determination of the mutual radiation resistances of a rectangular plate and their impact on the radiated sound power abstract the mutual radiation resistances resulting from cross modal coupling have been mostly excluded from sound power calculations on the belief or premise that either for some reasons they have an insignificant impact on the power radiation or consideration of them can be an enormous computational burden in this paper the characteristics of the mutual radiation resistances are investigated of a simply supported rectangular plate it is shown that once the self radiation resistances or the so called modal radiation efficiencies have been calculated the mutual radiation resistances can be readily obtained at virtually no cost of equal importance because no approximation is made the present formulation is fully accurate in the entire frequency range an asymptotic expression is also derived for large modal wavenumbers numerical results are presented to illustrate the spectral characteristics of the mutual radiation resistances and the corresponding impact on the radiated sound power

continued fractions and the potential models of confinement reply to a comment the analytic continued fractional formula for energies of the bound states in the harmonium potential v r ar 1 br cr2 as suggested by singh et al 1978 1979 and criticised by flessas 1982 is correct if and only if b 0 this is the special case of the more general result the author extends the analytic construction of the green function and the rigorous specification of its validity to the whole class of potentials with r2v r polynomial in ralpha alpha positive rational number

acoustic shape sensitivity analysis using the boundary integral equation boundary integral equations are formulated for the shape sensitivity analysis of the acoustic problems the concept of the material derivative is employed in deriving the sensitivity equations since the equation is derived by the direct differentiation of the boundary integrals containing the field values it is expected that the sensitivity would be computed more effectively and accurately than the conventional finite difference method in addition the equation has the potential to be applied to many complex acoustic problems because the derived equation is regularized by using the integral identity that incorporates the one dimensional propagating wave and its material derivative the validity of the formulations is demonstrated through examples having regular shapes such as the three dimensional pulsating sphere and the one dimensional duct for which the analytical solutions are available as an example for an irregular domain the two dimensional model of an automotive interior cavity is dealt with in the view point of the noise level at the passenger s ear position the results show that the present method can be an effective tool for the shape optimization in designing the desired sound field it is noted that the present method permits accurate sensitivities of the acoustic pressure on the boundary as well as at the field points the present method is thought to be an alternative to the previous finite difference techniques for computing the shape sensitivity using the boundary element method and the formal derivative method using the finite element method

the generalized anharmonic oscillator in three dimensions exact eigenvalues and eigenfunctions we study the generalized anharmonic oscillator in three dimensions described by the potentials of the form 2m 1k 1bkr 2k an asymptotic analysis of the schrodinger equation yields the leading asymptotic behavior of the energy eigenfunctions in terms of the dominant m 1 coupling constants bk m 1 k 2m 1 using an ansatz which incorporates this asymptotic behavior we reduce the eigenvalue equation to an m 2 term difference equation the corresponding hill determinant may be made to factorize with a finite determinant as a factor if a set of constraints on the couplings is satisfied an infinite sequence of such sets exists the exact energy eigenvalues appear as the real roots of the finite factor of the hill determinant the corresponding wavefunctions are gaussian weighted polynomials we consider the potentials 31bkr 2k and 51bkr 2k explicitly potentials of the form 2m1bjr j and 2m1bjr j r containing both even and odd terms are also considered finally we show that this method of constructi

polynomial solutions for a class of second order linear differential equations we analyze the polynomial solutions of the linear differential equation p 2 x y p 1 x y p 0 x y 0 where p j x is a jth degree polynomial we discuss all the possible polynomial solutions and their dependence on the parameters of the polynomials p j x special cases are related to known differential equations of mathematical physics classes of new soluble problems are exhibited general results are obtained for weight functions and orthogonality relations

