complete intersection k theory and chern classes the purpose of this paper is to investigate the theory of complete intersection in noetherian commutative rings from the k theory point of view by complete intersection theory we mean questions like when whether an ideal is the image of a projective module of appropriate rank the paper has two parts in part one section 1 5 we deal with the relationship between complete intersection and k theory the part two section 6 8 is essentially devoted to construction projective modules with certain cycles as the total chern class here chern classes will take values in the associated graded ring of the grothedieck filtration and as well in the chow group in the smooth case in this paper all our rings are commutative and schemes are noetherian to avoid unnecessary complications we shall assume that all our schemes are connected for a noetherian schemex k0 x will denote the grothendieck group of locally free sheaves of finite rank over x whenever it make sense for a coherent sheaf m over x m will denote the class of m in k0 x we shall mostly be concerned with x speca where a is a noetherian commutative ring and in this case we shall also use the notation k0 a for k0 x

asymptotic properties of the algebraic constant modulus algorithm the algebraic constant modulus algorithm acma is a noniterative blind source separation algorithm it computes jointly beamforming vectors for all constant modulus sources as the solution of a joint diagonalization problem we analyze its asymptotic properties and show that unlike cma it converges to the wiener beamformer when the number of samples or the signal to noise ratio snr goes to infinity we also sketch its connection to the related jade algorithm and derive a version of acma that converges to a zero forcing beamformer this gives improved performance in applications that use the estimated mixing matrix such as in direction finding

direction of arrival estimation using parametric signal models we consider the problem of estimating the directions of arrival doas of narrowband sources with known center frequency the paper evaluates the potential improvement in estimation accuracy by using spatial temporal processing for signals obeying a deterministic parametric model one would expect that prior information about the temporal structure of the signals will yield some gain in performance by deriving the cramer rao bound crb on the doa estimates we quantify this gain and identify the cases for which the gain is significant we show that for the single source case spatial temporal processing does not yield any gain in performance relative to conventional spatial processing for multiple noncoherent signals incorporating temporal processing can achieve the single source performance yielding a significant gain for the case of multiple sources with small spatial separation relative to the beamwidth of the array however spatial temporal processing cannot yield any gain in performance for multiple coherent signals

fundamental initial frequency and frequency rate estimation of random amplitude harmonic chirps we consider the problem of estimating the fundamental initial frequency and frequency rate of a linear chirp with random amplitudes harmonic components we develop an iterative nonlinear least squares estimator which involves a large number of computations as it requires high resolution search in the initial frequency and frequency rate parameter space as an alternative we suggest two suboptimal low complexity estimators the first is based on the high order ambiguity function which reduces the problem to a one dimensional search the second method applies our recently published harmonic separate estimate method which was used for constant amplitude harmonic chirps we present modifications of both methods for harmonic chirps with random amplitudes we also provide a framework for estimating the number of harmonic components numerical simulations show that the iterative nonlinear least squares estimator achieves its asymptotic accuracy in medium to high signal to noise ratio while the two sub optimal low complexity estimators perform well in high signal to noise ratio real data examples demonstrate the performance of the harmonic separate estimate method on random amplitude real life signals

strong euler class of a stably free module of odd rank abstract let r be a commutative noetherian ring of dimension n 3 following a suggestion of fasel we establish a group homomorphism from van der kallen s group um n 1 r e n 1 r to the n th euler class group e n r so that 1 when n is even coincides with the homomorphism given by bhatwadekar and sridharan through euler classes 2 when n is odd is non trivial in general for an important class of rings 3 the sequence um n 1 r e n 1 r e n r e 0 n r 0 is exact where e 0 n r is the n th weak euler class group if x spec r is a smooth affine variety of dimension n over r so that the complex points of x are complete intersections and the canonical module k r is trivial then the sequence is proved to be exact on the left as well more generally let r be a commutative noetherian ring of dimension d and n be an integer such that n d 2 n 3 we also indicate how to extend our arguments to this setup to obtain a group homomorphism from um n 1 r e n 1 r to e n r

