Galois self-dual constacyclic codes

On the ℓ-DLIPs of codes over finite commutative rings

General type-2 fuzzy logic systems (T2 FLS) constitute a powerful tool for coping with ubiquitous uncertainty in many engineering applications. However, the immense computational complexity associated with defuzzification of general T2 fuzzy sets still remains an unresolved issue and prohibits its practical use. This paper proposes a novel importance sampling based defuzzification method for general T2 FLS. Here, a subset from the domain of all embedded fuzzy sets is randomly sampled using a specific probability distribution function. The algorithm is compared with the previously published uniform sampling defuzzification method. Experimental results demonstrate that importance sampling substantially reduces the variance of the sampling defuzzification method. Comparison of T2FLS output surfaces showed that smoother and more stable response can be achieved with the proposed importance sampling based defuzzification method.

If the feasible set of non-convex optimization satisfies quasi-normal cone condition (QNCC) and under the hypothesis that a quasi-normal cone has been constructed, non-convex optimizations can be solved, theoretically, by the method of Homotopy Interior Point (HIP) Method with global convergence. But how to construct the quasi-normal cone for a general non-convex set is very difficult and there is no uniform and efficient method to do it. In this paper, we give a method to construct a quasi-normal cone for a class of sets satisfying QNCC, and realize HIP method algorithms under it. And we prove it is available by the numerical example at the same time.

It has proved that non-convex optimization with the feasible set satisfying quasi-normal cone condition (QNCC) can be solved by the method of Homotopy Interior Point (HIP) Method with global convergence under the hypothesis that a quasi-normal cone has been constructed. But how to construct the quasi-normal cone for a general non-convex set is very difficult and there is no uniform and efficient method to do it. In this paper, we give a method to construct a quasi-normal cone for a class of sets satisfying QNCC, and construct HIP function and realize the HIP method algorithms. And we prove it is available by the numerical example at the same time.

We introduce and study column cyclic rank metric (CCRM) codes over finite fields. We present natural questions for the existence and characterization of CCRM codes. We completely solve these questions only in the first nontrivial case: The case of the minimum rank distance [Formula: see text] and the number of rows [Formula: see text]. We also consider linear complementary dual rank metric (LCDRM) codes both in the setting of CCRM codes and in the general setting of rank metric codes. We also ask the natural questions for the existence and characterization of CCRM codes in the subclass of LCDRM codes. We also completely solve these questions for this subclass of LCDRM codes only in the first nontrivial case that [Formula: see text] and [Formula: see text]. Moreover we extend a characterization of linear complementary dual (LCD) codes of Massey to arbitrary rank metric codes in the general setting.

Analysis and design of gain scheduled sampled-data control systems

Necessary and sufficient conditions for the existence of diagonal, block-diagonal, and triangular decoupling controllers in linear multivariable systems for the most general setting are presented. The plant model in this study is sufficiently general to accommodate non-square plant and non-unity feedback cases with one-degree-of-freedom (1DOF) or two-degree-of-freedom (2DOF) controller configuration. The existence condition is described in terms of rank conditions on the coefficient matrices in partial fraction expansions.

Necessary and sufficient conditions for the existence of diagonal, block-diagonal and triangular decoupling controllers in linear multivariable systems are presented for the most general setting. The plant model in this paper is general enough to accommodate non-square plant and non-unity feedback cases with 1DOF (one-degree-of-freedom) or 2DOF controller configuration. It is shown that the existence condition is finally described in terms of rank conditions on coefficient matrices in partial fraction expansion.

A diagonal decoupling problem in linear multi-variable systems is formulated for the most general setting. A necessary and sufficient condition for the existence of a decoupling controller is presented and, when a solution exists, the class of all decoupling controllers is characterized in terms of free parameters of stable rational vectors.

