ergodic theory for markov fibred systems and parabolic rational maps a paraboiic rational map of the riemann sphere admits a non atomic h conformal measure on its julia set where h the hausdorff dimension of the julia set and satisfies 1 2 h 2 with respect to this measure the rational map is conservative exact and there is an equivalent a finite invariant measure finiteness of the measure is characterised central limit theorems are proved in the case of a finite invariant measure and return sequences are identified in the case of an infinite one a theory of markov fibred systems is developed and parabolic rational maps are considered within this framework

area and hausdorff dimension of julia sets of entire functions we show the julia set of a sin z has positive area and the action of a sin z on its julia set is not ergodic the julia set of a exp z has hausdorff dimension two but in the presence of an attracting periodic cycle its area is zero

a novel wavelet based generalized sidelobe canceller this paper presents a novel narrow band adaptive beamformer with the generalized sidelobe canceller gsc as the underlying structure the new beamformer employs a wavelet based approach for the design of the blocking matrix of the gsc which is now constituted by a set of regular m band wavelet filters such a construction of the blocking matrix can not only block the desired signals from the lower path as required provided the wavelet filters have sufficiently high regularity but it also encompasses the widely used one with ones and minus ones along the diagonals as a special case in addition it possesses two advantageous features first the eigenvalue spreads of the covariance matrices of the blocking matrix outputs as demonstrated in various scenarios are decreased as compared with those of previous approaches since the popular least mean squares lms algorithm has been notorious for its slow convergence rate the reduction of the eigenvalue spreads can in general accelerate the convergence speed of the succeeding lms algorithm second the new beamformer belongs to a specific type of partially adaptive beamformers wherein only a portion of the available degree of freedom is utilized in the adaptive processing as such the overall computational complexity is substantially reduced when compared to previous works the issues of choosing the parameters involved for superior performance are also addressed simulation results are furnished as well to justify this new approach

phase transitions for suspension flows this paper is devoted to studying the thermodynamic formalism for suspension flows defined over countable alphabets we are mostly interested in the regularity properties of the pressure function we establish conditions for the pressure function to be real analytic or to exhibit a phase transition we also construct an example of a potential for which the pressure has countably many phase transitions

iterated function system and ruelle operator abstract we consider a generalized iterated function system where the weights are variable functions by using the ruelle operator and a dynamical system consideration we prove that if the system is contractive and the weights are strictly positive functions and satisfy the dini condition then there exists a unique eigenmeasure corresponding to the ruelle operator on the attractor if in addition the maps are conformal and satisfy the open set condition then we prove that they satisfy the strong open set condition and by using this we can give a description of the l p scaling spectrum and the multifractal structure of the eigenmeasure the work extends some results of proc london math soc 73 1996 105 154 adv appl math 19 1997 486 513 j statist phys 86 1997 233 275 indiana univ math j 42 1993 367 411

common limits of fibonacci circle maps we show that limits for the critical exponent tending to exist in both critical circle homeomorphism of golden mean rotation number and fibonacci circle coverings moreover they are the same the limit map is not analytic at the critical point which is flat but has non trivial complex dynamics

calculating hausdorff dimension of julia sets and kleinian limit sets we present a new algorithm for efficiently computing the hausdorff dimension of sets x invariant under conformal expanding dynamical systems by locating the periodic points of period up to n we construct approximations s n which converge to dim x super exponentially fast in n this method can be used to give rigorous estimates for important examples including hyperbolic julia sets and limit sets of schottky and quasifuchsian groups

local dimensions of measures on infinitely generated self affine sets abstract we show the existence of the local dimension of an invariant probability measure on an infinitely generated self affine set for almost all translations this implies that an ergodic probability measure is exactly dimensional furthermore the local dimension equals the minimum of the local lyapunov dimension and the dimension of the space

