henselian implies large in this note we show that the quotient field of a domain which is henselian with respect to a nontrivial ideal is a large field and give some applications of this fact using a specialization theorem for ramified covers of the line over generalized krull fields

performance complexity comparison of receivers for a lte mimo ofdm system implementation of receivers for spatial multiplexing multiple input multiple output mimo orthogonal frequency division multiplexing ofdm systems is considered the linear minimum mean square error lmmse and the best list sphere detector lsd are compared to the iterative successive interference cancellation sic detector and the iterative best lsd the performance of the algorithms is evaluated in 3g long term evolution lte system the sic algorithm is found to perform worse than the best lsd when the mimo channels are highly correlated while the performance difference diminishes when the correlation decreases the receivers are designed for 22 and 4 4 antenna systems and three different modulation schemes complexity results for fpga and asic implementations are found a modification to the best lsd which increases its detection rate is introduced the asic receivers are designed to meet the decoding throughput requirements in lte and the best lsd is found to be the most complex receiver although it gives the best reliable data transmission throughput the sic receiver has the best performance complexity tradeoff in the system but in the 4 4 case the best lsd is the most efficient a receiver architecture which could be reconfigured to using a simple or a more complex detector as the channel conditions change would achieve the best performance while consuming the least amount of power in the receiver

far field boundary conditions for black scholes equations in this paper we consider the partial differential equations approach for valuing european style options in order to solve the equations numerically by finite difference or finite element methods it is necessary to introduce an artificial boundary in order to make the computational domain bounded we derive pointwise bounds for the error caused by various boundary conditions imposed on the artificial boundary the error estimates can be used to determine a priori a suitable location for the artificial boundary in terms of a given error tolerance

phase transitions in the condition number distribution of gaussian random matrices we study the statistics of the condition number ensuremath kappa ensuremath lambda mathrm max ensuremath lambda mathrm min the ratio between largest and smallest squared singular values of n ifmmode times else texttimes fi m gaussian random matrices using a coulomb fluid technique we derive analytically and for large n the cumulative mathcal p ensuremath kappa lx and tail cumulative mathcal p ensuremath kappa gx distributions of ensuremath kappa we find that these distributions decay as mathcal p ensuremath kappa lx ensuremath approx exp ensuremath ensuremath beta n 2 ensuremath phi ensuremath x and mathcal p ensuremath kappa gx ensuremath approx exp ensuremath ensuremath beta n ensuremath phi x where ensuremath beta is the dyson index of the ensemble the left and right rate functions ensuremath phi ifmmode pm else textpm fi x are independent of ensuremath beta and calculated exactly for any choice of the rectangularity parameter ensuremath alpha m n ensuremath 1g0 interestingly they show a weak nonanalytic behavior at their minimum ensuremath langle ensuremath kappa ensuremath rangle corresponding to the average condition number a direct consequence of a phase transition in the associated coulomb fluid problem matching the behavior of the rate functions around ensuremath langle ensuremath kappa ensuremath rangle we determine exactly the scale of typical fluctuations ensuremath sim o n ensuremath 2 3 and the tails of the limiting distribution of ensuremath kappa the analytical results are in excellent agreement with numerical simulations

subfields of ample fields rational maps and definability abstract pop proved that a smooth curve c over an ample field k with c k has k many rational points we strengthen this result by showing that there are k many rational points that do not lie in a given proper subfield even after applying a rational map this has several consequences for example we gain insight into the structure of existentially definable i e diophantine subsets of ample fields

split embedding problems over complete domains we prove that every finite split embedding problem is solvable over the field k x1 x n of formal power series in n 2 variables over an arbitrary field k as well as over the field quot a x 1 x n of formal power series in n 1 variables over a noetherian integrally closed domain a this generalizes a theorem of harbater and stevenson who settled the case k x1 x 2