structured singular values and stability analysis of uncertain polynomials part 1 the generalized m abstract one of the primary goals in this two part series is to establish a link between the structured singular value and results in stability analysis of uncertain polynomials another primary goal is to develop an improved method for accurately and efficiently computing the structured singular value for an important class of problems in robust stability analysis to achieve these goal we first introduce a generalized framework of structured singular values and next show how stability problems for uncertain polynomials may be studied in this framework part 1 of this series is devoted entirely to the generalized structured singular values specifically for the case when a certain matrix representing the nominal system is of rank one an analytical expression for the generalized notion is derived in this case which involves solving a convex optimization problem in one real variable and renders the structured singular value readily solvable in particular when the general framework is specialized to that of the standard structured singular value the expression is solved explicitly also for several additional important cases explicit solutions are obtained the framework as well as results will then be used in part 2 of this series to study stability problems for a class of polynomials whose coefficients are affine functions of real or complex uncertainties we demonstrate that the generalized structured singular value is a suitable notion for these problems and its solution unifies a number of results obtained previously via alternative approaches for several problems of interest we further demonstrate that stability conditions based upon the structured singular value and those in the spirit of kharitonov theorem can be derive from one another and hence establish a link between two drastically different type of results

computing the nearest polynomial to multiple given polynomials with a given zero via l2 q norm minimization abstract given multiple univariate or multivariate real polynomials f 1 f 2 f m and a desired real zero z we study the problem of computing a real polynomial f such that f z 0 and the distance between f and f 1 f 2 f m is minimal where the distance is measured by a pair of norms p q as the difficulty of finding solutions to this problem relies on selection of the norm pair p q previous works just discussed some special cases e g p q 2 2 2 and where the corresponding problems were translated in geometric views in this paper we revisit this problem from an optimization view for all the cases of 2 q with q 0 2 that is instead of directly finding the nearest polynomial we first transform the problem into solving a constrained minimization problem based on l 2 q norm minimization for all q in 0 2 then a unified iterative algorithm is proposed to solve the constrained optimization problem and also the convergence is uniformly demonstrated finally a simple example is presented to validate the effectiveness of the proposed algorithm

fluid structure coupling for an unbaffled elastic panel immersed in a diffuse field abstract the study of the structural response of a panel excited by a multiple plane wave acoustic field is presented a new semi analytical approach based on the integral equation method is proposed the two major difficulties lie in the fact that the panel is unbaffled and is excited by an acoustic field a system for which the fluid structure coupling cannot be neglecteda priori using the free space green function and a variational approach a linear system is obtained for the two unknowns of the problem the sound pressure jump and the panel deflection the formulation allows one to obtain a simple physical interpretation in terms of the diffraction and radiation phenomenon an efficient computation scheme is introduced for the admittance matrix as well as a multiexcitation procedure for the acoustic plane waves convergence of the method is discussed and a comparison with a modal cavity approach is presented finally the importance of the diffraction by the panel is discussed with regards to approximations usually performed in some numerical techniques

on the short wave acoustic radiation from planar panels or beams of rectangular shape an exact representation which involves single as opposed to double integrals is established for the time average power output generated by individual modes of normal surface velocity on a simply supported and baffled rectangular panel fluid loading is not taken into account the representation enables analytical estimates to be found in the short wavelength range and provides details hitherto unresolved by numerical analysis

the radiation efficiency of baffled plates and strips the average radiation efficiency of point excited rectangular plates including those with a very large aspect ratio strips is investigated by using a modal summation method based on the farfield sound intensity by taking an average over all possible forcing positions on the plate the cross modal contributions average out to zero the numerical results from the modal summation are compared with established formulae for rectangular plates for wavenumbers where acoustic circulation takes place it is shown that the previously published formulae are not applicable for predicting the average radiation efficiency for a strip the analysis for the strip reveals that the radiation efficiency at frequencies below the first structural natural frequency of the strip is proportional to the square of the shortest edge length at frequencies between the fundamental natural frequency and that of the second order mode of bending across the strip the average radiation efficiency is found to be proportional to the structural damping loss factor but differs from the results obtained from the usual model of the nearfield radiation from the forcing point of a rectangular plate approximate expressions for calculating the average radiation efficiency of the strip are derived the maximum radiation efficiency around the critical frequency is found to vary less with helmholtz number kca where kc is the wavenumber at the critical frequency and a is the width than previously published models suggest

