Zeros of the isomonodromic tau functions in constructive conformal mapping of polycircular arc domains: the n-vertex case

Abstract The prevertices of the conformal map between a generic, n-vertex, simply connected, polycircular arc domain and the upper half plane are determined by ﬁnding the zeros of an isomonodromic tau function. The accessory parameters of the associated Fuchsian equation are then found in terms of logarithmic derivatives of this tau function. Using these theoretical results a constructive approach to the determination of the conformal map is given and the particular case of 5 vertices is considered in detail. A computer implementation of a construction of the isomonodromic tau function described by Gavrylenko & Lisovyy [Comm. Math. Phys., 363, 2018)] is used to calculate some illustrative examples. A procedural guide to constructing the conformal map to a given polycircular arc domain using the method presented here is also set out.

Download Full-text

Generalization of Okamoto's Equation to Arbitrary2×2Schlesinger System

Advances in Mathematical Physics ◽

10.1155/2009/461860 ◽

2009 ◽

Vol 2009 ◽

pp. 1-14 ◽

Cited By ~ 1

Author(s):

Dmitry Korotkin ◽

Henning Samtleben

Keyword(s):

Arbitrary Number ◽

Logarithmic Derivative ◽

Virasoro Algebra ◽

Symmetric Form ◽

Schlesinger System ◽

Tau Function ◽

Painlevé Vi Equation ◽

Derivatives Of ◽

Logarithmic Derivatives ◽

Scalar Equations

The2×2Schlesinger system for the case of four regular singularities is equivalent to the Painlevé VI equation. The Painlevé VI equation can in turn be rewritten in the symmetric form of Okamoto's equation; the dependent variable in Okamoto's form of the PVI equation is the (slightly transformed) logarithmic derivative of the Jimbo-Miwa tau-function of the Schlesinger system. The goal of this note is twofold. First, we find a universal formulation of an arbitrary Schlesinger system with regular singularities in terms of appropriately defined Virasoro generators. Second, we find analogues of Okamoto's equation for the case of the2×2Schlesinger system with an arbitrary number of poles. A new set of scalar equations for the logarithmic derivatives of the Jimbo-Miwa tau-function is derived in terms of generators of the Virasoro algebra; these generators are expressed in terms of derivatives with respect to singularities of the Schlesinger system.

Download Full-text

ANALYSIS OF THE GENERAL EQUATIONS OF THE TRANSVERSE VIBRATION OF A PIECEWISE UNIFORM VISCOELASTIC PLATE

Computational nanotechnology ◽

10.33693/2313-223x-2020-7-3-52-56 ◽

2020 ◽

Vol 7 (3) ◽

pp. 52-56

Author(s):

MMATMATISA JALILOV ◽

◽

RUSTAM RAKHIMOV ◽

Keyword(s):

Cross Section ◽

Transverse Vibration ◽

Three Dimensional ◽

Viscoelastic Plate ◽

Constant Thickness ◽

Regional Problem ◽

Rigid Contact ◽

Under Construction ◽

Derivatives Of ◽

Theoretical Results

This article discusses the analysis of the general equations of the transverse vibration of a piecewise homogeneous viscoelastic plate obtained in the “Oscillation of inlayer plates of constant thickness” [1]. In the present work on the basis of a mathematical method, the approached theory of fluctuation of the two-layer plates, based on plate consideration as three dimensional body, on exact statement of a three dimensional mathematical regional problem of fluctuation is stood at the external efforts causing cross-section fluctuations. The general equations of fluctuations of piecewise homogeneous viscoelastic plates of the constant thickness, described in work [1], are difficult on structure and contain derivatives of any order on coordinates x, y and time t and consequently are not suitable for the decision of applied problems and carrying out of engineering calculations. For the decision of applied problems instead of the general equations it is expedient to use confidants who include this or that final order on derivatives. The classical equations of cross-section fluctuation of a plate contain derivatives not above 4th order, and for piecewise homogeneous or two-layer plates the elementary approached equation of fluctuation is the equation of the sixth order. On the basis of the analytical decision of a problem the general and approached decisions of a problem are under construction, are deduced the equation of fluctuation of piecewise homogeneous two-layer plates taking into account rigid contact on border between layers, and also taking into account mechanical and rheological properties of a material of a plate. The received theoretical results for the decision of dynamic problems of cross-section fluctuation of piecewise homogeneous two-layer plates of a constant thickness taking into account viscous properties of their material allow to count more precisely the is intense-deformed status of plates at non-stationary external loadings.

