an eigenanalysis interference canceler eigenanalysis methods are applied to interference cancellation problems while with common array processing methods the cancellation is effected by global optimization procedures that include the interferences and the background noise the proposed technique focuses on the interferences only resulting in superior cancellation performance furthermore the method achieves full effectiveness even for short observation times when the number of samples used for processing is of the the order of the number of interferences adaptive implementation is obtained with a simple fast converging algorithm

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

analysis of the performance and sensitivity of an eigenspace based interference canceler eigenspace based interference cancelers eics possess the advantages of providing maximal suppression of interference with fast convergence over conventional adaptive beamformers however the performance and sensitivity to steering angle error of eics have not been analyzed due to the use of a signal blocking matrix we first present a technique to construct a positive definite matrix based on the signal blocking matrix and then use this matrix to compensate the effect of the signal blocking matrix on the sensor noise received by an eic therefore the interference subspace required for finding the optimal weight vector can be obtained using conventional eigenvalue decomposition evd moreover the performance and sensitivity to the steering angle error of the eic can be analyzed simulation examples are provided for confirming the theoretical results

fastest recovery from feedback loss bounded overshoot abstractthe problem of designing robust optimal controllers to reduce in minimal time operating errors that had accumulated during a period of feedback loss is revisited with the objective of impo

vertex algebraic structure of principal subspaces of the basic modules for twisted affine lie algebras of type a2n 1 2 dn 2 e6 2 abstract we obtain a presentation of principal subspaces of the basic modules for the twisted affine kac moody lie algebras of type a 2 n 1 2 d n 2 and e 6 2 using this presentation we construct exact sequences among these principal subspaces and use these exact sequences to obtain recursions satisfied by graded dimensions of the principal subspaces solving these recursions we obtain the graded dimensions of the principal subspaces

fastest recovery after feedback disruption nonlinear delay differential systems abstractthe problem of reducing operating errors after a feedback disruption is considered for a class of nonlinear delay differential systems it is shown that there are optimal controllers that reduce such errors in minimal time once feedback has been restored it is further shown that optimal performance can be approximated by bang bang controllers controllers that are easy to design and implement

a quantum analog of the z algebra we define a natural quantum analog for the z algebra and which we refer to as the zq algebra by modding out the heisenberg algebra from the quantum affine algebra uq sl 2 with level k we discuss the representation theory of this zq algebra in particular we exhibit its reduction to a group algebra and to a tensor product of a group algebra with a quantum clifford algebra when k 1 and k 2 and thus we recover the explicit constructions of uq sl 2 standard modules as achieved by frenkel jing and bernard respectively moreover for arbitrary nonzero level k we show that the explicit basis for the simplest z generalized verma module as constructed by lepowsky and primc is also a basis for its corresponding zq module i e it is invariant under the q deformation for generic q we expect this zq algebra associated with uq sl 2 at level k to play the role of a dynamical symmetry in the off critical zk statistical models

a new family of algebras underlying the rogers ramanujan identities and generalizations abstract the classical rogers ramanujan identities have been interpreted by lepowsky milne and the present authors in terms of the representation theory of the euclidean kac moody lie algebra a1 1 also the present authors have introduced certain vertex differential operators providing a construction of a1 1 on its basic module and kac kazhdan and we have generalized this construction to a general class of euclidean lie algebras starting from this viewpoint we now introduce certain new algebras unk v which centralize the action of the principal heisenberg subalgebra of an arbitrary euclidean lie algebra unk on a highest weight unk module v we state a general tautological rogers ramanujan type identity which by our earlier theorem includes the classical identities and we show that unk v can be used to reformulate the general identity for unk a1 1 we develop the representation theory of unk v in considerable detail allowing us to prove our earlier conjecture that our general rogers ramanujan type identity includes certain identities of gordon andrews and bressoud in the process we construct explicit bases of all of the standard and verma modules of nonzero level for a1 1 with an explicit realization of a1 1 as operators in each case the differential operator constructions mentioned above correspond to the trivial case unk v 1 of the present theory

coding the principal character formula for affine kac moody lie algebras in this paper an algorithm for computing the principal character for affine lie algebras is discussed and presented the principal characters discovered using this program are given and or proven results include level 2 and 3 character formulas in a2n 1 2 and the sole existence of the rogers ramanujan products in a1 1 a2 1 a2 2 c3 1 f4 1 g2 1 a7 2

a framework of rogers ramanujan identities and their arithmetic properties the two rogers ramanujan q series where 0 1 play many roles in mathematics and physics by the rogers ramanujan identities they are essentially modular functions their quotient the rogers ramanujan continued fraction has the special property that its singular values are algebraic integral units we find a framework which extends the rogers ramanujan identities to doubly infinite families of q series identities if a 1 2 and m n 1 then we have infinite product modular function where the p x x q are hall littlewood polynomials these q series are specialized characters of affine kac moody algebras generalizing the rogers ramanujan continued fraction we prove in the case of a that the relevant q series quotients are integral units

a signal subspace method for adaptive interference cancellation an interference cancellation technique that combines a signal subspace approach with adaptive adjustment of the weight vector is derived the weight vector is constrained to lie in a signal subspace computed by eigendecomposition of the covariance matrix of the array outputs the weight vector is rotated to maximize the output signal to interference ratio the technique does not require array calibration as in other subspace methods this technique applies to receiver arrays for digital communication signals the case of a bpsk signal modulating an am transmitter is analyzed in some detail numerical examples illustrate the behavior of the algorithm

