operator norm inequalities in semi hilbertian spaces abstract in this work we extend cordes inequality mcintosh inequality and cpr inequality for the operator seminorm defined by a positive semidefinite bounded linear operator a

a m isometric operators in semi hilbertian spaces abstract in this work the concept of m isometry on a hilbert space are generalized when an additional semi inner product is considered this new concept is described by means of oblique projections

partial isometries and pseudoinverses in semi hilbertian spaces abstract in this article the concepts of partial isometries normal partial isometries and generalized projections in the context of operators defined on a semi hilbertian space are developed in particular we analyze the relationship between these operators and different notions of pseudoinverses in semi hilbertian spaces finally we apply the results obtained to describe the set of weighted projections into closed subspaces

antenna characterization in the time domain a theory for a complete far field transmit receive system characterization of short pulse antennas is derived in the time domain the transmit receive antenna system is characterized by a set of cascaded operators which transform the source waveform and power into similar quantities at the receiving antenna terminals two such sets are defined the first one is phrased in terms of the wave type time dependent effective height operator while the second one is defined in terms of the energy type gain operator both definitions fit within a complete transmit receive system description the latter being equivalent to the frequency domain friis equation however these operators are derived entirely in the context of the time domain field equation the starting point in the time domain analysis of the effective height is the slant stack transform sst of the time dependent current distribution in a manner equivalent to the spatial fourier transform used in the frequency domain the vector autocorrelation of the transmitting effective height is then used to define the time dependent gain operator under impulsive source excitation time domain reciprocity leads to the definitions of antenna parameters under receiving conditions and the corresponding equivalent circuit the parameters defined in this way fit within a consistent transmit receive convolution operator operating on the autocorrelation of the input signal this independent time domain representation is thus similar to the frequency domain representation however unlike the conventional frequency domain circuit parameters which relate voltage and current amplitudes the time domain circuit representation is based on incident and reflected wave type constituents in addition the use of appropriate norms facilitates the transformation of our operators to stand alone figures of merits the general concepts developed are demonstrated for a short dipole antenna

formulation of probe corrected planar near field scanning in the time domain probe corrected planar near field formulas in the time domain are derived for both acoustic and electromagnetic fields so that a single set of near field measurements in the time domain yields the fields of the test antenna directly in the time domain the time domain probe corrected formulas are first derived by taking the inverse fourier transform of the corresponding frequency domain formulas and then by using a time domain expansion for the fields of the test antenna and a time domain receiving characteristic of the probe because these general formulas which involve a double integral over the scan plane and an infinite time convolution integral are rather complicated we consider a special probe whose output due to an incoming time domain plane wave is proportional to the time derivative of the field of that plane wave for this special d dot probe the probe corrected formulas simplify to give the time domain far held pattern as a double spatial integral of the time domain output of the probe over the scan plane multiplied by the angular dependence of the inverse receiving characteristic of the probe time domain reciprocity relations are derived for reciprocal probes and their time domain receiving characteristics are related to their far fields finally a time domain sampling theorem is derived and a numerical example illustrates the use of the time domain probe corrected formulas

factorizations of linear relations abstract given two linear relations a and b we characterize the existence of a linear relation operator c such that a b c respectively a c b these factorizations extend and improve well known results by douglas and sebestyen

partial isometries in semi hilbertian spaces in this work the concepts of isometry unitary and partial isometry on a hilbert space are generalized when an additional semi inner product is considered these new concepts are described by means of oblique projections

on two classes of autonomous third order nonlinear ordinary differential equations abstract two autonomous nonlinear third order ordinary differential equations whose dynamics can be represented by second order nonlinear ordinary differential equations for the first order derivative of the solution are studied analytically and numerically the analytical study includes both the obtention of closed form solutions and the use of an artificial parameter method that provides approximations to both the solution and the frequency of oscillations it is shown that both the analytical solution and the accuracy of the artificial parameter method depend greatly on the sign of the nonlinearities and the initial value of the first order derivative

planar near field scanning in the time domain 2 sampling theorems and computation schemes for part 1 see ibid vol 47 no 9 p 1280 1994 two computation schemes for calculating the far field pattern in the time domain from sampled near field data are developed and applied the sampled near field data consists of the values of the field on the scan plane measured at discrete times and at discrete points on the scan plane the first computation scheme is based on a frequency domain near field to far field formula and applies frequency domain sampling theorems to the computed frequency domain near field the second computation scheme is based on a time domain near field to far field formula and computes the time domain far field directly from the time domain near field a time domain sampling theorem is derived to determine the spacing between sample points on the scan plane the computer time for each of the two schemes is determined and numerical examples illustrate the use and the general properties of the schemes for large antennas the frequency domain computation scheme takes less time to compute the full far field than the time domain computation scheme however the time domain computation scheme is simpler more direct and easier to program it is also found that planar time domain near field antenna measurements unlike single frequency near field measurements have the capability of eliminating the error caused by the finite scan plane and thus can be applied to broadbeam antennas