performance analysis of derivative constraint adaptive arrays with pointing errors the performance of adaptive arrays with arbitrary order derivative constraints to avoid the signal nulling caused by the error in the steering angle is investigated the generalized sidelobe canceller gsc is used to evaluate the bearing responses of adaptive arrays with pointing errors under the assumption of equispaced linear arrays the legendre polynomial is used to derive a closed form formula for the sidelobe leakage factor the ratio in which the signal leaks into the gsc sidelobe cancelling branch moreover the effective beamwidth the maximum range of pointing inaccuracy allowable to keep the signal loss in array output less than a given value is derived for the gsc with a delay and sum quiescent beamformer such adaptive arrays can achieve the maximum output signal to noise ratio when the presteering is perfect and the performance is independent of the location of the phase origin numerical results are presented to confirm the analysis

hausdorff dimension of harmonic measure for self conformal sets abstract under some technical assumptions it is shown that the hausdorff dimension of the harmonic measure on the limit set of a conformal infinite iterated function system is strictly less than the hausdorff dimension of the limit set itself if the limit set is contained in a real analytic curve if the iterated function system consists of similarities only or if this system is irregular as a consequence of this general result the same statement is proven for hyperbolic and parabolic julia sets finite parabolic iterated function systems and generalized polynomial like mappings also sufficient conditions are provided for a limit set to be uniformly perfect and for the harmonic measure to have the hausdorff dimension less than 1 some results in the spirit of przytycki et al ann of math 130 1989 1 40 stud math 97 1991 189 225 are obtained

rational curves dynkin diagrams and fano manifolds with nef tangent bundle a fano manifold x with nef tangent bundle is of flag type if it has the same kind of elementary contractions as a complete flag manifold in this paper we present a method to associate a dynkin diagram mathcal d x with any such x based on the numerical properties of its contractions we then show that mathcal d x is the dynkin diagram of a semisimple lie group as an application we prove that campana peternell conjecture holds when x is a flag type manifold whose dynkin diagram is a n i e we show that x is the variety of complete flags of linear subspaces in mathbb p n

the statistical performance of eigenspace based adaptive array beamformers in this paper we analyze the statistical performance of several eigenspace based adaptive array bearnformers including conventional direct form beamformers and generalized sidelobe canceler gsc it is shown that the convergence rate of eigenspace based adaptive array beamforming depends on the number of array elements the input signal to noise ratio snr and the number of interferers when the desired signal is present during the weight adaptation in contrast the misadjostment of the array output power is a function of the number of interferers and is independent of the number of array elements when the desired signal is absent several simulation examples are also provided to confirm the theoretical results

performance measures for optimal constrained beamformers in this paper the closed form expression is derived which relates the output signal to interference plus noise ratio to the minimum mean square error of constrained beamformers for narrowband and wideband signal environments

countable alphabet random subhifts of finite type with weakly positive transfer operator we deal with countable alphabet locally compact random subshifts of finite type the latter merely meaning that the symbol space is generated by an incidence matrix under the absence of big images property and under the absence of uniform positivity of the transfer operator we first establish the existence of random conformal measures along with good bounds for the iterates of the perron frobenius operator then using the technique of positive cones and proving a version of bowen s type contraction see equilibrium states and the ergodic theory of anosov diffeomorphisms 1975 we also establish a fairly complete thermodynamical formalism this means that we prove the existence and uniqueness of fiberwise invariant measures giving rise to a global invariant measure equivalent to the fiberwise conformal measures furthermore we establish the existence of a spectral gap for the transfer operators which in the random context precisely means the exponential rate of convergence of the normalized iterated transfer operator this latter property in a relatively straightforward way entails the exponential decay of correlations and the central limit theorem

p1 bundles admitting another smooth morphism of relative dimension one abstract we give the complete classification of p 1 bundles over projective manifolds of picard number one each of which admit another smooth morphism of relative dimension one