near field sound radiation from simply supported rectangular plates the sound radiation efficiency of a harmonically point forced and simply supported rectangular plate is obtained numerically and is compared with that of a circular plate the effect of aspect ratio and thickness on sound radiation efficiency is also studied since the radiation of sound from the plate is analyzed in the near field its characteristics near the critical frequency are revealed in numerical analysis the technique of co ordinate transformation which enables a quadruple integral of sound power to be shown in single integral representations is employed the radiation efficiency is at a maximum when the frequency of the applied force is slightly higher than the critical frequency when the aspect ratio of a rectangular plate is nearly equal to unity or its shape is similar to a square the radiation efficiency depends only on the frequency of the applied force but when the aspect ratio differs from unity the influence of the mode number on the radiation efficiency cannot be ignored in the frequencies below the critical frequency

extended continued fractions and energies of the anharmonic oscillators we describe the analytic solution to the schrodinger eigenvalue problem for the class of the central potentials v r za r where a 2 1 4 amax 0 z is an arbitrary finite set of the integer or rational exponents 2 1 0 the formalism is based on an analysis of the asymptotic behavior of the explicit regular solution r and issues in the formulation of the secular equation 1 l1 e 0 which determines the binding energies the main result is the rigorous construction of l1 e as a generalized extended and convergent continued fraction the method cannot be applied to the a i 1 0 cases this disproves the closely related hill determinant approach as conjectured recently by singh et al for the simplest potentials with z 2 2 4 6 and z 2 1 1 2

a unified approach to computing the nearest complex polynomial with a given zero suppose we have a complex polynomial f z whose coefficients are inaccurate and a prescribed complex number such that f 0 we study the problem of computing a complex polynomial f z such that f 0 and the distance between f and f i e f f is minimal considering that previous works usually took the usual l p norm weighted l p norm and block wise norm as distance measures we first introduce a new defined synthetic norm that integrates all these norms then we propose a unified approach to study the proposed problem and succeed in giving explicit expressions of the nearest polynomial the effectiveness of our approach is illustrated by two examples one of which shows an extension of finding the nearest complex polynomial with a zero in a given domain finally as an application of the new defined norm we discuss a matrix valued optimization problem that is very common in machine learning this paper introduces a new synthetic block wise norm and proves its dual norm which is very important here this paper for the first time proposes a unified approach to compute the nearest complex polynomial with a given zero this paper discusses a matrix valued optimization problem that is very common in machine learning as an application of the introduced norm

exact solutions for anharmonic oscillators completes the author s investigation see phys lett a vol 81 p 17 8 1981 and presents exact solutions and eigenvalues for anharmonic oscillators the solutions being given in the form of definite integrals the conditions for the validity of these results are investigated

acoustic radiation from periodic and sectionally aperiodic rib stiffened plates the far field and near field solutions for the radiated acoustic pressure from a line driven fluid loaded rib stiffened thin elastic plate have been obtained the plate has been configured to have two sets of rib stiffeners though the formulation given has been extended to include additional rib stiffener sets the stiffeners composing a given set are identical and are spaced periodically with distance l however one set of stiffeners is shifted by an amount from the other set in this manner portions of the plate may be configured with periodic repeating sections of arbitrary length l having aperiodic rib spacing the stiffeners exert reactive forces upon the plate but not angular moments fluid loading is included on the upper surface of the plate while the lower surface is unloaded except for a time harmonic line force applied normal to the lower surface the far field radiated pressure has been obtained using the method of stationary phase numerical integration techniques were used to obtain the near field acoustic pressure

radiation impedance matrices for rectangular interfaces within rigid baffles calculation methodology and applications the coupling of sound fields through a finite sized aperture in a plane rigid baffle where the region half space on one side is unbounded can be described by an integral equation which constitutes a boundary condition for the field on the other side of the aperture such a boundary condition when the pressure and the normal velocity are expanded in basis functions defined over the aperture can be recast into a matrix form relating the coefficients of the basis functions in the expansions the principal feature being a matrix of fourfold double area integrals analogous to those encountered in studies of radiation from flexible pistons in rigid baffles a substantial analytical reduction to sums of single nonsingular integrals is derived for the elements of this radiation impedance matrix when the aperture is rectangular and the basis functions are expressible as a sum of products of exponential functions of the cartesian coordinates of the aperture plane with the exponential coefficients being arbitrary complex numbers the validity of the result is substantiated by its reduction to previously published results for less general cases its utility is demonstrated with the example of diffraction by a square hole in a screen

