a theoretical and numerical analysis of the measured equation of invariance the measured equation of invariance mei has been previously introduced to efficiently and accurately handle the boundary truncation for finite methods the present authors give a theoretical analysis that provides several important insights into the capabilities of the mei from the numerical study they can explain why the mei works better than one would expect both the theoretical and the numerical analyses demonstrate that the accuracy of the solution is dependent on the electrical size of the geometry as well as the distance between the mesh boundary and the geometry from the analysis the authors propose a new set of metrons that is less sensitive to the excitation than the previously proposed sinusoidal metrons

compact expression for lowdin s alpha function a simple analytical expression for lowdin s alpha function is derived this expression is expected to be more convenient with the expansion of a general function about a displaced center than any other available in the literature

convergence properties of the sbar d transformation and a fast and accurate numerical evaluation of molecular integrals the present work concerns the study of the convergence properties of the nonlinear s transformation a fast and accurate numerical evaluation of highly oscillatory semi infinite integrals involved in the analytic expressions of molecular integrals over slater type orbitals is obtained using the s transformation these semi infinite integrals involve spherical and reduced bessel functions the convergence properties are analysed and they show that the approximations obtained using the s approach converge to the exact values of the semi infinite integrals without any constraint the numerical tables show that the s method gives unprecedented accuracy with speed up by a factor 2 over the h method and a factor 10 over the transformation this illustrates the superiority of this new approach

measured equation of invariance a new concept in field computations numerical computations of frequency domain field problems or elliptical partial differential equations may be based on differential equations or integral equations the new concept of field computation presented in this paper is based on the postulate of the existence of linear equations of the discretized nodal values of the fields different from the conventional equations but leading to the same solutions the postulated equations are local and invariant to excitation it is shown how the equations can be determined by a sequence of measures the measured equations are particularly useful at the mesh boundary where the finite difference methods fail the measured equations do not assume the physical condition of absorption so they are also applicable to concave boundaries using the measured equations one can terminate the finite difference mesh very close to the physical boundary and still obtain robust solutions it will definitely make a great impact on the way one applies finite difference and finite element methods in many problems computational results using the measured equations of invariance in two and three dimensions are presented

on some measures of noncompactness in the frechet spaces of continuous functions abstract in this paper the frechet spaces of continuous functions defined on a bounded or an unbounded interval with values in the space of all real sequences are considered for those frechet spaces new regular measures of noncompactness are constructed and several properties of these measures are established the results obtained are further applied to infinite systems of functional integral equations

convergence of translation formulas for the computation of multicenter integrals over slater orbitals abstract multicenter electron repulsion integrals are calculated using auxiliary functions and two kinds of translation formulas for slater type orbitals stos obtained from the expansion of stos in terms of exponential type orbitals at a displaced center that form complete orthonormal sets and are represented by linear combinations of stos the convergence of the series for real stos is tested by calculating concrete cases accuracy of the results is quite high for quantum numbers screening constants and location of stos

an analytical characterization of the error in the measured equation of invariance in previous publications the authors have numerically shown that the measured equation of invariance mei is not invariant to excitation the major implication is that an appropriate set of metrons should be selected for each geometry and excitation in question an argument however can be raised against these findings one can claim that the mei is indeed invariant and that any discrepancies are entirely due to the mesh discretization error the authors disprove this claim by a counterexample they perform an analytical study of the mei as applied to a perfectly conducting circular cylinder with a fixed choice of metrons they then investigate the behavior of the mei when the electrical radius of the cylinder becomes large and when the nodal separation goes to zero they prove that even as the mei residual goes to zero the error in the mei solution remains finite and cannot be reduced below a certain limit

