On the reduction of the multidimensional Schroedinger equation to a first order equation and its relation to the pseudoanalytic function theory

Given a particular solution of a one-dimensional stationary Schroedinger equation (SE) this equation of second order can be reduced to a first order linear differential equation. This is done with the aid of an auxiliary Riccati equation. We show that a similar fact is true in a multidimensional situation also. We consider the case of two or three independent variables. One particular solution of (SE) allows us to reduce this second order equation to a linear first order quaternionic differential equation. As in one-dimensional case this is done with the aid of an auxiliary Riccati equation. The resulting first order quaternionic equation is equivalent to the static Maxwell system. In the case of two independent variables it is the Vekua equation from theory of generalized analytic functions. We show that even in this case it is necessary to consider not complex valued functions only, solutions of the Vekua equation but complete quaternionic functions. Then the first order quaternionic equation represents two separate Vekua equations, one of which gives us solutions of (SE) and the other can be considered as an auxiliary equation of a simpler structure. For the auxiliary equation we always have the corresponding Bers generating pair, the base of the Bers theory of pseudoanalytic functions, and what is very important, the Bers derivatives of solutions of the auxiliary equation give us solutions of the main Vekua equation and as a consequence of (SE). We obtain an analogue of the Cauchy integral theorem for solutions of (SE). For an ample class of potentials (which includes for instance all radial potentials), this new approach gives us a simple procedure allowing to obtain an infinite sequence of solutions of (SE) from one known particular solution

On a factorization of second order elliptic operators and applications

We show that given a nonvanishing particular solution of the equation (divpgrad+q)u=0 (1) the corresponding differential operator can be factorized into a product of two first order operators. The factorization allows us to reduce the equation (1) to a first order equation which in a two-dimensional case is the Vekua equation of a special form. Under quite general conditions on the coefficients p and q we obtain an algorithm which allows us to construct in explicit form the positive formal powers (solutions of the Vekua equation generalizing the usual powers of the variable z). This result means that under quite general conditions one can construct an infinite system of exact solutions of (1) explicitly, and moreover, at least when p and q are real valued this system will be complete in ker(divpgrad+q) in the sense that any solution of (1) in a simply connected domain can be represented as an infinite series of obtained exact solutions which converges uniformly on any compact subset of . Finally we give a similar factorization of the operator (divpgrad+q) in a multidimensional case and obtain a natural generalization of the Vekua equation which is related to second order operators in a similar way as its two-dimensional prototype does

On a complex differential Riccati equation

We consider a nonlinear partial differential equation for complex-valued functions which is related to the two-dimensional stationary Schrodinger equation and enjoys many properties similar to those of the ordinary differential Riccati equation as, e.g., the famous Euler theorems, the Picard theorem and others. Besides these generalizations of the classical "one-dimensional" results we discuss new features of the considered equation like, e.g., an analogue of the Cauchy integral theorem

Multifractal detrended cross-correlation analysis for two nonstationary signals

It is ubiquitous in natural and social sciences that two variables, recorded temporally or spatially in a complex system, are cross-correlated and possess multifractal features. We propose a new method called multifractal detrended cross-correlation analysis (MF-DXA) to investigate the multifractal behaviors in the power-law cross-correlations between two records in one or higher dimensions. The method is validated with cross-correlated 1D and 2D binomial measures and multifractal random walks. Application to two financial time series is also illustrated.Comment: 4 RevTex pages including 6 eps figure

On the Klein-Gordon equation and hyperbolic pseudoanalytic function theory

Elliptic pseudoanalytic function theory was considered independently by Bers and Vekua decades ago. In this paper we develop a hyperbolic analogue of pseudoanalytic function theory using the algebra of hyperbolic numbers. We consider the Klein-Gordon equation with a potential. With the aid of one particular solution we factorize the Klein-Gordon operator in terms of two Vekua-type operators. We show that real parts of the solutions of one of these Vekua-type operators are solutions of the considered Klein-Gordon equation. Using hyperbolic pseudoanalytic function theory, we then obtain explicit construction of infinite systems of solutions of the Klein-Gordon equation with potential. Finally, we give some examples of application of the proposed procedure

