a new approach to multipath correction of constant modulus signals an adaptive digital filtering algorithm that can compensate for both frequency selective multipath and interference on constant envelope modulated signals is presented the method exploits the fact that multipath reception and various interference sources generate incidental amplitude modulation on the received signal a class of so called constant modulus performance functions is developed which sense this am term but are insensitive to the angle modulation simple adaptive algorithms for finite impulse response fir digital filters are developed which employ a gradient search of the performance function one of the resulting algorithms is simulated for the example of an fm signal degraded by specular multipath propagation substantial improvements in noise power ratio npr are observed e g 25 db with moderately rapid convergence time these results are then extended to include tonal interference on a fm signal and intersymbol interference on a qpsk data signal

fast and low complexity blind equalization via subgradient projections we propose a novel blind equalization method based on subgradient search over a convex cost surface this is an alternative to the existing iterative blind equalization approaches such as the constant modulus algorithm cma which often suffer from the convergence problems caused by their nonconvex cost functions the proposed method is an iterative algorithm called subgradient based blind algorithm sgba for both real and complex constellations with a very simple update rule it is based on the minimization of the l sub spl infin norm of the equalizer output under a linear constraint on the equalizer coefficients using subgradient iterations the algorithm has a nice convergence behavior attributed to the convex l sub spl infin cost surface as well as the step size selection rules associated with the subgradient search we illustrate the performance of the algorithm using examples with both complex and real constellations where we show that the proposed algorithm s convergence is less sensitive to initial point selection and a fast convergence behavior can be achieved with a judicious selection of step sizes furthermore the amount of data required for the training of the equalizer is significantly lower than most of the existing schemes

sk1 like functors for division algebras abstract we investigate the group valued functor g d d f d where d is a division algebra with center f and d the commutator subgroup of d we show that g has the most important functorial properties of the reduced whitehead group sk 1 we then establish a fundamental connection between this group its residue version and relative value group when d is a henselian division algebra the structure of g d turns out to carry significant information about the arithmetic of d along these lines we employ g d to compute the group sk 1 d as an application we obtain theorems of reduced k theory which require heavy machinery as simple examples of our method

valuations on algebras with involution let a be a central simple algebra with involution of the first or second kind let v be a valuation on the fixed part f of z a a special v gauge g on a is a kind of value function on a extending v on f such that g x x 2g x for all x in a it is shown under certain restrictions if the residue characteristic is 2 that if v is henselian then there is a special v gauge g if and only if is anisotropic and g is unique if v is not henselian it is shown that there is a special v gauge g if and only if remains anisotropic after scalar extension from f to the henselization of f with respect to v when this occurs g is the unique invariant v gauge on a

hasse principle for hermitian spaces over semi global fields abstract in a recent paper colliot thelene parimala and suresh conjectured that a local global principle holds for projective homogeneous spaces under connected linear algebraic groups over function fields of p adic curves in this paper we show that the conjecture is true for any linear algebraic group whose almost simple factors of its semisimple part are isogenous to unitary groups or special unitary groups of hermitian or skew hermitian spaces over central simple algebras with involutions the proof implements patching techniques of harbater hartmann and krashen as an application we obtain a springer type theorem for isotropy of hermitian spaces over odd degree extensions of function fields of p adic curves

totally ramified splitting fields of central simple algebras over henselian fields abstract let d be a central division algebra over a henselian field f with algebraically closed residue field f it is proved that if the degree of d is relatively prime to the characteristic of f then every finite extension of f which splits d contains a maximal subfield of d

the henselization of a valued division algebra the main result of this paper is the following if f v is a valued field fh its henselization d a division algebra with center f and d f then v extends to d iff d ffh is a division algebra it is also shown that if p char f p 1if char f 0 then d f d f d f pb for some nonnegative integer b