analytical and numerical development for the two centre overlap like quantum similarity integrals over slater type functions in molecular quantum similarity measure between two molecules using the molecular electron density the major task involves the accurate numerical evaluation of overlap between the two electron densities in the integral measure by expanding the electron densities in terms of atomic orbitals using the linear combination of atomic orbitals approach a large number of overlap like quantum similarity integrals over the basis functions in the two molecules will be required accurately for the calculation of a meaningful quantum similarity measure improvement of the computational methods of these integrals would be indispensable to a further development in computational studies of large molecular systems analytic expressions were obtained for these overlap like quantum similarity integrals over slater type functions in terms of the usual two centre overlap integrals over b functions different approaches were developed for the numerical evaluation of these two centre overlap integrals over b functions which can be used for the numerical evaluation of the two centre overlap like quantum similarity integrals over slater type functions in this work we present our approach which is based on the use of nonlinear transformations for improving convergence of highly oscillatory integrals in the case of more complicated multicentre integrals this approach is shown to be able to produce remarkably good results we also present different representations which were obtained by steinborn group and which can be used for a fast and accurate computation of the two centre overlap like quantum similarity integrals over slater type functions

simple expressions for radial functions appearing in the expansions of ym1l1 f m2l2 r and 2nym1l1 f m2l2 r in this paper simple analytic expressions for the radial functions r ll1l2 f r and glnl1l2 f r which appear in the expressions for ym1l1 fl2 r ym2l2 r and 2nym1l1 fl2 r ym2l2 r when expressed as linear combinations of yml r where ym1l1 is obtained from the solid harmonic ym1l1 r r l1ym1l1 r are derived by replacing x y and z in its representation as a polynomial of degree l1 by x y and z respectively writing r ll1l2 f r r ll1l20 r f r and glnl1l2 f r glnl1l20 r f r the expression for r ll1l20 r glnl1l20 r is found to be 2 r l1 2 r l1 2n times a product of commuting factors containing the single operator 1 2 r d dr and not two noncommuting operators r and 1 r d dr in the many equivalent previously obtained results which are thus synthesized in this approach also expressions for these operators manifest the symmetries in the problem in addition a simple connection glnl1l20 r r ll1 2nl20 r between these two operators and the c

comments on a theoretical and numerical analysis of the measured equation of invariance in the original paper see ibid vol 42 no 8 p 1097 1105 1994 the authors claimed to have found theoretical insights into the measured equations of invariance mei method their first insight was a proof that the postulate of invariance was wrong and their second insight led to the discovery of an optimum set of metrons metrons are considered to be possible induced current densities due to some unknown incident fields they also presented a series of computational results to highlight their theories this article points out the defects in the analyses and conclusions presented by the authors there are two things in the paper which are basically incorrect one is that the authors consider a zero in a numerical formulation to be an absolute zero the other is that they assume the invariance to excitations to be the same as the invariance to metrons based on these assumptions they have reached conclusions which are actually contradictory to their own calculations this article shows where the defects of their analyses occur and why their two insights are contradictory to each other

the hd and hd methods for accelerating the convergence of three center nuclear attraction and four center two electron coulomb integrals over b functions and their convergence properties abstract three center nuclear attraction and four center two electron coulomb integrals over slater type orbitals are required for ab initio and density functional theory dft molecular structure calculations they occur in many millions of terms even for small molecules and require rapid and accurate evaluation the b functions are used as a basis set of atomic orbitals these functions are well adapted to the fourier transform method that allowed analytical expressions for the integrals of interest to be developed rapid and accurate evaluation of these analytical expressions is now made possible by applying the hd and hd methods for accelerating the convergence of the semi infinite oscillatory integrals the convergence properties of the new methods are analysed the numerical results section shows the high predetermined accuracy and the substantial gain in the calculation times obtained using the new methods

weakly convergent expansions of a plane wave and their use in fourier integrals the fourier transform of an irreducible spherical tensor is normally computed with the help of the rayleigh expansion of a plane wave in terms of spherical bessel functions and spherical harmonics the angular integrations are then trivial however the remaining radial integral containing a spherical bessel function may be so complicated that the applicability of fourier transformation is severely restricted as an alternative the use of weakly convergent expansions of a plane wave in terms of complete orthonormal sets of functions is suggested the weakly convergent expansions of a plane wave are constructed in such a way that their application in fourier integrals leads to expansions of the fourier or inverse fourier transform that converge with respect to the norm of either the hilbert space l2 r3 or the sobolev space w 1 2 r3 accordingly these weakly convergent expansions may be viewed as distributions that are defined on either l2 r3 or w 1 2 r3 the properties of some complete orthonormal se