Accounting and Analytical Procurement of Predictive Appraisal of Synergistic Effect in Small Business Construction Companies

This study is aimed at the formation of accounting and analytical systems of predictive consolidated balance sheets, in accordance with certain trends of the synergistic effect. Based on this, the cluster analysis combined with the analysis of the portfolio of works performed by the development and construction companies was carried out, the business strategies and their relationship with the accounting processes were defined, the main trends of preparation and evaluation of the synergistic effect were formed, the value chains were analyze

Finite Element Model of Trenchless Pipe Laying

The paper focuses on the stress and strain state of the underground main pipeline section using Autodesk Inventor software

Synthesis and study of the antimicrobial activity of nifuroxazide derivatives

The number of infections caused by microorganisms that are resistant to antibiotics and synthetic antibacterial drugs is growing fast worldwide. This is one of the most important and urgent problems in health care. The main efforts of researchers around the world are focused on solving this issue. Nitrofurans represent one of the most effective classes of antibacterial drugs. We have synthesized 4 analogues of nifuroxazide – a well known nitrofuran antibiotic – and confirmed their structures by NMR, IR spectroscopy, and mass-spectrometry. All of the obtained compounds were studied for antimicrobial and antifungal activity. Activity against Escherichia coli, Staphylococcus aureus, Staphylococcus haemolyticus, and Pseudomonas aeruginosa was evaluated by the agar diffusion method. The synthesized compounds suppressed the growth of all the studied bacterial strains except Escherichia coli; the diameter of the inhibition zones ranged from 13.5 to 28 mm depending on the concentration of the tested compound and bacterial strain. One of the compounds studied in this project – the pyridine analogue of nifuroxazide – exceeded the activity of the standard (nifuroxazide) against the Staphylococcus aureus. The inhibitory activity of the synthesized compounds against the Candida albicans and Cryptococcus neoformans yeasts was determined using the microdilution method. The results were assessed according to the indicator color change. None of the studied compounds showed activity against these cultures. The obtained results confirm that substituted nifuroxazides have significant antimicrobial activity and, therefore, can be considered as promising candidates for developing new antibacterial drugs.The number of infections caused by microorganisms that are resistant to antibiotics and synthetic antibacterial drugs is growing fast worldwide. This is one of the most important and urgent problems in health care. The main efforts of researchers around the world are focused on solving this issue. Nitrofurans represent one of the most effective classes of antibacterial drugs. We have synthesized 4 analogues of nifuroxazide – a well known nitrofuran antibiotic – and confirmed their structures by NMR, IR spectroscopy, and mass-spectrometry. All of the obtained compounds were studied for antimicrobial and antifungal activity. Activity against Escherichia coli, Staphylococcus aureus, Staphylococcus haemolyticus, and Pseudomonas aeruginosa was evaluated by the agar diffusion method. The synthesized compounds suppressed the growth of all the studied bacterial strains except Escherichia coli; the diameter of the inhibition zones ranged from 13.5 to 28 mm depending on the concentration of the tested compound and bacterial strain. One of the compounds studied in this project – the pyridine analogue of nifuroxazide – exceeded the activity of the standard (nifuroxazide) against the Staphylococcus aureus. The inhibitory activity of the synthesized compounds against the Candida albicans and Cryptococcus neoformans yeasts was determined using the microdilution method. The results were assessed according to the indicator color change. None of the studied compounds showed activity against these cultures. The obtained results confirm that substituted nifuroxazides have significant antimicrobial activity and, therefore, can be considered as promising candidates for developing new antibacterial drugs

DIAGNOSTICS AND PREVENTION OF ZINC AND COBALT DEFICIENCY IN CATTLE IN MODERN CONDITIONS OF MILK PRODUCTION IN THE KHARKIV REGION