parameter estimation of chirp signals the problem of the parameter estimation of chirp signals is addressed several closely related estimators are proposed whose main characteristics are simplicity accuracy and ease of online or offline implementation for moderately high signal to noise ratios they are unbiased and attain the cramer rao bound monte carlo simulations verify the expected performance of the estimators it should be easy to extend this approach to signals having polynomials of any degree in the exponent all the derivations will be done under the assumption that the signal to noise ratio is sufficiently high

a differential quadrature analysis of vibration and buckling of an ss c ss c rectangular plate loaded by linearly varying in plane stresses abstract thin rectangular plates having two opposite edges simply supported with those edges subjected to linearly varying in plane stresses and the other two edges clamped are encountered in engineering practice recently leissa and kang used the classical power series method and obtained the first known exact vibration and some buckling solutions the classical plate theory based on the kirchhoff hypothesis is employed in the analysis the relatively wild character of the convergence is observed however and 20 or 30 more terms of the series are needed to obtain reasonably accurate results the differential quadrature dq method has proved an accurate and computationally efficient numerical method thus the dq method is used to study the vibration and buckling of an ss c ss c rectangular plate loaded by linearly varying in plane stresses convergence study shows that dq method with 15 15 or more non uniform grid points can yield very accurate results for cases considered exactly the same accurate results as of leissa and kang are easy to reproduce

estimating parameters of multiple wideband polynomial phase sources in sensor arrays we consider the problem of estimating the parameters of multiple wideband polynomial phase signal pps sources in sensor arrays a new maximum likelihood ml direction of arrival doa estimator is introduced and the exact cramer rao bound crb is derived for the general case of multiple constant amplitude polynomial phase sources since the proposed exact ml estimator is computationally intensive an approximate solution is proposed originating from the analysis of the log likelihood ll function in the single chirp signal case as a result a new form of spatio temporal matched filter referred to as the chirp beamformer is derived which is applicable to well separated sources that have distinct time frequency or and spatial signatures this beamforming approach requires solving a three dimensional 3 d optimization problem and therefore enjoys essentially simpler implementation than that entailed by the exact ml simulation results are presented illustrating the performance of the estimators and validating our theoretical crb analysis

free vibration analysis of rectangular plates with variously shaped holes an approximate method for analyzing the free vibration of rectangular plates with a hole of different shapes is proposed the shapes of the holes are circular semi circular elliptic square rectangular triangular rhombic etc these rectangular plates with a hole can be considered ultimately as a kind of rectangular plates with non uniform thickness a hole in a plate can be considered as an extremely thin part of the plate therefore the free vibration problem of a plate with a hole can be translated into the free vibration problem of the equivalent rectangular plate with non uniform thickness for some plates with different shaped holes the convergency and accuracy of the numerical solutions calculated by the proposed method are investigated

polynomial phase estimation by least squares phase unwrapping estimating the coefficients of a noisy polynomial phase signal is important in fields including radar biology and radio communications one approach attempts to perform polynomial regression on the phase of the signal this is complicated by the fact that the phase is wrapped modulo 2 and must be unwrapped before regression can be performed in this paper we consider an estimator that performs phase unwrapping in a least squares manner we call this the least squares unwrapping lsu estimator the lsu estimator can be computed in a reasonable amount of time for data sets of moderate size using existing general purpose algorithms from algebraic number theory under mild conditions on the distribution of the noise we describe the asymptotic properties of this estimator showing that it is strongly consistent and asymptotically normally distributed a key feature is that the lsu estimator is accurate over a far wider range of parameters than many popular existing estimators monte carlo simulations support our theoretical results and demonstrate the excellent statistical performance of the lsu estimator when compared with existing state of the art estimators

euler class group of a laurent polynomial ring local case abstract let r be a noetherian commutative ring of dimension n 2 and let a r t t 1 assume that the height of the jacobson radical of r is at least 2 let p be a projective a module of rank n dim a 1 with trivial determinant we define an abelian group called the euler class group of a denoted by e a let be an isomorphism from a to det p to the pair p we associate an element of e a called the euler class of p denoted by e p then we prove that a necessary and sufficient condition for p to have a unimodular element is the vanishing of e p in e a earlier bhatwadekar and raja sridharan have defined the euler class group of r denoted by e r and have proved similar results for projective r module of rank n later m k das defined the euler class group of the polynomial ring r t denoted by e r t and proved similar results for projective r t modules of rank n with trivial determinant

