Inverses of finite group systems

In this work core/shell (polystyrene(PS)/polymethylmethacrylate (PMMA)) latexes and inverse latex systems (PMMA/PS) were prepared by two-step emulsion polymerization. In order to avoid complications when characterizing the structured latexes, monodisperse PS and PMMA latexes of various diameters were prepared by seeded emulsion polymerization and used as core systems. In the second-step polymerization the formation of a new crop of latexes is avoided by the controlled level level of surfactant and initiator. For the characterization of the core, core/shell, and inverse system various experimental methods were used, e.g., electronmicroscopy (TEM, thin-sectioning, shadowcasting, SEM) [1], small-angle x-ray scattering (SAXS) [2,3], ultracentrifugation (UC), soap titration [1] and measurement of densities and refractive indexes. From the shadow-casting a very characteristic behavior of PMMA phase could be observed, and this was used for the determination of surface polymer phase of structured latex particles [1]. All these experimental results showed that the given system PS/PMMA exhibits the assumed core/shell structure. [1, 2] However, in the inverse system PMMA/PS more complicated, heterogeneous structures were observed [1], e.g., depending upon the addition method of the second monomer and particle size of the core.

Čech systems that induce approximate inverse systems

Inverse systems of linear systemsThe concept of inverse systems for standard and positive linear systems is introduced. Necessary and sufficient conditions for the existence of the positive inverse system for continuous-time and discrete-time linear systems are established. It is shown that: 1) The inverse system of continuous-time linear system is asymptotically stable if and only if the standard system is asymptotically stable. 2) The inverse system of discrete-time linear system is asymptotically stable if and only if the standard system is unstable. 3) The inverse system of continuous-time and discrete-time linear systems are reachable if and only if the standard systems are reachable. The considerations are illustrated by numerical examples.

There is a long tradition in placing I above YOU in linguistics and grammar. In our Western grammatical terminology, I is the “first person”. In the universal scale of agentivity, or “universal person hierarchy”, I is placed before YOU. The goal of this paper is to examine the proof for ordering I and YOU in such a fashion. The universal character of local person marking in human languages, and existing proposals concerning the person hierarchy are reviewed. The kind of grammatical phenomena governed by the so-called “universal hierarchy”: split ergativity, inverse systems, and pronominal marking, are discussed. First, we show that there are languages whose grammatical phenomena are governed by the other order, with YOU above I. Looking for the possibility that two person hierarchies share room within world languages, we then turn to the facts that support placing I above YOU, and demonstrate that this proof is non-existent. The egocentric perspective belongs to linguistics, and to certain habits of a Western school of thought, not to natural languages. The data examined here also shows that there are no languages where split ergativity or the inverse system would operate from a hierarchy placing 3rd persons above 2nd or 1st , thus confirming a 2, 1>3 hierarchy. As far as a hierarchy between singular persons or Speech Acts participants is concerned, the one for which there is clear evidence is the one where YOU outranks I: 2>I.

The LQ linear-quadratic problem of multiple-valued time-invariant discrete singular systems is discussed. The equivalence relation between this problem and that of standard state-space systems is given via an artificial feedback approach under some conditions, and the existence and uniqueness of the optimal control-trajectory pair are obtained. The state feedback synthesis of the optimal control is also derived, and the optimal closed-loop system is single-valued and asymptotically stable. >

The enhanced power graph [Formula: see text] of a group [Formula: see text] is the graph with vertex set [Formula: see text] such that two vertices [Formula: see text] and [Formula: see text] are adjacent if they are contained in the same cyclic subgroup. We prove that finite groups with isomorphic enhanced power graphs have isomorphic directed power graphs. We show that any isomorphism between undirected power graph of finite groups is an isomorphism between enhanced power graphs of these groups, and we find all finite groups [Formula: see text] for which [Formula: see text] is abelian, all finite groups [Formula: see text] with [Formula: see text] being prime power, and all finite groups [Formula: see text] with [Formula: see text] being square-free. Also, we describe enhanced power graphs of finite abelian groups. Finally, we give a characterization of finite nilpotent groups whose enhanced power graphs are perfect, and we present a sufficient condition for a finite group to have weakly perfect enhanced power graph.