speeding up the sphere decoder with h infty and sdp inspired lower bounds it is well known that maximum likelihood ml decoding in many digital communication schemes reduces to solving an integer least squares problem which is np hard in the worst case on the other hand it has recently been shown that over a wide range of dimensions n and signal to noise ratios snrs the sphere decoding algorithm can be used to find the exact ml solution with an expected complexity that is often less than n3 however the computational complexity of sphere decoding becomes prohibitive if the snr is too low and or if the dimension of the problem is too large in this paper we target these two regimes and attempt to find faster algorithms by pruning the search tree beyond what is done in the standard sphere decoding algorithm the search tree is pruned by computing lower bounds on the optimal value of the objective function as the algorithm proceeds to descend down the search tree we observe a tradeoff between the computational complexity required to compute a lower bound and the size of the pruned tree the more effort we spend in computing a tight lower bound the more branches that can be eliminated in the tree using ideas from semidefinite program sdp duality theory and hinfin estimation theory we propose general frameworks for computing lower bounds on integer least squares problems we propose two families of algorithms one that is appropriate for large problem dimensions and binary modulation and the other that is appropriate for moderate size dimensions yet high order constellations we then show how in each case these bounds can be efficiently incorporated in the sphere decoding algorithm often resulting in significant improvement of the expected complexity of solving the ml decoding problem while maintaining the exact ml performance

galois theory over complete local domains complete local domains play an important role in commutative algebra and algebraic geometry and their algebraic properties were already described by cohen s structure theorem in 1946 however the galois theoretic properties of their quotient fields only recently began to unfold in 2005 harbater and stevenson considered the two dimensional case they proved that the absolute galois group of the field k x y where k is an arbitrary field is semi free in this work we settle the general case and prove that if r is a complete local domain of dimension exceeding 1 then the quotient field of r has a semi free absolute galois group

a fast high order finite difference algorithm for pricing american options we describe an improvement of han and wu s algorithm h han x wu a fast numerical method for the black scholes equation of american options siam j numer anal 41 6 2003 2081 2095 for american options a high order optimal compact scheme is used to discretise the transformed black scholes pde under a singularity separating framework a more accurate free boundary location based on the smooth pasting condition and the use of a non uniform grid with a modified tridiagonal solver lead to an efficient implementation of the free boundary value problem extensive numerical experiments show that the new finite difference algorithm converges rapidly and numerical solutions with good accuracy are obtained comparisons with some recently proposed methods for the american options problem are carried out to show the advantage of our numerical method

finite element error estimates for a nonlocal problem in american option valuation based on new exact formulations of american option problems on bounded domains error estimates are established for finite element approximations of american option prices under admissible regularity some numerical results are also presented

distribution of the demmel condition number of wishart matrices this paper studies the demmel condition number of wishart matrices a quantity which has numerous applications to wireless communications such as adaptive switching between beamforming and diversity coding link adaptation and spectrum sensing for complex wishart matrices we give an exact analytical expression for the probability density function p d f of the demmel condition number and also derive simplified expressions for the high tail regime these results indicate that the condition of complex wishart matrices is dominantly decided by the difference between the matrix dimension and degree of freedom dof i e the probability of drawing a highly ill conditioned matrix decreases considerably when the difference between the matrix dimension and dof increases we further investigate real wishart matrices and derive new expressions for the p d f of the smallest eigenvalue when the difference between the matrix dimension and dof is odd based on these results we succeed to obtain an exact p d f expression for the demmel condition number and simplified expressions for the high tail regime

mathbb a 1 connected varieties of rank one over nonclosed fields in this paper we prove two results regarding the arithmetics of separably mathbb a 1 connected varieties of rank one first we prove that over a large field there is an mathbb a 1 curve through any rational point of the boundary if the boundary divisor is smooth and separably rationally connected secondly we generalize a theorem of hassett tschinkel for the zariski density of integral points over function fields of curves

embedding problems over large fields in this paper we study galois theoretic properties of a large class of fields a class which includes all fields satisfying a universal local global principle for the existence of rational points on varieties as applications we give a positive answer to a long standing conjecture which originates in an unpublished note of roquette and asserts that the absolute galois group of a countable hilbertian pac field is profinite free see f j problem 24 41 secondly we give new evidence for the conjecture of shafarevich which asserts that the absolute galois group of qab is profinite free finally one of the most interesting applications of the theory we develop here is the insight in the galois structure of the totally eg adic numbers

the error probability of the fixed complexity sphere decoder the fixed complexity sphere decoder fsd has been previously proposed for multiple input multiple output mimo detection in order to overcome the two main drawbacks of the sphere decoder sd namely its variable complexity and its sequential structure although the fsd has shown remarkable quasi maximum likelihood ml performance and has resulted in a highly optimized real time implementation no analytical study of its performance existed for an arbitrary mimo system herein the error probability of the fsd is analyzed proving that it achieves the same diversity as the maximum likelihood detector mld independent of the constellation used in addition it can also asymptotically yield ml performance in the high signal to noise ratio snr regime those two results together with its fixed complexity make the fsd a very promising algorithm for uncoded mimo detection

