some model theory of polish structures we introduce a notion of polish structure and in doing so provide a setting which allows the application of ideas and techniques from model theory descriptive set theory topology and the theory of profinite groups we define a topological notion of independence in polish structures and prove that it has some nice properties using this notion we prove counterparts of some basic results from geometric stability theory in the context of small polish structures then we prove some structural theorems about compact groups regarded as polish structures each small nm stable compact g group is solvable by finite each small compact g group of finite n m rank is nilpotent by finite examples of small polish structures and groups are also given

the polynomial ring over a goldie ring need not be a goldie ring rings satisfying chain conditions have been of interest for quite some time the famous wedderburn theorem states that semisimple artinian rings must be finite direct sums of matrix rings goldie s theorem links rings with ascending chain conditions to rings with descending chain conditions thus extending wedderburn s result a ring r is said to be a right goldie ring if r satisfies the ascending chain condition on right annihilator ideals and r contains no infinite direct sum of right ideals from goldie s theorem we know that a semiprime right goldie ring must be an order in a semisimple right artinian ring a natural question to arise is whether the matrix and polynomial rings over right goldie rings are also necessarily right goldie rings under certain additional hypotheses such as if the ring is an order in a right artinian ring 4 or if the ring contains a certain type of uncountable set in its center i the answer is yes moreover the second goldie condition is always preserved 3 hence as in the case for the matrix ring counterexample 2 we must explore the ascending chain condition on right annihilator ideals in the next section we construct a commutative goldie ring r whose polynomial ring r t contains two infinite sets of polynomials p t and qj t such that pi t qj t 0 iff i j this condition forces qk t to be in ann p t i k and qk t to be excluded from ann p t i k1 thus r t has an infinite ascending chain of annihilator ideals

amenability definable groups and automorphism groups abstract we prove several theorems relating amenability of groups in various categories discrete definable topological automor phism group to model theoretic invariants quotients by connected components lascar galois group g compactness among the main tools which is possibly of independent interest is the adaptation and generalization of theorem 12 of 27 to other settings including amenable topological groups whose topology is generated by a family of subgroups on the side of definable groups we prove that if g is definable in a model m and g is definably amenable then the connected components g m 00 and g m 000 coincide answering positively a question from 22 we also prove some natural counterparts for topological groups using our generalizations of 27 by finding a dictionary relating quotients by connected components and galois groups of categorical theories we conclude that if m is countable and categorical and aut m is amenable as a topological group then t th m is g compact i e the lascar galois group gal l t is compact hausdorff equivalently the natural epimorphism from gal l t to gal k p t is an isomorphism we also take the opportunity to further develop the model theoretic approach to topological dynamics obtaining for example some new invariants for topological groups as well as allowing a uniform approach to the theorems above and the various categories

generalized fitting modules and rings abstract an r module m is called strongly hopfian respectively strongly co hopfian if for every endomorphism f of m the chain ker f ker f 2 respectively im f im f 2 stabilizes the class of strongly hopfian respectively co hopfian modules lies properly between the class of noetherian respectively artinian and the class of hopfian respectively co hopfian modules for a quasi projective respectively quasi injective module m if m is strongly co hopfian respectively strongly hopfian then m is strongly hopfian respectively strongly co hopfian as a consequence we obtain a version of hopkins levitzki theorem for strongly co hopfian rings namely a strongly co hopfian ring is strongly hopfian also we prove that for a commutative ring a the polynomial ring a x is strongly hopfian if and only if a is strongly hopfian

suppression of time aliasing in the solution of the equations of motion of an impacted beam with partial constrained layer damping abstract signal processing issues encountered when an analytical spectrum is converted in the time domain with an inverse discrete fourier transform are investigated in the analytical model of the transient time response of an impacted beam with partial constrained layer damping pcld developed in ref d granger a ross effects of partial constrained viscoelastic layer damping parameters on the initial transient response of impacted cantilever beams experimental and numerical results journal of sound and vibration 321 1 2 2009 45 64 doi 10 1016 j jsv 2008 09 039 noncausal effects were observed for lightly damped structures as discussed in the present paper the noncausal effects were due to time aliasing occurring when continuous frequency spectra were discretized to suppress such errors the numerical laplace transform is introduced and applied to the previous model which was based on fourier transforms the equations of motion of the system and the viscoelastic properties of the core are formulated in the laplace domain a window is used in the laplace domain to avoid amplification of the gibbs oscillations that are caused by the truncation of the spectrum the new solution technique is compared to the previous method it is shown that noncausal effects appearing in the first milliseconds of time signals with the use of discrete fourier transforms are avoided with the laplace transform solution method numerical results are validated for transient responses using experimental impact force signals the results are in good agreement with experimental data

