Indefinite Sturm-Liouville operators with the singular critical point zero

We present a new necessary condition for similarity of indefinite Sturm-Liouville operators to self-adjoint operators. This condition is formulated in terms of Weyl-Titchmarsh $m$-functions. Also we obtain necessary conditions for regularity of the critical points 0 and $\infty$ of $J$-nonnegative Sturm-Liouville operators. Using this result, we construct several examples of operators with the singular critical point zero. In particular, it is shown that 0 is a singular critical point of the operator -\frac{(\sgn x)}{(3|x|+1)^{-4/3}} \frac{d^2}{dx^2} acting in the Hilbert space $L^2(\R, (3|x|+1)^{-4/3}dx)$ and therefore this operator is not similar to a self-adjoint one. Also we construct a J-nonnegative Sturm-Liouville operator of type (\sgn x)(-d^2/dx^2+q(x)) with the same properties.Comment: 24 pages, LaTeX2e <2003/12/01

Temperature deformations of the mirror of a radio telescope antenna

The stress informed state of the mirror of an antenna, with a diameter of 3 m, for a radio interferometer used in space, and located in a temperature field is examined. The mirror represents a parabolic shell, consisting of 19 identical parts. The problem is based on representations of the thermoelasticity of thin shells

Особливості геному великої рогатої худоби

Boss taurus is not only an important agricultural species, which during the last 8–10 thousand years since domestication served to humanity as a reliable source of milk, meat, skin, and cattle, is a successful object for the study of obesity, gynecological and infectious diseases of man. Cows are successfully used as a model organism in endocrinology, physiology and reproductive biotechnology. Today, in the world, the number of ruminants – large and small cattle, namely – buffaloes, sheep and goats is estimated at around 3.4 billion. About three-fourths of the world's agricultural land produces fodder suitable for the grazing of these ruminants, which have an amazing ability to effectively convert low-quality vegetable fibers, which are often not suitable for human use, into energy-intensive fat, muscle and milk. This biological process has long been used by humanity, which in the process of breeding has created more than 800 breeds of cattle, which is an important world heritage and a unique scientific resource. The B. taurus genome is estimated at 3000 MB, arranged in 29 pairs of acrocentric autosomes and two sex chromosomes. The sequencing of the bovine genome was conducted by a consortium of more than 300 scientists from 25 different countries. The results of the analysis of the genome are presented in the database ncbi. For the first time, it was sequenced by the genome of one inverted cow of the Hereford breed, L1 Dominette. In addition, today's well-known information on the sequence of six species animals, which identified SNP, was the main resource for the HapMap project, which used 34.470 of them in their analyzes, the EST collection and about 10.000 full-screen cDNA sequences. A genomic card of cattle based on high-density bonds is also reported. The World Society has created and actively used databases containing information on the sequence of genomes, genes, proteins, and their polymorphism. Particular attention deserves descriptions of the results of the analysis of single-nucleotide polymorphism, which allows us to analyze the evolutionary history of phylogenetic bonds in the middle of the species and between different species. The analysis of the associated quantitative features of the loci gives the scientific community additional confidence in identifying the polymorphism of genes, which is the basis of animal productivity. The QTL database contains data on 108 040 bovine cattle, which are associated with 579 different quantitative features. With the polymorphism of individual genes, harmful mutations are associated with the genetic load of populations. To date, 519 traits (disorders) have been described, 203 of them are considered by potential models for research on human diseases. A connection was found between the mutations that caused the 145 polymorphisms.Boss taurus – не лише важливий сільськогосподарський вид, який протягом останніх 8–10 тисяч років з моменту одомашнення слугує людству надійним джерелом молока, м’яса, шкіри, тварини великої рогатої худоби є вдалим об’єктом для дослідження ожиріння, гінекологічних та інфекційних захворювань людини. Корів успішно використовують як модельний організм в ендокринології, фізіології та репродуктивній біотехнології. На сьогодні у світі поголів’я жуйних тварин – великої та малої рогатої худоби, а саме – буйволів, овець та кіз налічує близько 3,4 мільярда. Близько трьох чвертей світових сільськогосподарських угідь землі продукують корм, придатний для випасу цих жуйних тварин, які мають дивовижну здатність ефективно перетворювати низькоякісне рослинне волокно, що часто не підходить для людського використання, в енергоємний жир, м’язи та молоко. Цей біологічний процес давно використовується людством, яке в процесі селекції створило понад 800 порід великої рогатої худоби, що є важливою всесвітньою спадщиною та унікальним науковим ресурсом. Геном B. taurus оцінюється у 3000 МБ, організованих в 29 пар акроцентричних аутосом і дві статеві хромосоми. Секвенування геному великої рогатої худоби було проведено консорціумом, що налічував понад 300 вчених з 25 різних країн. Результати аналізу геному подані в базі даних ncbi. Вперше було секвеновано геном однієї інбредної корови породи Херефорд, L1 Dominette. Крім того, на сьогодні відома інформація про послідовності тварин шести порід, що дозволило виявити SNP, основний ресурс для проекту HapMap, який використовував 34 470 з них у своїх аналізах, EST колекції та близько 10 000 повноекранних послідовностей кДНК . Також повідомляється про геномну карту великої рогатої худоби на основі зв'язків високої щільності. На сьогодні накопичені значні масиви даних, які стосуються аналізу геномів тварин. Світовим товариством були створені й активно використовуються бази даних, що містять інформацію про послідовності геномів, генів, білків, їх поліморфізм. Особливої уваги заслуговують описи результатів аналізу однонуклеотидного поліморфізму, який дозволяє проаналізувати еволюційну історію філогенетичних зв’язків всередині виду та між різними видами. Аналіз локусів, асоційованих з кількісними ознаками, дає науковому співтовариству додаткову впевненість у ідентифікації поліморфізму генів, що є основою продуктивності тварин. База даних QTL містить дані щодо 108 040 локусів великої рогатої худоби, які асоційовані з 579 різними кількісними ознаками. З поліморфізмом окремих генів пов’язані шкодочинні мутації, що складають генетичний вантаж популяцій. На сьогодні описано 519 ознак великої рогатої худоби, 203 з них вважються потенційними моделями для досліджень захворювань людини. Знайдено зв'язок з мутаціями, що були причиною поліморфізму 145 ознак