an extremely efficient approach for accurate and rapid evaluation of three centre two electron coulomb and hybrid integrals over b functions analytic expressions of three centre two electron coulomb and hybrid integrals over b functions are obtained using the fourier transform method thoroughly explored by steinborn s group these analytic expressions involve semi infinite integrals which are slowly convergent due to the presence of hypergeometric and spherical bessel functions in the integrands we have proven that these hypergeometric functions can be expressed as finite expansions and the integrands involving these series satisfy all the conditions required to apply the h approach which greatly simplifies the application of the nonlinear transformation this work presents a rapid and accurate evaluation of these integrals obtained by using a new approach which we called s this new method is based on the h and methods and some practical properties of spherical bessel reduced bessel and sine functions the s method has greatly simplified the calculations avoiding the long and difficult implementation of the successive zeros of the spherical bessel function and a method for solving linear systems which are required by h and

new representations for the spherical tensor gradient and the spherical delta function in this article we analyze representations for the product ym1l1 fm2l2 r with yml specifying a solid harmonic whose argument is the nabla operator r instead of the vector r since both ym1l1 and fm2l2 r are irreducible spherical tensors we can use angular momentum algebra for evaluating the product accordingly the problem of finding a representation for the product is reduced to the determination of the radial functions generated by the product analytical expressions for these radial functions are derived by direct differentiation and with the help of fourier transforms closely related to the spherical tensor gradient yml is the spherical delta function ml r we derive new representations for ml by considering convolution integrals involving b functions these functions are closely related to the modified bessel functions and also to the yukawa potential e r r we show that the definition of the b functions can be extended to include a large class of derivatives of the delta func

on a nonlocal problem for semilinear differential equations with upper semicontinuous nonlinearities in general banach spaces abstract sufficient conditions on the existence of mild solutions for the following semilinear nonlocal evolution inclusion with upper semicontinuous nonlinearity u t a t u t f t u t 0 t d u 0 g u are given when g is completely continuous and lipschitz continuous in general banach spaces respectively an example concerning the partial differential equation is also presented

existence of nondensely defined evolution equations with nonlocal conditions abstract this paper is concerned with the existence for nondensely defined evolution equations with nonlocal conditions using the techniques of fixed point theory and approximate solutions existence results are obtained for integral solutions when the nonlocal item is lipschitz continuous or continuous respectively examples are also given to illustrate our results

mild solutions of functional semilinear evolution volterra integrodifferential equations on an unbounded interval abstract in this paper we study the existence of mild solutions for initial value problems for semilinear volterra integrodifferential equations in a banach space the arguments are based on the concept of measure of noncompactness in frechet space and the tikhonov fixed point theorem

existence results and asymptotic behavior for nonlocal abstract cauchy problems the purpose of this paper is to study the existence and asymptotic behavior of solutions for cauchy problems with nonlocal initial datum generated by accretive operators in banach spaces

discretized boundary equation method for two dimensional scattering problems a unified approach named discretized boundary equation dbe method is introduced for two dimensional 2 d scattering problems it is based on the discretization of field expressions for one or two components of the scattered field the dbes can be used either on the object surface to obtain the solution directly or on the truncation boundary of a finite difference fd or finite element fe mesh as termination conditions this paper describes the general theory of the dbe method and key points or limitations for its implementation a new on surface formulation for the solution of scattering by perfectly conducting cylinders is presented as an application of the two component version of the dbe method and validated through numerical examples mesh termination conditions for the fd or fe method are derived based on the one component formulation of the dbe method and their equivalence and difference to the measured equation of invariance are discussed in particular the dbe obtained with the minimum norm least squares solution is investigated thoroughly and its validity and features are demonstrated through numerical results generated together with the fd method for scattering by cylinders with various material properties