dynamic stability of cylindrical panels with transverse shear effects abstract the dynamic stability of simply supported isotropic cylindrical panels under combined static and periodic axial forces are investigated an extension of donnells shell theory to a first order shear deformation theory is used and a system of mathieu hill equations are obtained via a normal mode expansion and the parametric resonance response was analyzed using bolotins method results are compared with those obtained using the classical shell theory the effects of the thickness to radius ratio on the instability regions are examined in detail

vanishing of euler class groups abstract in this paper we prove some theorems about vanishing of euler class groups for example suppose b a x f 1 where a x is a polynomial ring f a x is a non zero divisor and dim b dim a 1 3 then we prove that the euler class group e b l 0 for any rank one projective b module l

an analytical constant modulus algorithm iterative constant modulus algorithms such as godard 1980 and cma have been used to blindly separate a superposition of cochannel constant modulus cm signals impinging on an antenna array these algorithms have certain deficiencies in the context of convergence to local minima and the retrieval of all individual cm signals that are present in the channel we show that the underlying constant modulus factorization problem is in fact a generalized eigenvalue problem and may be solved via a simultaneous diagonalization of a set of matrices with this new analytical approach it is possible to detect the number of cm signals present in the channel and to retrieve all of them exactly rejecting other non cm signals only a modest amount of samples is required the algorithm is robust in the presence of noise and is tested on measured data collected from an experimental set up

direction of arrival estimation for constant modulus signals in many cases where direction finding is of interest the signals impinging on an antenna array are known to be phase modulated and hence to have a constant modulus cm this is a strong property by itself it is already sufficient for source separation and can be used to construct improved direction finding algorithms we first derive the relevant cramer rao bounds crbs for arbitrary array configurations and specialize to uniform linear arrays we then propose a simple suboptimal direction estimation algorithm in which the signals are separated using the cm property followed by direction finding on the decoupled signals compared with the esprit algorithm and the crb for arbitrary signals the algorithm shows good results

stably free modules in su prob 3 suslin had asked the following question let a be any affine algebra of dimension n over an algebraically closed field what is the smallest integer m such that all stably free projective modules of rank bigger than m are free all the examples in the literature of stably free non free modules have rank less than or equal to n 1 2 the aim of this note is to construct examples of such modules of large rank we construct rank p stably free non free modules over p 2 dimensional affine algebras over algebraically closed fields wherep is any prime these varieties are actually smooth and rational over c these are trivial as holomorphic vector bundles forp 2 this is classical forp 2 see ms so these are strictly algebraic examples i had described this construction in mk 1 and proved the result for p 2 we will reproduce the construction with necessary modifications in this note let p be any prime number and k any field letf x be any polynomial of degree p over k letf 0 a e k and fi xo xl f xo x1 xp f x0 x1 also let

local coefficients and euler class groups abstract in this paper we establish an isomorphism between the euler class group e r x l for a real smooth affine variety x spec a and the 0 th homology group h 0 m c g with local coefficients in a bundle g of groups constructed from the line bundle l over m corresponding to the orientation rank 1 projective module l where m c is the compact part of the manifold m of real points in x then by steenrod s poincare duality between homology and cohomology groups with local coefficients this isomorphism is identified with the whitney class homomorphism

efficient estimation of a narrow band polynomial phase signal impinging on a sensor array the parameters of interest of a polynomial phase signal observed by a sensor array include the direction of arrival and the polynomial coefficients the direct maximum likelihood estimation of these parameters requires a nonlinear multidimensional search in this paper we present a two step estimation approach the estimation requires only a one dimensional search in the direction of arrival space and involves a simple least squares solution for the polynomial coefficients the efficiency of the estimates is corroborated by monte carlo simulations

estimation and classification of polynomial phase signals the measurement of the parameters of complex signals with constant amplitude and polynomial phase measured in additive noise is considered a novel new integral transform that is adapted for signals of this type is introduced this transform is used to derive estimation and classification algorithms that are simple to implement and that exhibit good performance the algorithms are extended to constant amplitude and continuous nonpolynomial phase signals

