a new asymptotically optimal code for the positive integers a new universal binary code for the positive integers is proposed as a modified version of m wang s see ibid vol 34 p 324 6 mar 1988 flag encoding scheme the codeword length of the new scheme is shorter than wang s on an average for large initial segments of the positive integers the performance of the new scheme is also compared with that of other universal schemes furthermore it is shown that an asymptotically optimal code can be achieved by modifying the new flag scheme such that the flag length varies dynamically

almost asymptotically optimal flag encoding of the integers a simple prefix free encoding scheme for the positive integers is proposed in which a flag of f zeros is used to mark the end of a codeword and bit stuffing is used to prevent premature appearance of the flag in the conventional binary coding of the integers it is shown that this coding scheme is universal in the sense defined by p elias 1975 and that for large f its asymptotic efficiency is virtually 1

meta fibonacci codes efficient universal coding of natural numbers in this paper we address the problem of the universal coding of natural numbers a new numeration system is introduced which is based on variable r meta fibonacci sequences and it is a generalization of the zeckendorf numeration system this new numeration system is used to construct binary prefix free uniquely decodable universal codes called meta fibonacci codes the main advantage of these codes is that they are parametrized by a sequence of numbers the sequence o by controlling the growth of the values of this sequence we can control the length of the code word this means that we can provide a general framework for building efficient universal coders for natural numbers such framework is applied to the upper bounds of the code word length defined by leung yan cheong and cover 1978 levenshtein 1968 and ahlswede 1997 there is no other code meeting these bounds in each case we build meta fibonacci codes and demonstrate that the upper bound of their code word length is satisfied up to an additive constant thereby solving these open problems the framework may be applied to other upper bounds that satisfy kraft inequality

state feedback impulse elimination of linear time varying singular systems abstract linear time varying singular systems e t x a t x b t u are treated a necessary and sufficient condition for the existence of linear state feedback to eliminate impulsive behavior is derived the condition obtained is a natural extension of existing time invariant theory

a universal prior for integers and estimation by minimum description length of the number of bits required to write down the observed data has been reformulated to extend the classical maximum likelihood principle the principle permits estimation of the number of the parameters in statistical models in addition to their values and even of the way the parameters appear in the models i e of the model structures the principle rests on a new way to interpret and construct a universal prior distribution for the integers which makes sense even when the parameter is an individual object truncated realvalued parameters are converted to integers by dividing them by their precision and their prior is determined from the universal prior for the integers by optimizing the precision 1 introduction in this paper we study estimation based upon the principle of minimizing the total number of binary digits required to rewrite the observed data when each observation is given with some precision instead of attempting at an absolutely shortest description which would be futile we look for the optimum relative to a class of parametrically given distributions this minimum description length mdl principle which we introduced in a less comprehensive form in 25 turns out to degenerate to the more familiar maximum likelihood ml principle in case the number of parameters in the models is fixed so that the description length of the parameters themselves can be ignored in another extreme case where the parameters determine the data it similarly degenerates to jaynes s principle of maximum entropy 14 but the main power of the new criterion is that it permits estimates of the entire model its parameters their number and even the way the parameters appear in the model i e the model structure hence there will be no need to supplement the estimated parameters with a separate hypothesis test to decide whether a model is adequately parameterized or perhaps over parameterized

disturbance decoupling of linear time varying singular systems the problem of disturbance decoupling by state feedback is defined for a linear time varying singular system it is required that the closed loop system has a unique impulse free solution and its output is not affected by disturbances an algorithm namely disturbance decoupling algorithm is proposed it is proved that the feasibility of the disturbance decoupling algorithm is invariant under any regular feedback control law based on the disturbance algorithm a constructive method is provided to design a disturbance decoupling feedback control law sufficient conditions for the solvability of the disturbance decoupling problem are derived it is proved that one of the sufficient conditions is also necessary provided that other conditions are satisfied

input output block decoupling of linear time varying singular systems the input output block decoupling problem by state feedback is studied for linear time varying singular systems first an algorithm the regularization algorithm is developed such that the system can be made by state feedback to have a unique impulse free solution second another algorithm the block decoupling algorithm is proposed which provides sufficient conditions for the solvability of the input output block decoupling problem then a decoupling feedback law is constructed such that the corresponding closed loop system is regular impulse free and noninteractive finally an example is given to illustrate the applicability of the algorithms