on the dec group of finite abelian galois extensions over global fields abstract if k f is a finite abelian galois extension of global fields whose galois group has exponent t we prove that there exists a short exact sequence 0 dec k f br t k f q p r q z z 0 where r q q and p is a finite set of primes of f that is empty if t is square free in particular we obtain that if t is square free then dec k f br t k f which we use to show that prime exponent division algebras over henselian valued fields with global residue fields are isomorphic to a tensor product of cyclic algebras finally we construct a counterexample to the result for higher exponent division algebras

li yau type estimates for a nonlinear parabolic equation on complete manifolds abstract let m g be a complete noncompact riemannian manifold with the m dimensional bakry emery ricci curvature bounded below in this paper we give a local li yau type gradient estimate for the positive solutions to a general nonlinear parabolic equation u t u u a u log u q u in m 0 where a r is a c 2 smooth function and q q x t is a function which generalizes many previous well known gradient estimate results

prime to p extensions of the generic abelian crossed product in this paper we prove that the non cyclic generic abelian crossed product p algebras constructed by amitsur and saltman in s a amitsur d saltman generic abelian crossed products and p algebras j algebra 51 1 1978 76 87 remain non cyclic after tensoring by any prime to p extension of their centers we also prove that an example due to saltman of an indecomposable generic abelian crossed product with exponent p and degree p2 remains indecomposable after any prime to p extension

the l theory of laurent extensions and genus 0 function fields the stable classification of quadratic forms over a field is given by the witt group topology via surgery theory has embedded the witt groups in a general theory of forms over any ring with involution in this paper we use geometrically inspired methods to make computations general results on the l theory of a laurent polynomial extension are used to study the witt groups of genus 0 function fields

integral semihereditary orders inside a bezout maximal order in this paper we show that over a commutative valuation ringv a semihereditaryv orderhin a finite dimensional simple artinian ring is a finite intersection of bezout maximal v orders iff eitherhis bezout orhis contained in a bezoutv order andj v is a principal ideal ofv

integral semihereditary orders extremality and henselization abstract in this paper we study integral semihereditary orders over a valuation ring in a finite dimensional simple artinian ring in the first section we prove that such orders are extremal consequently in a central division algebra admitting a total valuation ring the intersection of all the conjugates of the total valuation ring is the unique integral semihereditary order over the center of the total valuation ring in the second section we characterize up to conjugacy integral semihereditary orders over a henselian valuation ring in the last section we show that an integral order r over an arbitrary valuation ring v is semihereditary iff its henselization r v v h where v h is the henselization of v is a semihereditary v h order in this case there is an inclusion preserving bijective correspondence between semihereditary v orders inside r and semihereditary v h orders inside r v v h

maximal orders over valuation rings abstract in this paper we study maximal orders over commutative valuation rings in central simple algebras we are particularly interested in maximal orders which are either bezout or semihereditary we construct a class of bezout maximal orders and a class of semihereditary maximal orders and show that for any valuation ring v resp v with value group z m any bezout resp semihereditary maximal order over v belongs to the class constructed furthermore we classify all maximal orders in m2 f over a valuation ring with value group z m and in mn f given a mild defectless assumption

on the parabolic kernel of the schrodinger operator etude des equations paraboliques du type q x t t u x t 0 sur une variete riemannienne generale introduction estimations de gradients inegalites de harnack majorations et minorations des solutions fondamentales equation de la chaleur et noyau de green operateur de schrodinger