a robust transfer matrix formulation for the ultrasonic response of multilayered absorbing media an improved version of the transfer matrix approach is presented for ultrasonic wave interaction in multilayered media generalized expressions are obtained for reflection and transmission coefficients in either fluid or solid half space and problems associated with numerical stability are solved efficiently the formulation is applicable to longitudinal and shear input waves alike at arbitrary incidence angles and for any sequence of solid or fluid layers also allowance is made for viscoelastic behavior by means of relaxation functions in the laplace transform domain finally the response to arbitrary incident pulse shapes and beam profiles is described through application of two dimensional numerical laplace inversion

commutative rings with acc on n generated ideals abstract a commutative ring with unity has n acc iff every ascending chain of n generated ideals stabilizes this paper shows that any polynomial ring or formal power series ring over a noetherian ring has n acc for all n the method involves a sufficient condition for n acc in the quasilocal case and another for globalizing the n acc property examples are given to show that n acc does not imply n 1 acc for every positive integer n and that n acc does not behave well in general under localization globalization and passage to a polynomial ring it is also noted that a prufer domain with 2 acc is dedekind

matrix propagator method for layered porous media analytical expressions and stability criteria we fully expand the thomson haskell propagator matrix method to obtain closed form analytical expressions for the reflectivity and transmittivity of a horizontally stratified poroelastic biot type medium that is bounded from above and below by fluid half spaces stable and unstable regions of the propagator matrix method are determined by means of comparison with the inherently stable reflectivity method it was found that the stability is mainly determined by the imaginary part of the vertical wavenumber of the biot slow wave

small profinite structures we propose a model theoretic framework for investigating profinite structures we prove that in many cases small profinite structures interpret infinite groups this corresponds to results of hrushovski and peterzil on interpreting groups in locally modular stable and o minimal structures

connected components of definable groups and o minimality i abstract we give examples of definable groups g in a saturated model sometimes o minimal such that g 00 g 000 yielding also new examples of non g compact theories we also prove that for g definable in a saturated o minimal structure g has a bounded orbit i e there is a type of g whose stabilizer has bounded index if and only if g is definably amenable giving a positive answer to a conjecture of newelski and petrykowski in this special case of groups definable in o minimal structures

generalized hopfian modules a module is called generalized hopfian gh if any of its surjective endomorphisms has a small kernel such modules are in a sense dual to weakly co hopfian modules that were defined and extensively studied in a haghany m r vedadi j algebra 243 2001 765 779 several equivalent formulations are given for gh modules and used in their study generalized hopfian modules form a proper subclass of dedekind finite modules but this subclass is rather large in that it properly contains hopfian and in particular noetherian modules as well as artinian modules and modules with finite dual goldie dimension for quasi projective modules the properties dedekind finite hopfian and gh are all equivalent yielding a ring r stably finite iff all finitely generated free r modules are gh the gh property is shown to be a morita invariant and rings are characterized over which all finitely generated modules are gh some other classes of rings are also studied these rings satisfy one of the conditions all right ideals are gh all annihilator right ideals are small right domain all left regular elements have small right annihilators right directly finite we will show right domain right directly finite directly finite and these cannot be reversed these results are by products of the study of special gh modules

legendre and laguerre polynomial approach for modeling of wave propagation in layered magneto electro elastic media a numerical method to compute propagation constants and mode shapes of elastic waves in layered piezoelectric piezomagnetic composites potentially deposited on a substrate is described the basic feature of the method is the expansion of particle displacement stress fields electric and magnetic potentials in each layer on different polynomial bases legendre for a layer of finite thickness and laguerre for the semi infinite substrate the exponential convergence rate of the method for propagation of love waves is numerically verified the main advantage of the method is to directly determine complex wave numbers for a given frequency via a matricial eigenvalue problem in a way that no transcendental equation has to be solved results are presented and the method is discussed

modules whose injective endomorphisms are essential abstract an r module m is called weakly co hopfian if any injective endomorphism of m is essential the class of weakly co hopfian modules lies properly between the class of co hopfian and the class of dedekind finite modules several equivalent conditions are given for a module to be weakly co hopfian being co hopfian weakly co hopfian or dedekind finite are all equivalent conditions on quasi injective modules some other properties of weakly co hopfian modules are also obtained the ring r is said to be right strong stably finite if all the finitely generated free right r modules are weakly co hopfian we shall characterize such rings and show that they are stably finite and satisfy the right strong rank condition examples show that stably finite rings and rings with the right strong rank conditions need not be strong stably finite both weakly co hopfian and right strong stably finite are morita invariants although the right and left strong stably finite are different properties the class of commutative rings and the class of rings with finite right uniform dimension are proper subclasses of the class of right strong stably finite rings we shall also investigate conditions that are relevant to weakly co hopfian modules equivalent statements are found on a ring to have all its finitely generated right modules weakly co hopfian