a numerical method for the computation of the resonance frequencies and modes of a fluid loaded plate application to the transient response of the system in previous papers we have shown that the time response of a fluid loaded structure can be expressed in terms of the resonance modes of the fluid structure system we first show the efficiency of such a representation by comparing numerical predictions to experimental results the main objective of this paper is to consider the numerical aspects of this representation namely the computation of the coupling term in the variational equation and the computation of the resonance frequencies and modes three methods are proposed to compute the resonance frequencies an iterative technique a warburton approximation and a perturbation technique light fluid approximation numerical results are presented to compare these three methods for air and water loading the last part of the paper discusses the choice of the number of resonance modes which is required to obtain a representation of the transient radiated pressure with a sufficient accuracy

a general formulation for the sound radiation from rectangular baffled plates with arbitrary boundary conditions the radiation of sound from a baffled rectangular plate with edges elastically restrained against deflection and rotation is analyzed the elastic constants along the contour can be varied to reproduce simply supported clamped free or guided edges as limiting cases the formulation is based on a variational method for the vibration of the plate and assumes no fluid loading of the structure the elastic boundary conditions appear in the hamiltonian of the plate through a dynamic contribution which is expressed in terms of nondimensional edge parameters the extremalization of the hamiltonian is achieved using a rayleigh ritz method and both the free vibrations and the forced vibrations of the plate are presented the radiation of sound from the plate is analyzed in the far field and is calculated from one dimensional fourier transforms numerical results are presented for the radiation efficiency of modes of simply supported clamped free and guided plates the values found agree well with predic

nearest matrix with two prescribed eigenvalues abstract given a square complex matrix a and two complex numbers z1 and z2 we find the distance from a to the set of matrices that have z1 z2 as some of their eigenvalues we use the distance between two matrices associated with the spectral norm

on the radiation impedance of a rectangular piston abstract single integral representations for the resistive and reactive components of the radiation impedance appropriate to a rectangular piston are established thereby enabling a systematic refinement of estimates at both short and long wavelengths comparisons with previous analyses are made explicit as well as extensions and corrections thereto

a series expansion of the acoustic power radiated from planar sources a series expansion in ascending powers of the wavenumber k is derived for the acoustic power delivered by baffled or unbaffled planar sources this series provides a relatively simple means of deriving expressions for the power radiated by a baffled source with a known velocity distribution and can be used for unbaffled plates when the velocity field outside the plate is also known the terms in the series are calculated from the moments of this velocity distribution in the plane containing the source if these moments are written as derivatives in wavenumber space it is shown that a maclaurin expansion of the fourier transformed velocity provides an easy technique for computing the first few terms of the acoustic power examples are provided for baffled rectangular plates with various boundary conditions the arbitrarily shaped plate with free boundaries is particularly interesting it is proven that the volume flow across its surface must be zero and as a result corner and edge mode radiation cannot e

an improved state space method for coupled fluid structure interaction analysis this paper presents an improved state space method for incorporating fluid structure interaction into structural acoustic analyses giordano and koopmann j a giordano and g h koopmann state space boundary element finite element coupling for fluid structure interaction analysis j acoust soc am 98 363 372 1995 introduced a state space approach for the coupled analysis of fluid loaded structures giordano s method employed a third order interpolation of the fluid impedance coupled with state space formalism permitting the direct eigenvalue analysis of the coupled system and thereby yielding the fluid loaded modes and natural frequencies this is in contrast to the common technique of sweeping through a range of frequencies so as to identify the natural frequencies and mode shapes the original state space approach yielded system matrices of order 4n where n is the number of degrees of freedom in the underlying model where giordano s method employed an interpolation based on surface velo

analytical approximations for the modal acoustic impedances of simply supported rectangular plates coupling of the in vacuo modes of a fluid loaded vibrating structure by the resulting acoustic field while known to be negligible for sufficiently light fluids is still only partially understood a particularly useful structural geometry for the study of this problem is the simply supported rectangular flat plate since it exhibits all the relevant physical features while still admitting an analytical description of the modes here the influence of the fluid can be expressed in terms of a set of doubly infinite integrals over wave number the modal acoustic impedances closed form solutions for these impedances do not exist and while their numerical evaluation is possible it greatly increases the computational cost of solving the coupled system of modal equations there is thus a need for accurate analytical approximations in this work such approximations are sought in the limit where the modal wavelength is small in comparison with the acoustic wavelength and the plate dimensions it is shown that contour integration techniques can be used to derive analytical formulas for this regime and that these formulas agree closely with the results of numerical evaluations previous approximations davies j sound vib 15 1 107 126 1971 are assessed in the light of the new results and are shown to give a satisfactory description of real impedance components but in general erroneous expressions for imaginary parts

