, probabilistic interpretation, eigenstructure, and impact on the smoothness of a function have been examined. In this paper, the functional-analytic properties of are studied. Our main result states that there exists an infinite-dimensional subspace of such that the restriction is an isomorphic embedding. Also we show that each such subspace contains an isomorphic copy of the Banach space . 1. Introduction The limit q-Bernstein operator comes out naturally as an analogue of the Szász-Mirakyan operator, which is related to the Euler probability distribution—also referred to as the “ -deformed Poisson distribution” (see [1, 2]). The latter is used in the -boson theory, which is a -deformation of the quantum harmonic oscillator formalism [3]. Namely, the -deformed Poisson distribution describes the energy distribution in a -analogue of the coherent state [3, 4]. The -analogue of the boson operator calculus has proved to be a powerful tool in theoretical physics by providing explicit expressions for the representations of the quantum group , which is by now known to play a profound role in a variety of different problems, such as integrable models in the field theory, exactly solvable lattice models of statistical mechanics, and conformal field theory among others. Therefore, properties of the -deformed Poisson distribution and its related linear operators are of significant interest for applications. In the sequel, the following notations and definitions are employed (cf., e.g., [5]). Let . For any , the -integer is defined by and the -factorial by Besides, denotes the -analogue of , that is, while For , the -analogues of the exponential function are given by (see [5], formulae (9.7) and (9.10)) By Euler’s Identities (cf., e.g., [5], formulae (9.3) and (9.4)), whence Clearly, for , we have Now, for , let be a random variable possessing a discrete distribution with the probability mass function: When , we recover the classical Poisson distribution with parameter . If is a function defined on , then the mathematical expectation of equals We notice that in the case , , operator is the classical Szász-Mirakyan operator. Taking and , we

Abstract:
The origin of fast radio bursts remains a puzzle. Suggestions have been made that they are produced within the Earth atmosphere, in stellar coronae, in other galaxies or at cosmological distances. If they are extraterrestrial, the implied brightness temperature is very high, and therefore, the induced scattering places constraints on possible models. In this paper, constraints are obtained on flares from coronae of nearby stars. It is shown that the radio pulses with the observed power could not be generated if the plasma density within and in the nearest vicinity of the source is as high as it is necessary in order to provide the observed dispersion measure. However, one cannot exclude a possibility that the pulses are generated within a bubble with a very low density and pass through the dense plasma only in the outer corona.

Abstract:
Given a Banach space $X$ and a locally finite metric space $A$, it is known that if all finite subsets of $A$ admit bilipschitz embeddings into $X$ with distortions $\le C$, then the space $A$ itself admits an embedding into $X$ with distortion $\le D\cdot C$, where $D$ is an absolute constant. The goal of this paper is to show that $D>1$, implying that, in general, there is a "deterioration of distortion" in the aforementioned situations.

Abstract:
Diamond graphs and Laakso graphs are important examples in the theory of metric embeddings. Many results for these families of graphs are similar to each other. In this connection, it is natural to ask whether one of these families admits uniformly bilipschitz embeddings into the other. The well-known fact that Laakso graphs are uniformly doubling but diamond graphs are not, immediately implies that diamond graphs do not admit uniformly bilipschitz embeddings into Laakso graphs. The main goal of this paper is to prove that Laakso graphs do not admit uniformly bilipschitz embeddings into diamond graphs.

Abstract:
The aim of this paper is to present new results related to the convergence of the sequence of the -Bernstein polynomials {,(;)} in the case >1, where is a continuous function on [0,1]. It is shown that the polynomials converge to uniformly on the time scale ={？}∞=0∪{0}, and that this result is sharp in the sense that the sequence {,(;)}∞=1 may be divergent for all ∈？. Further, the impossibility of the uniform approximation for the Weierstrass-type functions is established. Throughout the paper, the results are illustrated by numerical examples.