global existence theory and chaos control of fractional differential equations in this paper the initial value problem for a class of fractional differential equations is discussed which generalizes the existent result to a wide class of fractional differential equations also the theoretical result established in the paper ensures the validity of chaos control of fractional differential equations in particular feed back control of chaotic fractional differential equation is theoretically investigated and the fractional lorenz system as a numerical example is further provided to verify the analytical result

multilevel codes based on partitioning following v v ginzburg 1984 a hierarchy of codes is proposed to match the geometric partitioning of a signal set the authors show that coset codes including ungerboeck lattice and binary codes and indeed any codes which rely on partitioning of the signal set are all subclasses of the proposed coding scheme the combination of such codes in a multilevel scheme often leads to reduced complexity in comparison with previously published schemes a variety of decoder structures is discussed

the poisson boundary of the mapping class group a theory of random walks on the mapping class group and its non elementary subgroups is developed we prove convergence of sample paths in the thurston compactification and show that the space of projective measured foliations with the corresponding harmonic measure can be identified with the poisson boundary of random walks the methods are based on an analysis of the asymptotic geometry of teichmuller space and of the contraction properties of the action of the mapping class group on the thurston boundary we prove in particular that teichmuller space is roughly isometric to a graph with uniformly bounded vertex degrees using our analysis of the mapping class group action on the thurston boundary we prove that no non elementary subgroup of the mapping class group can be a lattice in a higher rank semi simple lie group

on train track splitting sequences we present a structure theorem for the subsurface projections of train track splitting sequences for the proof we introduce induced tracks efficient position and wide curves as a consequence of the structure theorem we prove that train track sliding and splitting sequences give quasi geodesics in the train track graph this generalizes a result of hamenstadt

stationary measures for projective transformations the blackwell and furstenberg measures in this paper we study the blackwell and furstenberg measures which play an important role in information theory and the study of lyapunov exponents for the blackwell measure we determine parameter domains of singularity and give upper bounds for the hausdorff dimension for the furstenberg measure we establish absolute continuity for some parameter values our method is to analyze linear fractional iterated function schemes which are contracting on average have no separation properties that is we do not assume that the open set condition holds see hutchinson in indiana univ math j 30 713 747 1981 and in the case of the blackwell measure have place dependent probabilities in such a general setting even an effective upper bound on the dimension of the measure is difficult to achieve

a class of optimum block codes in signal space by using convolutional coding coupled with expanded sets of channel signals ungerboeck showed that it is possible to obtain coding gains of several decibels at a given data rate without increasing the transmission bandwidth in this paper we construct a class of optimum signal space codes using short binary block as opposed to convolutional codes our results are compared to those obtained by ungerboeck a simplified decoding procedure that is asymptotically optimum is also presented

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

ulam hyers stability of fractional langevin equations in this paper we discuss ulam hyers stability of nonlinear fractional langevin equations by using the boundedness monotonicity and nonnegative properties of classical and generalized mittag leffler functions further the same problem for the associated impulsive systems is investigated finally an example is given to illustrate our theoretical results

combination of bcm and tcm with 90 spl deg 180 spl deg and 270 spl deg phase rotational invariance two systematic schemes to combine block coded modulation bcm and trellis coded modulation tcm are proposed in the first scheme the signal points which are used in tcm should be partitioned by the proper bcm systems constructed by a multilevel construction method the asymptotic coding gain will be 6 02 3 01 n db where n is the length of the bcm systems since the average transmission power can be reduced by using a denser signal lattice the main idea of the second scheme is to construct the tcm system based on the signal points of a denser lattice formed by a proper bcm system hence we can get a higher coding gain which is a combination of both the distance gain of tcm and the density gain of bcm theoretically the net coding gain of this proposed scheme can reach 5 27 db in the case of an 8 d constellation and 7 15 db in the case of a 16 d constellation for practical implementation the phase ambiguity problems for both schemes are considered and solved by a differential encoder decoder