Північні райони Харківської області, до якихі належить і Дергачівський район, належить до центральної біогеохімічної зони, у грунтах якої бракує засвоюваних форм Цинку і Кобальту. Тому метою роботи стало встановлення діагностичних критеріїв нестачі Кобальту і Цинку у великої рогатої худоби за сучасних умов виробництва молока в Харківській області.Матеріалом для дослідження були проби кормів та крові з 5-ти ферм одного господарства Дергачівського району, Харківської області (лактуючі корови червоної степової породи, віком 3-6 років). Усього досліджено 59 проб кормів та 100 проб крові від корів.Встановлено основні діагностичні критерії нестачі Цинку і Кобальту в організмі корів, а саме: симптомокомплекс, що включає зниження продуктивності, виникнення захворювань репродуктивної системи, спотворення смаку, ураження шкіри, випадіння шерсті, блідість видимих слизових оболонок; низький вміст мікроелементів у раціоні ВРХ; зниження рівня мікроелементів у сироватці крові корів відносно фізіологічної норми.Для профілактики нестачі вищевказаних мікроелементів в організмі ВРХ виробникам комбікормів необхідно суворо дотримуватися рецептури виготовлення, враховувати вміст Цинку і Кобальту у сировині для комбікормів, а особливо у кормових добавках (преміксах, БВМД). Спеціалістам господарств бажано два рази на рік проводити діагностичні дослідження крові на вміст вищевказаних мікроелементів, а також контролювати їх вміст у раціоні ВРХ.Северные районы Харьковской области, к которым пренадлежит и Дергачевский район, относится к центральной биогеохимической зоны, в почвах которой не хватает усваиваемых форм цинка и кобальта. Поэтому целью работы стало установление диагностических критериев недостатка кобальта и цинка у крупного рогатого скота в современных условиях производства молока в Харьковской области.Материалом для исследования послужили пробы кормов и крови с 5-ти ферм одного хозяйства Дергачевского района, Харьковской области (животные красной степной породы в возрасте 3-6 лет, лактирующие). Всего происследовано 59 проб кормов и 100 проб крови от коров.Установлены основные диагностические критерии недостатка цинка и кобальта в организме коров, а именно: симптомокомплекс, включающий снижение продуктивности, возникновение заболеваний репродуктивной системы, извращение вкуса, поражения кожи, выпадение шерсти, бледность видимых слизистых оболочек; низкое содержание микроэлементов в рационе КРС; снижение уровня металлов в сыворотке крови коров относительно физиологической нормы.Для профилактики недостатка вышеуказанных микроэлементов в организме КРС производителям комбикормов необходимо строго соблюдать рецептуры изготовления, учитывать содержание цинка и кобальта в сырье для комбикормов, а особенно в кормовых добавках (премиксы, БВМД). Специалистам хозяйств желательно 2 раза в год проводить диагностические исследования крови на содержание вышеуказанных металлов, а также контролировать их содержание в рационе КРС.Northern areas of Kharkiv region, which belongs to Dergachevsky region, which refers to the central biogeochemical zone, in the soil which lacks digestible forms of zinc and cobalt. Therefore, the aim of the work was to establish diagnostic criteria of cobalt and zinc deficiency in cattle in modern conditions of production of milk in the Kharkiv region.Material for the study is based on a sample of blood and fodder from 5 farms of the one householdfrom of the feed and 5 trusses of Dergachevsky area, Kharkiv region (red steppe breed lactating animals aged 3-6 years). It have been studied 59 samples of feed and 100 blood samples from cows.It was estublished the basic diagnostic criteria of zinc and cobalt deficiency in the body of cows, namely: syndrome that including loss of productivity, the emergence of diseases of the reproductive system, taste perversion, skin lesions, wool loss, paleness visible mucous membranes; low content of microelements in the diet of cattle; reducing metal cows serum in compared whith the physiological norm.For the prevention of a lack of microelements in the cattle producers of feed must be strictly observed formulation manufacturing, to consider the content of zinc and cobalt in raw materials for animal feed, especially in feed additives (premixes). Experts of farms desirable 2 times a year to carry out diagnostic blood tests for the maintenance of the aforementioned metals, as well as to monitor their content in the diet of cattle