We show in a rather general setting that Hoelder and Lipschitz stability properties ofsolutions to variational problems can be characterized by convergence of more or less abstract iteration schemes. Depending on the principle of convergence, new and intrinsic stability conditions can be derived. Our most abstract models are (multi-) functions on complete metric spaces. The relevance of this approach is illustrated by deriving bothclassical and new results on existence and optimality conditions, stability of feasible and solution sets and convergence behavior ofsolution procedures.

Recent advances in DFT codes based quantized frame expansions for erasure channels

A unified treatment is given of the class of low-frequency P–SV modes whose complex phase velocities do not approach zero as fast as the frequency when the frequency is decreased toward zero. Utilizing the analyticity of the dispersion function, a complete characterization is given of these modes and the linearly viscoelastic fluid–solid media in which they occur. The two Lamb plate modes and the classical interface waves (Rayleigh, Scholte, Stoneley) all appear in a general setting, and asymptotic low-frequency expressions are given for modal slownesses and mode forms. The corresponding phase velocities will either tend to a nonzero constant or approach zero like the square root of frequency. In addition, slow modes appear whose phase velocities approach zero like three other powers of frequency: 1/3, 3/5, and 2/3. Concerning 1/3, a correction is made to a paper by Ferrazzini and Aki; 3/5 and 2/3 appear for certain bending-type waves that are slower than the classical bending wave. A less known type of interface wave also emerges from the analysis, and precise conditions for existence and uniqueness are obtained. The results are extended to interface conditions with slip. In an extreme case, yet another kind of interface wave is obtained.

The aim of this paper is to deal with the general decoupling problem of linear constant ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A, B, C, D</tex> )-quadruples under the assumption of (regular) output feedback. In its most general setting, this problem was hitherto unsolved. Here we give a complete characterization of solutions by (regular) output feedback by means of necessary and sufficient conditions of existence. They generalize the result previously obtained by Denham [4] for the linear constant ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A, B, C</tex> )-triples.

The problem of clustering a sample set on the basis of a fuzzy resemblance structure is considered. A rigorous mathematical theory is developed for general (i.e., non-necessary finite) sample sets in order to allow for future studies of an statistical nature relating the classification of a general set with that of its finite samples. The theory is presented in two major steps. The first step deals with the formalization of the concept of cluster. Unlike previous approaches which defined clusters as the fuzzy sets obtained as a result of the application of an algorithmic procedure (frequently based on an optimization goal) to the sample set, in this work clusters are characterized as fuzzy subsets which must satisfy certain conditions (independent of the classification goals being pursued) in order to qualify as potential taxonomical elements. The qualifying conditions are expressed as fuzzy relational equations derived extending simple relational equations in the conventional set domain. The problems in making such transition are discussed. Conditions for existence of fuzzy classifications are derived in terms of a class of fuzzy resemblance relations, called relations. These conditions are shown to be much less restrictive than the corresponding conditions for the conventional case. In addition, the resulting cluster families provide richer representations of the underlying taxonomical structures. The problem of likeness relation derivation is analyzed from several viewpoints. The second step in this theoretical development deals with the problem of optimal representation of a sample set as a union of clusters. Using again the procedure of extending conventional set formulations, it is shown that approaches based on the minimization of functionals defined over all possible cluster representations, which satisfy certain desirable properties, must necessarily optimize one member of a uniparametric functional family. It is also shown that the extension of conventional concepts to the fuzzy domain provides a generalization of the concept of a number of clusters (which is no longer required to be an integer) and of prototype element of a cluster.

We give a simplified definition of topological T-duality that applies to arbitrary torus bundles. The new definition does not involve Chern classes or spectral sequences, only gerbes and morphisms between them. All the familiar topological conditions for T-duals are shown to follow. We determine necessary and sufficient conditions for existence of a T-dual in the case of affine torus bundles. This is general enough to include all principal torus bundles as well as torus bundles with arbitrary monodromy representations. We show that isomorphisms in twisted cohomology, twisted K-theory and of Courant algebroids persist in this general setting. We also give an example where twisted K-theory groups can be computed by iterating T-duality.