a computationally efficient technique for estimating the parameters of polynomial phase signals from noisy observations many real world applications are characterized by the presence of polynomial phase signals embedded in noise these applications include radar sonar telemetry communications and power systems in a significant number of these applications it is highly desirable to be able to accurately estimate the polynomial phase signal parameters this correspondence presents a computationally efficient method for estimating any or all of the parameters of polynomial phase signals in white gaussian noise and provides a first order statistical analysis of the technique simulations are also presented to support the theoretical analysis

zero cycles and projective modules let a be a reduced affine k algebra of dimension n over an algebraically closed field k let fnko a denote the sub group of ko a generated by the images of all the residue fields of all smooth maximal ideals of height n for a module of finite projective dimension m let m denote the image of m in ko a for a projective a module p of rank n we define the nth chern class of p to be cn p e l i aip where p is the dual of p suppose fnko a has no n 1 torsion then our main result th 3 8 is that p has a free direct summand of rank one if and only if cn p 0 when the characteristic of k is zero or a is normal and n 3 it is known that fnko a is torsion free le sr hence our theorem is applicable in these cases also when a is regular fnko a coincides with chn x the chow group of zero cycles of spec a and cn p coincides with the usual nth chern class as defined by grothendieck see fu when n 3 and a is regular this result was proved in mkm when n 3 and the characteristic of k is not equal to two this result in mkm was extended to the singular case by m levine in this paper we extend the results of mkm to all dimensions with the assumption stated above on torsion in fnko a we first show that cor 3 4 if i c a is a local complete intersection of height n then a i is zero in ko a if and only if i is a complete intersection corollary 3 4 together with a result of mohan kumar mk cor 1 9 here at once gives theorem 3 8 in section 1 we give some preliminaries and generalize results in mk2 these results are crucially used in the rest of the paper the basic ideas in section 1 are all taken from mk2 in section 2 we prove theorem 2 2 which strengthens a result of boratynski bo for local complete intersections with trivial co normal bundle theorem 2 2 is one of the crucial ingredients in the proofs of the results in section 3 as an amusing application of theorem 2 2 we give a new proof of a theorem of srinivas sr about torsion in zero cycles

murthy s conjecture on 0 cycles we show that the levine weibel chow group of 0 cycles mathrm ch d a of a reduced affine algebra a of dimension d ge 2 over an algebraically closed field is torsion free among several applications it implies an affirmative solution to an old conjecture of murthy in classical k theory

on unique localization of multiple sources by passive sensor arrays necessary and sufficient conditions are derived for the unique localization of narrowband sources having the same known center frequency by passive sensor arrays the conditions specify the maximum number of sources that can be uniquely localized by a general array that satisfies some mild geometric constraints the conditions are expressed in terms of the number of sensors and the rank of the correlation matrix of the sources two different conditions are presented the first guarantees uniqueness for every batch of sampled data the second which is weaker guarantees uniqueness for almost every batch of sampled data with the exception of a set of batches of measure zero it is shown that a condition that is slightly weaker than the second one is also necessary

good invariants for bad ideals abstract we generalize the notion of the segre class of ideals defined by murthy and obtain various analogous results using the theory of the euler class groups

on algebras which are locally mathbb a 1 in codimension one let r be a noetherian normal domain call an r algebra a locally a1 in codimension one if rp r a is a polynomial ring in one variable over rp for every height one prime ideal p in r we shall describe a general structure for any faithfully flat r algebra a which is locally a1 in codimensionone and deduce results giving sufficient conditions for such an r algebra to be a locally polynomial algebra we also give a recipe for constructing r algebras which are locally a1 in codimension one when r is a normal affine spot i e a normal local domain obtained by a localisation of an affine domain we give criteria for a faithfully flat r algebra a which is locally a1 in codimensionone to be krull and a further condition for a to be noetherian the results are used to construct intricate examples of faithfully flat r algebras locally a1 in codimension one which are noetherian normal but not finitely generated