patching and thickening problems in recent years much progress has been made on the structure of fundamental groups of algebraic curves by means of patching techniques in formal and rigid geometry a number of these results have concerned curves over algebraically closed fields of characteristic p e g the proofs of the abhyankar conjecture ra ha5 and of the geometric case of the shafarevich conjecture po1 ha6 and the realization of galois groups over projective curves sa1 st1 while the rigid approach to patching is often regarded as more intuitive than the formal approach its foundations are less well established but constructions involving the formal approach have tended to be technically more cumbersome the purpose of the current paper is to build on previous formal patching results in order to create a framework in which such constructions are facilitated in the process we prove a result asserting that singular curves over a field k can be thickened to curves over k t with prescribed behavior in a formal neighborhood of the singular locus and similarly for covers of curves afterwards we obtain applications to fundamental groups of curves over large fields the structure of the paper is as follows section 1 concerns patching problems for projective curves x over a power series ring r k t1 tn it is shown theorem 1 that giving a coherent projective module over x is equivalent to giving such modules compatibly on a formal neighborhood of each singular point of the closed fibre x and on the formal thickening along the complement of the singular locus s of x section 2 applies this to thickening problems in both the absolute and relative senses namely it shows theorem 3 that such an x can be constructed from its closed fibre x and from complete local thickenings near s such that x is a trivial deformation away from s moreover theorem 2 given a morphism x z and a thickening z of z such that the local thickenings near s are compatible with that of z there is a unique such thickening x of x that is compatible with the given data in section 3 these results are applied to the problem of thickening and deforming covers theorem 4 there combines the results of sections 1 and 2 to show that covers of reducible k curves can be thickened to covers of curves over k t and theorem 5 then shows how this can be used over large fields to

the boundedness of degree of fano varieties with picard number one contents 0 introduction 1 rational curves 1 1 deformation theory of morphisms 1 2 free rational curves 1 3 the invariant d m 2 special subvarieties in fano varieties of large degree 2 1 the statement 2 2 a siegel type lemma 2 3 multiplicity subspaces 2 4 the product theorem part i 2 5 the product theorem part ii 2 6 the proof 3 the covering lemma 4 collections of subsets 4 1 base change and push forward 4 2 an example 4 3 universally open morphisms 4 4 flat families 5 proof of theorem a

a front fixing finite element method for the valuation of american options a front fixing finite element method is developed for the valuation of american options on stocks stability and solution nonnegativity are established under some appropriate assumptions numerical results are presented to examine our method and to compare it with the other methods

a fast numerical method for the black scholes equation of american options this paper introduces a fast numerical method for computing american option pricing problems governed by the black scholes equation the treatment of the free boundary is based on some properties of the solution of the black scholes equation an artificial boundary condition is also used at the other end of the domain the finite difference method is used to solve the resulting problem computational results are given for some american call option problems the results show that the new treatment is very efficient and gives better accuracy than the normal finite difference method

weak approximation over function fields of curves over large or finite fields let k k c be the function field of a curve over a field k and let x be a smooth projective separably rationally connected k variety with x k neq emptyset under the assumption that x admits a smooth projective model pi mathcal x to c we prove the following weak approximation results 1 if k is a large field then x k is zariski dense 2 if k is an infinite algebraic extension of a finite field then x satisfies weak approximation at places of good reduction 3 if k is a nonarchimedean local field and r equivalence is trivial on one of the fibers mathcal x p over points of good reduction then there is a zariski dense subset w subseteq c k such that x satisfies weak approximation at places in w as applications of the methods we also obtain the following results over a finite field k 4 if k 10 then for a smooth cubic hypersurface x k the specialization map x k longrightarrow prod p in p mathcal x p kappa p at finitely many points of good reduction is surjective 5 if mathrm char k neq 2 3 and k 47 then a smooth cubic surface x over k satisfies weak approximation at any given place of good reduction