Download Full-text

Experimental and Theoretical Investigations of Complex Formation of Substituted Phenylazo-Derivatives of Methylphloroglucinol

JOURNAL OF ADVANCES IN CHEMISTRY ◽

10.24297/jac.v12i8.2837 ◽

2016 ◽

Vol 12 (8) ◽

pp. 295-300

Author(s):

Olga Kovalchukova ◽

Amangdam A.T. ◽

Strashnova S.B. ◽

Strashnov P.V. ◽

Romashkina E.P. ◽

...

Keyword(s):

Complex Formation ◽

Organic Ligand ◽

Spectrophotometric Titration ◽

Organic Ligands ◽

Oh Groups ◽

Tautomeric Forms ◽

Theoretical Investigations ◽

Derivatives Of ◽

Theoretical Results ◽

Titration Technique

Using spectrophotometric titration technique, the processes of complex formation of some phenylazo-derivatives of methylphloroglucinol (MPG) containing hydroxo-, nitro- and nitroso-substituents were studied. The spectral criteria of neutral and ionized forms of the organic ligands in their different tautomeric forms were determined.It was detected that the complex formation is accompanied by formation of one or two chelate cycles which involve azo- or nitroso-fragments and neighboring OH-groups of the organic ligands. Different types of coordination lead to different changes in the electronic absorption spectra.The DFT-B3LYP modeling of a Ni(II) complex of α-hydroxyphenylazo MPG established the most probable coordination mode of the organic ligand: tridentate chelating dianion, distorted square coordination of Ni-cations including one water molecule. The theoretical results are in a good accordance with the experimental data.

Download Full-text

Simultaneous determination of eight derivatives of propranolol in cornea perfusate in vitro by high performance liquid chromatography

Chinese Journal of Chromatography ◽

10.3724/sp.j.1123.2012.06039 ◽

2013 ◽

Vol 30 (11) ◽

pp. 1183-1187

Author(s):

Haitao WU ◽

Chuanbing CHEN ◽

Ningsheng WANG ◽

Suiqing MI ◽

Nanying LIAO

Keyword(s):

High Performance Liquid Chromatography ◽

Liquid Chromatography ◽

Simultaneous Determination ◽

High Performance ◽

Derivatives Of

Download Full-text

Spectrophotometric study of the complexation equilibria of cadmium ions with 5-bromo and 5-chloro derivatives of 2-(2-pyridylazo)-5-diethylaminophenol (BrPADAP, ClPADAP)

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19830052 ◽

1983 ◽

Vol 48 (1) ◽

pp. 52-59 ◽

Cited By ~ 4

Author(s):

Vlastimil Kubáň ◽

Miroslav Macka

Keyword(s):

Equilibrium Constants ◽

Spectrophotometric Study ◽

Graphical Analysis ◽

Optimal Conditions ◽

Cadmium Ions ◽

Brij 35 ◽

Ethanol Medium ◽

Triton X ◽

Derivatives Of

The composition, optical characteristics, molar absorption coefficients and equilibrium constants of the reactions of formation of the ML and ML2 complexes of both reagents with cadmium(II) ions were determined by graphical analysis and numerical interpretation of the absorbance-pH curves by the modified SQUAD-G program. Optimal conditions were proposed for the spectrophotometric determination of Cd in 10% v/v ethanol medium in the presence of 0.1% w/v Triton X-100 or 1% w/v Brij 35. BrPADAP and ClPADAP are the most sensitive spectrophotometric reagents for the determination of cadmium(II) ions (ε = 1.28-1.44 . 105 mmol-1 cm2 at 560 nm and pH 8.0-9.5) with a high colour contrast in the reaction (Δλmax ~117 nm) and a selectivity similar to that of other N-heterocyclic azodyes (PAR, PAN, etc.).