low complexity residual doppler shift estimation for underwater acoustic multicarrier communication we propose two computationally efficient residual doppler shift estimation methods for underwater acoustic multicarrier communication the first method is based on computing the phase of the root of a low order polynomial the second method is a closed form least squares estimate given the unwrapped phases of the minimal eigenvector of a small data matrix the complexities of both estimates are significantly lower compared to the methods commonly used in underwater acoustic multicarrier communication which result in nonlinear least squares estimators and thus require a fine grid search in the frequency domain numerical simulations show that the mean square errors of the proposed methods have similar performance as the common estimation techniques achieve the cramer rao lower bounds at low noise levels and agree with their theoretically derived variances pool experiments and sea trial results further demonstrate that the suggested estimates yield similar results as the common nonlinear least squares estimates but at a lower complexity

displacement structure approach to polynomial vandermonde and related matrices abstract we introduce a new class of what we call polynomial vandermonde like matrices this class generalizes the polynomial vandermonde matrices studied earlier by various authors who derived explicit inversion formulas and fast algorithms for inversion and for solving the associated linear systems a displacement structure approach allows us to carry over all these results to the wider class of polynomial vandermonde like matrices

identifiability and aliasing in polynomial phase signals polynomial phase signals have numerous applications including radar sonar geophysics and radio communication many techniques for estimating the parameters of polynomial phase signals have been described in the literature despite the significant interest aliasing of polynomial phase parameters has not been fully clarified we address the problem of identifiability and aliasing in polynomial phase signals we fully describe the region in which aliasing does not occur for polynomial phase signals of any order we call this the identifiable region we find that this region is the voronoi region of a lattice generated by the coefficients of a set of polynomials known as the integer valued polynomials we show how aliasing can be resolved by solving the nearest lattice point problem we discuss some of the consequences of these results on a popular estimator for polynomial phase signals that is based on the discrete polynomial phase transform dppt it is shown that the range of parameters suitable for the dppt estimator is very small compared to the identifiable region

on invariance of the euler class groups under a subintegral base change abstract let r be a commutative noetherian ring and r s be a subintegral extension it is proved that the top euler class group of r is isomorphic to the top euler class group of s an example is given to show that similar conclusion does not hold for integral but not subintegral extension of rings

joint model order selection and parameter estimation of chirps with harmonic components we consider the problem of jointly determining the number of harmonic components of a fundamental linear chirp and estimating its parameters i e its initial frequency and frequency rate given time samples of the observed signal common model order criteria select the number of harmonics based on the maximum likelihood estimator we develop exact and approximated maximum likelihood estimators of these parameters to avoid an exhaustive search in the initial frequency frequency rate space involved by those estimators we propose an alternative low complexity two step estimation method the first step separates the signal to its harmonic components then in the second step the parameters of interest are estimated using least squares method given the phases of the harmonic components the method is compared to the exact and approximated maximum likelihood estimators and to the well known high order ambiguity function based method numerical simulations and real data examples demonstrate that the proposed low complexity method can successfully replace the maximum likelihood estimator in the model order criteria at moderate to high signal to noise ratio since the estimates obtained by the proposed method achieve the cramer rao lower bound at these signal to noise ratios

a low complexity blind estimator of narrowband polynomial phase signals consider the problem of estimating the parameters of multiple polynomial phase signals observed by a sensor array in practice it is difficult to maintain a precisely calibrated array the array manifold is then assumed to be unknown and the estimation is referred to as blind estimation to date only an approximated maximum likelihood estimator amle was suggested for blindly estimating the polynomial coefficients of each signal however this estimator requires a multidimensional search over the entire coefficient space instead we propose an estimation approach which is based on two steps first the signals are separated using a blind source separation technique which exploits the constant modulus property of the signals then the coefficients of each polynomial are estimated using a least squares method applied to the unwrapped phase of the estimated signal this estimator does not involve any search in the coefficient spaces the computational complexity of the proposed estimator increases linearly with respect to the polynomial order whereas that of the amle increases exponentially simulation results show that the proposed estimator achieves the cramer rao lower bound at moderate or high signal to noise ratio

dynamic stability of curved panels with cutouts the parametric instability behaviour of curved panels with cutouts subjected to in plane static and periodic compressive edge loadings are studied using finite element analysis the first order shear deformation theory is used to model the curved panels considering the effects of transverse shear deformation and rotary inertia the theory used is the extension of dynamic shear deformable theory according to sanders first approximation for doubly curved shells which can be reduced to love s and donnell s theories by means of tracers the effects of static and dynamic load factors geometry boundary conditions and the cutout parameters on the principal instability regions of curved panels with cutouts are studied in detail using bolotin s method quantitative results are presented to show the effects of shell geometry and load parameters on the stability boundaries results for plates are also presented as special cases and are compared with those available in the literature