zero cycles on homogeneous varieties abstract in this paper we study the group a 0 x of zero dimensional cycles of degree 0 modulo rational equivalence on a projective homogeneous algebraic variety x to do this we translate rational equivalence of 0 cycles on a projective variety into r equivalence on symmetric powers of the variety for certain homogeneous varieties we then relate these symmetric powers to moduli spaces of etale subalgebras of central simple algebras which we construct this allows us to show a 0 x 0 for certain classes of homogeneous varieties for groups of each of the classical types extending previous results of swan karpenko of merkurjev and of panin

galois theory over rings of arithmetic power series let r be a domain complete with respect to a norm which denes a non discrete topology on r we prove that the quotient eld of r is ample generalizing a theorem of pop we then consider the case where r is a ring of arithmetic power series which are holomorphic on the closed disc of radius 0 r 1 around the origin and apply the above result to prove that the absolute galois group of the quotient eld of r is semi free this strengthens a theorem of harbater who solved the inverse galois problem over these elds

approximation of the heat equation in a variable domain with application to the stefan problem a discretization of the one dimensional heat equation in a time dependent domain is considered with particular emphasis on a generalization of the crank nicholson scheme for the discretization with respect to time application to a one dimensional stefan problem is given with an iterative algorithm to follow the moving boundary numerical results agree well with the theoretical error bounds

the distribution of free path lengths in the periodic lorentz gas and related lattice point problems the periodic lorentz gas describes the dynamics of a point particle in a periodic array of spherical scatterers and is one of the fundamental models for chaotic diffusion in the present paper we investigate the boltzmann grad limit where the radius of each scatterer tends to zero and prove the existence of a limiting distribution for the free path length we also discuss related problems such as the statistical distribution of directions of lattice points that are visible from a fixed position

construction de revetements de courbes pointees resume si k est un corps fertile large field chez f pop g un k schema en groupes fini etale et x un g torseur on construit un g revetement ramifie c p 1k ou c est lisse et geometriquement connexe sur k induisant en 0 p 1 k le torseur x lorsque k est de caracteristique nulle c est un resultat recent de colliot thelene on termine l article par des commentaires sur l utilisation du langage des champs algebriques dans ce type de probleme copyright 2001 academic press if k is a large field in the sense of f pop g a finite etale k group scheme and x a g torsor we construct a ramified g covering c p 1k where c is smooth and geometrically connected over k inducing at 0 p 1 k the given x when k has characteristic zero this was proved recently by colliot thelene we end with some comments on how the language of algebraic stacks can be used for such problems

improved methods for calculating vectors of short length in a lattice including a complexity analysis the standard methods for calculating vectors of short length in a lattice use a reduction procedure followed by enumerating all vectors of z in a suitable box however it suffices to consider those x e z which lie in a suitable ellipsoid having a much smaller volume than the box we show in this paper that searching through that ellipsoid is in many cases much more efficient if combined with an appropriate reduction procedure our method allows to do computations in lattices of much higher dimensions several randomly constructed numerical examples illustrate the superiority of our new method over the known ones

closed form solutions for perpetual american put options with regime switching this paper studies an optimal stopping time problem for pricing perpetual american put options in a regime switching model an explicit optimal stopping rule and the corresponding value function in a closed form are obtained using the modified smooth fit technique the solution is then compared with the numerical results obtained via a dynamic programming approach and also with a two point boundary value differential equation tpbvde method

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

quadratic families of elliptic curves and unirationality of degree 1 conic bundles we study families of elliptic curves whose coefficients are degree 2 polynomials in a variable t all such curves together form an algebraic surface which is birational to a conic bundle with 7 singular fibers we prove that such conic bundles are unirational as a consequence one obtains that for infinitely many values of t the resulting elliptic curve has rank at least 1

a low complexity generalized sphere decoding approach for underdetermined linear communication systems performance and complexity evaluation for underdetermined linear systems original sphere decoding sd algorithms fail due to zero diagonal elements in the upper triangular matrix of the qr or cholesky factorization of the underdetermined matrix to solve this problem this paper presents a low complexity generalized sphere decoding gsd approach by transforming the original underdetermined problem into the full column rank one so that standard sd can be directly applied on the transformed problem since the introduced transformation maintains the dimension of the original problem for all m qam s the proposed gsd approach provides significant reduction in complexity as compared to other gsd schemes especially for m qam with large signaling constellation both performance and expected complexity are analyzed to provide the comprehensive relationships between the performance and complexity of the proposed gsd and its parameters illustrative simulation and analytical results are in good agreement in terms of both the performance and complexity and indicate that with the properly selected design parameters the proposed gsd scheme can approach the optimum maximumlikelihood decoding mld performance with low complexity for underdetermined linear communication systems including underdetermined mimo systems and the proposed expected complexity analysis can be used as reliable complexity estimation for practical implementation of the proposed algorithm and serve as reference for other gsd algorithms

