Khazar University

In this work, we construct new Bailey pairs for the integral pentagon identity in terms of q-hypergeometric functions. The pentagon identity considered here represents the equality of the partition functions of certain three-dimensional supersymmetric dual theories. It can be also interpreted as the star-triangle relation for the Ising-type integrable lattice model.

Tea, coffee, and cocoa are all popular beverages in Azerbaijan, and each has its own unique cultural significance. Tea is the most popular beverage in Azerbaijan and is often consumed throughout the day. It is also a common accompaniment to meals and social gatherings. Coffee is also popular in Azerbaijan but is more typically consumed as a morning beverage. Cocoa is less popular than tea or coffee but is still enjoyed by many Azerbaijanis. This article will explore the cultural significance of tea, coffee, and cocoa in Azerbaijan. It will discuss the history of each beverage in this country, as well as different ways in which they are served, consumed and enjoyed. The article will also examine the role that these beverages play in Azerbaijani society and culture. The article will conclude by discussing the importance of tea, coffee, and cocoa to Azerbaijani culture. It will argue that these beverages are more than just drinks; they are also important symbols of Azerbaijani hospitality, friendship, and community.

Genetic diversity of 45 genotypes were shown in the list of genotypes Azerbaijani durum wheat (Triticum durum Desf.) genotypes were screened using simple sequence repeats (SSRs). These accessions were collected from various bioclimatic regions of Azerbaijan. Out of the used 22 primers, 13 primers showed polymorphism and were selected for the analyses. Among the genotypes under study, 31 alleles were detected. The highest number of alleles was detected in locus gwm 335 (on chromosome 5B) and on locus gwm 445 (on chromosome 2A) with 5 and 4 alleles, respectively. The lowest number of alleles was found in locus gwm 617 with only 1 allele. For A, B, and D genomes, the total number of alleles detected was 14, 15, and 2, respectively. PIC value between studied SSR markers was 0.912 and this result shows high genetic diversity between Azerbaijani durum wheat genotypes. Therefore, these primers can be recommended for studying the genetic diversity of Azerbaijani durum wheat accessions. The genetic structure of the genotypes was analyzed and the Unweighted Pair Group Method with Arithmetic Mean (UPGMA) dendrogram revealed five major clusters using Nei genetic distance index. The results revealed that SSR markers can efficiently evaluate genetic variation in the wheat samples. Based on the previous characterization of the drought response of these genotypes, links could be established between the SSR markers and drought tolerance. If some of the SSR markers are confirmed for their association with drought tolerance, then, they can be used as markers for the identification of drought-tolerant cultivars needed to enhance wheat productivity for farmers dealing with harsh conditions.

Distributed Denial of Service (DDoS) attacks pose a significant threat to online services, causing disruption and financial losses to victim organizations. To enhance the preparedness of potential targets, this research paper introduces the concept of a DDoS simulation portal. The portal, exemplified by ddosattack.online, aims to simulate DDoS attacks and provide valuable insights to help targets understand their limits and devise effective mitigation strategies. The paper reviews Layer 7 attacks, outlines the development and usage of the simulation portal, and discusses future plans for incorporating Layer 4 attacks and expanding attack locations.

The current research focuses on optimizing the Nusselt number (Nu) and pressure drop (ΔP) in a bionic fractal heat sink. The artificial neural network (ANN) and response surface methodology (RSM) were used to model the thermos-hydraulic behavior of the MCHS. The aspect ratios of t/b (cavities' upper side to bottom side ratio) and h/b (cavities’ height to bottom side ratio), as well as the Reynolds number, were set as the independent variables in both ANN and RSM models. After finding the optimum state for the copper-made MCHS (containing the optimum design of the cavities along with the best applied velocity), different materials were tested and compared with the base case (heat sink made of copper). The obtained results indicated that both ANN and RSM models (with determination coefficient of 99.9 %) could exactly anticipate heat transfer and ΔP to a large extent. To achieve the optimal design of the microchannel heat sink (MCHS) with the objective of maximizing Nu and minimizing ΔP, the efficiency index of the device was evaluated. The analysis revealed that the highest efficiency index (1.070 by RSM and 1.067 by ANN methods) was attained when the aspect ratios were t/b = 0.2, h/b = 0.2, and the Reynolds number was 1000. Next, the effect of the different materials on heat sink performance was investigated, and it was observed that by reducing the thermal conductivity, the thermal resistance of the heat sink increased and its overall performance decreased.

In this paper, the Titchmarsh–Weyl theory of the impulsive [Formula: see text]-Dirac equation is studied.

