An algebraic proof of a result by Gonzagaand Lara

AbstractThe equality of two condition numbers of a rectangular matrix recently established by C.C. Gonzaga and H.J. Lara [Linear Algebra Appl. 261 (1997) 269–273] is now proved by purely algebraic means

A note on an unusual type of polar decomposition

AbstractMotivated by applications in the theory of unitary congruence, we introduce the factorization of a square complex matrix A of the form A=SU, where S is complex symmetric and U is unitary. We call this factorization a symmetric–unitary polar decomposition or an SUPD. It is shown that an SUPD exists for every matrix A and is always nonunique. Even the symmetric factor S can be chosen in infinitely many ways. Nevertheless, we show that many properties of the conventional polar decomposition related to normal matrices have their counterparts for the SUPD, provided that normal matrices are replaced with conjugate–normal ones

Numerical Study of the Oregonator Models on the Basis of the Two-Phase Rozenbrock's Method with Complex Coefficients

Chemical transformations typically occur according to multiphase schemes. Changes in the concentrations of the starting materials and intermediates with time are not always described with increasing or decreasing functions. A detailed study of a complex process kinetics showed that at the presence of feedback far from equilibrium there may occur vibrational modes - periodic increase or decrease in the concentration of one of the components in time. In a numerical study of oscillating reactions there appears a problem in solving a rigid system of typical differential equations. The purpose of this study is to develop an algorithm and a program to solve the direct kinetic problem and to investigate multicomponent chemical systems with complex nonlinear dynamics

The possibility of using microwaves to obtain extracts from berry press residues and jelly products with bioactive characteristics

The paper explores the possibility of development a microwave technology for obtaining water extracts from berry press residues (wild bilberries and cranberries as the objects) and jelly products based on them, which will allow using the waste of freshly squeezed juices in business, such as restaurants and catering services. The antioxidant activity (DPPH and FRAP methods), content of phenolic compounds, flavonoids, anthocyanins, ascorbic acid were determined in berries and in berry press residues. The antioxidant activity of bilberry press residues was due to anthocyanins, and the activity of cranberry press residues was due to flavonoids. Using the microwave oven (magnetron power 800 W, frequency 2,450 MHz), water extracts were obtained in the ratio: for cranberries 1.5:10, for bilberries 1:10. The antioxidant activity of extracts depended on the type of berries and was greater in extracts from bilberry press residues. Extracts of bilberries and cranberries and their compositions (sugar-free and sugaradded) with gelatin as a gelling agent were used to produce the jelly products. Combining bilberry and cranberry extracts (70:30) with gelatin makes it possible to obtain jelly products without sugar. Heating of the ready recipe mixture after preliminary swelling of gelatin and without swelling of gelatin was carried out in the microwave oven. The antioxidant activity of jelly products was higher when using bilberry extracts than cranberries. An increase in the antioxidant activity of the extracts led to a slowdown in structure formation, but increased the plasticity of the products

IMPLEMENTATION OF THE CONCESSION IN DEVELOPING UZBEKISTAN TRANSPORT INFRASTRUCTURE

The article considers concession as a potential method of financing the transport infrastructure in Uzbekistan. The concession is suggested as an optimal policy option within public-private partnership (PPP). The paper defines directions targeted to build-up PPP conditions in the country.Concession, transport infrastructure, transport policy, lack of resources, public-private partnership., Public Economics, L92, R40,

AN APPROACH OF REDUCING COMPOUNDS' SET BASED ON MOLECULAR SIGNATURES

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Influence of flow hydraulic characteristics on the ridge lower escarpment angle

In the riverbeds and canals that run on non-cohesive grounds, bedload sediments move in the ridges form. Ridge forms determine the flow rate of bedload sediments, hydraulic resistances, the types and rates of deformations in alluvial channels. The main elements of ridge formations are height, gentle and steep length with corresponding escarpments. The ridge's steep length and this corresponding escarpment change with changes in the flow hydraulic characteristics. With a change in the ridge's steep length and its steep escarpment, the hydraulic resistance of the channel, the flow rate of bedload sediments, the types, and the channel deformation rates change. In the laboratory, a series of experiments with different sediments compositions and diameters were carried out on the hydraulic tray to determine the main elements (total, gentle and steep length, and the ridge height) and the dynamic characteristics of the ridge formations and the flow hydraulic characteristics. Calculation formulas for determining the coefficient of the ridge lower escarpments with and without taking into account the angle of the natural ground escarpment under water and in the dry state, and the dependence of the steepness of the relative ridge on the relative flow velocity, are obtained. The obtained dependencies allow to accurately determine the geometric and dynamic characteristics of bedload ridges and the corresponding hydraulic characteristics that may define the view ridge formations, ridges resistance of the channel, and the flow rate of bedload sediments, and to design sustainable escarpments large channels

Unitary similarity of algebras generated by pairs of orthoprojectors

It is shown that the unitary similarity of two matrix algebras generated by pairs of orthoprojectors { P1, Q1} and {P 2,Q2} can be verified by comparing the traces of P 1, Q1, and (P1Q1)i, i = 1, 2, n, with those of P2, Q2, and (P2Q 2)i. The conditions of the unitary similarity of two matrices with quadratic minimal polynomials presented in [A. George and Kh. D. Ikramov, Unitary similarity of matrices with quadratic minimal polynomials, Linear Algebra Appl., 349, 11-16 (2002)] are refined. Bibliography: 10 titles. © 2006 Springer Science+Business Media, Inc

A criterion for unitary congruence between complex matrices

Let A and B be square complex matrices of the same order n. Based on an important result Y. P. Hong and R. A. Horn, we propose a criterion for verifying unitary congruence of these matrices. The criterion requires that a finite number of arithmetic operations be performed. No criteria with this finiteness property were previously known. Bibliography: 7 titles. © 2012 Springer Science+Business Media, Inc