branching processes in the annni model the mean field equations of the simple cubic annni model are studied on finite lattices the results are consistent with the sequence of distinct commensurate phases 2k 13 k 1 2 3 springing from the multiphase point found using low temperature series expansions moreover evidence for new structure combination branching processes is presented which generate phases of type 2l3 m 2l 13 n or 23l m 23l 1 n where l m and n are integers

on the classical theory of ordinary linear differential equations of the second order and the schrodinger equation for power law potentials the power law potentials in the schrodinger equation solved recently are shown to come from the classical treatment of the singularities of a linear second order differential equation this allows one to enlarge the class of solvable power law potentials

a simple calculation method for the self and mutual radiation impedance of flexible rectangular patches in a rigid infinite baffle a numerical model has been developed to calculate the self and mutual radiation impedance in the cases of uniformly and flexibly vibrating rectangular patches in a rigid infinite baffle the spatial convolution approach is employed here to derive general expressions for the radiation impedance of a rectangular radiator in the form of simple integrals which allows a fast evaluation numerically the presented integral solution agrees with that obtained for the mutual radiation impedance of a uniformly vibrating rectangular piston by the use of the classical approach the numerical results of self radiation impedance of a square piston are compared with the tabulated values published previously as examples of flexibly vibrating rectangular patch a closed form expression is first given for the radiation impedance in the normal mode of vibration the numerical results reveal that the computation time in obtaining accurate calculations is greatly reduced by using the proposed method

the nearest polynomial with a zero in a given domain for a real univariate polynomial f and a closed domain email protected c whose boundary c is represented by a piecewise rational function we provide a rigorous method for finding a real univariate polynomial email protected such that email protected has a zero in d and email protected email protected is minimal first we prove that if a nearest polynomial exists there is a nearest polynomial email protected such that the absolute value of every coefficient of email protected is email protected email protected with at most one exception using this property and the representation of c we reduce the problem to solving systems of algebraic equations each of which consists of two equations with two variables

the effect of different combinations of boundary conditions on the average radiation efficiency of rectangular plates the boundary conditions of a vibrating plate are known to have an influence on its sound radiation for frequencies below the critical frequency to investigate this effect in a systematic way the average radiation efficiency and radiated power are calculated for a rectangular plate set in an infinite baffle using a modal summation approach whereas analytical expressions exist for simply supported boundary conditions a numerical approach is required for other cases nine combinations of boundary conditions are considered consisting of simply supported clamped and free edges on different plate edges the structural vibration is approximated by using independent beam functions in orthogonal directions allowing simple approximate formulae for mode shapes and natural frequencies this assumption is checked against a finite element model and shown to give reliable results it is shown that a free plate has the lowest radiation efficiency and a clamped plate the highest for most frequencies between the fundamental panel natural frequency and the critical frequency other combinations of boundary condition give intermediate results according to the level of constraint introduced the differences depend on frequency excluding the extreme case of a fully free plate all the other boundary conditions give results within a range of 8 db in the middle part of the short circuiting region decreasing towards the critical frequency at low frequency the differences can be even greater in some cases up to 20 db these conclusions are shown to hold for a range of plate thicknesses and dimensions

on the αx2 βx4 interaction by applying the laplace transform method the authors obtain a class of exact solutions for the schrodinger equation with the potential v x alpha x2 beta x4 x 0 alpha or 0 beta 0 the corresponding energy spectrum being continuous a particular feature of these eigen solutions is that they may not be accessible to perturbation theory the properties of the solutions obtained are investigated and their relation to the case where x or 0 is included is discussed

