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

littlewood paley theory and the t 1 theorem with non doubling measures let be a radon measure on rd which may be non doubling the only condition that must satisfy is b x r crn for all x rd r 0 and for some fixed 0 n d in this paper littlewood paley theory for functions in lp is developed one of the main difficulties to be solved is the construction of reasonable approximations of the identity in order to obtain a calderon type reproducing formula moreover it is shown that the t 1 theorem for n dimensional calderon zygmund operators without doubling assumptions can be proved using the littlewood paley type decomposition that is obtained for functions in l2 as in the classical case of homogeneous spaces

on a system of differential equations with fractional derivatives arising in rod theory we study a system of equations with fractional derivatives that arises in the analysis of the lateral motion of an elastic column fixed at one end and loaded by a concentrated follower force at the other end we assume that the column is positioned on a viscoelastic foundation described by a constitutive equation of fractional derivative type the stability boundary is determined it is shown that as in the case of an elastic winkler type of foundation the stability boundary remains the same as for the column without a foundation thus with the solution analysed here the column exhibits the so called hermann smith paradox

global monotonic solutions of multi term fractional differential equations abstract based on the leray schauder principle a fixed point theorem is established to study the existence of a global monotonic solution for some multi term differential equations of fractional type some existence result for the inclusion problem is proved

characterization and semiadditivity of the c 1 harmonic capacity the c 1 harmonic capacity c plays a central role in problems of approximation by harmonic functions in the c 1 norm in n 1 in this paper we prove the comparability between the capacity c and its positive version c as a corollary we deduce the semiadditivity of c this capacity can be considered as a generalization in n 1 of the continuous analytic capacity in c moreover we also show that the so called inner boundary conjecture fails for dimensions n 1 unlike in the case n 1

the planar cantor sets of zero analytic capacity and the local t b theorem in this paper we obtain rather precise estimates for the analytic capacity of a big class of planar cantors sets in fact we show that analytic capacity and positive analytic capacity are comparable for these sets the main tool for the proof is an appropriate version of the t b theorem

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

the semiadditivity of continuous analytic capacity and the inner boundary conjecture let a e be the continuous analytic capacity of a compact set e c c in this paper we obtain a characterization of a in terms of curvature of measures with zero linear density and we deduce that a is countably semiadditive this result has important consequences for the theory of uniform rational approximation on compact sets in particular it implies the so called inner boundary conjecture 1 introduction the continuous analytic capacity a was introduced by erokhin and vitushkin see vi in the 1950s in order to study problems of uniform rational approximation in compact subsets of the complex plane up to now the geometric properties of the capacity a have not been well understood it has been an open question if a is semiadditive as a set function that is to say if

on the existence of continuous solutions for a singular system of non linear fractional differential equations abstract in the this paper we establish the existence of continuous solutions to some non linear fractional integral and differential equations quadratic system of fractional integral equations cases will be considered our analysis rely on krasnoselskii s fixed point theorem on a cone

positive solutions of a system of non autonomous fractional differential equations abstract existence of positive solutions for the following system of fractional differential equations d i u i f i t u 1 u 2 u n u i 0 0 0 i 1 1 i n where d i denotes riemann liouville derivative of order i has been studied

the molecular characterization of the hardy space h 1 on non homogeneous metric measure spaces and its application national natural science foundation of china 11171027 11101339 specialized research fund for the doctoral program of higher education of china 20120003110003 natural science foundation of fujian province of china 2013j01020 fundamental research funds for central universities of china 2013121004

riesz transforms and harmonic lip1 capacity in cantor sets we estimate the l norm of the s dimensional riesz transforms on some cantor sets in rd to this end we show that the riesz transforms truncated at different scales behave in quasiorthogonal way as an application we obtain some precise numerical estimates for the lipschitz harmonic capacity of these sets

the tb theorem on non homogeneous spaces 0 introduction main objects and results 3 0 1 main results 4 0 2 an application of t1 heorem electric intensity capacity 7 0 3 how to interpret calderon zygmund operator t 9 0 3 1 bilinear form is defined on lipschitz functions 10 0 3 2 bilinear form is defined for smooth functions 11 0 3 3 apriori boundedness 12 0 4 plan of the paper 15

numerical solution of fractional integro differential equations by a hybrid collocation method fractional integro differential equations have been recently solved by many methods such as adomian decomposition method differential transform method collocation method and taylor expansion approach in this paper a hybrid collocation method is used which combines a non polynomial collocation used on the first subinterval and graded piecewise polynomial collocation used on the rest of the interval a theoretical analysis for the convergence order of the method is presented some numerical examples are given which confirm the theoretical results

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