validity of the measured equation of invariance the measured equation of invariance mei is derived without any postulates it is shown that the coefficients of the mei are invariant to the field of excitation however the accuracy of the mei solution is closely related to the number of nodes in the mei coupling more nodes improves progressively the accuracy of the mei solution with increasing nodes the matrix problem for the determination of the mei coefficients becomes seriously ill conditioned and generally must be solved using multiple precision arithmetic the consequences of the ill conditioning phenomenon are discussed

comment on compact expression for lowdin s alpha function j math phys 26 940 1985 recently antone j math phys 26 940 1985 has presented a compact expression for lowdin s function and expected that in calculation on the electronic properties of molecules and solids it is the most convenient of all the expressions available in literature but in the present paper it is shown that the expression for the function obtained from the expansion formula of silverstone and moats phys rev a 16 1731 1977 is remarkably more compact and therefore more convenient than antone s expression though not visibly it is proved with the aid of some manipulation that the formula of silverstone and moats can be reduced to the well known expansion formula of a solid harmonic in the special case where the center of the function to be expanded and that of the function both are located on the z axis some mistakes are found that lead to antone s expression for the function

addition theorem of slater type orbitals a numerical evaluation of barnett coulson lowdin functions when using the one centre two range expansion method to evaluate multicentre integrals over slater type orbitals stos it may become necessary to compute numerical values of the corresponding fourier coefficients also known as barnett coulson lowdin functions bclfs bouferguene and jones 1998 j chem phys 109 5718 to carry out this task it is crucial to not only have a stable numerical procedure but also a fast algorithm in previous work bouferguene and rinaldi 1994 int j quantum chem 50 21 bclfs were represented by a double integral which led to a numerically stable algorithm but this turned out to be disappointingly time consuming the present work aims at exploring another path in which bclfs are represented either by an infinite series involving modified bessel functions or by an integral whose integrand is a smooth function both of these representations have the advantage of being symmetrical with respect to the cusp parameter a and the radial variable r as a consequence it is no longer necessary to split the integrals over r 0 into several components with a different analytical form in each of these a numerical study is also carried out to help select the most appropriate method to be used in practice

on a new class of gradient formulas in the angular momentum theory recently b f bayman has derived the formula for ylm r ylm r where ylm r is a solid spherical harmonic in terms of the derivatives of the function r by the scalar parameter r this result is clarified and essentially generalized for the case of the tensor product ynl r yl r where ynlm nylm in this paper applications to the taylor series in the three dimensional euclidean space as well as some other expansions are discussed briefly

simple calculation of lowdin s alpha function a function of the type f r yml around a specific center b is expanded about another center a as f r yml l m 1 r l flm a r y ml where yml and yml are the complex spherical harmonics around the respective centers which have been assumed to be quantized in the direction of a to b the distances from the respective centers are r and r and the separation between the two centers is a the expansion coefficient l flm a r which is usually called lowdin s function can be expressed in a remarkably simple form by using silverstone and moats formula owing to the simplicity the properties of the coefficients bkk lm l appearing in the function are manifested and the recurrence formulas for evaluating bkk lm l are derived furthermore when r 0 the asymptotic expression for the function is given in a compact form

generating differential operators for the basis functions in the variational lcao type methods the analytical expressions for operators which allow us to generate the basis functions from the simplest ground states by means of differentiating by parameters are obtained some important properties of these operators are indicated this approach allows us to simplify the structure of molecular matrix elements whose calculation presents considerable difficulties in the variational lcao type methods

a new algorithm for accurate and fast numerical evaluation of hybrid and three centre two electron coulomb integrals over slater type functions recently we developed a new algorithm for a fast and accurate numerical evaluation of three centre nuclear attraction integrals over slater type functions the results obtained were very satisfactory now it is shown that this new algorithm can also be applied to hybrid and three centre two electron coulomb integrals over slater type functions these integrals which are numerous are very difficult to evaluate to a high accuracy because of the presence of spherical bessel functions and hypergeometric series in the integrands we have proved that the integrands that occur in the analytic expressions of the integrals under consideration satisfy all the conditions to apply the approach the hypergeometric functions which occur in the semi infinite integrals can be expressed as a finite expansion and the semi infinite integrals involving the spherical bessel functions can be transformed into semi infinite integrals involving the simple sine function the numerical results obtained with linear and non linear systems illustrate clearly a further improvement of accuracy and a substantial reduction in calculation times comparisons with existing codes stop developed by bouferguene et al 1996 int j quantum chem 57 801 and adggstngint developed by rico et al 1997 comp phys commun 105 216 are listed