the geometry of julia sets the long term analysis of dynamical systems inspired the study of the dynamics of families of mappings many of these investigations led to the study of the dynamics of mappings on cantor sets and on intervals julia sets play a critical role in the understanding of the dynamics of families of mappings in this paper we introduce another class of objects called hairy objects which share many properties with the cantor set and the interval they are topologically unique and admit only one embedding in the plane these uniqueness properties explain the regular occurrence of hairy objects in pictures of julia sets hairy objects are ubiquitous hairy arcs will be used to give a complete topological description of the julia sets of many members of the exponential family

entire functions with julia sets of positive measure let f be a transcendental entire function for which the set of critical and asymptotic values is bounded the denjoy carleman ahlfors theorem implies that if the set of all z for which f z r has n components for some r 0 then the order of f is at least n 2 more precisely we have log log m r f n 2 log r o 1 where m r f denotes the maximum modulus of f we show that if f does not grow much faster than this then the escaping set and the julia set of f have positive lebesgue measure however as soon as the order of f exceeds n 2 this need not be true the proof requires a sharpened form of an estimate of carleman and tsuji related to the denjoy carleman ahlfors theorem

trees and hairs for some hyperbolic entire maps of finite order let f be an entire transcendental map of finite order such that all the singularities of f 1 are contained in a compact subset of the immediate basin b of an attracting fixed point it is proved that there exist geometric coding trees of preimages of points from b with all branches convergent to points from hat mathbb c this implies that the riemann map onto b has radial limits everywhere moreover the julia set of f consists of disjoint curves hairs tending to infinity homeomorphic to a half line composed of points with a given symbolic itinerary and attached to the unique point accessible from b endpoint of the hair these facts generalize the corresponding results for exponential maps

dimension spectra of hyperbolic flows for flows with a conformal hyperbolic set we establish a conditional variational principle for the dimension spectra of holder continuous functions we consider simultaneously birkhoff averages into the future and into the past we emphasize that the description of the spectra is not a consequence of the existing results for birkhoff averages into the future or into the past the main difficulty is that even though the local product structure is bi lipschitz the level sets of the birkhoff averages are never compact our proof is based on the use of markov systems and is inspired in earlier arguments in the case of discrete time

thermodynamic formalism and variations of the hausdorff dimension of quadratic julia sets let d c denote the hausdorff dimension of the julia set of the polynomial the function d restricted to 0 is real analytic in ru2 is left continuous at bo zi but not continuous do se zi we prove that tends to from the left at as in particular the graph of d has a vertical tangent on the left at a result which supports the numerical experiments

on fano manifolds with nef tangent bundles admitting 1 dimensional varieties of minimal rational tangents let x be a fano manifold of picard number 1 with numerically effective tangent bundle according to the principal case of a conjecture of campana peternell s x should be biholomorphic to a rational homogeneous manifold g p where g is a simple lie group and p g is a maximal parabolic subgroup in our opinion there is no overriding evidence for the campana peternell conjecture for the case of picard number 1 to be valid in its full generality as part of a general programme that the author has undertaken with jun muk hwang to study uniruled projective manifolds via their varieties of minimal rational tangents a new geometric approach is adopted in the current article in a special case consisting of a recovering the generic variety of minimal rational tangents c x and b recovering the structure of a rational homogeneous manifold from c x the author proves that when b 4 x 1 and the generic variety of minimal rational tangents is 1 dimensional x is biholomorphic to the projective plane p 2 the 3 dimensional hyperquadric q 3 or the 5 dimensional fano homogeneous contact manifold of type g 2 to be denoted by k g 2 the principal difficulty is part a of the scheme we prove that c x c pt x x is a rational curve of degrees 3 and show that d 1 resp 2 resp 3 corresponds precisely to the cases of x p 2 resp q 3 resp k g 2 let be the normalization of a choice of a chow component of minimal rational curves on x nefness of the tangent bundle implies that is smooth furthermore it implies that at any point x x the normalization x of the corresponding chow space of minimal rational curves marked at is smooth after proving that x is a rational curve our principal object of study is the universal family u of giving a double fibration p u u x which gives p 1 bundles there is a rank 2 holomorphic vector bundle v on whose projectivization is isomorphic to p u we prove that v is stable and deduce the inequality d 4 from the inequality c 2 1 v 4c 2 v resulting from stability and the existence theorem on hermitian einstein metrics the case of d 4 is ruled out by studying the structure of the curvature tensor of the hermitian einstein metric on v in the special case where c 2 1 v 4c 2 v