disturbance decoupling for descriptor systems by state feedback we study the disturbance decoupling problem for linear time invariant descriptor systems we give necessary and sufficient conditions for the existence of a solution to the disturbance decoupling problem with or without stability via a proportional and or derivative feedback that also makes the resulting closed loop system regular and or of index at most one all results are proved constructively based on condensed forms that can be computed using orthogonal matrix transformations i e transformations that can be implemented in a numerically stable way

periodic and non concurrent error detection and identification in one hot encoded fsms state transition faults in digital sequential systems such as finite state logic controllers have traditionally been handled by embedding the given system into a larger one in a way that preserves the state evolution of the original system while enabling an external mechanism to concurrently perform checks to detect identify and correct errors in this paper we develop a methodology for systematically constructing embeddings of one hot encoded finite state machines fsms in a way that allows the external mechanism to capture transient state transition faults via checks that are performed in a non concurrent manner e g periodically more specifically by employing coding techniques over finite fields we completely characterize an appropriate class of redundant fsm embeddings and its corresponding non concurrent error detecting identifying capabilities these embeddings can be used to construct a redundant version of the given one hot encoded fsm so that the external mechanism can detect and identify errors due to past state transition faults based on an analysis of the current possibly corrupted fsm state as a result the proposed error detection and identification approach relaxes the stringent requirements on the reliability of the checker and avoids the slowdown associated with concurrent checking

the disturbance decoupling problem for implicit linear discrete time systems the disturbance decoupling problem for implicit linear discrete time systems is studied in detail necessary and sufficient conditions for the problem to be solved are given the results are obtained with the aid of the concepts of almost invariant sliding and coasting subspaces for implicit systems

regular universal codeword sets corresp proof is given that no regular or synchronizable universal codeword sets can achieve optimality some asymptotic properties of a remarkable class of regular codeword sets related to the fibonacci representation of integers are also obtained

non complex representations and their relation to antiunitary symmetry equivalent eigenvalue problems in real complex and quaternionic hilbert spaces are discussed in all cases a compact symmetry group is assumed to exist in the complex case also an antiunitary operator commuting with both the self adjoint operator and the elements of the symmetry group and satisfying 2 1 it is shown that the extra degeneracies caused by the existence of can also be obtained by consideration of an equivalent eigenvalue problem in a noncomplex hilbert space

on universal codeword sets the set of all binary strings terminated by a specific pattern is countably infinite and regular and satisfies the prefix property some properties of such codeword sets in the context of source coding are studied it is shown that some of them are universal and some of them are not but none is asymptotically optimal

type adapted subduction matrices if an irreducible representation is restricted to a subgroup it becomes reducible in general the matrices transforming this reducible representation into a direct sum of irreducible constituents are called subduction matrices their structure is discussed for real complex and quaternionic representations where all these representations are assumed to show a peculiar structure characteristic for the type of this representation character test 0 the choice of these type adapted representations a convention possible for all compact groups considerably reduces the number of parameters needed to fix a subduction matrix

comments and additions to robust transmission of unbounded strings using fibonacci representations an ambiguous point in the paper by apostolico and fraenkel see ibid vol it 33 no 2 p 238 45 march 1987 is clarified new codes that have better asymptotic performances and better synchronization capability are introduced

type adapted representations of semidirect product groups irreducible representations of compact groups can be partitioned into three classes character test 0 this classification is the same for real complex and quaternionic representations and in all three cases a peculiar type adapted form of the representation matrices may be chosen t reps in this paper it is shown how to construct t reps of semidirect products g s g starting with t reps of g and t reps of some covering groups of subgroups of g the advantage of using t reps shows up in that the factor system of the little cogroups is real in two of three cases and that real complex and quaternionic representations are obtained simultaneously the method is specialized to direct products and generalized to induction from normal subgroups

a solution to the disturbance decoupling problem in singular systems via analogy with state space systems abstract this paper presents an approach for solving the disturbance decoupling problem in a square linear time invariant singular system a simple criterion and an efficient algorithm for solving the underlying problem by applying a state feedback which preserves the uniqueness property of the closed loop singular system has been established the present algorithm is based on a well established approach borrowed from state space system theory