existence of mild solutions for the semilinear nonlocal problem in banach spaces abstract in this paper we study the existence of mild solutions of the semilinear nonlocal initial value problem on a bounded and on an unbounded interval in our considerations we apply a new calculation method based on the technique of modulus of continuity in conjunction with idea of the family of measures of noncompactness in frechet space the results obtained in this paper generalize several ones obtained earlier by many authors

nonlocal differential equations with multivalued perturbations in banach spaces abstract we discuss the existence of mild solutions for nonlocal differential inclusions with multivalued perturbations in banach spaces and establish new existence theorems for related cauchy problems which extend some existing results in this area using the established results we investigate a special nonlocal problem finally we also consider a partial functional differential equation

addition theorems for b functions and other exponentially declining functions in this paper addition theorems are derived for a special class of exponentially declining functions the so called b functions bmn l r e filter and e o steinborn phys rev a 18 1 1978 although these b functions have a relatively complicated analytical structure they nevertheless have some mathematical properties that are particularly advantageous in connection with multicenter problems also all the commonly occurring exponentially declining functions like for instance bound state hydrogen eigenfunctions and slater type functions can be expressed by simple finite sums of b functions consequently addition theorems for these functions can also be written down immediately the various addition theorems for b functions are derived by applying suitable generating differential operators to the well known addition theorem of the special b function bm l l which is that solution of the modified helmholtz equation that is irregular at the origin and regular at infinity e j weniger and e o

a simple derivation of the addition theorems of the irregular solid harmonics the helmholtz harmonics and the modified helmholtz harmonics in this article a simple derivation of the addition theorems of the irregular solid harmonics the helmholtz harmonics and the modified helmholtz harmonics is presented our derivation is based upon properties of the differential operator yml which is obtained from the regular solid harmonic yml r by replacing the cartesian components of r by the cartesian components of with the help of this differential operator yml which is an irreducible spherical tensor of rank l the addition theorems of the anisotropic functions are obtained by differentiating the addition theorems of the isotropic functions the performance of the necessary differentiations is greatly facilitated by a systematic exploitation of the tensorial nature of the differential operator yml

a new gauss quadrature for multicentre integrals over stos in the gaussian integral transform approach when computing multicentre integrals over slater type orbitals stos by means of the shavitt and karplus gaussian integral transforms shavitt and karplus 1962 j chem phys 36 550 one usually ends up with a multiple integral of the form shavitt and karplus 1965 j chem phys 43 398 in which all the integrals are inter related the most widely used approach for computing such an integral is to apply a product of gauss legendre quadratures for the integrals over 0 1 while the semi infinite term is evaluated by a special procedure although numerous approaches have been developed to accurately perform the integration over 0 efficiently it is the aim of this work to add a new tool that could be of some benefit in carrying out the hard task of multicentre integrals over stos the new approach relies on a special gauss quadrature referred to as gauss bessel to accurately evaluate the semi infinite integral of interest in this work emphasis is put on accuracy rather than efficiency since its aim is essentially to bring a proof of concept showing that gauss bessel quadrature can successfully be applied in the context of multicentre integrals over stos the obtained accuracy is comparable to that obtained with other methods available in the literature

an extremely efficient and rapid algorithm for numerical evaluation of three centre nuclear attraction integrals over slater type functions the present work concerns the development of an extremely accurate and rapid algorithm for the numerical evaluation of the three centre nuclear attraction integrals over slater type functions these integrals are numerous they occur in many millions of terms even for small molecules and they require rapid and accurate evaluation the new algorithm is based on nonlinear transformation methods on numerical quadrature and on properties of the sine and bessel functions the section with numerical results shows the high accuracy and the substantial gain in calculation time realized using the new algorithm the complete expressions of the three centre nuclear attraction integrals over b functions and over slater type functions are evaluated for different values of the quantum numbers to show the efficiency of the new approach numerical results obtained with linear and nonlinear systems and comparisons with numerical results from the literature are listed