fano 5 folds with nef tangent bundles and picard numbers greater than one we prove that smooth fano 5 folds with nef tangent bundles and picard numbers greater than one are rational homogeneous manifolds

a fast null steering algorithm for linearly constrained adaptive arrays a fast null steering algorithm for adaptive arrays with a look direction constraint is investigated in this algorithm the least mean square lms algorithm is used to adaptively adjust the positions of the array response zeros one after another in a time multiplexed manner to track unknown jammers to ensure that the look direction response and the other zeros remain unchanged when a particular null is being updated the element signals are suitably transformed before the lms updating despite this signal transformation the new algorithm has almost the same implementation complexity as when the lms algorithm is employed directly as only one zero is being adaptively updated at any instant however with each null being independently steered the convergence behavior of the new algorithm is significantly faster and is almost independent of the external noise environment

dynamics of infinitely generated nicely expanding rational semigroups and the inducing method we investigate the dynamics of semigroups of rational maps on the riemann sphere to establish a fractal theory of the julia sets of infinitely generated semigroups of rational maps we introduce a new class of semigroups which we call nicely expanding rational semigroups more precisely we prove bowen s formula for the hausdorff dimension of the pre julia sets which we also introduce in this paper we apply our results to the study of the julia sets of non hyperbolic rational semigroups for these results we do not assume the cone condition which has been assumed in the study of infinite contracting iterated function systems similarly we show that bowen s formula holds for the limit set of a contracting conformal iterated function system without the cone condition

a dynamical dimension transference principle for dynamical diophantine approximation diophantine approximation in dynamical systems concerns the diophantine properties of the orbits in classic diophantine approximation the powerful mass transference principle established by beresnevich and velani provides a general principle to the dimension for a limsup set in this paper we aim at finding a general principle for the dimension of the limsup set arising in a general expanding dynamical system more precisely let x t be a topological dynamical system where x is a compact metric space and t x rightarrow x is an expanding continuous transformation given y o in x we consider the following limsup set mathcal w t f driven by the dynamical system x t begin aligned big x in x x in b z e s n f log t z text for some z in t n y o text with infinitely many n in mathbb n big end aligned where log t is a function reflecting the local conformality of the transformation t f is a non negative continuous function over x and s n f log t z denotes the ergodic sum f log t z cdots f log t t n 1 z by proposing a dynamical ubiquity property assumed on the system x t we obtain that the dimensions of x and mathcal w t f are both related to the bowen manning mccluskey formulae namely the solution to the pressure functions begin aligned texttt p t log t 0 text and texttt p t log t f 0 text respectively end aligned we call this phenomenon a dynamical dimension transference principle because of its partial analogy with the mass transference principle this general principle unifies and extends some known results which were considered only separatedly before these include the b adic expansions expanding rational maps over julia sets inhomogeneous diophantine approximation on the triadic cantor set and finite conformal iterated function systems

performance analysis of a wavelet based generalized sidelobe canceller in this paper we carry out a detailed performance analysis of the recently addressed wavelet based generalized sidelobe canceller gsc which employs a set of p regular m band wavelet filters in the design of the blocking matrix involved we begin our analysis by developing a closed form expression of the output signal to interference plus noise ratio sinr of partially adaptive beamformers with the gsc as the underlying structure under a one jammer or multiple jammer environment this new expression is shown to encompass several previous works as special cases we then examine the relationship between the choices of the parameters p and m in the wavelet based gsc and the corresponding output sinr based on this expression some guidelines for the choices of these parameters can thus be induced to achieve superior performance simulation results are also furnished to justify these suggestions