on disturbance decoupling in descriptor systems the disturbance decoupling problem for a linear multivariable control system is to determine when and how a state feedback may be chosen so that some class of disturbances has no effect on the system output the development of necessary and sufficient conditions for the solvability of this problem for state space systems by wonham and his co workers has profoundly influenced geometric control theory particularly by means of the concept of an a b invariant subspace this paper develops necessary and sufficient conditions for solvability of this problem for linear systems described by a mixture of algebraic and differential equations although the argument presented has the same structure as in the state space case and incorporates a generalisation of a b invariant subspaces to descriptor systems there are some additional issues demanding particularly careful attention is the ensuring of existence and uniqueness of classical solutions of the underlying differential equations which cannot be tak

representation theory of compact groups over fields of characteristic zero the group algebras over the reals the complex numbers and the quaternions are discussed and compared for a fixed compact group special emphasis is put on the properties of ring bases of the minimal two sided ideals and their relation to the matrix representation of the group irreducible over the fields cited above

disturbance rejection of left invertible generalized state space systems a new approach is presented for the study of the disturbance rejection of left invertible generalized state space systems via pure proportional state feedback reducing the problem to that of solving a linear algebraic system of equations on the basis of this system of equations the necessary and sufficient conditions for the problem to have a solution are established in a form of simple algebraic criteria thus reducing the computational effort over known results and the general analytical expressions of the controller matrices are derived the structural properties of the closed loop system feedback invariant poles disturbance rejection with simultaneous elimination of the infinite poles are studied

robust transmission of unbounded strings using fibonacci representations families of fibonacci codes and fibonacci representations are defined their main attributes are robustness manifesting itself by the local containment of errors and simple encoding and decoding the main application explored is the transmission of binary strings in which the length is in an unknown range using robust fibonacci representations instead of the conventional error sensitive logarithmic ramp representation though the former is asymptotically longer than the latter the former is actually shorter for very large initial segments of integers

determination of the symmetries characterising separable systems in euclidean spaces the additively separable coordinate systems for the hamilton jacobi equation of classical mechanics in n dimensional complex euclidean space cn are characterised explicitly in terms of the lie symmetry algebra of cn specifically a formula is given by which the n separation constants regarded as functions of position and momentum can be expressed as members of the enveloping algebra of cn i e as elements of the vector space spanned by products of the members of the lie algebra of cn by quantising these n integrals of the motion the author easily obtains the commuting sets of n partial differential operators characterising the multiplicatively separable systems for the corresponding helmholtz equation a package including this formula has been implemented in the symbolic language macsyma the resulting program is also capable of calculating many of the time consuming details separation equations etc of separation on cn

a new recursive universal code of the positive integers a new recursive universal code of the positive integers is proposed in which any given sequence can be used as a delimiter of codeword while bit 0 is used as a delimiter in known universal codes e g levenshtein code elias spl omega code even rodeh code stout code bentley yao code etc the codeword length of the proposed code is shorter than log sub 2 sup n n in almost all of sufficiently large positive integers although the known codes are longer than log sub 2 sup n n for any positive integer n

optimal sinusoidal disturbances damping for singularly perturbed systems with time delay abstract this paper considers an optimal damping vibration control problem for linear time delay singularly perturbed systems affected by external sinusoidal disturbances by using the slow fast decomposition theory of singularly perturbed systems the system is first decomposed into a fast subsystem without time delay and a slow subsystem with time delay affected by external sinusoidal disturbances then the successive approximation approach saa and the feedforward compensation techniques are proposed to solve the slow time scale time delay optimal control problem and damp the external sinusoidal disturbances respectively the conditions of existence and uniqueness of the finite and infinite horizon feedforward and feedback composite control ffcc laws are presented and the design approaches are given the ffcc laws consist of nondelay feedback terms disturbances compensation terms and a time delay compensation term which is the limit of the solution sequence of the adjoint vector equations simulation examples indicate that the saa is valid and the ffcc laws are easy to implement and more effective with respect to damping the external sinusoidal disturbances than that of the classical feedback composite control fcc laws