coset codes i introduction and geometrical classification practically all known good constructive coding techniques for bandlimited channels including lattice codes and various trellis coded modulation schemes can be characterized as coset codes a coset code is defined by a lattice partition lambda lambda and by a binary encoder c that selects a sequence of cosets of the lattice lambda the fundamental coding gain of a coset code as well as other important parameters such as the error coefficient the decoding complexity and the constellation expansion factor are purely geometric parameters determined by c lambda lambda the known types of coset codes as well as a number of new classes that systematize and generalize known codes are classified and compared in terms of these parameters

center stable manifold for planar fractional damped equations in this paper we discuss the existence of a center stable manifold for planar fractional damped equations by constructing a suitable lyapunovperron operator via giving asymptotic behavior of mittagleffler function we obtain an interesting center stable manifold theorem finally an example is provided to illustrate the result

smoothness and stability of the solutions for nonlinear fractional differential equations this paper first obtains the differentiability properties of the solutions for nonlinear fractional differential equations and then the sufficient conditions for the local asymptotical stability of nonlinear fractional differential equations are also derived

conditions for 90 degrees phase invariant block coded qam based on v a zinoviev s 1981 generalized concatenated codes conditions for the construction of 90 degrees phase invariant qam are derived furthermore a proposal for the necessary differential encoding decoding is made the conditions for phase invariance are specialized for the case of reed muller codes as outer codes of the generalized concatenation

exponential asymptotics of the mittag leffler function we consider the exponentially improved asymptotics of the mittag leffler function e a z and show how certain exponentially small terms make their appearance in the asymptotic expansion of e a z when z is large a new terminant function is introduced a generalized mittag leffler function e a b z and the stokes phenomenon in both arg z and the parameter a is examined

tight geodesics in the curve complex the curve graph mathcal g associated to a compact surface is the 1 skeleton of the curve complex defined by harvey masur and minsky showed that this graph is hyperbolic and defined the notion of a tight geodesic therein we prove some finiteness results for such geodesics for example we show that a slice of the union of tight geodesics between any pair of points has cardinality bounded purely in terms of the topological type of we deduce some consequences for the action of the mapping class group on mathcal g in particular we show that it satisfies an acylindricity condition and that the stable lengths of pseudoanosov elements are rational with bounded denominator

trellis coded modulation with multidimensional constellations trellis coded modulation schemes using four eight or 16 dimensional constellations have a number of potential advantages over the usual two dimensional schemes a smaller constituent two dimensional constellation easier tolerance to phase ambiguities and a better trade off between complexity and coding gain a number of such schemes are presented and evaluated starting with a variety of multidimensional lattices we show how to select multidimensional constellations how to partition them into subsets how to construct trellis codes using those subsets and how to map hits to constellation points simplifications of the viterbi decoding algorithm are presented we conclude that there are multidimensional trellis coded modulation schemes that perform better for the same complexity than do two dimensional schemes

trellis coding with multidimensional qam signal sets trellis coding using multidimensional quadrature amplitude modulation qam signal sets is investigated finite size 2d signal sets are presented that have minimum average energy are 90 degrees rotationally symmetric and have from 16 to 1024 points the best trellis codes using the finite 16 qam signal set with two four six and eight dimensions are found by computer search the multidimensional multi d signal set is constructed from the 2 d signal set the best moderate complexity trellis codes for infinite lattices with two four six and eight dimensions are also found the minimum free squared euclidean distance and number of nearest neighbors for these codes were used as the selection criteria many of the multi d codes are fully rotationally invariant and give asymptotic coding gains up to 6 0 db from the infinite lattice codes the best codes for transmitting j j 1 4 j 1 3 j 1 2 j 2 3 and j 3 4 b sym j an integer are presented

on multilevel block modulation codes the multilevel technique for combining block coding and modulation is investigated a general formulation is presented for multilevel modulation codes in terms of component codes with appropriate distance measures a specific method for constructing multilevel block modulation codes with interdependency among component codes is proposed given a multilevel block modulation code c with no interdependency among the binary component codes the proposed method gives a multilevel block modulation code c that has the same rate as c a minimum squared euclidean distance not less than that of c a trellis diagram with the same number of states as that of c and a smaller number of nearest neighbor codewords than that of c finally a technique is presented for analyzing the error performance of block modulation codes for an additive white gaussian noise awgn channel based on soft decision maximum likelihood decoding error probabilities of some specific codes are evaluated by simulation and upper bounds based on their euclidean weight distributions