on the hausdorff dimension of the escaping set of certain meromorphic functions let f be a transcendental meromorphic function of finite order for which the set of finite singularities of f 1 is bounded suppose that is not an asymptotic value and that there exists m n such that the multiplicity of all poles except possibly finitely many is at most m for r 0 let ir f be the set of all z c for which lim infn fn z r as n here fn denotes the n th iterate of f let i f be the set of all z c such that fn z as n that is i f t r 0 ir f denote the hausdorff dimension of a set a c by hd a it is shown that limr hd ir f 2m 2 m in particular hd i f 2m 2 m these estimates are best possible for given and m we construct a function f such that hd i f 2m 2 m and hd ir f 2m 2 m for all r 0 if f is as above but of infinite order then the area of ir f is zero this result does not hold without a restriction on the multiplicity of the poles

on transfer operators for continued fractions with restricted digits for any non empty subset i of the natural numbers let lambda i denote those numbers in the unit interval whose continued fraction digits all lie in i define the corresponding transfer operator formula for formula where re rs theta i is the abscissa of convergence of the series formula when acting on a certain hilbert space hi rs we show that the operator li rs is conjugate to an integral operator ki rs if furthermore rs is real then ki rs is selfadjoint so that li rs hi rs hi rs has purely real spectrum it is proved that li rs also has purely real spectrum when acting on various hilbert or banach spaces of holomorphic functions on the nuclear space c omega 0 1 and on the frechet space c infty 0 1 the analytic properties of the map rs m li rs are investigated for certain alphabets i of an arithmetic nature for example i primes i squares i an arithmetic progression i the set of sums of two squares it is shown that rs m li rs admits an analytic continuation beyond the half plane re rs theta i

projective manifolds whose tangent bundles are numerically effective in 1979 mori mo proved the so called hartshorne frankel conjecture every projective n dimensional manifold with ample tangent bundle is isomorphic to the complex projective space p a differential geometric analogon assuming the existence of a k ihler metric on x with positive holomorphic bisectional curvature is independently due to siu yau sy thus it seems natural to classify projective manifolds x whose tangent bundle tx satisfy a degenerate condition of ampleness numerical effectivity abbreviated by nef this means that the tautological quotient line bundle d 1 on f tx is numerically effective i e c 0

valuations of languages with applications to fractal geometry abstract valuations morphisms from to 0 1 are a simple generalization of bernoulli morphisms distributions measures as introduced by berstel and perrin 1988 berstel and reutenauer 1988 blanchard and hansel 1984 eilenberg 1974 and hansel and perrin 1983 1989 this paper shows that valuations are useful not only within the theory of codes but also when dealing with ambiguity especially in context free grammars or for defining outer measures on the space of words which are of some importance to the theory of fractals these connections yield new formulae to determine the hausdorff dimension of fractal sets especially in euclidean spaces defined via formal languages the class of fractals describable with context free languages strictly includes that of mrfs fractals introduced by culik and dube 1990 and mauldin and williams 1988 some of the results of this paper also appear as part of the author s ph d thesis and other works fernau 1992a b 1993

convergence speeds of iterations of ruelle operator with weakly contractive ifs abstract given ruelle operator sg induced by a summable variation potential function g on a symbolic space fan and pollicott math proc cambridge philos soc 129 2000 99 115 gave an estimate of the convergence speed of iterations sgnf n 1 later on fan and jiang comm math phys 223 2001 143 159 extended it to locally expansive dini dynamical system it is known that the systems they considered have the bounded distortion property bdp and the bdp is a key condition in the papers we extend their results to weakly contractive dini iterated function systems x wj j 1m pj j 1m which may not have the bdp and allows to have overlapping

the box dimensions of inhomogeneous self conformal sets with overlaps abstract we investigate the box dimensions of inhomogeneous self conformal sets with overlaps firstly we significantly generalize the result of fraser concerning upper box dimension under some mild overlap conditions secondly we give corresponding formula of lower box dimension for condense set c with special construction these results extend the bowen s equation for inhomogeneous ifs

