Abstract:
Analysis and generalization of various factual materials makes it possible to come to conclusion, that the city of Ordubad, which had complicated, full of many military-political events history, was one of important economic and cultural centre of Azerbaijan. Due to its various goods and aquaculture products Ordubad had links (connection) with a number of trading centre of the East and Russia.

Abstract:
The perturbed systems of sines, which appear when solving some partial differential equations by the Fourier method, are considered in this paper. Basis properties of these systems in weighted Sobolev spaces of functions are studied. 1. Introduction When solving many problems in mathematical physics by Fourier method (see e.g., [1–4]), there appear perturbed systems of sines and cosines of the following form: where , are real parameters. Using Fourier method requires the study of basis properties of the above systems in Lebesgue and Sobolev spaces of functions. Relevant investigations date back to the well-known works by Paley and Wiener [5] and Levinson [6]. For , basis properties of these systems in spaces , , are completely studied in [7–12]. The case of weighted was considered by E. I. Moiseev in [13, 14]. Basis properties of some perturbed systems of exponents in Sobolev spaces are studied in [15–19]. Further references include [20–23]. Our paper is devoted to the study of basis properties of these systems in weighted Sobolev spaces. Unlike previous works, we offer a different method of investigation. 2. Auxiliary Facts Let and be weighted Lebesgue and Sobolev spaces with the following norms: where , , . Denote by the following direct sum: where is a complex plane. The norm in this space is defined as follows: , where . The following easily provable lemmas play an important role in obtaining our main result. Lemma 1. Let . Then the operator performs an isomorphism between the spaces and ; that is, the spaces and are isomorphic. Proof. First we show the boundedness of this operator. We have the following: Applying Hlder's inequality, we obtain the following: Consequently, where . Let us show that . Let ; that is, where , . Differentiating this equation, we obtain a.e. on . It follows that . From (9) it directly follows that a.e. on and this implies that . Show that . Let be an arbitrary function. Assume . It is clear that and . Then by Banach theorem we find that the operator has a bounded inverse. This proves Lemma 1. Now let us prove the following lemma. Lemma 2. Let and . Then for all , where . Proof. Let ,？？ . We have the following: As and , then . Similarly, we find that and . It is easy to see that and, moreover, This proves the lemma. From results of the paper [24] it follows the validity of the following lemma. Lemma 3. Let , , , and in . Then the series converges absolutely. 3. Main Result Theorem 4. Let , . Then system (2) forms a basis for if and only if system (1) forms a basis for , where , . Proof. First let us assume that the system

Abstract:
The paper presents the results of studies surface microrelief, frequency-temperature characteristics of the imaginary part of the dielectric permittivity and dielectric loss of PE+TlInSe_{2} composite materials in 25^{。}C - 150^{。}C temperature and 25 Hz - 1 MHz frequency range before and after application of the aluminum nano-particles with a size of 50 nm. The change in the amount of semicon-ductor filler TlInSe_{2} and aluminum nano-particles changes the state of the surface and the frequency-temperature characteristics of composite materials PE+xvol.%TlInSe_{2}, which allows to obtain composites with the desired dielectric permittivity and dielectric loss.

Abstract:
Super-microscopic techniques like scanning tunnelling microscopy, atomic force microscopy or scanning near-field optical microscopy allows investigate micro- and/or nano-scale surfaces and structures. In this paper, both Environmental scanning electron microscope (ESEM) and Scanning near field optical microscope (SNOM) have been applied to more closely study of biomaterials. The results of visualization of human osteo-sarcoma cell line (U2OS) are compared. SNOM and ESEM yield different, however, comparable and complementary information on studied biological samples.

Abstract:
For the transportation problem, Sharma and Sharma [1] have given a very computationally efficient heuristic (runs in O(c*n^{2}) time) to give very good dual solution to transportation problem. Sharma and Prasad [2] have given an efficient heuristic (complexity O(n^{3}) procedure to give a very good primal solution (that is generally non-basic feasible solution) to transportation problem by using the very good dual solution given by Sharma and Sharma [2]. In this paper we use the solution given by Sharma and Prasad [2] to get a very good Basic Feasible Solution to transportation problem, so that network simplex (worst case complexity (O(n^{3}*(log(n))) can be used to reach the optimal solution to transportation problem. In the second part of this paper, we give a simple heuristic procedure to get a very good BFS to linear programming problem from the solution given by Karmarkar [3] (that generally produces a very good non-basic feasible solution in polynomial time (O(n^{5.5})). We give a procedure to obtain a good BFS for LP by starting from the solution given by Karmarkar [3]. We note that this procedure (given here) is significantly different from the procedure given in [4].

We report a case of a 56-year-old female with a confirmed diagnosis of Dermatomyositis on muscle biopsy, which was refractory to 5 different disease modifying drugs as well as intravenous immunoglobulins and symptoms improved dramatically with a single course of Rituximab. We hereby wish to highlight the importance of Rituximab in this highly resistant case and that anti CD 20 biologic drugs can be considered as standard treatment protocol in refractory Dermatomyositis.