the laskerian property in commutative rings 1 introduction primary decomposition is a venerable tool in commutative algebra indeed emmy noether studied rings with the ascending chain condition on ideals because primary decomposition was available there 9 j though many results for which it was once used are now proved by other means primary decomposition itself is still finding new applications 15 161 and provides an often informative representation of ideals 2 in this paper we study the class of rings always commutative with unity in which primary decom position holds and related classes recall definition let m be a finitely generated module over ring r 1 a submodule n is primary if for any r in r and m in m whose product rm is in n either m e n or some power rk of r satisfies rkm g n it is strongly primary if in addition the radical p fl r e r rkm l n for some k has a power pk which satisfies pkm e n 2 m is a strongly laskerian module if every submodule of m is an intersection of a finite number of strongly primary submodules 3 m is a zd module if for every submodule n of m the set z m n r e r rm e n for some m e m n of zero divisors on m n in r is the union of a finite number prime ideals in r of course a ring is laskerian or strongly laskerian or zd if it has the property as a module over itself in section 2 we prove the ascent of these properties in certain ring extensions in particular finite integral extensions

groups measures and the nip we discuss measures invariant measures on definable groups and genericity often in an nip failure of the independence property environment we complete the proof of the third author s conjectures relating definably compact groups g in saturated o minimal structures to compact lie groups we also prove some other structural results about such g for example the existence of a left invariant finitely additive probability measure on definable subsets of g we finally introduce a new notion compact domination domination of a definable set by a compact space and raise some new conjectures in the o minimal case

rings with the dual of the isomorphism theorem ar ingr satisfies the dual of the isomorphism theorem if r ra l a for all elements a of r where l a denotes the left annihilator we call these rings left morphic examples include all unit regular rings and certain left uniserial local rings we show that every left morphic ring is right principally injective and use this to characterize the left perfect right and left morphic rings 2004 elsevier inc all rights reserved

the ascending chain condition for principal left or right ideals of skew generalized power series rings let r be a ring s a monoid and s end r a monoid homomorphism in this paper we prove that if the monoid s is strictly totally ordered or s is commutative torsion free cancellative semisubtotally ordered then the ring r s of skew generalized power series with coefficients in r and exponents in s is a domain satisfying the ascending chain condition on principal left resp right ideals if and only if r is a domain r and s satisfy the ascending chain condition on principal left resp right ideals and each s is injective resp is injective and preserves nonunits of r as an immediate consequence we obtain characterizations of power series rings laurent series rings skew power series rings skew laurent series rings and generalized power series rings that are domains satisfying the ascending chain condition on principal left or right ideals we construct examples of skew generalized power series domains for which the ascending chain conditions on principal one sided ideals are not symmetric

forward projection of transient sound pressure fields radiated by impacted plates using numerical laplace transform forward propagation of the transient sound pressure radiated by an impacted plate is presented it is shown that direct and inverse time domain discrete fourier transforms involved in fourier transform based near field acoustical holography nah lead to aliasing errors in the reconstructed time signals adding trailing zeros to the initial time signals is an inefficient way to reduce time aliasing errors hence the numerical laplace transform is introduced and a fourier transform based transient nah tnah approach is formulated an error measure is introduced to compare both nah and tnah with respect to the propagation distance and the location of the observation point in the projection plane the percentage of error with tnah is reduced by more than a factor of 10 without adding trailing zeros to the initial signals simulation results are validated experimentally using a free plexiglas plate impacted at its center

eberlein oligomorphic groups we study the fourier stieltjes algebra of roelcke precompact non archimedean polish groups and give a model theoretic description of the hilbert compactification of these groups we characterize the family of such groups whose fourier stieltjes algebra is dense in the algebra of weakly almost periodic functions those are exactly the automorphism groups of 0 stable 0 categorical structures this analysis is then extended to all semitopological semigroup compactifica tions s of such a group s is hilbert representable if and only if it is an inverse semigroup we also show that every factor of the hilbert compactification is hilbert representable

modules with n acc and the acc on certain types of annihilators abstract a unitary module m over a commutative ring r with unity satisfies acc on d colons if for every submodule n of m and every sequence a n n of elements of r the ascending chain n a 1 n a 1 a 2 stabilizes in this paper we study the acc on d colons and show that it implies the acc on n generated submodules for every n pan acc generalizing a result of w heinzer and d lantz the method involves a generalized nakayama s lemma for these modules further it is shown that every r module r i for a noetherian ring r satisfies pan acc and we give a sufficient condition for the acc on principal ideals to rise to the polynomial ring