face recognition by sparse discriminant analysis via joint l2 1 norm minimization abstract recently joint feature selection and subspace learning which can perform feature selection and subspace learning simultaneously is proposed and has encouraging ability on face recognition in the literature a framework of utilizing l 2 1 norm penalty term has also been presented but some important algorithms cannot be covered such as fisher linear discriminant analysis and sparse discriminant analysis therefore in this paper we add l 2 1 norm penalty term on flda and propose a feasible solution by transforming its nonlinear model into linear regression type in addition we modify the optimization model of sda by replacing elastic net with l 2 1 norm penalty term and present its optimization method experiments on three standard face databases illustrate flda and sda via l 2 1 norm penalty term can significantly improve their recognition performance and obtain inspiring results with low computation cost and for low dimension feature

state space boundary element finite element coupling for fluid structure interaction analysis state space coupling is a new approach for handling computational fluid structure interaction problems in the low to medium frequency range the method is based on standard boundary element bem and finite element fem discretizations of the acoustic and structural domains respectively the implicit frequency dependence of a traditional acoustic impedance matrix is made explicit through a power series expansion on circular frequency and considering time harmonic motion once expanded the acoustic energy of the fluid is directly coupled to that of the structure via hamilton s principle the coupled system is then recast in a canonical state space form which is also in the form of a standard eigenvalue problem solution of this system produces a series of complex eigenvalues and eigenvectors which represent a modal decomposition of the fluid loaded structure biorthogonality properties of the state space eigensystem allow for an uncoupled modal solution of the forced problem results for a submerged spherical shell and a finite plate in an infinite ridged baffle are given to illustrate the state space approach

root neighborhoods of a polynomial the root neighborhoods of p z a polynomial over the complex field are the sets of complex numbers that are the roots of polynomials which are near to p z the term near means that the coefficients of the polynomials are within some fixed magnitude of the coefficients of p z a necessary and sufficient condition for a complex number to be in the root neighborhoods is given and it is proved that each root neighborhood contains at least one root of p z and the same number of roots of each near polynomial finally a necessary and sufficient condition is given for a root neighborhood to contain more than one root of p z and consequently more than one root of any of the near polynomials

modal sound transmission loss of a single leaf panel asymptotic solutions in a previously published paper c wang j acoust soc am 137 6 3514 3522 2015 the modal sound transmission coefficients of a single leaf panel were discussed with regard to the inter modal coupling effects by incorporating such effect into the equivalent modal radiation impedance which is directly related to the modal sound transmission coefficient of each mode the overall sound transmission loss for both normal and randomized sound incidences was computed through a simple modal superposition benefiting from the analytical expressions of the equivalent modal impedance and modal transmission coefficients in this paper behaviors of modal sound transmission coefficients in several typical frequency ranges are discussed in detail asymptotic solutions are also given for the panels with relatively low bending stiffnesses for which the sound transmission loss has been assumed to follow the mass law of a limp panel results are also compared to numerical analysis and the renowned mass law theories

structured singular values and stability analysis of uncertain polynomials part 2 a missing link abstract in part 1 of this paper a generalized notion of structured singular value is introduced and studied specifically in the case when a certain matrix is of rank one in part 2 of this series we demonstrate that the framework developed in part 1 is particularly suitable for a class of stability problems and its unifies several frequency based stability conditions obtained via alternative approaches generally these problems correspond to a class of uncertain polynomials whose coefficients are perturbed in an affine fashion several stability conditions are derived readily from solution of the structured singular value presented in part 1 which either extend or coincide with previously known results in particular for family of interval and diamond polynomials we further show that the stability conditions based on the structured singular value and the corresponding results in the spirit of kharitonov theorem lead to one another thus establishing a link between the two types of drastically different results and accomplishing one of our main goals in this series a related robust stabilization problem is also investigated in this framework

acoustic modeling of a three dimensional rectangular opened enclosure coupled with a semi infinite exterior field at the baffled opening a modeling method is proposed for the acoustic analysis of a three dimensional 3d rectangular opened enclosure coupled with a semi infinite exterior field by a rectangular opening of arbitrary size and with general wall impedance in contrast to existing modeling methods that solve the differential equations the energy principle in combination with a 3d modified fourier cosine series is employed in the present method for the modeling of this system under this theoretical framework the effect of an opening in the wall of a rectangular enclosure is taken into account via the work done by the sound pressure acting on the opening between the finite enclosure and exterior domain the sound pressure inside the opened enclosure is expressed as the combination of a 3d trigonometric cosine series and one supplementary 2d expansion introduced to ensure uniform convergence of the solution over the entire solution domain including opening boundary the acoustic responses of the opened enclosure are obtained bas