planar near field scanning in the time domain 1 formulation time domain planar near field measurement techniques are formulated for acoustic and electromagnetic fields probe correction is ignored in that it is assumed that the probe measures the exact values of the field on the scan plane two fundamentally different approaches are used in deriving three sets of formulas that give the fields in the source free half space z z sub 0 in terms of their values on the scan plane z z sub 0 in the first approach the time domain formulas are obtained by inverse fourier transforming the corresponding frequency domain formulas in the second approach the time domain formulas are derived directly in the time domain by working with time domain green s functions

functional calculus for semigroup generators via transference abstract in this article we apply a recently established transference principle in order to obtain the boundedness of certain functional calculi for semigroup generators in particular it is proved that if a generates a c 0 semigroup on a hilbert space then for each 0 the operator a has a bounded calculus for the closed ideal of bounded holomorphic functions on a sufficiently large right half plane that satisfy f z o e re z as z the bound of this calculus grows at most logarithmically as 0 as a consequence f a is a bounded operator for each holomorphic function f on a right half plane with polynomial decay at then we show that each semigroup generator has a so called strong m bounded calculus for all m n and that this property characterizes semigroup generators similar results are obtained if the underlying banach space is a umd space upon restriction to so called bounded semigroups the hilbert space results actually hold in general banach spaces

one dimensional quaternion homogeneous polynomial differential equations in this paper we study the dynamics of real four dimensional polynomial differential equations of the forms q aqkq m or q qkaqm where q a are quaternions q is the conjugate of q and k and m are non negative integers in many parts of the work the quaternion structure is used along the proofs

optimal time domain field interpolation from plane polar samples new time domain sampling series for representing radiated fields on a plane in terms of plane polar samples are presented the representations make it possible for the advanced sampling field interpolations introduced in the frequency domain to be generalized to the time domain thus enabling minimum redundance when using either a cardinal sampling scheme or a central interpolation one numerical analysis is then conducted to prove the effectiveness of the new representations

symmetry properties and solutions of nonlinear dispersive thin film equations in three dimensions the lie point symmetries are obtained for each one of two nonlinear dispersive thin film equations in 2 1 variables by means of the invariants of the one and two dimensional subgroups all reductions to ordinary differential equations and to partial differential equations in two variables are obtained solutions are provided for a number of the reduced equations it is also ascertained that neither one of the two considered thin film equations is integrable in some cases solitary and periodic wave solutions having curved wavecrests are obtained

on tuples of commuting operators in positive semidefinite inner product spaces abstract this paper is concerned with the study of certain properties of operator tuples on a complex hilbert space h when a semi inner product induced by a positive operator a on h is considered in particular we show that r a t a t for every commuting operator tuple t t 1 t d such that each t k admits an a adjoint operator where r a t and a t denote respectively the a joint spectral radius and the a joint numerical radius of t this study allows to establish that r a t a t t a for every a normal commuting tuple of operators t where t a is denoted to be the a joint operator seminorm of t in addition the a joint spectral radius of an a m isometric tuple of commuting operators is studied

quasi isometries in semi hilbertian spaces abstract the concept of quasi isometry on a hilbert space h studied by patel s m patel a note on quasi isometries glas mat 35 55 2000 307 312 s m patel a note on quasi isometries ii glas mat 38 58 2003 111 120 is generalized in the context of a contractions t i e t at a a 0 and t being bounded linear operators on h in fact the new concept is related on the semi inner product induced by a on h other results on operator ranges and invariant null subspaces for certain a contractions are obtained

partial isometries and the conjecture of c k fong and s k tsui abstract we investigate some bounded linear operators t on a hilbert space which satisfy the condition t re t we describe the maximum invariant subspace for a contraction t on which t is a partial isometry to obtain that in certain cases the above condition ensures that t is self adjoint in other words we show that the fong tsui conjecture holds for partial isometries contractive quasi isometries or 2 quasi isometries and brownian isometries of positive covariance or even for a more general class of operators