on univoque and strongly univoque sets abstract much has been written about expansions of real numbers in noninteger bases particularly for a finite alphabet 0 1 and a real number base 1 1 the so called univoque set of numbers which have a unique expansion in base has garnered a great deal of attention in recent years motivated by recent applications of expansions to bernoulli convolutions and a certain class of self affine functions we introduce the notion of a strongly univoque set we study in detail the set d of numbers which are univoque but not strongly univoque our main result is that d is nonempty if and only if the number 1 has a unique nonterminating expansion in base and in that case d is uncountable we give a sufficient condition for d to have positive hausdorff dimension and show that on the other hand there are infinitely many values of for which d is uncountable but of hausdorff dimension zero

dimension and measures for a curvilinear sierpinski gasket or apollonian packing in this paper we apply some results about general conformal iterated function systems to a the residual set of a standard apollonian packing or a curvilinear sierpinski gasket within this context it is straightforward to show that h the hausdorff dimension of a is greater than 1 and the packing dimension and the upper and lower box counting dimensions are all the same as the hausdorff dimension among other things we verify sullivan s result that 0 h h a p h a

anomalies in multifractal formalism for local time of brownian motion the renyi function for the logical time measure of brownian motion is found it is shown that this function the legendre transform of the multifractal spectrum of and the function derived by the reciprocal measure formalism are not identical more examples of having similar anomalies are discussed

fractal curvature measures and minkowski content for self conformal subsets of the real line abstract we show that the fractal curvature measures of invariant sets of one dimensional conformal iterated function systems satisfying the open set condition exist if the associated geometric potential function is nonlattice moreover we prove that if the maps of the conformal iterated function system are all analytic then the fractal curvature measures do not exist in the lattice case further in the nonlattice situation we obtain that the minkowski content exists and prove that the fractal curvature measures are constant multiples of the conformal measure where denotes the minkowski dimension of the invariant set for the first fractal curvature measure this constant factor coincides with the minkowski content of the invariant set in the lattice situation we give sufficient conditions for the minkowski content of the invariant set to exist disproving a conjecture of lapidus and standing in contrast with the fact that the minkowski content of a self similar lattice fractal never exists however every self similar set satisfying the open set condition exhibits a minkowski measurable c 1 diffeomorphic image both in the lattice and in the nonlattice situation average versions of the fractal curvature measures are shown to always exist

hausdorff dimension and conformal measures of feigenbaum julia sets 1 1 statement of the results one of the first questions usually asked about a fractal subset of r is whether it has the maximal possible hausdorff dimension n it certainly happens if the set has positive lebesgue measure on the other hand it is easy to construct fractal sets of zero measure but of dimension n moreover this phenomenon is often observable for fractal sets produced by conformal dynamical systems iterated rational functions or kleinian groups in particular the analogy with kleinian groups suggested that the julia sets of feigenbaum maps should have hausdorff dimension two in this paper we will show that this is not always the case a quadratic polynomial or more generally a quadratic like map is called feigenbaum if it is infinitely renormalizable of bounded combinatorial type with a priori bounds see 2 for a precise definition feigenbaum polynomials are remarkable dynamical systems whose geometry has been a focus of research for the past 25 years by analogy with kleinian groups it was anticipated that their julia sets have dimension 2 and this problem has been around for a while however in this paper we will show that this is not always the case

fano n folds with nef tangent bundle and picard number greater than n 5 we prove that fano n folds with nef tangent bundle and picard number greater than n 5 are rational homogeneous manifolds