Entropy represents
a universal concept in science suitable for quantifying the uncertainty of a series of random events. We define and describe this notion in an appropriate
manner for physicists. We start with a brief recapitulation of the basic
concept of the theory probability being useful for the determination of the
concept of entropy. The history of how this concept came into its to-day exact
form is sketched. We show that the Shannon entropy represents the most adequate
measure of the probabilistic uncertainty of a random object. Though the notion
of entropy has been introduced in classical thermodynamics as a thermodynamic
state variable it relies on concepts studied in the theory of probability and
mathematical statistics. We point out that whole formalisms of statistical
mechanics can be rewritten in terms of Shannon entropy. The notion “entropy” is
differently understood in various science disciplines: in classical physics
it represents the thermodynamical state variable; in communication theory it
represents the efficiency of transmission of communication; in the theory of
general systems the magnitude of the configurational order; in ecology the
measure for bio-diversity; in statistics the degree of disorder, etc. All these
notions can be mapped on the general mathematical concept of entropy. By means
of entropy, the configurational order of complex systems can be exactly
quantified. Besides the Shannon entropy, there exists a class of Shannon-like
entropies which converge, under certain circumstances, toward Shannon
entropy. The Shannon-like entropy is sometimes easier to handle mathematically
then Shannon entropy. One of the important Shannon-like entropy is well-known
Tsallis entropy. The application of the Shannon and Shannon-like entropies in
science is really versatile. Besides the mentioned statistical physics, they
play a fundamental role in the quantum information, communication theory, in the
description of disorder, etc.

Abstract:
Given a regular compact set E in , a unit measure μ supported by , a triangular point set , and a function f , holomorphic on E , let π^{β,f}_{n,m} be the associated multipoint β-Padé approximant of order (n,m) . We show that if the sequence π^{β,f}_{n,m} , n∈Λ , ∧∈n,k are uniformly distributed on with respect to u as n∈Λ . Furthermore, a result about the behavior of the zeros of the exact maximally convergent sequence Λ is provided, under the condition that Λ is “dense enough”.

Abstract:
In his paper “On quasi-separative ‘semigroup’s’”, Krasilnikova, Yu. I. and Novikov, B. V. have studied congruences induced by certain relations on a “semigroup”. They further showed that if the “semigroup” is quasi separative then the induced congruence is a semilattice congruence. In this paper we continue the study of these relations and the induced congruences i.e., the congruences induced by certain relations on ‘‘semigroup’s”. In this paper mainly it is observed that if S is a quasi-separative and regular “semigroup” then the necessary and sufficient condition for to be the smallest semilattice congruence η is obtained.

Abstract:
Background. Atherosclerosis is a systemic disease. That is why the damage is not restricted by one vascular area in 18-50% of patients. High serum level of lipoprotein(a) [Lp(a)] is an independent risk factor for coronary, carotid and peripheral atherosclerosis. However the correlation of apoprotein(a) [apo(a)] polymorphism with the multifocal atherosclerosis in coronary heart disease (CHD) is not sufficiently studied.Aim. To study the correlation of apo(a) phenotype with the multifocal atherosclerosis in CHD patients.Material and Methods. 220 patients aged 32- 76 y.o. with the proven coronary and carotid atherosclerosis were split into two groups depending on the presence (n=22) or absence (n=198) of peripheral atherosclerosis. Evaluation of lipid profile, Lp(a) and determination of apo(a) isoforms by SDS electrophoresis in polyacrylamide gel and immunoblotting was performed in all patients.Results. Both groups of patients were comparable by age, sex, classical cardiovascular risk factors, including frequency of hyperlipidemia and diabetes mellitus, lipid profile. The Lp(a) serum level ≥30 mg/dL and low molecular weight (LMW) apo(a) phenotype were found more often in patients with multifocal than coronary and carotid atherosclerosis: 55 and 45% (р=0.372); 73 and 44% (p<0.05), respectively. According to multiple regression analysis (including sex, age, smoking status, and Lp(a) serum level) only smoking status (β=0.203, p=0.0003) and a size of apo(a) isoforms (β=0.191, p=0.0133) correlated with the peripheral atherosclerosis in patients with CHD. LMW apo(a) phenotype was the most significant predictor of peripheral atherosclerosis (β=0.281, p=0.0089) regardless of the Lp(a) serum level in patients under 55 y.o. High Lp(a) serum level combined with LMW apo(a) phenotype associated with more significant coronary, carotid and peripheral atherosclerosis.Conclusion. LMW apo(a) phenotype relates to the presence of multifocal atherosclerosis in CHD patients regardless of the Lp(a) serum level. Apo(a) phenotype can be a marker of generalized atherosclerosis especially among young adults. Next studies of correlations Lp(a) and apo(a) phenotype with lower limb arteries lesions are needed in various patients.