The similarity problem for JJ-nonnegative Sturm-Liouville operators

Sufficient conditions for the similarity of the operator $A := 1/r(x) (-d^2/dx^2 +q(x))$ with an indefinite weight r(x)=(\sgn x)|r(x)| are obtained. These conditions are formulated in terms of Titchmarsh-Weyl $m$-coefficients. Sufficient conditions for the regularity of the critical points 0 and $\infty$ of $J$-nonnegative Sturm-Liouville operators are also obtained. This result is exploited to prove the regularity of 0 for various classes of Sturm-Liouville operators. This implies the similarity of the considered operators to self-adjoint ones. In particular, in the case r(x)=\sgn x and $q\in L^1(R, (1+|x|)dx)$, we prove that $A$ is similar to a self-adjoint operator if and only if $A$ is $J$-nonnegative. The latter condition on $q$ is sharp, i.e., we construct $q\in \cap_{\gamma <1} L^1(R, (1+|x|)^\gamma dx)$ such that $A$ is $J$-nonnegative with the singular critical point 0. Hence $A$ is not similar to a self-adjoint operator. For periodic and infinite-zone potentials, we show that $J$-positivity is sufficient for the similarity of $A$ to a self-adjoint operator. In the case $q\equiv 0$, we prove the regularity of the critical point 0 for a wide class of weights $r$. This yields new results for "forward-backward" diffusion equations.Comment: 36 pages, LaTeX2e, version 2; addresses of the authors added, the reference [38] update

Simulation of the short-range order in disordered cubic titanium monoxide TiO1.0

A model of the atomic structure with the short-range order in the vacancy distribution for the disordered cubic phase of titanium monoxide TiO1.0 has been proposed. The effect of the short-range order on the electronic structure and the stability of the compound has been studied by the supercell method within the DFT-GGA approximation with the use of pseudopotentials. It has been established that the appearance of the short-range order considerably decreases the total energy. The decrease in the energy is comparable with the energy gain during the ordering of the vacancies according to the type of monoclinic superstructure Ti5O5 to the long-range order parameter η = 0.7. It has been shown that the discrepancies between the theoretical and experimental electronic spectra of titanium monoxide can be explained by allowance for the short range order. © 2013 Pleiades Publishing, Ltd