on manifolds whose tangent bundle is big and 1 ample a line bundle over a complex projective variety is called big and 1 ample if a large multiple of it is generated by global sections and a morphism induced by the evaluation of the spanning sections is generically finite and has at most 1 dimensional fibers a vector bundle is called big and 1 ample if the relative hyperplane line bundle over its projectivisation is big and 1 ample the main theorem of the present paper asserts that any complex projective manifold of dimension 4 or more whose tangent bundle is big and 1 ample is equal either to a projective space or to a smooth quadric since big and 1 ample bundles are almost ample the present result is yet another extension of the celebrated mori paper projective manifolds with ample tangent bundles ann of math 110 1979 593 606 the proof of the theorem applies results about contractions of complex symplectic manifolds and of manifolds whose tangent bundles are numerically effective in the appendix we re prove these results

families of rationally connected varieties recall that a proper variety x is said to be rationally connected if two general points p q x are contained in the image of a map g p x this is clearly a birationally invariant property when x is smooth this turns out to be equivalent to the a priori weaker condition that two general points can be joined by a chain of rational curves and also to the a priori stronger condition that for any finite subset x there is a map g p x whose image contains and such that gtx is an ample bundle

explicit eigenvalue estimates for transfer operators acting on spaces of holomorphic functions abstract we consider transfer operators acting on spaces of holomorphic functions and provide explicit bounds for their eigenvalues more precisely if is any open set in c d and l is a suitable transfer operator acting on bergman space a 2 its eigenvalue sequence n l is bounded by n l a exp a n 1 d where a a 0 are explicitly given

iterated function systems and control languages valuations morphisms from e to 0 1 are a generalization of bernoulli morphisms introduced by eilenberg automata languages and machines academic press new york 1974 here we show how to generalize the notion of entropy of a language in order to obtain new formulas to determine the hausdorff dimension of fractal sets also in euclidean spaces especially defined via regular languages by doing this we can sharpen and generalize earlier results in two ways first we treat the case where the underlying basic iterated function system contains noncontractive mappings and second we obtain results valid for nonregular languages as well

conformal geometric and invariant measures for transcendental expanding functions we describe the fractal structure of expanding meromorphic maps of the form h circ exp circ q where h and q are rational functions whose most transparent examples are among the functions of the form frac a exp z p b exp z p c exp z p d exp z p with ad bc ne 0 in particular we show that depending upon whether the hausdorff dimension of the julia set is greater or less than 1 the finite non zero geometric measure is provided by the hausdorff or packing measure in order to describe this fractal structure we introduce and explore in detail walters expanding conformal maps and jump like conformal maps

nowhere differentiable hairs for entire maps devaney and krych ergod theory dyn syst 4 35 52 1984 showed that for the exponential family lambda e z where 0 lambda 1 e the julia set consists of uncountably many pairwise disjoint simple curves tending to infty which they called hairs viana proved that these hairs are smooth baranski as well as rottenfuser ruckert rempe and schleicher gave analogues of the result of devaney and krych for more general classes of functions in contrast to viana s result we construct in this article an entire function where the julia set consists of hairs which are nowhere differentiable

steady state analysis of the generalized sidelobe canceller by adaptive noise cancelling techniques narrow band adaptive noise cancelling techniques are used to study the generalized sidelobe canceller gsc a general form of linearly constrained adaptive beamforming structure in an environment which consists of a look direction signal one jammer and additive receiver noise exact expressions are derived for the wiener solution the steady state output signal to interference plus noise ratio sinr 0 and performance improvement due to adaptation pia defined as the ratio of sinr 0 after adaptation to sinr0 before adaptation these expressions are in terms of the signal directions and power levels an arbitrary array geometry and a general signal blocking matrix next easily evaluated scalar equations for pia are given for two classes of constraints the first is constant gain in the look direction and the second is constant gain plus a main beam zero first derivative in the look direction under the further assumption of an equally spaced line array even simpler equations for pia result and are used to show that for jammers arriving outside the heamwidth between first nulls bwfn region of the unadapted beampattern the introduction of the additional main beam zero first derivative constraint leads to negligible degradation in pia