on the existence of mild solutions of semilinear evolution differential inclusions abstract in this paper we deal with a cauchy problem governed by the following semilinear evolution differential inclusion x t a t x t f t x t and with initial data x 0 x 0 e where a t t 0 d is a family of linear operators in the banach space e generating an evolution operator and f is a caratheodory type multifunction we prove the existence of local and global mild solutions of the problem moreover we obtain the compactness of the set of all global mild solutions in order to obtain these results we define a generalized cauchy operator our existence theorems respectively contain the analogous results provided by kamenskii obukhovskii and zecca condensing multivalued maps and semilinear differential inclusions in banach spaces de gruyter ser nonlinear anal appl vol 7 de gruyter berlin 2001 for inclusions with constant operator

multicentre two electron coulomb and exchange integrals over slater functions evaluated using a generalized algorithm based on nonlinear transformations when calculating molecular electronic energies the contributions involving the coulomb operator for bielectronic terms are required rapidly and to high chemically significant accuracy the atomic orbital basis functions chosen in the present work are slater type functions stfs these functions can be expressed as finite linear combinations of b functions which are suitable to apply the fourier transform method the difficulties of the numerical evaluation of the analytic expressions of the integrals of interest arise mainly from the presence of two or three dimensional integral representations in this work we present a generalized algorithm for a precise and fast numerical evaluation of molecular integrals over stfs numerical results obtained with c2h2 c2h4 and ch4 molecules show the efficiency of the approach presented in this work comparisons with the existing codes are also listed

the properties of sine spherical bessel and reduced bessel functions for improving convergence of semi infinite very oscillatory integrals the evaluation of three centre nuclear attraction integrals over b functions this paper focuses on the use of useful properties of sine spherical bessel and reduced bessel functions to simplify the application of the nonlinear d and transformations for accelerating the convergence of semi infinite very oscillatory integrals and to reduce the calculation times keeping a high predetermined accuracy three centre nuclear attraction integrals which are one of the most difficult type involved in density functional theory methods when using a basis set of b functions are evaluated using the new approach the numerical results show the efficiency of the new method compared with other alternatives

a fast finite difference method for propagation predictions over irregular inhomogeneous terrain propagation of electromagnetic waves over irregular inhomogeneous terrain is solved by a finite difference scheme the method is fast and requires considerably less memory than the integral equation methods the method requires a storage space of order o n and an execution time of order o n sup 2 fields generated by a te sub 2 line source are represented in an integral form in terms of the field over a flat constant impedance plane the incident field and the field scattered by the terrain irregularities and inhomogeneities accurate expressions are provided for the incident field and the green s function whose evaluation is otherwise accomplished by the rather time consuming sommerfeld s integrals measured equation of invariance is used to terminate the computational domain the sparse matrix generated by the method is inverted by the ricatti transform numerical results are presented for the ground wave as well as for the sky wave comparison is made for known geometries to establish the validity and limitations of the method

simple calculation of lowdin s alpha function ii easier procedure for evaluating bk k l m l and vanishing of hn 2n i l m l for special values of i and n this paper subsequent to the one j math phys 25 1133 1984 referred to as part i presents the following new results it is found out that for m l and l 1 the coefficients bk k l m l in lowdin s function have properties other than manifested in part i the expression for bk k l m l is shown to be equivalent to the one into which sharma s expression obtained in a different manner from that in part i is simplified by rashid the use of rashid s expression leads to the recurrence formula for bk k l m l with respect to m only this formula and the expression for the bk k l m l with m l provide an easier procedure for successively evaluating bk k l m l than in part i furthermore it is proved that the coefficients hn 2n i l m l in the asymptotic form of the function vanish for i l m and for n l

