clean rings some clean and almost clean baer rings and von neumann algebras a ring is clean resp almost clean if each of its elements is the sum of a unit resp regular element and an idempotent in this paper we define the analogous notion for rings a ring is clean resp almost clean if its every element is the sum of a unit resp regular element and a projection although clean is a stronger notion than clean for some rings we demonstrate that it is more natural to use the theorem on cleanness of unit regular rings from camillo and khurana 2001 4 is modified for cleanness of regular rings that are abelian or reduced or armendariz using this result it is shown that all finite type i baer rings that satisfy certain axioms considered in berberian 1972 2 and vas 2005 26 are almost clean in particular we obtain that all finite type i aw algebras thus all finite type i von neumann algebras as well are almost clean we also prove that for a baer ring satisfying the same axioms the following properties are equivalent regular unit regular left right morphic and left right quasi morphic if such a ring is finite and type i it is clean finally we present some examples related to group von neumann algebras and list some open problems

on expressing a cubic form as a sum of cubes of linear forms abstract sufficient conditions for a cubic form in n variables to be representable as a sum of cubes of n m m n 2 2 linear forms are derived for m 0 1 the conditions are also necessary whether it is true for m 1 is an open question in each case the corresponding algorithm requires besides arithmetic operations over the coefficients of solving one algebraic equation of degree m n

the value of a kurtosis metric in estimating the hazard to hearing of complex industrial noise exposures a series of gaussian and non gaussian equal energy noise exposures were designed with the objective of establishing the extent to which the kurtosis statistic could be used to grade the severity of noise trauma produced by the exposures here 225 chinchillas distributed in 29 groups with 6 to 8 animals per group were exposed at 97 db spl the equal energy exposures were presented either continuously for 5 d or on an interrupted schedule for 19 d the non gaussian noises all differed in the level of the kurtosis statistic or in the temporal structure of the noise where the latter was defined by different peak interval and duration histograms of the impact noise transients embedded in the noise signal noise induced trauma was estimated from auditory evoked potential hearing thresholds and surface preparation histology that quantified sensory cell loss results indicated that the equal energy hypothesis is a valid unifying principle for estimating the consequences of an exposure if and only if the equivalent energy exposures had the same kurtosis furthermore for the same level of kurtosis the detailed temporal structure of an exposure does not have a strong effect on trauma

noise levels and hearing thresholds in the drop forging industry a weighted equivalent continuous noise levels for hammer and press operations in a drop forging industry were determined using both tape recordings of the noise and personal noise dosimeters the results indicated average a weighted leq values of 108 db for hammer operators and 99 db for press operators comparison of hearing level statistics for 716 hammer and press operators and 293 control subjects indicated the severe hazard to hearing of impact noise exposures for mean exposure times of less than 10 years hearing levels for the press 99 db and hammer 108 db operator age groups are nearly identical and in the latter case are less than those predicted for exposure to equivalent continuous noise for long term exposures of 10 years or more the results of this study indicate that hearing losses resulting from impact noise in the drop forging industry are as great or greater than those resulting from continuous noise

development of a noise metric for assessment of exposure risk to complex noises many noise guidelines currently use a weighted equivalent sound pressure level laeq as the noise metric and the equal energy hypothesis to assess the risk of occupational noises because of the time averaging effect involved with the procedure the current guidelines may significantly underestimate the risk associated with complex noises this study develops and evaluates several new noise metrics for more accurate assessment of exposure risks to complex and impulsive noises the analytic wavelet transform was used to obtain time frequency characteristics of the noise 6 basic unique metric forms that reflect the time frequency characteristics were developed from which 14 noise metrics were derived the noise metrics were evaluated utilizing existing animal test data that were obtained by exposing 23 groups of chinchillas to respectively different types of noise correlations of the metrics with the hearing losses observed in chinchillas were compared and the most promising noise metric was identified