on the performance of the generalized sidelobe canceller in coherent situations the convergence rate for the adaptive weights to reach the optimum value in an adaptive array system depends on the eigenvalue spread ratio of the autocovariance matrix how the eigenvalue spread ratio in a generalized sidelobe canceller gsc is affected by the various parameters is studied expressions for the output power of the gsc in coherent situations are derived and numerical results are included

the limited rademacher functions and bernoulli convolutions associated with pisot numbers abstract in this paper we give a systematical study of the local structures and fractal indices of the limited rademacher functions and bernoulli convolutions associated with pisot numbers for a given pisot number in the interval 1 2 we construct a finite family of non negative matrices maybe non square such that the corresponding fractal indices can be re expressed as some limits in terms of products of these non negative matrices we are especially interested in the case that the associated pisot number is a simple pisot number i e the unique positive root of the polynomial x k x k 1 x 1 k 2 3 in this case the corresponding products of matrices can be decomposed into the products of scalars based on which the precise formulas of fractal indices as well as the multifractal formalism are obtained

adaptive beamforming with conjugate symmetric weights the hermitian persymmetric maximum likelihood estimator mle is better than the conventional mle in estimating the covariance matrix of a symmetrically distributed antenna array though using the hermitian persymmetric mle improves the performance of adaptive beamforming it increases the computational load due to the forward backward averaging of array input sample data by observing that the weight vector obtained from the hermitian persymmetric mle is conjugate symmetric if the phase origin is chosen at the array geometry center methods are developed to reduce the computational load of the direct form beamformer and the generalized sidelobe canceler gsc the weights of both beamformers can be adapted with real computations with significant savings in computation time

random walks on homogeneous spaces and diophantine approximation on fractals we extend results of y benoist and j f quint concerning random walks on homogeneous spaces of simple lie groups to the case where the measure defining the random walk generates a semigroup which is not necessarily zariski dense but satisfies some expansion properties for the adjoint action using these dynamical results we study diophantine properties of typical points on some self similar fractals in mathbb r d as examples we show that for any self similar fractal mathcal k subseteq mathbb r d satisfying the open set condition for instance any translate or dilate of cantor s middle thirds set or of a koch snowflake almost every point with respect to the natural measure on mathcal k is not badly approximable furthermore almost every point on the fractal is of generic type which means in the one dimensional case that its continued fraction expansion contains all finite words with the frequencies predicted by the gauss measure we prove analogous results for matrix approximation and for the case of fractals defined by mobius transformations

the output sinr of the linearly constrained beamformer the authors derive expressions of the output signal to interference plus noise ratio sinr of the linearly constrained narrowband beamformer in noncoherent situations using a vector approach numerical results are included

dimensions and measures in infinite iterated function systems the hausdorff and packing measures and dimensions of the limit sets of iterated function systems generated by countable families of conformal contractions are investigated conformal measures for such systems reflecting geometric properties of the limit set are introduced proved to exist and to be unique the existence of a unique invariant probability equivalent to the conformal measure is derived our methods employ the concepts of the perron frobenius operator symbolic dynamics on a shift space with an infinite alphabet and the properties of the above mentioned ergodic invariant measure a formula for the hausdorff dimension of the limit set in terms of the pressure function is derived fractal phenomena not exhibited by finite systems are shown to appear in the infinite case in particular a variety of conditions are provided for hausdorff and packing measures to be positive or finite and a number of examples are described showing the appearance of various possible combinations for these quantities one example given special attention is the limit set associated to the complex continued fraction expansion in particular lower and upper estimates for its hausdorff dimension are given a large natural class of systems whose limit sets are dimensionless in the restricted sense is described

on euler jaczewski sequence and remmert van de ven problem for toric varieties let x be a complete toric variety and y a smooth projective variety with rho y 1 we prove that if varphi x to y is a surjective morphism then y simeq mathbb p n

constructing entire functions by quasiconformal folding we give a method for constructing transcendental entire functions with good control of both the singular values of f and the geometry of f among other applications we construct a function f with bounded singular set whose fatou set contains a wandering domain