a new construction of noncrossed product algebras new examples of noncrossed product division algebras are obtained using methods different from all previous noncrossed product constructions the examples are division algebras over intersections of henselian valued fields and they have schur index and exponent p for any prime number p and any integers m n 2 n 3if 2 the basic tools used in the construction are valuation theory and galois cohomology no generic methods are applied and there is no p i theory along the way local global principles are proved for central simple algebras over intersections of p henselian valued fields the first examples of central simple division algebras which are not crossed products were obtained by amitsur in am in 1972 amitsur thereby settled a question that had been one of the outstanding open problems in the theory of algebras for at least thirty years his examples were the generic division algebras ud q n of index n over q the rational numbers for any natural number n such that p2 n p an odd prime or 8 all subsequent constructions of noncrossed products in ss 83 883 r r an ti have heretofore been based on amitsur s specialization argument and they are all generic division algebras or extensions of generic division algebras the centers of these noncrossed product algebras are not known nor are the brauer groups nor the absolute galois groups of the centers we present here a new method of constructing noncrossed product algebras in our approach the noncrossed product is realized as the underlying division algebra d of a tensor product of suitably chosen cyclic algebras over a field f l n l2 where each l is a pth root henselian valued field we prove local global principles relating the splitting fields of d to those of d f lt i 1 2 it is shown that the part of the brauer group of f is completely determined by that of ll and l2 computations for central simple f algebras thus become very tractable for exam ple we not only show that d is not a crossed product but also calculate exactly how large r must be so that the matrix ring mr d is a crossed product and how large s must be so that ms d is a tensor product of cyclic algebras indeed the structure of the brauer group of f is so nice that we were somewhat surprised that noncrossed products could possibly exist over f

nontriviality of certain quotients of k1 groups of division algebras for a division algebra d finite dimensional over its center z d f it is a conjecture that ck1 d coker k1f k1d is trivial if and only if d 1 1f with f a formally real pythagorean field since ck1 d is very difficult to work with we consider here nk1 d nrdd d f ind d which is a homomorphic image of ck1 d a field e is said to be nknt if for every noncommutative division algebra d finite dimensional over e z d nk1 d is nontrivial it is proved that if e is finitely generated but not algebraic over some subfield then e is nknt as a consequence if z d is finitely generated over its prime subfield or over an algebraically closed field then ck1 d is nontrivial

totally ramified valuations on finite dimensional division algebras division algebras d with valuation v are studied where d is lsnite dimensional and totally ramified over its center f i e the ramification index of v over wlf equals d f such division algebras have appeared in some important constructions but the structure of these algebras has not been systematically analyzed before when vlf is henselian a full classification of the f subalgebras of d is given when f has a henselian valuation v with separably closed residue field and a is any tame central simple f algebra an algorithm is given for computing the underlying division algebra of a from a suitable subgroup of a f some examples are constructed using this valuation theory including the first example of finitbdimensional f central division algebras d1 and d2 with d1 xf d2 not a division ring but d1 and d2 having no common subfield k d f valuation theory long a basic tool in commutative algebra has been relatively neglected in the study of division algebras until quite recently nontheless valuations are naturally present in a number of division algebras that have been constructed to exhibit special properties particularly algebras over iterated laurent power series fields for example such division algebras have been key ingredients in amitsur s noncrossed product construction am and in platonov s construction p of division algebras d with sk1 d 7 1 valuations are not so prevalent on division algebras as on fields but if a division algebra d does have a valuation this structure contains a substantial amount of information about d which would scarcely be accessible otherwise we consider here valued divisioll algebras d for which d is totqlly ramified and tame over its center f i e for which the ramification index ird rfi equals the dimension d f of d over f and the characteristic char d does not divide d f here rd is the value group of the valuation on d and d is the residue division algebra we assume throughout that d f oo valued division algebras of this type appear e g in amitsur s noncrossed product paper am 2 in saltman s work on indecomposable division algebras sa in certain of the malcevneumann division algebras considered by the first author and amitsur ta2 4 etc however the intrinsic structure of totally ramified tame division algebras has apparently not been examined closely before this may be because most past work on valued division algebras has concentrated on discrete valuations when rd z for such a valuation d is never totally ramified over its center f unless d f cf 3 2 below received by the editors june 26 1986 1980 mathematics subject clmsification 1985 reon primary 16a39 2supported in part by f n r s 2supported in part by the national science foundation 1987 american mathematlcal society 0002 9947 87 00 25 per page

sk1 of azumaya algebras over hensel pairs let a be an azumaya algebra of constant rank n2 over a hensel pair r i where r is a semilocal ring with n invertible in r then the reduced whitehead group sk1 a coincides with its reduction sk1 a i a this generalizes a result of hazrat j algebra 305 687 703 2006 to non local henselian rings