computing multiple roots of inexact polynomials we present a combination of two algorithms that accurately calculate multiple roots of general polynomials algorithm i transforms the singular root finding into a regular nonlinear least squares problem on a pejorative manifold and it calculates multiple roots simultaneously from a given multiplicity structure and initial root approximations to fulfill the input requirement of algorithm i we develop a numerical gcd finder containing a successive singular value updating and an iterative gcd refinement as the main engine of algorithm ii that calculates the multiplicity structure and the initial root approximation while limitations exist in certain situations the combined method calculates multiple roots with high accuracy and consistency in practice without using multiprecision arithmetic even if the coefficients are inexact this is perhaps the first blackbox type root finder with such capabilities to measure the sensitivity of the multiple roots a structure preserving condition number is proposed and error bounds are established according to our computational experiments and error analysis a polynomial being ill conditioned in the conventional sense can be well conditioned with the multiplicity structure being preserved and its multiple roots can be computed with high accuracy

the forced sound transmission of finite single leaf walls using a variational technique the single wall is the simplest element of concern in building acoustics but there still remain some open questions regarding the sound insulation of this simple case the two main reasons for this are the effects on the excitation and sound radiation of the wall when it has a finite size and the fact that the wave field in the wall is consisting of two types of waves namely forced waves due to the exciting acoustic field and free bending waves due to reflections in the boundary the aim of the present paper is to derive simple analytical formulas for the forced part of the airborne sound insulation of a single homogeneous wall of finite size using a variational technique based on the integral differential equation of the fluid loaded wall the so derived formulas are valid in the entire audible frequency range the results are compared with full numerical calculations measurements and alternative theory with reasonable agreement

computing the nearest singular univariate polynomials with given root multiplicities in this paper we derive explicit expressions for the nearest singular polynomials with given root multiplicities and its distance to the given polynomial these expressions can be computed recursively these results extend previous results of zhi et al 2004 10 and zhi and wu 1998 11

acoustic radiation from a rectangular plate reinforced by springs at arbitrary locations abstract the vibration of a simply supported rectangular plate which is reinforced by a finite number of springs at arbitrary locations is sought as a linear combination of the flexural modes of the corresponding unloaded or simple plate although these modes cannot be directly used to decouple the dynamic equations of the motion of the reinforced plate it is still advantageous to use them as a complete set of basis functions to represent the interested quantities such as the deflection of the plate a linear transformation is established between the two modal spaces spanned by the modes respectively for the reinforced and the unloaded plates the radiation characteristics of the spring reinforced plate are investigated by using a near field formulation in order to reduce computational burden a frequency interpolation technique is employed so that numerical integration now needs to be carried out only at some key frequencies the specific radiation resistances of the basis modes are first determined as a set of invariants from which the modal radiation efficiency of the reinforced plate can be readily extracted the effects of cross modal coupling between the basis modes have been considered which is necessary for an accurate determination of the modal radiation efficiency for the reinforced plate a qualitative procedure is also described for locating the coincidence frequencies where the modal radiation efficiencies of the reinforced plate tend to reach their peak values

the average specific forced radiation wave impedance of a finite rectangular panel the average specific forced radiation wave impedance of a finite rectangular panel is of importance for the prediction of both sound insulation and sound absorption in 1982 thomasson published numerical calculations of the average specific forced radiation wave impedance of a square of side length 2e for wave number k in half octave steps of ke from 0 25 to 64 thomasson s calculations were for the case when the forced bending wave number kb was less than or equal to k thomasson also published approximate formulas for values of ke above and below the published results this paper combines thomasson s high and low frequency formulas and compares this combined formula with thomasson s numerical calculations the real part of the approximate formula is between 0 7 db higher and 1 db lower than the numerical calculations the imaginary part of the approximate formula is between 2 3 db higher and 2 6 db lower than the numerical calculations this paper also gives approximate formulas for the case when kb is greater than or equal to k the differences are between 0 8 and 1 2 db for the imaginary part and between 6 2 and 2 4 db for the real part