vibration analysis of a thick plate with an interior cut out by a finite element method abstract plates with interior openings are often used in industrial design such as machines bridges aircraft etc many advantages can be obtained by this design such as reduced weight easy access for maintenance and an easy assembling process however when interior holes are cut from a plate structure the mechanical behavior of the structure is changed to avoid induced acoustic noise and or mechanical failure due to mechanical resonance vibration problems of such plate structures must be studied the work reported here is a study of the vibration of a plate with an interior cut out by a finite element method hamilton s variational principal and potential theory are used to derive the governing equations for a mindlin plate a quadratic element of eight nodes is used selective reduced integration is used for integration of the stiffness matrix the locking phenomenon is avoided by this particular integration technique eigenvalues and eigenvectors are calculated by subspace iteration computations are significantly reduced by this numerical technique results are compared with nagaya s work and good agreements are obtained

algebraic cycles and vector bundles over affine three folds on any smooth affine surface over an algebraically closed field it is easy to construct rank two projective modules with given determinant as the first chern class and an arbitrary rational equivalence class of a zero cycle as the second chern class we will briefly indicate this method in section 1 here we construct projective modules over smooth affine 3 folds with prescribed chern classes and of the right rank that is to say we construct rank two projective modules with prescribed first and second chem classes and rank three projective modules with prescribed first second and third chern classes theorem 2 1 as a corollary using roitman s theorem on torsion in zero cycles and suslin s cancellation theorem one gets that a rank three projective module over a smooth affine threefold with top chem class zero has a free direct summand of rank one cor 2 4 for example over a rational threefold any projective module splits into a free module and a rank two projective module thus we obtain necessary and sufficient conditions in terms of appropriate chern classes for modules to be efficiently generated for example on an affine rational 3 fold any line bundle is 3 generated and any rank two projective module is 4 generated we also prove that any maximal ideal over a smooth affine variety of dimension d is the zero of a section of a rank d projective module theorem 3 1 for an affine 3 fold if a3 x 0 we prove the validity of the eisenbud evans estimate for finitely generated modules we do not know the answers for most of these questions in higher dimensions sometimes we assume that the characteristic of the ground field is different from 2 3 and 5 due to technical reasons

projective modules over smooth real affine varieties let x spec a be a smooth affine variety of dimension n 2 over a field k and p be a projective a module of rank n a result of murthy mu theorem 3 8 says that if k is an algebraically closed field and if the top chern class cn p in ch0 x is zero then p splits off a free summand of rank 1 i e p a q we note that over any base field the vanishing of the top chern class is a necessary condition for p to split off a free summand of rank 1 however as is shown by the example of the tangent bundle of an even dimensional real sphere this condition is not sufficient in view of these examples it is of interest to explore whether one can classify examples of projective modules over smooth real varieties which have the property that the top chern class of the projective module vanishes but the projective module does not split off a free summand of rank one more precisely we ask the following

estimating the doa and the polarization of a polynomial phase signal using a single polarized vector sensor this paper introduces a novel algorithm to estimate the direction of arrival doa and the polarization of a completely polarized polynomial phase signal of an arbitrary degree the algorithm utilizes a polarized vector sensor comprising a spatially collocated six component electromagnetic vector sensor a dipole triad or a loop triad this esprit based algorithm is based on a time invariant matrix pencil pair derived from the time delayed data sets collected by a single polarized vector sensor the high order difference function of the signal s phase constructs the invariant factor used in the esprit algorithm the steering vector is estimated from the signal subspace eigenvector of the data correlation matrix following which the closed form doa and polarization can be obtained given the degree of the polynomial phase signal this approach resolves the two dimensional azimuth elevation angle and the polarization of the source and requires neither a priori knowledge of the polynomial phase signal s coefficients nor a priori knowledge of the polynomial phase signal s frequency spectrum the efficacy of the proposed algorithm is verified by monte carlo simulations estimation accuracies of the doa and the polarization parameters are evaluated by the closed form cramer rao bounds which are independent of the polynomial coefficients the degree of the polynomial phase signal and the azimuth angle of the source