handbook of differential equations chapter headings definitions and concepts transformations exact analytical methods exact methods for odes exact methods for pdes approximate analytical methods numerical methods concepts numerical methods for odes numerical methods for pdes list of tables list of programs list of figures subject index

approximate methods based on order reduction for the periodic solutions of nonlinear third order ordinary differential equations four approximate methods based on order reduction the introduction of a book keeping parameter and power series expansions for the solution and the frequency of oscillation are used to analyze three autonomous nonlinear third order ordinary differential equations which have analytical periodic solutions the first method introduces the velocity in both sides of the equation if this linear term is not present the second one is based on the first one but employs a new independent variable whereas in the third and fourth techniques a term equal to the velocity times the square of the unknown frequency of oscillation is introduced in both sides of the equation the third method uses the original independent variable whereas the fourth one employs a new independent variable which depends linearly on the unknown frequency of oscillation it is shown that the second method provides accurate solutions only for initial velocities close to unity whereas the third one is found to yield very accurate results for the first and second equations considered here and only for large initial velocities for the third one the fourth technique provides as accurate results as or more accurate results than parameter perturbation techniques which deal with the third order equations directly and are based on the expansion of certain constants that appear in the differential equations in terms of a book keeping parameter

a numerical radius inequalities for semi hilbertian space operators abstract let a be a positive bounded operator on a hilbert space h the semi inner product x y a a x y x y h induces a semi norm a on h let t a and w a t denote the a operator semi norm and the a numerical radius of an operator t in semi hilbertian space h a respectively in this paper we prove the following characterization of w a t w a t sup 2 2 1 t t a 2 t t a 2 i a where t a is a distinguished a adjoint operator of t we then apply it to find upper and lower bounds for w a t in particular we show that 1 2 t a max 1 cos a 2 t 2 2 w a t w a t where cos a t denotes the a cosine of angle of t some upper bounds for the a numerical radius of commutators anticommutators and products of semi hilbertian space operators are also given

a boundary element numerical scheme for the two dimensional convection diffusion equation in this study the theoretical and numerical fundamentals of biem techniques for the two dimensional convection diffusion problem are presented after an extended presentation of the basic integral formulation the discretizing and iterative processes for its resolution are introduced interesting remarks on general expressions versus previously published particularized results are worth mentioning a numerical solution scheme is provided which has been completely developed and designed to the physical problem posed a novel scheme based in the simultaneous solving of the potential and the gradient of the potential boundary integral equations is included a diversity of problems is tested to prove the possibilities of the method copyright 2008 john wiley sons ltd

on lifting of operators to hilbert spaces induced by positive selfadjoint operators we introduce the notion of induced hilbert spaces for positive unbounded operators and show that the energy spaces associated to several classical boundary value problems for partial differential operators are relevant examples of this type the main result is a generalization of the krein reid lifting theorem to this unbounded case and we indicate how it provides estimates of the spectra of operators with respect to energy spaces 2004 elsevier inc all rights reserved

joint numerical ranges of operators in semi hilbertian spaces abstract in this paper we aim to investigate the concept of numerical range and maximal numerical range relative to a positive operator of a d tuple of bounded linear operators on a hilbert space some properties and applications of these sets are studied mainly it is proved that they are convex for d 1 this generalizes the well known toeplitz hausdorff theorem 24 16 and stampfli s result 23 moreover under additional hypotheses we show that these sets are convex for d 2

on an instability exhibited by the ballistic diffusive heat conduction model of xu and hu we show that the constitutive relation for the thermal flux proposed by xu hu 2011 admits an unconditional instability we also highlight the difference between mathematical models containing delay and those that include relaxation effects

a volterra integral formulation for determining the periodic solutions of some autonomous nonlinear third order ordinary differential equations a volterra integral formulation based on the introduction of a term proportional to the velocity times the square of the unknown frequency of oscillation a new independent variable equal to the original one times the unknown frequency of oscillation the method of variation of parameters and series expansions of both the solution and the frequency of oscillation is used to determine the periodic solutions to three nonlinear autonomous third order ordinary differential equations it is shown that the first term of the series expansion of the frequency of oscillation coincides with that determined from a first order harmonic balance procedure whereas the two term approximation to the frequency of oscillation is shown to be more accurate than that of a parameter perturbation procedure for the second equation considered in this paper for the third equation it is shown that the two term approximation presented in this paper is more accurate than the corresponding one for one of the parameter perturbation methods and for initial velocities less than one for the other parameter perturbation approach