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

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

Self-Propagating High-Temperature Synthesis of Chromium Substituted Lanthanide – Barium – Copper Oxides, LnBa2Cu3-xCrxO7-y (Ln = Y; La; Nd; Sm and Yb)

A series of MBa2Cu3-xCrxO7-y (M = Y; La; Nd; Sm and Yb; x = 0, 0.05, 0.15, 0.25) materials were synthesized in air by self-propagating high-temperature synthesis (SHS) involving reaction of stoichiometric mixtures of rare-earth metal (III) oxide, barium peroxide, copper metal, chromium (III) oxide and sodium perchlorate. All the SHS processes were followed by sintering in oxygen at 950 °C for 2 h. The products were characterized by SEM, X-ray powder diffraction, UV, superconductive transition temperatures (Tc) and magnetic susceptibility (χ) measurements. X-ray diffraction data showed that single phase orthorhombic (or tetragonal for M = Nd) materials were produced. All series of materials showed a systematic increase in lattice parameters and unit cell volume with chromium content (M = Y: x = 0, V = 174.25 Å3; x = 0.25, V = 175.10 Å3). Thermal stability of all the SHS prepared materials increased with x. Oxygen content of all the samples increased with x, but did not exceed 7.0. Superconductivity transition temperature decreased with chromium substitution in all systems (98-77 K). Magnetic susceptibility decreased with chromium substitution

Lipid Regulators during Atherogenesis : expression of LXR, PPAR, and SREBP mRNA in the Human Aorta

Transcription factors LXRs, PPARs, and SREBPs have been implicated in a multitude of physiological and pathological processes including atherogenesis. However, little is known about the regulation of these transcription factors at different stages of atherosclerosis progression. Quantitative real-time polymerase chain reaction (qRT-PCR) was used to compare the contents of mRNAs in pairs intact-injured aorta fragments taken from the same donors. Only minor changes in LXR?, LXR?, PPAR?, PPAR?, SREBP1, and SREBP2 mRNA levels were found in initial lesions as compared with intact non-diseased tissue. The contents of all mRNAs but SREBP2 mRNA were found to be progressively up-regulated in fatty streaks and fibrous lipoid plaques. These changes were only partially reproduced in cultured macrophages upon lipid loading. Wave-shaped changes in abundance of correlations between given group of mRNAs and 28 atherosclerosis-related mRNA species in the course of atherogenesis were observed. The impact of specific mRNA correlations on the total correlations also significantly varied between different lesion types. The study suggests that the extent and forms of LXR/PPAR/SREBP participation in intima functions vary nonlinear in individual fashion in atherogenesis. We speculate that the observed changes in mRNAs expression and coupling reflect shifts in lipid ligands availability and cellular composition in the course of atherosclerosis progression

Prospects for the Development of the Oil and Gas Industry in the Regional and Global Economy

Problems of energy efficiency, along with increasing environmental safety of production and increasing social responsibility, are becoming a central object of research. Therefore, the main goal of the work is to analyze the prospects for the development of the oil and gas industry. It was established that innovative technologies play an important role in the development of energy. In the structure of public administration, the definition of the place in the close relationship with commodity-money relations, mediating its implementation. But refusal of oil resources will lead to negative consequences. It is established that the maximum production of conventional oil in the world in the amount of 4.5-4.8 billion tons per year will be achieved in 2020-2030. Major areas of conventional oil production in this period will be oil and gas basins of the Persian Gulf, Western and Eastern Siberia, the Caspian sea, the Atlantic shelves of Africa and South America. The achieved level of oil production can be maintained by large-scale involvement in the development of non-traditional sources (bitumen and shale oil). According to the raw material base, the leaders of unconventional oil production should be Venezuela, Canada, Russia and the United States. Keywords: environmental policy, oil production, forecast, coal-fired power plants, economic crisis. JEL Classifications: L100, Q400, Q430

How close can one approach the Dirac point in graphene experimentally?

The above question is frequently asked by theorists who are interested in graphene as a model system, especially in context of relativistic quantum physics. We offer an experimental answer by describing electron transport in suspended devices with carrier mobilities of several 10^6 cm^2V^-1s^-1 and with the onset of Landau quantization occurring in fields below 5 mT. The observed charge inhomogeneity is as low as \approx10^8 cm^-2, allowing a neutral state with a few charge carriers per entire micron-scale device. Above liquid helium temperatures, the electronic properties of such devices are intrinsic, being governed by thermal excitations only. This yields that the Dirac point can be approached within 1 meV, a limit currently set by the remaining charge inhomogeneity. No sign of an insulating state is observed down to 1 K, which establishes the upper limit on a possible bandgap