hearing loss from interrupted intermittent and time varying gaussian noise exposures the applicability of the equal energy hypothesis eight groups of chinchillas n 74 were exposed to various equivalent energy 100 or 106 db a sound pressure level spl noise exposure paradigms six groups received an interrupted intermittent time varying iitv gaussian noise exposure that lasted 8 h d 5 d week for 3 weeks the exposures modeled an idealized workweek at each level three different temporal patterns of gaussian iitv noise were used the 100 db a iitv exposure had a db range of 90 108 db spl while the range of the 106 db a iitv exposure was 80 115 db spl two reference groups were exposed to a uniform 100 or 106 db a spl noise 24 h d for 5 days each reference group and the three corresponding iitv groups comprised a set of equivalent energy exposures evoked potentials were used to estimate hearing thresholds and surface preparation histology quantified sensory cell populations all six groups exposed to the iitv noise showed threshold toughening effects of up to 40 db all iitv exposures produced hearing and sensory cell loss that was similar to their respective equivalent energy reference group these results indicate that for gaussian noise the equal energy hypothesis for noise induced hearing loss is an acceptable unifying principle

class of baer rings defined by a relaxed set of axioms abstract we consider a class c of baer rings also treated in s k berberian baer rings grundlehren math wiss vol 195 springer berlin 1972 and l vas dimension and torsion theories for a class of baer rings j algebra 289 2005 614 639 defined by nine axioms the last two of which are particularly strong we prove that the ninth axiom follows from the first seven this gives an affirmative answer to the question of s k berberian if a baer ring r satisfies the first seven axioms is the matrix ring m n r a baer ring

reduced forms and reduced witt rings of higher level the present paper and its successor s deal with an extension of the socalled reduced theory of quadratic forms over a formally real field k 5 7 lo this theory deals with the reduced witt ring wred k w k nil w k and its natural embedding into c x z the ring of integer valued continuous functions on the space x x k of orderings of k recently it has been found that there is a far reaching generalization of the notion of ordering namely the orderings of higher level 11 the orderings of level s where s divides a given natural number n are related to sums of 2nth powers in the same way as the usual orderings are to sums of squares their intersection is the set of all sums of 2nth powers in k 11 in 6 orderings of levels were replaced by signatures of this level these are those characters x i s of order 2s whose kernels are additively closed where k k o it is exactly this change in point of view which leads to a natural definition of reduced witt rings of higher level let x x k denote the set of all signatures of k whose order divides 2n so that x k x k x being a closed subspace of the compact character group of x the set x k is also a compact topological space each element a e i induces a continuous function a x c in c x c defined by x x a where c is given the discrete topology by analogy with the natural representation of the ordinary reduced witt ring as a subring of 477 0021 8693 85 3 00

a generalized approach to random noise synthesis theory and computer simulation a generalized approach to the synthesis of gaussian and non gaussian random noises as well as purely impulsive waveforms having a preselected amplitude spectrum has been developed the basic idea behind the synthesis is to construct the amplitude time waveform from the frequency domain i e from the amplitude and phase spectra by maintaining a predetermined reference amplitude spectrum and performing certain specific manipulations of the phase spectrum within any selected band of frequencies and then applying the inverse discrete fourier transform idft peaks in the non gaussian random waveform can be constructed from the selected band of frequencies that have been phase manipulated entire families of signals can thus be produced having the same energy spectrum but statistical characteristics that vary along the continuum from gaussian skewness 0 and kurtosis 3 through non gaussian variable skewness kurtosis and crest factor to purely impulsive shock transient signals the theoretical background and the results of a series of numerical simulations will be presented which demonstrate the functional relation between various phase spectrum manipulations and the descriptors of the synthesized random noise the results show that the approach is viable and that the synthesized random waveforms can be easily tailored to simulate a variety of real world acoustic vibration signals e g high kurtosis impulsive industrial noises helicopter noises missile vibrational signals etc

applicability of the leq as a damage risk criterion an animal experiment within the european communities the leq8h is used as a damage risk criterion drc for hearing protection the use of such a drc supposes that sound exposures with equal energy imply equal risk for noise induced hearing loss nihl the aim of the present study carried out with guinea pigs was to test the applicability of the leq8h for estimating the hazard of different noises having the same spectrum and acoustic energy therefore only the temporal structure of noises was a variable continuous intermittent or impulsive and each noise had a leq8h of 92 db the results indicate the leq8h is not an accurate drc it overestimates the nihl for intermittent and short continuous noises whereas it seems to be useful for moderate intensity noises 95 db and for the impulse noise 101 db furthermore the data point out the notion of critical intensity which seems to play a determining role in the transition between metabolic and mechanical mechanisms involved in the acoustic trauma since the criti