Internet Commerce As a Possible Direction for the Development of Entrepreneurship Supply Chain and Information Management

Information and communications technology in supply chain management has enabled corporations to use offshore facilities for outsourcing commercial activities. One of the current trends in the global economic space is the formation of an information economy that allows fulfilling the requirements for the interaction organization between business entities at a high organizational level. At the same time, the traditional economy is significantly lagging behind in the development of new economic trends such as digitalization, supply chain and information management, which necessitates to create effective measures aimed at developing the economic information space: in particular, the Internet entrepreneurship supply chain management. To solve this problem, it is proposed to use a combination of quantitative and qualitative methods, including test analysis method, logical-structural and causal analysis, as well as synthesis of literature, strategic analysis method, content analysis, applied economic and statistical methods, and sociological survey. Using these methods allowed determining the set of factors affecting the growth and development of the Internet entrepreneurship supply chain. We classified e-commerce models according to various criteria, formed different directions of the impact of government regulation on the e-commerce market and information management in the supply chain system. The identification of factors holding back the development of e-commerce made it possible to determine the nature of their negative impact on the development of the Internet entrepreneurship supply chain and to give some recommendations on improving the efficiency of state regulation of this sphere and ensuring its greater attractiveness in the minds of consumers. Application of the obtained results will make it possible to prepare regulatory and program documents in the field of state regulation of the Internet entrepreneurship supply chain and determine possible directions for its development in the future

Heliosystem of Auxiliary Heat Supply for a Mining Enterprise

In the conditions of the global ecological crisis in the world and Ukraine, the issue of finding alternative energy sources becomes relevant. One of the most common types of renewable energy is solar energy. In Ukraine today, the most promising direction of using solar energy is its direct transformation into low-potential thermal energy. To get electric power, solar radiation is the mere alternative to electric power generated from mined fuel, and without the pollution of air and water, or adverse consequences manifested in global warming. The disadvantage of this type of installation is the limitation of the duration of light time, as well as the effect of cloudiness. During the day, the number of solar radiation changes, to stabilize it is necessary to accumulate and accumulate it for further use, the technical implementation of stable operation of solar installation due to the use of terrestrial radiation and the accumulator of a specific part of solar energy is proposed. The purpose of the work is experimental studies to ensure the stable operation of the solar collector under cloudy conditions. The paper is aimed at the stabilization of the operation of the solar installation and to obtain additional heat after the Sun’s cloud cover. The use of a solar thermal collector is advisable in solar heating and hot water systems in conditions of alternating solar radiation. The results of physical modeling have proved the efficiency of the method of combining types of thermal radiation, due to the accumulation of energy it is possible to increase the quantitative index of solar energy in the conditions of cloudiness by 3 times

Diagnostics of formedness of system of values of future economists in professional preparation process

The article presents the results of the diagnostics of the formation of the value sphere of future economists. The problem of diagnostics of the formedness of the axiosphere of future economic profile specialist is becoming increasingly relevant in the context of modern socio-economic and political conditions. The notion of "value" is considered in the article as a material or spiritual object, which matters for a particular person and causes a valuable relation to it. We define the valuable orientations of the person as a relatively stable orientation of the needs of an individual towards a certain group of values. The purpose of the research is to carry out the diagnostics of the formation of the value sphere of future specialists of the economic profile. Students studying economics on 1-3 courses participated in the study. The methods of conversations, interviews, questionnaires, and observations were used to diagnose the formedness of the value sphere of future specialists in the economic field in the process of carrying out their vocational training. The conducted research testifies to the formedness of certain social image of democratic and totalitarian values of future economic specialists. However, there is a need for further work on clarifying the essence of such socially important values as discipline and law-abidingness and the formation of proper awareness of them by future economists. The development of a methodology for formation of the value sphere of the future specialist in the economic profile is the prospects for further research.peer-reviewe

Spectral Asymptotics for Perturbed Spherical Schr\"odinger Operators and Applications to Quantum Scattering

We find the high energy asymptotics for the singular Weyl--Titchmarsh m-functions and the associated spectral measures of perturbed spherical Schr\"odinger operators (also known as Bessel operators). We apply this result to establish an improved local Borg-Marchenko theorem for Bessel operators as well as uniqueness theorems for the radial quantum scattering problem with nontrivial angular momentum.Comment: 20 page