A Study on the Minimal-Time Control Problem of a Quantized Linear Discrete System with Rational Coefficients

A method of synthesis and decomposition of autonomous linear sequential circuits

The concepts of inverse and left inverse systems, weakly equivalent and strongly equivalent systems, and discretetime and finite memory systems are examined. Various relations between these concepts are found, and the role of the decomposition property of the system input-output state relation is investigated. Among the results obtained are 1) under suitable controllability assumptions, left inverse systems are inverse systems, 2) weakly equivalent finite memory systems with the decomposition property are strongly equivalent, and 3) finite-state systems with the decomposition property have finite memory.

In general, designing Gain-Scheduled (GS) controllers for Linear Parameter-Varying (LPV) systems using Parameter-Dependent Lyapunov Functions (PDLFs) yields controllers that depend on the derivatives of parameters. This makes their implementation impractical because ideal parameter derivatives are not available in the real world. In contrast to this, for open-loop system design, such as filter design and inverse system design, we propose a GS controller design method using PDLFs that gives controllers which do not depend on parameter derivatives. Although the proposed method uses structured PDLFs, we show that it is as conservative as existing methods. Numerical examples of designing GS filters and GS right inverse systems for LPV systems are included to demonstrate our conclusion.

Rigid body dynamics are traditionally formulated by Lagrangian or Newton-Euler methods. A particular state space form using Euler angles and angular velocities expressed in the body coordinate system is employed here to address constrained rigid body dynamics. We study gliding and rolling, and we develop inverse systems for estimation of internal and contact forces of constraint. A primitive approximation of biped locomotion serves as a motivation for this work. A class of constraints is formulated in this state space. Rolling and gliding are common in contact sports, in interaction of humans and robots with their environment where one surface makes contact with another surface, and at skeletal joints in living systems. This formulation of constraints is important for control purposes. The estimation of applied and constraint forces and torques at the joints of natural and robotic systems is a challenge. Direct and indirect measurement methods involving a combination of kinematic data and computation are discussed. The basic methodology is developed for one single rigid body for simplicity, brevity, and precision. Computer simulations are presented to demonstrate the feasibility and effectiveness of the approaches presented. The methodology can be applied to a multilink model of bipedal systems where natural and/or artificial connectors and actuators are modeled. Estimation of the forces is accomplished by the inverse of the nonlinear plant designed by using a robust high gain feedback system. The inverse is shown to be stable, and bounds on the tracking error are developed. Lyapunov stability methods are used to establish global stability of the inverse system.

In this note, we briefly introduce the theory of fusion systems and some recent progress. Fusion systems were introduced by Puig in the early 1990s as a common framework for fusion systems of finite groups or $p$-blocks of finite groups. Fusion systems are also very important in algebraic topology, the long-open conjecture by Martino and Priddy is thus solved. In recent two decades the theory develops very quickly with deep applications. A simplified proof of the classification theorem of finite simple groups is highly expected.

We show that the class of groups which have monoid presentations by means of finite special [λ]-confluent string-rewriting systems strictly contains the class of plain groups (the groups which are free products of a finitely generated free group and finitely many finite groups), and that any group which has an infinite cyclic central subgroup can be presented by such a string-rewriting system if and only if it is the direct product of an infinite cyclic group and a finite cyclic group.

The present article devotes to the study of linear time invariant discrete fractional order state space systems using a novel approach. First, we replace the conventional Grünwald-Letnikov-type backward difference operator with the equivalent Riemann-Liouville-type nabla difference operator and obtain the system response using variation of constants and discrete Laplace transform methods. Next, we present three different algorithms to construct state transition matrix of the system. Finally, we provide an example to illustrate the applicability of established result.

On the controllability of a class of discrete bilinear systems