centers of higher degree forms let be a symmetric d linear form on a vector space v of dimension n over a field k its center cent is the analog of the space of symmetric matrices for a bilinear form if d 2 the center is a commutative subalgebra of end v it seems difficult to determine which subalgebras can be realized as cent for some some d linear form as a first step we conjecture that the center has dimension at most n the conjecture is proved for n 5

dimension and torsion theories for a class of baer rings abstract many known results on finite von neumann algebras are generalized by purely algebraic proofs to a certain class c of finite baer rings the results in this paper can also be viewed as a study of the properties of baer rings in the class c first we show that a finitely generated module over a ring from the class c splits as a direct sum of a finitely generated projective module and a certain torsion module then we define the dimension of any module over a ring from c and prove that this dimension has all the nice properties of the dimension studied in w luck j reine angew math 495 1998 135 162 for finite von neumann algebras this dimension defines a torsion theory that we prove to be equal to the goldie and lambek torsion theories moreover every finitely generated module splits in this torsion theory if r is a ring in c we can embed it in a canonical way into a regular ring q also in c we show that k 0 r is isomorphic to k 0 q by producing an explicit isomorphism and its inverse of monoids proj p proj q that extends to the isomorphism of k 0 r and k 0 q

energy independent factors influencing noise induced hearing loss in the chinchilla model the effects on hearing and the sensory cell population of four continuous non gaussian noise exposures each having an a weighted l eq 100 db spl were compared to the effects of an energy equivalent gaussian noise the non gaussian noise conditions were characterized by the statistical metric kurtosis beta computed on the unfiltered beta t and the filtered beta f time domain signals the chinchilla n 58 was used as the animal model hearing thresholds were estimated using auditory evoked potentials aep recorded from the inferior colliculus and sensory cell populations were obtained from surface preparation histology despite equivalent exposure energies the four non gaussian conditions produced considerably greater hearing and sensory cell loss than did the gaussian condition the magnitude of this excess trauma produced by the non gaussian noise was dependent on the frequency content but not on the average energy content of the impacts which gave the noise its non gaussian character these results indicate that beta t is an appropriate index of the increased hazard of exposure to non gaussian noises and that beta f may be useful in the prediction of the place specific additional outer hair cell loss produced by non gaussian exposures the results also suggest that energy based metrics while necessary for the prediction of noise induced hearing loss are not sufficient

indecomposable forms of higher degree all nondegenerate indecomposable forms of higher degree over a perfect field k can be realized as traces of nondegenerate absolutely indecomposable forms of higher degree over a suitable algebraic field extension of k with the help of trace forms of certain nonassociative algebras we construct classes of indecomposable forms of degree d 3

the application of frequency and time domain kurtosis to the assessment of hazardous noise exposures five computer synthesized broadband noises each having the same average spectrum and the same unweighted leq of 100 db spl but very different temporal structures were used to produce hearing loss in chinchillas despite the same exposure energies and spectra each noise exposure produced a different magnitude and frequency distribution of hearing loss and sensory cell loss the results indicate that the statistical properties of a signal are important in the determination of hearing loss when the audiometric and histological results are compared to a metric based upon kurtosis measured in the time and the frequency domain for each exposure there is a clear indication that these statistical metrics are good predictors of the relative magnitude and frequency distribution of the acoustic trauma

on waring s problem for cubic forms let w be a cubic form in n variables over the complex field and r be the smallest integer such that w can be expressed as a sum of cubes of r linear forms some theorems are proved that connect r with the ranks of certain matrices associated with w for arbitrary n and for n 5 based on these theorems an algorithm to express a cubic form in five variables as a sum of cubes of linear forms is proposed the paper is concluded with two examples of indecomposable cubic forms for the first form it is shown that r 7 and that there exists a one parameter set of representations of the form as a sum of cubes of seven linear forms while for the second form it is shown that r 8

hearing loss in the chinchilla from impact and continuous noise exposure the relative hazard posed to the peripheral auditory system by impact impulse and continuous noise of the same power spectrum was determined impact noise was generated by striking a nail with a hammer and was digitally recorded the acoustical power spectrum of the impact was determined and pink noise was filtered to produce a continuous noise stimulus with the same acoustic power spectrum pre exposure auditory evoked response aer thresholds were obtained at 1 2 4 and 8 khz on 16 adult chinchillas the pool of animals was divided into two equal groups based upon pre exposure aer thresholds one group was exposed to impact noise and the other group to the filtered pink noise exposures were 4 h day for 5 days thirty days following the exposure auditory evoked response thresholds were remeasured changes in auditory sensitivity were determined by subtracting the pre exposure thresholds from the post exposure thresholds hearing threshold shifts of the impact noise group were significantly greater