averaging analysis of local stability of a real constant modulus algorithm adaptive filter the constant modulus algorithm cma of adaptive filtering was developed for usage when the modulus of the desired signal is known but its specific value at every sample instant is not known a real arithmetic version of cma was recently proposed and studied using simulations by j r treichler and m g larimore ibid vol assp 33 p 420 31 apr 1985 local stability of their arithmetic version of cma is proven in two applications channel equalization for a transmitted sequence of plus and minus ones and the separation of a sinusoidal signal from its sum with a number of sinusoidal interferers at separate frequencies the proofs utilize dynamic system stability theorems from averaging theory which is a technique currently being utilized in the stability analysis of a variety of adaptive systems

a note on valued division algebras let d be a finite dimensional division algebra with center f and let b be a valuation ring of d i e xeb or x 1 e b holds for all nonzero x in d then b is called an extension of v f b let s be the set of all extensions of v to d and let p b be the group of all bijections of s which are induced by the inner automorphisms of d in this note we investigate p b it is shown that p b is solvable and an upper bound for p b is given finally theorem 4 5 gives a necessary and sufficient condition for b such that p b is equal to this bound

new improved exact sequences of witt groups abstract two exact sequences of witt groups are constructed extending ones obtained earlier by the author they involve witt groups of forms over a base field k quadratic extension l and quaternion division algebra d containing l as a maximal subfield the mappings in these sequences arise by use of the tensor product for going up in the inclusions k l d and by use of trace maps for going down the sequences exhibit a pleasing degree of symmetry and yield results on the relative sizes of the witt groups also a result on the relative sizes of the groups of square classes of k and l is obtained

performance analysis of the matrix pair method for blind channel identification we study the estimation variance performance of the matrix pair mp method for estimating the impulse responses of multiple fir channels driven by an unknown input sequence a first order perturbation analysis of the large data size performance of the mp method is presented and an explicit expression for the estimation variance is derived both the theoretical and simulation results are used to investigate the statistical performance of the mp method and a number of new insights are revealed

relationships between the constant modulus and wiener receivers the godard 1980 or the constant modulus algorithm cma is an effective technique for blind receiver design in communications however due to the complexity of the constant modulus cm cost function the performance of the cm receivers has primarily been evaluated using simulations theoretical analysis is typically based on either the noiseless case or approximations of the cost function the following question while resolvable numerically for a specific example remains unanswered in a generic manner in the presence of channel noise where are the cm local minima and what are their mean squared errors mse in this paper a geometrical approach is presented that relates the cm to wiener or minimum mse receivers given the mse and the intersymbol user interference of a wiener receiver a sufficient condition is given for the existence of a cm local minimum in the neighborhood of the wiener receiver the mse bounds on cm receiver performance are derived and shown to be tight in simulations the analysis shows that while in some cases the cm receiver performs almost as well as the nonblind wiener receiver it is also possible that due to its blind nature the cm receiver may perform considerably worse than a nonblind wiener receiver

division algebras over henselian fields in this chapter we focus on the tame division algebras d with center a field f with henselian valuation v as usual we approach this by first obtaining results for graded division algebras then lifting back from operatorname mathsf gr d to d this is facilitated by results in 8 1 on existence and uniqueness of lifts of tame subalgebras from operatorname mathsf gr d to d in 8 2 we describe four fundamental canonical up to conjugacy subalgebras of d that reflect its valuative structure the rest of the chapter is devoted to brauer group factorizations of d corresponding to the noncanonical direct product decomposition of operatorname mathit br t f given in cor 7 85 the factor operatorname mathit hom c operatorname mathcal g overline f mathbb t gamma f is represented by a type of division algebra n called decomposably semiramified defined in 8 3 and characterized by the property that n contains a maximal subfield inertial over f and another totally ramified over f we show in 8 4 that every tame division algebra d is brauer equivalent to some s f t where s is inertially split and t is tame and totally ramified over f we show further that every inertially split division algebra s is brauer equivalent to some i f n where i is inertial over f and n is decomposably semiramified the classes overline i for the i appearing in the i f n decompositions of s are shown to range over a single coset of mathit dec z overline s overline f in operatorname mathit br overline f called the specialization coset of s in the final subsection 8 4 6 we summarize what happens in the special case that v is discrete of rank 1 where substantial simplifications occur

