Arun K. Mitra

On a geometry of the flat violin boundary

Abstract An analytic expression for the shape of the flat boundary of the violin is suggested. The polar equation in the form ( r / a ) n = 1 − 2 Σ m = 1 N − 1 c m sin 2 ( mθ /2) has been assumed for the upper and lower bouts, whereas the C-bout has been represented by a rotated and translated ellipse. The parameters and the coefficients, computed numerically to fit a 1720 Stradivarius, are tabulated in the text.

Minimal Boolean sum-of-product forms in prolog

Abstract The method of consensus taking has been used to develop a program in PROLOG for the symbolic computation of the prime implicants and all the minimal sums for a Boolean expression given in a sum-of-product form.

Second-order functionals for spectral synthesis with discontinuous trial functions

Abstract As an extension of earlier work, the most general second-order variational functional for the two-region multigroup neutron diffusion problem has been derived from the Generalized Roussopoulos Principle. Several special cases of this general functional have been identified with second-order functionals previously proposed in the literature. A theorem on the equivalence of the first- and second-order synthesis has been proved under certain assumptions. This theorem provides a criterion for discriminating between the pure first-order and pure second-order cases. It is evident that the second-order synthesis is advantageous over the first-order, because one has to choose fewer trial functions. Some numerical results, based on the pure first- and pure second-order synthesis, for a prototype two-region two-group reactor model have been given. For the purpose of illustration, two special cases, viz. Galerkin weighting and unity weighting, for the choice of adjoint trial functions for the second-order synthesis have been considered.

Classical functionals for spectral synthesis with discontinuous trial functions

Abstract Pomraning2 introduced the variational principle of Roussopoulos3 into transport theory. Nelson4 presented a Generalized Roussopoulos Principle (GRP) suitable for discontinuous trial functions, and initiated a program of systematically using this principle to derive various types of functionals. In Ref. 4 the GRP was used to obtain functionals admitting trial functions con- taining an interface value which is independent of the limiting values from either side. Our purpose in this work is to continue the program initiated in Ref. 4 by applying the GFP to functionals of classical type, by which we mean functionals in which there are no approximations at an interface other than the limiting values from either side.

A c-version of minimal boolean sum-of-product forms

A code in c for symbolic computation of all the minimal sums for a Boolean sum-of-product form has been developed by using the method of consensus taking. This code is capable of handling longer expressions with ease and is significantly faster than the one previously given in PROLOG.

A neighborhood magnification method for solving implicit equations in two variables

A geometric approach for solving simultaneous equations in the form f(x,y) = 0 and g(x,y) = 0 in two real variables in a given region is suggested. The method, called the neighborhood magnification method, primarily locates a neighborhood of a point of intersection of the graphs of the functions and, by magnification of successively smaller neighborhoods, computes the numerical values of the coordinates of the point of intersection. A simple procedure for generating rough sketches of implicit functions in a given region is also suggested.

A massive parallel computation in Boolean logic

Abstract A code in MasPar MPL for the computation of the prime implicants and all the minimal sums of a Boolean sum-of-product form has been presented. This is an extension to parallel computation of a previously published serial code in C [3] based on the method of consensus taking.

An eigenvalue problem arising in a patch formation model

A simple numerical scheme has been developed for the solution of the eigenvalue problem arising in a patch formation model given by Del Grosso et al. [1]. The scheme is based on finding bounds which separate the eigenvalues. The exact eigenvalues are obtained by solving an algebraic equation given by the corresponding regular Frobenius series solution. At the same time eigenfunctions may also be obtained from this series solution.

An eigenlength problem arising from a model of patch formation

Abstract The patch formation model of Del Grosso, Gerardi and Marchetti[1] is reformulated as an eigenlength problem. The latter is then solved numerically by using recent results of Elder[2, 3], in which the method of invariant imbedding is extended to linear problems having a singularity of the first kind. The results agree very well with those previously obtained[4] for the eigenvalue problem by means of the Frobenius series, Sturmian theory, and a certain monotone iteration.