rationally connected varieties over local fields let x be a proper variety defined over a field k following ma we say that two points x x x k are r equivalent if they can be connected by a chain of rational curves defined over k cf 4 1 in essence two points are r equivalent if they are obviously rationally equivalent several authors have proved finiteness results over local and global fields cubic hypersurfaces ma sd linear algebraic groups ct sa vo1 gi vo2 rational surfaces ct co ct1 ct sk1 quadric bundles and intersections of two quadrics ct sa sd pa su r equivalence is only interesting if there are plenty of rational curves on x at least over k such varieties have been studied in the series of papers komi mo1 ko mi mo3 see also ko1 there are many a priori different ways of defining what plenty of rational curves should mean fortunately many of these turn out to be equivalent and this leads to the notion of rationally connected varieties see ko mi mo2 ko1 iv 3 ko2 4 1 2

local galois theory in dimension two this paper proves a generalization of shafarevich s conjecture for fields of laurent series in two variables over an arbitrary field this result says that the absolute galois group gk of such a field k is quasi free of rank equal to the cardinality of k i e every non trivial finite split embedding problem for gk has exactly cardk proper solutions we also strengthen a result of pop and haran jarden on the existence of proper regular solutions to split embedding problems for curves over large fields our strengthening concerns integral models of curves which are two dimensional

power series over generalized krull domains we resolve an open problem in commutative algebra and field arithmetic posed by jarden let r be a generalized krull domain is the ring r x of formal power series over r a generalized krull domain we show that the answer is negative moreover we show that essentially the opposite theorem holds we prove that if r is a generalized krull domain which is not a krull domain then r x is never a generalized krull domain

analysis of a robust finite element approximation for a parabolic equation with rough boundary data the approximation of parabolic equations with nonhomogeneous dirichlet boundary data by a numerical method that consists of finite elements for the space discretization and the backward euler time discretization is studied the boundary values are assumed in a least squares sense it is shown that this method achieves an optimal rate of convergence for rough only l2 boundary data and for smooth data as well the results of numerical computations which confirm the robust theoretical error estimates are also presented

rationally connected varieties over finite fields let x be a geometrically rational or more generally separably rationally connected variety over a finite field k we prove that if k is large enough then x contains many rational curves defined over k as a consequence we prove that r equivalence is trivial on x if k is large enough these results imply the following conjecture of j l colliot thelene let y be a rationally connected variety over a number field f for a prime p let y p denote the corresponding variety over the local field f p then for almost all primes p the chow group of 0 cycles on y p is trivial and r equivalence is trivial on y p

quasi maximum likelihood detector based on geometrical diversification greedy intensification this letter proposes a quasi optimum maximum likelihood detection technique based on geometrical diversification and greedy intensification gdgi the presented detector scheme is shown to achieve almost optimal performance for all signal to noise ratio snr values and a cubic computation complexity in the problem dimension it possesses a regular structure well suited for hardware implementation simulation results show that for a system with a high dimension of n 60 the loss is approximately 0 35 db at ber 10 5 compared to an optimal decoding

boundary behavior and the martin boundary problem for p harmonic functions in lipschitz domains boundary behavior and the martin boundary problem for p harmonic functions in lipschitz domains

efficient detection algorithms for mimo channels a geometrical approach to approximate ml detection it is well known that suboptimal detection schemes for multiple input multiple output mimo spatial multiplexing systems equalization based schemes as well as nulling and cancelling schemes are unable to exploit all of the available diversity and thus their performance is inferior to ml detection motivated by experimental evidence that this inferior performance is primarily caused by the inability of suboptimal schemes to deal with bad i e poorly conditioned channel realizations we study the decision regions of suboptimal schemes for bad channels based on a simplified model for bad channels we then develop two computationally efficient detection algorithms that are robust to bad channels in particular the novel sphere projection algorithm spa is a simple add on to standard suboptimal detectors that is able to achieve near ml performance and significantly increased diversity gains the spa s computational complexity is comparable with that of nulling and cancelling detectors and only a fraction of that of the fincke phost sphere decoding algorithm for ml detection