signatures of hermitian forms and prime ideals of witt groups in this paper a further study is made of h signatures of hermitian forms introduced previously by the authors it is shown that a tuple of reference forms h may be replaced by a single form and that the h signature is invariant under morita equivalence of algebras with involution the prime ideals of the witt group are studied obtaining results that are analogues of the classification of prime ideals of the witt ring by harrison and lorenz leicht it follows that h signatures canonically correspond to morphisms into the integers

a matrix li yau hamilton estimate for kahler ricci flow in this paper we prove a new matrix li yau hamilton lyh estimate for kahler ricci flow on manifolds with nonnegative bisectional curvature the form of this new lyh estimate is obtained by the interpolation consideration originated in ch by chow this new inequality is shown to be connected with perelman s entropy formula through a family of differential equalities in the rest of the paper we show several applications of this new estimate and its corresponding estimate for linear heat equation these include a sharp heat kernel comparison theorem generalizing the earlier result of li and tian lt a manifold version of stoll s theorem st on the characterization of algebraic divisors and a localized monotonicity formula for analytic subvarieties which sharpens the bishop volume comparison theorem motivated by the connection between the heat kernel estimate and the reduced volume monotonicity of perelman p we prove a sharp lower bound heat kernel estimate for the time dependent heat equation which is in a certain sense dual to perelman s monotonicity of the reduced volume as an application of this new monotonicity formula we show that the blow down limit of a certain type long time solution is a gradient expanding soliton we also illustrate the connection between the new lyh estimate and the hessian comparison theorem of fin on the forward reduced distance local monotonicity formulae on entropy and forward reduced volume are also derived

gradient estimates for the heat equation under the ricci flow the paper considers a manifold m evolving under the ricci flow and establishes a series of gradient estimates for positive solutions of the heat equation on m

gradient estimates for a simple elliptic equation on complete non compact riemannian manifolds in this paper we study the local gradient estimate for the positive solution to the following equation u aulog u bu 0i nm where a 0 b are real constants m is a complete non compact riemannian manifold our result is optimal in the sense when m g is a complete non compact expanding gradient ricci soliton by definition m g is called an expanding gradient ricci soliton if for some constant c 0 it satisfies that rc cg d 2 f

interpolating between constrained li yau and chow hamilton harnack inequalities for a nonlinear parabolic equation abstract we establish a one parameter family of harnack inequalities connecting the constrained trace li yau differential harnack inequality for a nonlinear parabolic equation to the constrained trace chow hamilton harnack inequality for this nonlinear equation with respect to evolving metrics related to the ricci flow on a 2 dimensional closed manifold this result can be regarded as a nonlinear version of the previous work of y zheng and the author j y wu y zheng interpolating between constrained li yau and chow hamilton harnack inequalities on a surface arch math 94 2010 591 600

on the behaviour of brauer p dimensions under finitely generated field extensions abstract the present paper shows that if q p or q 0 where p is the set of prime numbers then there exist characteristic q fields e q k k n of brauer dimension brd e q k k and infinite absolute brauer p dimensions abrd p e q k for all p p not dividing q 2 q this ensures that brd p f q k p q 2 q for every finitely generated transcendental extension f q k e q k we also prove that each sequence a p b p p p satisfying the conditions a 2 b 2 and 0 b p a p equals the sequence abrd p e brd p e p p for a field e of characteristic zero

the hasse principle for similarity of hermitian forms the hasse principle for similarity is established for restricted classes of skew hermitian forms over quaternion division algebras with canonical involution and for hermitian forms over division algebras with involution of the second kind a counterexample is produced to show that the principle cannot hold for skew hermitian forms over quaternion division algebras in general this settles the two final cases of hasse principles for similarity of forms that were missing in the literature