on partial polynomial interpolation thealexander hirschowitztheoremsaysthatageneralcollectionof k double points in p n imposes independent conditions on homogeneous polynomials of degree d with a well known list of exceptions we generalize this theorem to arbitrary zero dimensional schemes contained in a general union of double points we work in the polynomial interpolation setting in this framework our main result says that the affine space of polynomials of degree d in n variables with assigned values of any number of general linear combinations of first partial derivatives has the expected dimension if d 2w ith only five exceptional cases if d 2 the exceptional cases are fully described

the kurtosis metric as an adjunct to energy in the prediction of trauma from continuous nongaussian noise exposures data from an earlier study hamernik et al 2003 j acoust soc am 114 386 395 were consistent in showing that for equivalent energy leq 100 db a and spectra exposure to a continuous nongaussian nong noise could produce substantially greater hearing and sensory cell loss in the chinchilla model than a gaussian g noise exposure and that the statistical metric kurtosis computed on the amplitude distribution of the noise could order the extent of the trauma this paper extends these results to leq 90 and 110 db a and to nong noises that are generated using broadband noise bursts and band limited impacts within a continuous g background noise data from nine new experimental groups with 11 or 12 chinchillas group is presented evoked response audiometry established hearing thresholds and surface preparation histology quantified sensory cell loss at the lowest level leq 90 db a there were no differences in the trauma produced by g and nong exposures for leq 90 db a nong exposures produced increased trauma relative to equivalent g exposures removing energy from the impacts by limiting their bandwidth reduced trauma the use of noise bursts to produce the nong noise instead of impacts also reduced the amount of trauma

determinants of r fold symmetric multilinear forms in hi harrison has constructed and investigated higher degree forms and the witt grothendieck ring of forms we speculate that the signature theory of ordered fields may be extended to the signature theory of partially ordered fields which will be needed for higher degree forms cf br k it seems that higher degree forms and the witt grothendieck ring have important meaning for it in this paper we introduce a notion of determinant as an extension of ordinary determinant and an invariant of forms we shall use the terminologies and notations in h let r be a commutative ring with identity 1 for an r module e let 8 e x e x x e r be an r fold symmetric multilinear form that is 0 x x2 x 0 x x x for every permutation p of 1 2 r and 8 ax byl x2 x ao x

on trace forms of higher degree let ti be a central simple algebra over a field k and let tr denote its reduced trace then qd x tr x is the trace form of degree d on a similarity of w vd is a linear map f d d for which there exists a e k such that

on symmetric operators of higher degree and their applications abstract the concept of a symmetric operator relative to a quadratic form is extended to a k form acting in n space ln for any k 2 it is shown how to embed l2 into lr with the smallest possible r and expand to a k form g4 acting in lr such that there exists an operator lr lr that is symmetric with respect to g4 and whose eigenvalues are all distinct as an application it is shown how to express a polynomial in one variable as a sum of r kth powers of the linear binomials with the smallest possible r as a particular case a formula that generalizes the cardan formula for solving cubic equations is derived

a simplification of morita s construction of total right rings of quotients for a class of rings the total right ring of quotients qtotr r sometimes also called the maximal flat epimorphic right ring of quotients or right flat epimorphic hull is usually obtained as a directed union of a certain family of extension of the base ring r in k morita flat modules injective modules and quotient rings math z 120 1971 25 40 qtotr r is constructed in a different way by transfinite induction on ordinals starting with the maximal right ring of quotients qmaxr r its subrings are constructed until qtotr r is obtained here we prove that morita s construction of qtotr r can be simplified for rings satisfying condition c that every subring of the maximal right ring of quotients qmaxr r containing r is flat as a left r module we illustrate the usefulness of this simplification by considering the class of right semihereditary rings all of which satisfy condition c we prove that the construction stops after just one step and we obtain a simple description of qtotr r in this case lastly we study conditions that imply that morita s construction ends in countably many steps