THEORY OF INFRA-RED ABSORPTION OF MOLECULES

In this paper, we apply the adiabatic approximation model to the IR absorption of molecules. Expressions of the band shape functions for isothermal and isolated systems are obtained and using Einstein model we discuss the dependence of the band shape functions on temperature, normal coodinate shifts and energy.We also obtain a very simple expression of the correlation function when Svv′< 1 and discuss its effect on the band shape function.     

THE DISTRIBUTION OF ZEROS OF SOLUTIONS OF NEUTRAL DIFFERENTIAL EQUATIONS WITH A VARIABLE DELAY

In this paper, the distribution of zeros of solutions of the first-order neutral differential equation with a variable delayis studied. The estimate for the distance between adjacent zeros of the oscillatory solution of the above equation is obtained.     

ON THE RATE OF CONVERGENCE OF CONJUGATE LEGENDRE-FOURIER SERIES OF FUNCTION OF BOUNDED VARIATION

This paper gives the degree of approximation of function of bounded variation by the partial sums of con-jngate Legendre-Fourier Series.     

THEORY OF INFRA-RED ABSORPTION OF MOLECULES

In this paper, we apply the adiabatic approximation model to the IR absorption of molecules. Expressions of the band shape functions for isothermal and isolated systems are obtained and using Einstein model we discuss the dependence of the band shape functions on temperature, normal coodinate shifts and energy.We also obtain a very simple expression of the correlation function when Svv ′<1 and discuss its effect on the band shape function.     

ON THE LINEARITY OF TESTING PLANARITY OF GRAPHS

In 1978, the author published a paper in which a characteristic theorem of 'planarity of a graph was provided as determining if another graph has a fundamental circuit with a certain property. However, the new graph is with, at worst, quadratic order of the vertex number of the original graph.This paper presents a new criterion of testing planarity of a graph based on what the author obtained before. Fortunately, it is equivalent to finding a spanning tree in another graph with only linear order of the vertex number of the original one in the worst case.     

EXTREMES OF RATIOS OF DETERMINANTS AND CANONICAL CORRELATION VARIABLES

This article develops some extremes of the ratios of determinants. The results are themultivariate extensions of the extremes of quadratic forms, and can be applied to finding thecanonicai correlation variables of two random vectors. Hence a group of canonical correlationvariables is a solution of the extreme of the ratio of determinants.     

OPTIMIZATION OF ADAPTIVE DIRECT METHOD FOR APPROXIMATE SOLUTION OF INTEGRAL EQUATIONS OF SEVERAL VARIABLES

This paper determines the exact error order on optimization of adaptive directmethods of approximate solution of the class of Fredholm integral equations of the secondkind with kernel belonging to the anisotropic Sobolev classes, and also gives an optimalalgorithm.     

PROJECTIVE DIFFERENTIAL GEOMETRY OF SINGULARITIES OF PLANE CURVES

<正> In a recent paper the present author has established somerepresentations for a plane curve C in the neighbourhood of a singularpoint O characterized by the property that the tangent t(?) of C at O hasa contact of order m—1((?)2) with the curve.For convenience'sakewe have adopted non-homogeneous coordinates x,y of a point to represent the expansion of the curve.     

ON THE GROWTH OF SOLUTIONS OF HIGHER-ORDER ALGEBRAIC DIFFERENTIAL EQUATIONS

Using Nevanlinna theory of the value distribution of meromorphic functions, the author investigates the problem of the growth of solutions of two types of algebraic differential equation and obtains some results.