The complex application of modern analysis methods (FT-IR, NMR, GC–MS and UV/Vis) allowed us to study in detail the composition of the crude Surakhani light oil with a complex composition. An accurate and comprehensive study of the composition of crude oils makes it easier to find the necessary field of application for them. For this purpose, the studied crude oil was separated into two fractions, such as paraffinic–naphthenic and aromatic (groups 1st, 2nd, 3rd and tar), by absorption column chromatography. The results show that Surakhani light oil is a paraffin–naphthene-based oil that contains 74% of paraffin–naphthene, 11.15% of aromatic hydrocarbons and 14.8% of gases. It has been shown that the aromatic group of compounds is mainly composed of mono- and bicyclic compounds and has alkyl chains with different lengths and branches (with the presence of methylene and methine groups). Based on the parameters of the structural group, it was found that the portion of H atoms in the aromatic nucleus and alkyl chain was 4.4–20.1% and 79.9–95.6%, respectively. The degree of aromaticity of the separated aromatic group is approximately 50%, which proves that these compounds are alkylated. The structure of the isolated paraffin–naphthene fraction has also been investigated by spectroscopic techniques, and it has been determined that this fraction is composed of iso- and cycloalkanes with alkyl chains of different lengths. As it is seen from the obtained results, unlike the other oils existing on the Absheron Peninsula, Surakhani light oil consists of one- and two-ring naphthene and isostructured paraffinic hydrocarbons. The composition of this petroleum mainly consists of isosubstituted alkyl cycloalkanes and relict, viz. biologically active hydrocarbons such as sterane and hopane used in medicine. It seems that the methodology developed for the petroleum industry can be used in other fields such as medicine. Graphical abstract

Let X be a compact metric space, C(X) be the space of continuous real-valued functions on X and $A_{1},A_{2}$ be two closed subalgebras of C(X) containing constant functions. We consider the problem of approximation of a function $f\in C(X)$ by elements from $A_{1}+A_{2}$. We prove a Chebyshev-type alternation theorem for a function $u_{0} \in A_{1}+A_{2}$ to be a best approximation to f.

We study some problems of operator theory by using Berezin symbols approach. Namely, we investigate in terms of Berezin symbols invariant subspaces of isometric composition operators on \({\mathcal {H}}\left( \Omega \right) .\) We discuss operator corona problem, in particular, the Toeplitz corona problem. Further, we characterize unitary operators in terms of Berezin symbols. We show that the well known inequality \(w\left( A\right) \ge \frac{1}{2}\left\| A\right\| \) for numerical radius is not true for the Berezin number of operators, which is defined by \({\textrm{ber}}\left( A\right) :=\sup _{\lambda \in \Omega }\left| {\tilde{A}}\left( \lambda \right) \right| ,\) where \({\tilde{A}}\left( \lambda \right) :=\left\langle A\hat{k}_{\lambda },{\hat{k}}_{\lambda }\right\rangle \) is the Berezin symbol of operator \(A:{\mathcal {H}}\left( \Omega \right) \rightarrow {\mathcal {H}}\left( \Omega \right) .\) Finally, we provide a lower bound for \({\textrm{ber}}\left( A\right) .\)

We study the Titchmarsh–Weyl theory of the impulsive dynamic Dirac system. The limit-circle/limit-point classification will be obtained for this system. Later, it has been proven that just like the classical Dirac systems, only the limit-point case occurs in the impulsive dynamic Dirac system. Finally, an example is given for the results in the article.

The paper considers the scattering problem for the first-order system of hyperbolic equations on the half-axis with a nonhomogeneous boundary condition. This problem models the phnomennon of wave propagation in a nonstationary medium where an incoming wave unaffected by a potential field. The scattering operator on the half-axis with a nonzero boundary condition is defined and the uniqueness of the inverse scattering problem (the problem of finding the potential with respect to scattering operator) is studied.

We discuss an elementary derivation of variational symmetries and corresponding integrals of motion for the Lagrangian systems depending on acceleration. Providing several examples, we make the manuscript accessible to a wide range of readers with an interest in higher-order Lagrangians and symmetries. The discussed technique is also applicable to the Lagrangian systems with higher-order derivatives.

This paper considers the method of Riemann boundary value problems of the theory of analytic functions to study basis properties of perturbed systems of exponents in rearrangement invariant Banach function spaces. This method is demonstrated by the example of a system of exponents with a linear phase, depending on a complex parameter. The study of the basis properties of this system has a deep history starting with the classical results of Paley–Wiener and Levinson. The basis properties of this system in Lebesgue spaces were finally established in the works of Sedletskii and Moiseev. As special cases of rearrangement invariant Banach function spaces (r.i.s. for short), we can mention Lebesgue, Orlicz, Lorentz, Lorentz–Orlicz, Marcinkiewicz, grand-Lebesgue and other classical and non-standard spaces. A subspace of r.i.s. is considered where continuous functions are dense and the conditions on phase parameter are found, depending on the Boyd indices, which are sufficient for basicity of the system of exponents for this subspace. In the special case, where the Boyd indices coincide with each other, these conditions become a basicity criterion. A new proof method, different from the previously known ones, is proposed. In particular, previously known results are obtained for some Banach function spaces.