Download Full-text

Spectrophotometric study of the acid-base and optical properties of the 5-bromo and 5-chloro derivatives of 2-(2-pyridylazo)-5-(diethylamino)phenol (BrPADAP, ClPADAP) and their complexation equilibria with zinc(II) ions

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19822676 ◽

1982 ◽

Vol 47 (10) ◽

pp. 2676-2691 ◽

Cited By ~ 6

Author(s):

Miroslav Macka ◽

Vlastimil Kubáň

Keyword(s):

Equilibrium Constants ◽

Spectrophotometric Study ◽

Graphical Analysis ◽

Alkaline Media ◽

Acid Base ◽

Ethanol Medium ◽

Triton X ◽

Mixed Water ◽

Derivatives Of

The optical and acid-base characteristics of BrPADAP and ClPADAP were studied in mixed water-ethanol and water-DMF media and in 10% ethanol medium in the presence of cationic, anionic and nonionic tensides. The composition, optical characteristics, molar absorption coefficients and equilibrium constants of the ML and ML2 complexes with zinc(II) ions were found by graphical analysis and numerical interpretation of the absorbance curves by the modified SQUAD-G program. Optimal conditions were found for the spectrophotometric determination of Zn(II) in the presence of 0.1% Triton X-100 or 1% Brij 35 in alkaline media with pH = 6.5-10. BrPADAP and ClPADAP are the most sensitive reagents (ε = 1.3-1.6 . 105 mmol-1 cm2 at 557 and 560 nm, respectively) for the determination of zinc with high colour contrast of the reaction (Δλ = 104 nm) and selectivity similar to that for the other N-heterocyclic azodyes (PAN, PAR, etc.).

Download Full-text

SYNTHESIS AND DETERMINATION OF LYCOMARASMIN ACTIVITY OF SOME DERIVATIVES OF ASPARTIC ACID

Journal of Biological Chemistry ◽

10.1016/s0021-9258(18)57142-8 ◽

1948 ◽

Vol 176 (3) ◽

pp. 1299-1308 ◽

Cited By ~ 1

Author(s):

D.W. Woolley

Keyword(s):

Aspartic Acid ◽

Derivatives Of

Download Full-text

IV. On the dynamical theory of incompressible viscous fluids and the determination of the criterion

Philosophical Transactions of the Royal Society of London. (A.) ◽

10.1098/rsta.1895.0004 ◽

1895 ◽

Vol 186 ◽

pp. 123-164 ◽

Cited By ~ 696

Keyword(s):

Singular Solution ◽

Physical State ◽

Theoretical Calculations ◽

Equations Of Motion ◽

Dynamical Theory ◽

Viscous Fluids ◽

Linear Functions ◽

Incompressible Viscous Fluids ◽

Theoretical Results

1. The equations of motion of viscous fluid (obtained by grafting on certain terms to the abstract equations of the Eulerian form so as to adapt these equations to the case of fluids subject to stresses depending in some hypothetical manner on the rates of distortion, which equations Navier seems to have first introduced in 1822, and which were much studied by Cauchy and Poisson) were finally shown by St. Venant and Sir Gabriel Stokes, in 1845, to involve no other assumption than that the stresses, other than that of pressure uniform in all directions, are linear functions of the rates of distortion, with a co-efficient depending on the physical state of the fluid. By obtaining a singular solution of these equations as applied to the case of pendulums in steady periodic motion, Sir G. Stokes was able to compare the theoretical results with the numerous experiments that had been recorded, with the result that the theoretical calculations agreed so closely with the experimental determinations as seemingly to prove the truth of the assumption involved. This was also the result of comparing the flow of water through uniform tubes with the flow calculated from a singular solution of the equations so long as the tubes were small and the velocities slow. On the other hand, these results, both theoretical and practical, were directly at variance with common experience as to the resistance encountered by larger bodies moving with higher velocities through water, or by water moving with greater velocities through larger tubes. This discrepancy Sir G. Stokes considered as probably resulting from eddies which rendered the actual motion other than that to which the singular solution referred and not as disproving the assumption.

Download Full-text