elementary bound states for the power law potentials the author shows how the exact polynomial exp polynomial bound state solutions to the radial schrodinger equation may be constructed for any potential of the form v r sigma delta in d gdelta rdelta where d is a finite set of arbitrary rational numbers and some of the couplings gdelta are not independent

a unified approach for predicting sound radiation from baffled rectangular plates with arbitrary boundary conditions this paper discusses sound radiation from a baffled rectangular plate with each of its edges arbitrarily supported in the form of elastic restraints the plate displacement function is universally expressed as a 2 d fourier cosine series supplemented by several 1 d series the unknown fourier expansion coefficients are then determined by using the rayleigh ritz procedure once the vibration field is solved the displacement function is further simplified to a single standard 2 d fourier cosine series in the subsequent acoustic analysis thus the sound radiation from a rectangular plate can always be obtained from the radiation resistance matrix for an invariant set of cosine functions regardless of its actual dimensions and boundary conditions further this radiation resistance matrix unlike the traditional ones for modal functions only needs to be calculated once for all plates with the same aspect ratio in order to determine the radiation resistance matrix effectively an analytical formula is derived in the form of a power series of the non dimensional acoustic wavenumber the formula is mathematically valid and accurate for any wavenumber several numerical examples are presented to validate the formulations and show the effect of the boundary conditions on the radiation behavior of planar sources

on exact solutions of the schrodinger equation in the one and three dimensional schrodinger equation a broad class of the regular potentials rational functions of the rational powers of r may admit exact bound state solutions in the generalised harmonic oscillator elementary form psi r rsigma polynomial exp polynomial the necessary and sufficient conditions of this phenomenon are derived in the form of coupled algebraic equations the methods of their solution and a few examples are discussed in particular the well known coulombic and oscillator solvability and the similar recent results of singh et al 1978 and whitehead et al 1982 are reproduced as the two simplest special cases

an analytical solution for the self and mutual radiation resistances of a rectangular plate it is widely accepted that for an arbitrary acoustic wavenumber the radiation resistance of a simply supported rectangular plate has to be calculated through numerical integration in this study an analytical solution for the self and mutual radiation resistances is obtained in the form of the power series of the non dimensional acoustic wavenumber unlike the previous analytical or asymptotic solutions it is not subject to any of the restrictions usually imposed upon the acoustic wavenumber a few numerical examples are given simply to verify the solution and elucidate the reliance of the self and mutual radiation resistances on the acoustic wavenumber and the plate aspect ratio it is shown that the present formulae are extremely efficient by cutting the cpu time by orders of magnitude in comparison with the traditional numerical integration scheme this investigation successfully fills the long existing gap in solutions for the moderate wavenumbers that are often of primary concern in an acoustic analysis

dynamic analysis of generally supported beams using fourier series the applicability of fourier series to the dynamic analysis of beams having arbitrary boundary conditions is explored for the simplicity of presenting the analysis procedure beams having zero end displacement are used in the discussion numerical results for free vibration and dynamic response based on the present analysis procedure are compared with existing results for natural frequencies and dynamic behavior obtained by the conventional modal analysis these results indicate that the present analysis is accurate and provides a unified and systematic procedure which is seemingly simpler and more straightforward than the conventional modal analysis

the nearest complex polynomial with a zero in a given complex domain given a univariate complex polynomial f and a closed complex domain d whose boundary c is a curve parameterized by a piecewise rational function we propose two computational algorithms for finding a univariate complex polynomial email protected such that email protected has a zero in d and the distance between f and email protected is minimal our approach is composed of two steps first in the case of d consisting of one point a we give explicit formulas of email protected and the minimal distance in terms of a next the case of a general closed domain d is considered by using the property that a nearest polynomial email protected has a zero on the boundary c the curve c is parameterized piecewisely and on each piece we search for the minimum of the distance between f and email protected at this step we exploit the explicit formula of the minimal distance as a function of a point a then the global minimum and the nearest polynomial are obtained by comparing the piecewise minima some examples are presented one of them confirms that the distance between a nearest complex polynomial and a given polynomial is less than that between a nearest real polynomial and the given polynomial