shells of twisted flag varieties and the rost invariant we introduce two new general methods to compute the chow motives of twisted flag varieties and settle a 20 year old conjecture of markus rost about the rost invariant for groups of type e 7

value functions and associated graded rings for semisimple algebras we introduce a type of value function y called a gauge on a finite dimensional semisimple algebra a over a field f with valuation v the filtration on a induced by y yields an associated graded ring gr y a which is a graded algebra over the graded field gr v f key requirements for y to be a gauge are that gr y a be graded semisimple and that dim gr v f gr y a dim f a it is shown that gauges behave well with respect to scalar extensions and tensor products when v is henselian and a is central simple over f it is shown that gr y a is simple and graded brauer equivalent to gr w d where d is the division algebra brauer equivalent to a and w is the valuation on d extending v on f the utility of having a good notion of value function for central simple algebras not just division algebras and with good functorial properties is demonstrated by giving new and greatly simplified proofs of some difficult earlier results on valued division algebras

differential harnack estimates for backward heat equations with potentials under the ricci flow abstract in this paper we derive a general evolution formula for possible harnack quantities as a consequence we prove several differential harnack inequalities for positive solutions of backward heat type equations with potentials including the conjugate heat equation under the ricci flow we shall also derive perelman s harnack inequality for the fundamental solution of the conjugate heat equation under the ricci flow

an analysis of constant modulus receivers this paper investigates connections between non blind wiener receivers and blind receivers designed by minimizing the constant modulus cm cost applicable to both t spaced and fractionally spaced fir equalization the main results include 1 a test for the existence of cm local minima near wiener receivers 2 an analytical description of cm receivers in the neighborhood of wiener receivers 3 mean square error mse bounds for cm receivers when the channel matrix is invertible we also show that the cm receiver is approximately colinear with the wiener receiver and provide a quantitative measure of the size of neighborhoods that contain the cm receivers and the accuracy of the mse bounds

new processing techniques based on the constant modulus adaptive algorithm this paper presents three extensions of the constant modulus algorithm cma introduced in an earlier paper as a means of correcting degradations in constant enyelope waveforms as originally formulated the cma employs an fir filter with complex coefficients and accepts complex quadrature input data in this paper first a real input real coefficient version of the algorithm is shown to perform arbitrarily close to the fully complex version secondly the algorithm is extended for the enhancement of signals having a nonconstant but known envelope as might arise in data signals with pulse shaping lastly a multichannel version of cma wherein several observations are linearly combined is presented for joint adaptation of multiple filters this approach can be used for example as a means of spatial or polarization beamsteering to reject additive interferers and compensate for channel induced polarization rotation

a springer theorem for hermitian forms throughout this paper we let d be a central f division algebra with involution such that f d f d d is a henselian valued field by 11 the valuation on f extends uniquely to a valuation on d we denote this valuation by v moreover we assume that the characteristic of the residue field open image in new window is not 2 if the valuation on f is discrete then any quadratic form q can be written as q q1 q2 where is a uniformizer and qi are unit forms springer s theorem states that q is isotropic if and only if at least one of the residue forms open image in new window and open image in new window is isotropic in this paper we generalize this result to hermitian forms in section 4 we use the connection between involutions on algebras and hermitian forms to prove an analog of the springer theorem for involutions

on the nonvanishing stability of undesirable equilibria for fir godard blind equalizers the existence of undesirable equilibria of godard 1980 or constant modulus algorithms cma is demonstrated for all finite dimensional fir equalizers sufficient stability conditions are presented for these equilibria it is shown that for the godard 2 algorithm these undesirable equilibria are locally stable as long as the equalizer length remains finite results indicate that merely increasing the equalizer length does not necessarily nullify the potential for local convergence by godard algorithms