bott periodicity and calculus of euler classes on spheres a variety of computations regarding the euler class group e an an and the grothendieck group k0 an of the algebraic sphere spec an is done the euler class of the algebraic tangent bundle on spec an is computed it is also investigated whether every element in the euler class group e an an is the euler class of a projective an module of rank n

generalized high order phase function for parameter estimation of polynomial phase signal the high order phase function hpf has been introduced recently to estimate the parameters of a polynomial phase signal pps in this correspondence we generalize the standard hpf by introducing multiple time instants thus the standard hpf can be treated as a special example of the generalized hpf with identical time instants we propose a procedure for finding time instants minimizing the mean square error mse the proposed method achieves better performances than the high order ambiguity function haf and polynomial wigner ville distribution pwvd the theoretical analysis as well as the monte carlo simulations verify the advantages such as lower mse and lower snr threshold for the pps

parameter estimation of multicomponent 2d polynomial phase signals using the 2d phaf based approach this paper considers parameter estimation of multicomponent 2d polynomial phase signals mc 2d ppss the main contributions included are i derivation of the cramer rao lower bound crlb for mc 2d ppss ii two dimensional product high order ambiguity function 2d phaf based estimation procedure recently proposed by barbarossa for the estimation of third order mc 2d ppss is extended to signals of arbitrary orders iii procedure for optimal lag set selection in the proposed 2d phaf has been proposed iv since the 2d phaf is characterized by large mean squared error mse for higher order signals refinement procedure is introduced that is able to improve the estimation accuracy and to reduce mse up to the crlb the proposed estimator has been used for target focusing in radar images

mathbb p 1 p 1 gluing for local complete intersections we prove an analogue of the affine horrocks theorem for local complete intersection ideals of height n in r t where r is a regular domain of dimension d which is essentially of finite type over an infinite perfect field of characteristic unequal to 2 and 2n ge d 3

a riemann roch theorem in this paper we prove an analogue of this theorem for weak euler classes weak euler classes take values in weak euler class groups the definitions of the weak euler class group and weak euler classes were achieved by relaxing the definitions of the euler class group and euler classes the original definitions of the euler class group and the euler classes for smooth affine algebras over fields were given by m v nori for background literature we refer to 1 2 8 11 12 15 for noetherian commutative rings a with dima n 2 and a line bundle l on spec a the weak euler class group e0 a l has been defined in 2 as the quotient

estimation of multicomponent polynomial phase signals impinging on a multisensor array using state space modeling this contribution addresses the problem of estimating the parameters of multicomponent polynomial phase signals when impinging on a multisensor array an original approach is proposed based on a state space modelization of the signal and the application of an extended kalman filter for the state estimation the use of a multisensor array allows the exploitation of a spatial information and leads to the consideration of multiple filters with different observation equations computer simulations are used to demonstrate the effectiveness of the proposed algorithm

projective modules over smooth affine varieties over real closed fields abstract let x spec a be a smooth affine variety of dimension n 2 over the field r of real numbers let p be a projective a module of rankn such that its nth chern class c n p ch 0 x is zero in this set up bhatwadekar das mandal showed amongst many other results that p a q in the case that either n is odd or the topological space x r of real points of x does not have a compact connected component in this paper we prove that similar results hold for smooth affine varieties over an arbitrary real closed field r the proof is algebraic and does not make use of tarski s principle nor of the earlier result for r

the euler class group of a polynomial algebra in this paper we continue our study on the theory of the euler class group of a polynomial algebra a t where a is a commutative noetherian ring containing q of dimension n for such a ring a in 9 we defined the notion of the nth euler class group en a t of a t for simplicity let us call it e a t in 9 we also studied the relations between e a t and e a where e a is the nth euler class group of a for example there is canonical map e a e a t which is an injective group homomorphism and it is an isomorphism when a is a smooth affine domain 9 proposition 5 7 in general these two groups are not isomorphic see discussion preceding 9 proposition 5 7 in this context the following question is natural