existence of mild solutions for semilinear evolution equations with non local initial conditions abstract in this paper we study the existence of mild solutions for a class of semilinear evolution equations with non local initial conditions and extend some related results in this direction

mild solutions of semilinear evolution equation on an unbounded interval and their applications the aim of this paper is to give an existence theorem for a semilinear equation of evolution on an unbounded interval in the case when the generator of a semigroup depends on time parameter the considerations of this paper are based on the concept of a measure of noncompactness in frechet space and the classical tichonov fixed point principle moreover an application of the main theorem to the second order parabolic pde is given

efficient and rapid numerical evaluation of the two electron four center coulomb integrals using nonlinear transformations and useful properties of sine and bessel functions two electron four center coulomb integrals are undoubtedly the most difficult type involved in ab initio and density functional theory molecular structure calculations millions of such integrals are required for molecules of interest therefore rapidity is the primordial criterion when the precision has been reached this work presents an extremely efficient approach for improving convergence of semi infinite very oscillatory integrals based on the nonlinear d transformation and some useful properties of spherical bessel reduced bessel and sine functions the new method is now shown to be applicable to evaluating the two electron four center coulomb integrals over b functions the section with numerical results illustrates the unprecedented efficiency of the new approach in evaluating the integrals of interest

regular article efficient and rapid evaluation of three center two electron coulomb and hybrid integrals using nonlinear transformations among the two electron integrals occurring in the molecular context the three center coulomb and hybrid integrals are numerous and difficult to evaluate to high accuracy the analytical and numerical difficulties arise mainly from the presence of the spherical bessel function and hypergeometric series in these integrals the present work pursues the acceleration of convergence for three center two electron coulomb and hybrid integrals we have proven that the hypergeometric function can be expressed as a finite expansion and that the integrand involving this series and a product of bessel functions satisfies a linear differential equation with coefficients having a power series expansion in the reciprocal of the variable suitable for application of the nonlinear d and d transformations these transformations depend strongly on the order of the differential equation that the integrand of interest satisfies this work concentrates on reduction of this order to two exploiting properties of spherical and reduced bessel functions leading to greatly simplified calculations to evaluate the integrals precisely by reducing the order of linear systems to be solved it also avoids the long and difficult implementations of successive derivatives of the integrands the numerical results section illustrates clearly the reduction of the calculation time we obtained for a high predetermined accuracy

nonlinear differential equations with nonlocal conditions in banach spaces abstract in this paper we study the existence of integral solutions for nonlinear differential equations with nonlocal initial conditions in banach spaces we derive conditions under which the integral solutions exist

interpolation extrapolation and application of the measured equation of invariance to scattering by very large cylinders using the conventional method of moment mom calculations a cylinder of circumferential dimension of 100 wavelengths is considered to be large using the measured equation of invariance mei approach a cylinder of 10000 wavelengths is within the storage capacity and numerical tolerance of a workstation although the mei has greatly reduced the storage and solution time of the matrix its overhead to generate the matrix elements is about the same order as that of the mom when the target is very large that overhead can be very time consuming this paper presents an interpolation and extrapolation technique such that the boundary equations of the mei for high frequencies may be predicted from those of low frequencies it is demonstrated that in the optical limit the same set of coefficients may be used for all frequencies which is consistent with the concept of geometric optics where the same rule is applied to all frequencies

existence and asymptotic properties of solutions of nonlinear multivalued differential inclusions with nonlocal conditions abstract this paper deals with a nonlocal problem governed by the nonlinear differential inclusions with multivalued perturbations in banach spaces first using the approach of geometry of banach space hausdorff metric the measure of noncompactness and fixed point existence results are obtained we have removed from previous papers the crucial restriction on the semigroup then we establish the asymptotic properties of integral solutions when t finally for illustration a partial differential equation is worked out

expansion of a function about a displaced center an extremely simple closed expression is obtained for the coefficients which appear in the expansion of a function of a special type about a displaced center a conjecture about the vanishing of a certain coefficient which appear in the expansion of a slater type orbital about a displaced center is also proved