ill convergence of godard blind equalizers in data communication systems the existence of stable undesirable equilibria for the godard algorithm is demonstrated through a simple autoregressive ar channel model these undesirable equilibria correspond to local but nonglobal minima of the underlying mean cost function and thus permit the ill convergence of the godard algorithms which are stochastic gradient descent in nature simulation results confirm predicted misbehavior for channel input of constant modulus it is shown that attaining the global minimum of the mean cost necessarily implies correct equalization a criterion is also presented for allowing a decision at the equalizer as to whether a global or nonglobal minimum has been reached

reduced k theory of azumaya algebras abstract in the theory of central simple algebras often we are dealing with abelian groups which arise from the kernel or co kernel of functors which respect transfer maps for example k functors since a central simple algebra splits and the functors above are trivial in the split case one can prove certain calculus on these functors the common examples are kernel or co kernel of the maps k i f k i d where k i are quillen k groups d is a division algebra and f its center or the homotopy fiber arising from the long exact sequence of above map or the reduced whitehead group sk 1 in this note we introduce an abstract functor over the category of azumaya algebras which covers all the functors mentioned above and prove the usual calculus for it this for example immediately shows that k theory of an azumaya algebra over a local ring is almost the same as k theory of the base ring the main result is to prove that reduced k theory of an azumaya algebra over a henselian ring coincides with reduced k theory of its residue central simple algebra the note ends with some calculation trying to determine the homotopy fibers mentioned above

a gradient estimate for all positive solutions of the conjugate heat equation under ricci flow abstract we establish a point wise gradient estimate for all positive solutions of the conjugate heat equation this contrasts to perelman s point wise gradient estimate which works mainly for the fundamental solution rather than all solutions like perelman s estimate the most general form of our gradient estimate does not require any curvature assumption moreover assuming only lower bound on the ricci curvature we also prove a localized gradient estimate similar to the li yau estimate for the linear schrodinger heat equation the main difference with the linear case is that no assumptions on the derivatives of the potential scalar curvature are needed a classical harnack inequality follows

galois subfields of inertially split division algebras abstract let d be a valued division algebra finite dimensional over its center f assume d has an unramified splitting field the paper shows that if d contains a maximal subfield which is galois over f i e d is a crossed product then the residue division algebra d contains a maximal subfield which is galois over the residue field f this theorem captures an essential argument of previously known noncrossed product proofs in the more general language of noncommutative valuations the result is particularly useful in connection with explicit constructions

new criteria for blind deconvolution of nonminimum phase systems channels a necessary and sufficient condition for blind deconvolution without observing the input of nonminimum phase linear time invariant systems channels is derived based on this condition several optimization criteria are proposed and their solution is shown to correspond to the desired response these criteria involve the computation only of second and fourth order moments implying a simple tap update procedure the proposed methods are universal in the sense that they do not impose any restrictions on the probability distribution of the unobserved input sequence it is shown that in several important cases e g when the additive noise is gaussian the proposed criteria are essentially unaffected

fractionally spaced equalization using cma robustness to channel noise and lack of disparity in the noise free case the fractionally spaced equalization using constant modulus fse cm criterion has been studied previously its minima were shown to achieve perfect equalization when zero forcing zf conditions are satisfied and to be able to still achieve fair equalization when there is lack of disparity however to our best knowledge the effect of additive channel noise on the fse cm cost function minima has not been studied in this paper we show that the noisy fse cm cost function is subject to a smoothing effect with respect to the noise free cost function the result of which is a tradeoff between achieving zero forcing and noise enhancement furthermore we give an analytical closed form expression for the loss of performance due to the noise in terms of input output mean square error mse under the zf conditions the fse cm mse is shown to be mostly due to output noise enhancement and not to residual intersymbol interference isi when there is lack of disparity an irreducible amount of isi appears independently of the algorithm it is the lower equalizability bound for given channel conditions and equalizer length the so called minimum mse mmse the mmse lower bound is the sum of the mmse and of additional mse mostly due to noise enhancement finally we compare the fse cm mse to this lower bound