Number Theoretic Arithmetic Functions and Dirichlet Series

In this study, we will study number theoretic functions and their associated Dirichlet series. This study lay the foundation for deep research that has applications in cryptography and theoretical studies. Our work will expand known results and venture into the complex plane

Approaches to the Erdős–Straus Conjecture

The Erdős–Straus conjecture, initially proposed in 1948 by Paul Erdős and Ernst G. Straus, asks whether the equation 4/n = 1/x + 1/y + 1/z is solvable for all n ∈ N and some x, y, z ∈ N. This problem touches on properties of Egyptian fractions, which had been used in ancient Egyptian mathematics. There exist many partial solutions, mainly in the form of arithmetic progressions and therefore residue classes. In this work we explore partial solutions and aim to expand them

Results of experimental study of friction effect on mechanical properties of salt rocks

The purpose of the work is to study influence of friction between samples and press plates on mechanical parameters of salt rocks. The main source of information for determining values of mechanical parameters of salt rocks is laboratory tests of rock samples for compression. It is known that values of mechanical parameters determined from results of compression of samples essentially depend on magnitude of frictional force between fronts and plates of a press. Wherein, empirical coefficients of shape used in calculation of values of mechanical parameters corresponding to uniaxial compression do not take into account specific frontal conditions. This leads to a known inaccuracy in formulation of an experiment and interpretation of its results. Thus, relevant studies correspond to more detailed study of influence of friction between samples and press plates on mechanical properties of salt rocks. During experimental studies 75 samples of fine to medium grained rock salt from Verkhnekamsk deposit of potassium salts were tested. The paper presents results of experimental studies directed to determine coefficient of friction of salt rocks according to a scheme "shear with compression" over various surfaces. Studies were carried out on compression of samples of different heights under known contact conditions. The necessary friction value was modeled using manufactured gaskets placed between fronts of samples to be tested for compression and press plates. A full diagram of deformation was build from the compression results of each sample and a set of mechanical parameters was determined. Dependences that reflect an effect of frictional forces between fronts of samples and press plates under compression on values of strength limit, destructive deformation and specific energy consumption of rock salt deformation are determined. Results of the study are intended to improve a method of testing rocks for compression

Mathematical model of the mechanical properties of Ti-alloyed hypoeutectic cast iron for mixer blades

The object of research is hypoeutectic cast iron intended for cast parts operating under abrasive friction conditions. Such parts are mixer blades, the operational properties of which include durability, assessed by abrasion resistance and strength. To give the blades such properties, cast irons, which are materials of the blades, are alloyed with elements that contribute to the formation of carbides of various compositions. The main problem that impedes the targeted selection of materials for mixer blades or finished blades from different materials or different chemical composition is the lack of substantiated selection criteria. If the shipment is carried out only with the provision of data on the chemical composition of the alloy, it is necessary to be able to evaluate the expected mechanical properties, in particular abrasion resistance and strength. Using the methods of regression analysis, a mathematical model has been obtained that includes two regression equations, which allows for a targeted selection of the chemical composition that provides the maximum possible value of mechanical properties – ultimate strength and coefficient of wear resistance. Optimization of the chemical composition, carried out according to this model, made it possible to determine the following chemical composition: C=2.94 %, Ceq=3.3 %, Ti=1.56 %, providing the maximum ultimate strength σb=391 MPa; C=2.78 %, Ceq=3.14 %, Ti=1.61 %, providing a maximum wear resistance coefficient Kwr=12 %. In the case of priority of the strength criterion, the calculated optimal chemical composition makes it possible to reduce the mass-dimensional characteristics of the mixing units of the mixers. A procedure is proposed for using this model to select a batch of blades with the expected best performance propertie

Motivation of personnel in an innovative business climate

With increasing understanding of the importance of labor motivation in the personnel management system it is necessary to study the examples of practical implementation of personnel motivation programs that have been tested in successful companies. This work is designed to give answers to the following questions: How and what should motivate employees under the conditions of innovative business development? How is it done in Russia and around the world? What motivating programs are offered by employers today, what are their common features and fundamental differences? The main goal is to identify the best practices of motivation by using the examples of the leading foreign and Russian companies. The main conclusion – even considering the Russian specifics, one large salary is not enough in innovative conditions, therefore progressive companies introduce multifactorial motivation systems, including material and non-material components. The work is of practical value for the Russian business. The continuation of this original research can develop in two directions: "in breadth" and "in depth". In the first case a similar analysis carried out with a large sample of enterprises will reveal additional dependencies. In the second case an empirical study of the reaction to certain motivators and the ways of their implementation within a separate company is proposed.peer-reviewe

Matrix models as conformal field theories: genus expansion

We obtain the topological expansion of the hermitian matrix model using its representation as a CFT on a hyperelliptic Riemann surface. To each branch point of the Riemann surface we associate an operator which represents a twist field dressed by the modes of the twisted boson. The partition function of the matrix model is computed as a correlation function of such dressed twist fields. The perturbative construction of the dressing operators yields a set of Feynman rules for evaluating the free energy and the loop observables at any genus.Comment: 17 pages, 4 figure