exploring delayed mittag leffler type matrix functions to study finite time stability of fractional delay differential equations abstract in this paper we introduce a concept of delayed two parameters mittag leffler type matrix function which is an extension of the classical mittag leffler matrix function with the help of the delayed two parameters mittag leffler type matrix function we give an explicit formula of solutions to linear nonhomogeneous fractional delay differential equations via the variation of constants method in addition we prove the existence and uniqueness of solutions to nonlinear fractional delay differential equations thereafter we present finite time stability results of nonlinear fractional delay differential equations under mild conditions on nonlinear term finally an example is presented to illustrate the validity of the main theorems

new trellis codes based on lattices and cosets a new technique is proposed for constructing trellis codes which provides an alternative to ungerboeck s method of set partitioning the new codes use a signal constellation consisting of points from an n dimensional lattice lambda with an equal number of points from each coset of a sublattice lambda one part of the input stream drives a generalized convolutional code whose outputs are cosets of lambda while the other part selects points from these cosets several of the new codes are better than those previously known

on systems of linear fractional differential equations with constant coefficients abstract this paper deals with the study of linear systems of fractional differential equations such as the following system 1 y a x y b x where y is the riemann liouville or the caputo fractional derivative of order 0 2 a x a 11 x a 1 n x a n 1 x a nn x b x b 1 x b n x are matrices of known real functions in a way analogous to the usual case we show how a generalized matrix exponential function and certain fractional green function in connection with the mittag leffler type functions would allow us to obtain an explicit representation of the general solution to the system 1 when a is a constant matrix

harmonic measures for distributions with finite support on the mapping class group are singular kaimanovich and masur showed that a random walk on the mapping class group for an initial distribution whose support generates a nonelementary subgroup when projected into teichmuller space converges almost surely to a point in the space pmf of projective measured foliations on the surface this defines a harmonic measure on pmf here we show that when the initial distribution has finite support the corresponding harmonic measure is singular with respect to the natural lebesgue measure class on pmf

multilevel codes and multistage decoding h imai and s hirakawa have proposed 1977 a multilevel coding method based on binary block codes that admits a staged decoding procedure the author extends the coding method to coset codes and shows how to calculate minimum squared distance and path multiplicity in terms of the norms and multiplicities of the different cosets the multilevel structure allows the redundancy in the coset selection procedure to be allocated efficiently among the different levels it also allows the use of suboptimal multistage decoding procedures that have performance complexity advantages over maximum likelihood decoding

decay of correlations for the rauzy veech zorich induction map on the space of interval exchange transformations and the central limit theorem for the teichmuller flow on the moduli space of abelian differentials the aim of this paper is to prove a stretched exponential bound for the decay of correlations for the rauzy veech zorich induction map on the space of interval exchange transformations theorem 4 a corollary is the central limit theorem for the teichm ller flow on the moduli space of abelian differentials with prescribed singularities theorem 10 the proof of theorem 4 proceeds by the method of sinai 13 and bunimovich sinai 14 the induction map is approximated by a sequence of markov chains satisfying the doeblin condition the main loss of memory estimate is lemma 4

trellis coded multidimensional phase modulation a 2l dimensional multiple phase shift keyed l mpsk signal set is obtained by forming the cartesian product of l two dimensional mpsk signal sets a systematic approach to partitioning l mpsk signal sets that is based on block coding is used an encoder system approach is developed it incorporates the design of a differential precoder a systematic convolutional encoder and a signal set mapper trellis coded l 4psk l 8psk and l 16psk modulation schemes are found for 1

on stable manifolds for planar fractional differential equations in this paper we establish a local stable manifold theorem near a hyperbolic equilibrium point for planar fractional differential equations the construction of this stable manifold is based on the associated lyapunov perron operator an example is provided to illustrate the result