System Of Linear Integral Equations Research Articles

The regularization of systems of linear integral equations of the first kind of the convolution type

The regularization of systems of linear integral equations of the first kind of the convolution type

A kinetic theory of gas mixtures with regard to the laws of the thermodynamics of irreversible processes

The derivation of the hydrodynamic equations for a gaseous mixture from the system of kinetic Boltzmann equations is analyzed. The form of the hydrodynamic equations is a unique consequence of necessary and sufficient conditions for the solvability of systems of linear integral equations with symmetrical kernels, which define the terms in the expansion of the distribution functions in a series with respect to a parameter of spatial non-homogeneity (actually, the Knudsen number). The transport laws are presented in a form for which the Onsager symmetry relations hold. In deriving the Onsager relations use is made of symmetry properties of integral operators, which are a consequence of the invariance of the equations of mechanics with respect to a transformation involving changing the sign of the time and the impulses of the particles. The Onsager relations are also derived from expressions for the kinetic coefficients in terms of correlation functions.

Axial and transverse Stokes flow past slender axisymmetric bodies

This paper deals with Stokes flow due to a stationary axially symmetric slender body in a uniform stream, which may be either parallel or perpendicular to the axis of the body. The effect of the body is represented by distributions of singularities along a segment of its axis of symmetry. Systems of linear integral equations for these distributions are obtained, and the first few terms of uniformly valid (in the Stokes region) asymptotic expansions in the slenderness ratio are discussed. The leading terms yield the expected result that the drag on the body in a transverse stream is double that in an axial stream. The second approximation to the ratio of these two drags is also independent of the body shape.

Thermomechanical analysis of viscoelastic solids

AbstractThis paper is concerned with the development of a computational algorithm for the solution of the uncoupled, quasi‐static boundary value problem for a linear viscoelastic solid undergoing thermal and mechanical deformation. The method evolves from a finite element discretization of a stationary value problem, leading to the solution of a system of linear integral equations determining the motion of the solid. An illustrative example is included.

A multidimensional age-dependent branching process with applications to natural selection. I

A multidimensional version of an age-dependent branching process of Bellman and Harris is studied. In the Introduction the model is described and some of its biological limitations are discussed; in Section 2 it is shown that the mean functions of the process satisfy a system of linear integral equations of the renewal type, and a solution to the system of integral equations is obtained; and in Section 3 the limiting behavior of the mean functions is studied. The analytic techniques used rely heavily on the theory of the Laplace transform and the Perron-Frobenius theory of positive matrices. Further analytic results as well as applications to the theory of natural selection will be developed in a companion article.

Theory of Stochastic Linear Systems with Gaussian Parameter Variations

A theory of linear systems with randomly varying parameters is developed under the assumption that the parameter processes are Gaussian processes obtained by linear filtering of white noise. By this device, the restriction to white-noise parameter processes of previous studies has been removed. By a method related somewhat to a technique used in the theory of the multiple scattering of light, a system of linear integral equations for the determination of various second-order moments of the system output is derived. This system can be solved explicitly in some interesting cases. A theory of stability in mean and in mean square is given for random systems. It was found that mean square stability depended only on the values of the auto- and cross-correlation functions of the parameter processes at the origin and not on the detailed structure of these functions. The stability theory is applied to an RLC circuit with randomly varying capacitance. The possibility of stabalizing unstable deterministic systems with random noise is discussed.

Normalisable transformations in Hilbert space and systems of linear integral equations

Normalisable transformations in Hilbert space and systems of linear integral equations

On Infinite Systems of Linear Integral Equations

On Infinite Systems of Linear Integral Equations