on principal realization of modules for the affine lie algebra a_1 1 at the critical level we present complete realization of irreducible a 1 1 modules at the critical level in the principal gradation our construction uses vertex algebraic techniques the theory of twisted modules and representations of lie conformal superalgebras we also provide an alternative z algebra approach to this construction all irreducible highest weight a 1 1 modules at the critical level are realized on the vector space m tfrac 1 2 z 1 otimes 2 where m tfrac 1 2 z 1 is the polynomial ring c alpha 1 2 alpha 3 2 explicit combinatorial bases for these modules are also given

the statistical performance of the music and the minimum norm algorithms in resolving plane waves in noise this paper presents an asymptotic statistical analysis of the null spectra of two eigen assisted methods music 1 and minimum norm 2 for resolving independent closely spaced plane waves in noise particular attention is paid to the average deviation of the null spectra from zero at the true angles of arrival for the plane waves these deviations are expressed as functions of signal to noise ratios number of array elements angular separation of emitters and the number of snapshots in the case of music an approximate expression is derived for the resolution threshold of two plane waves with equal power in noise this result is validated by monte carlo simulations

vertex operators and principal subspaces of level one for u_q widehat mathfrak sl _2 abstract we consider two different methods of associating vertex algebraic structures with the level 1 principal subspaces for u q sl 2 in the first approach we introduce certain commutative operators and study the corresponding vertex algebra and its module we find combinatorial bases for these objects and show that they coincide with the principal subspace bases found by b l feigin and a v stoyanovsky in the second approach we introduce the so called nonlocal q vertex algebras investigate their properties and construct the nonlocal q vertex algebra and its module generated by frenkel jing operator and koyama s operator respectively by finding the combinatorial bases of their suitably defined subspaces we establish a connection with the sum sides of the rogers ramanujan identities finally we discuss further applications to quantum quasi particle relations

robust optimal control low error operation for the longest time the problem of maximising the time during which an open loop system can operate without exceeding a specified error bound is considered for linear systems that are subject to uncertainties about their parameters and their initial conditions and whose operation is hampered by disturbance signals the objective is to characterise an optimal input signal that keeps performance errors within specified bounds for the longest time it is shown that such an input signal exists and that it can be approximated by a bang bang input signal without significantly affecting performance

periodic sampling maximising the sampling period the process of periodic sampling is investigated for a class of nonlinear systems the objective is to achieve the longest sampling period that is compatible with a specified error bound it is sho

the rogers ramanujan identities lie theoretic interpretation and proof abstract the two rogers ramanujan identities which equate certain infinite products with infinite sums are among the most intriguing of the classical formal power series identitites it has been found by lepowsky and milne that the product side of each of them differs by a certain factor from the principally specialized character of a certain standard module for the euclidean kac moody lie algebra a1 1 on the other hand the present authors have introduced an infinite dimensional heisenberg subalgebra unk of a1 1 which leads to a construction of a1 1 in terms of differential operators given by the homogeneous components of an exponential generating function in the present announcement we use unk to formulate a natural abstract rogers ramanujan identity for an arbitrary standard a1 1 module which turns out to coincide with the classical identities in the cases of the two corresponding standard modules the abstract identity equates two expressions one a product and the other a sum for the principally specialized character of the space of highest weight vectors or vacuum states for unk in the module the construction of a1 1 leads to a concrete realization of as the span of certain spaces of symmetric polynomials occurring as the homogeneous components of exponential generating functions the summands in the rogers ramanujan identities turn out to count the dimensions of these spaces for general standard a1 1 modules we conjecture that the abstract identities agree with generalizations of the rogers ramanujan identities due to gordon andrews and bressoud

representation of the affine superalgebras a 4 0 2l a 2 0 2l 1 and their subalgebras a2l 2 a2l 1 2 by vertex operators abstract the structure theory of standard modules of affine lie algebras given by j lepowsky and r l wilson in lw is stated for representations of affine superalgebras as an application the standard modules of level one for the superalgebras a 4 0 2l a 2 0 2l 1 and their affine subalgebras a2l 2 a2l 1 2 are constructed explicitly these modules are realized as the tensor product of symmetric and exterior algebras with an irreducible representation of a certain finite 2 group the affine superalgebra acts on this space by tensor products of vertex operators operators of clifford type and elements of the 2 group as a corollary the spin representations of the lie algebras bl and dl are obtained from the 2 group representation

combinatorial bases of feigin stoyanovsky s type subspaces of higher level standard sl l 1 c modules abstract let g be an affine lie algebra of the type a l 1 we find a combinatorial basis of feigin stoyanovsky s type subspace w given in terms of difference and initial conditions linear independence of the generating set is proved inductively by using coefficients of intertwining operators a basis of the standard g module l is obtained as an inductive limit of the basis of w

a new optimization technique for adaptive antenna arrays an adaptive nulling algorithm for adjusting the array weights under the soft constraint of the weight norm being very much less than 1 or equal to 1 based on the measured correlations between the array and element outputs is described the algorithm can be regarded as an extension of the constrained least mean square algorithm it is derived from the same concept of signal and noise subspaces defined in the multiple signal classification music algorithm one of the unique features of the present algorithm is that the number of the iterations required to adapt the array weights to form nulls is exactly equal to the number of interferers

stability of model based networked control systems with time varying transmission times in model based networked control systems mb ncss an explicit model of the plant is used to produce an estimate of the plant state behavior between transmission times in this paper the stability of mb ncss is studied when the controller actuator is updated with the sensor information at nonconstant time intervals networked control systems with transmission times that are varying either within a time interval or are driven by a stochastic process with identically independently distributed and markov chain driven transmission times are studied sufficient conditions for lyapunov stability are derived for stochastically modeled transmission times almost sure stability and mean square sufficient conditions for stability are introduced