Distributed Minimum-Energy Containment Control of Continuous-Time Multi-Agent Systems by Inverse Optimal Control

Dear Editor,This letter focuses on the distributed optimal containment control of continuous-time multi-agent systems(CTMASs)with respect to the minimum-energy performance index over fixed topology.To achieve this,we firstly investigate the optimal containment control problem using the inverse optimal control method,where all states of followers asymptotically converge to the convex hull spanned by the leaders while some quadratic performance indexes get minimized.A sufficient condition for existence of the distributed optimal containment control protocol is derived.By introducing the parametric algebraic Riccati equation(PARE),it is strictly proved that the global performance index can be used to approximate the standard minimumenergy performance index as the parameters tends to infinity.In consequence,the standard minimum-energy cooperative containment control can be solved by local steady state feedback protocols.

Characterizations of semihoops based on derivations

In this paper,we discuss the related properties of some particular derivations in semihoops and give some characterizations of them.Then,we prove that every Heyting algebra is isomorphic to the algebra of all multiplicative derivations and show that every Boolean algebra is isomorphic to the algebra of all implicative derivations.Finally,we show that the sets of multiplicative and implicative derivations on bounded regular idempotent semihoops are in oneto-one correspondence.

AGGREGATE SPECIAL FUNCTIONS TO APPROXIMATE PERMUTING TRI-HOMOMORPHISMS AND PERMUTING TRI-DERIVATIONS ASSOCIATED WITH A TRI-ADDITIVEψ-FUNCTIONAL INEQUALITY IN BANACH ALGEBRAS

In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.

Groupoid Approach to Ergodic Dynamical System of Commutative von Neumann Algebra

Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bounded functions L∞(X, μ) on X. We confirm that the commutative von Neumann algebras M⊂B(H), with H=L2(X, μ), are unitary equivariant to the maximal ideals of the commutative algebra C(X). Subsequenly, we use the measure groupoid to formulate the algebraic and topological structures of the commutative algebra C(X) following its action on M(X) and define its representation and ergodic dynamical system on the commutative von Neumann algebras of M of B(H) .

Exploring the Implications of the Deformation Parameter and Minimal Length in the Generalized Uncertainty Principle

The breakdown of the Heisenberg Uncertainty Principle occurs when energies approach the Planck scale, and the corresponding Schwarzschild radius becomes similar to the Compton wavelength. Both of these quantities are approximately equal to the Planck length. In this context, we have introduced a model that utilizes a combination of Schwarzschild’s radius and Compton length to quantify the gravitational length of an object. This model has provided a novel perspective in generalizing the uncertainty principle. Furthermore, it has elucidated the significance of the deforming linear parameter β and its range of variation from unity to its maximum value.

Relationship of Edge States to Anomaly and Construction of Dual Systems in Quantum Hall Systems

The hierarchy of bulk actions is developed which are associated with Chern-Simons theories. The connection between the bulk and edge arising from the requirement there is a cancelation of an anomaly which arises in the theory. A duality transformation is studied for the Chern-Simons example. The idea that is used has been employed to describe duality in a scalar theory. The link between the edge theory with the Chern-Simons theory in the bulk then suggests that similar transformations can be implemented in the bulk Chern-Simons theory as well.

Quantum Computingvia Entanglement in Geometric Algebra Approach

The superiority of hypothetical quantum computers is not due to faster calculations but due to different scheme of calculations running on special hardware. At the same time, one should realize that quantum computers would only provide dramatic speedups for a few specific problems, for example, factoring integers and breaking cryptographic codes in the conventional quantum computing approach. The core of quantum computing follows the way a state of a quantum system is defined when basic things interact with each other. In the conventional approach, it is implemented through the tensor product of qubits. In the suggested geometric algebra formalism simultaneous availability of all the results for non-measured observables is based on the definition of states as points on a three-dimensional sphere, which is very different from the usual Hilbert space scheme.

An Eighth Order A-Stable Rational Integrator

In this work we derived and analyzed the stability structure of an order eight rational integrator wherein our numerator and denominator is 4 (i.e. m = n = 4) for the solution of problems in ordinary differential equations. The integrator was observed to be A-stable and also L-stable.

On Some Properties of Graph of Prefix Code

We investigate decomposition of codes and finite languages. A prime decomposition is a decomposition of a code or languages into a concatenation of nontrivial prime codes or languages. A code is prime if it cannot be decomposed into at least two nontrivial codes as the same for the languages. In the paper, a linear time algorithm is designed, which finds the prime decomposition. If codes or finite languages are presented as given by its minimal deterministic automaton, then from the point of view of abstract algebra and graph theory, this automaton has special properties. The study was conducted using system for computational Discrete Algebra GAP. .

ORDER RESULTS FOR ALGEBRAICALLY STABLEMONO-IMPLICIT RUNGE-KUTTA METHODS

It is well known that mono-implicit Runge-Kutta methods have been applied in the efficient numerical solution of initial or boundary value problems of ordinary differential equations. Burrage (1994) has shown that the order of an s-stage monoimplicit Runge-Kutta method is at most s+1 and the stage order is at most 3. In this paper, it is shown that the order of an s-stage mono-implicit Runge-Kutta method being algebraically stable is at most min((s) over tilde, 4), and the stage order together with the optimal B-convergence order is at most min(s, 2), where [GRAPHICS]

An Introduction to the Theory of Field Extensions

This paper unfolds and reviews the theory of abstract algebra, field extensions and discusses various kinds of field extensions. Field extensions are said to be algebraic or transcendental. We pay much attention to algebraic extensions. Finally, we construct finite extensions of Q and finite extensions of the function field over finite field Fp using the notion of field completion, analogous to field extensions. With the study of field extensions, considering any polynomial with coefficients in the field, we can find the roots of the polynomial, and with the notion of algebraically closed fields, we have one field, F, where we can find the roots of any polynomial with coefficients in F.

REAL PALEY-WIENER THEOREMS FOR THE SPACE-TIME FOURIER TRANSFORM

This paper presents an extension of certain forms of the real Paley-Wiener theorems to the Minkowski space-time algebra. Our emphasis is dedicated to determining the space-time valued functions whose space-time Fourier transforms(SFT) have compact support using the partial derivatives operator and the Dirac operator of higher order.

Some results on derivations of MV-algebras

In this paper, we review some of their related properties of derivations on MValgebras and give some characterizations of additive derivations. Then we prove that the fixed point set of Boolean additive derivations and that of their adjoint derivations are isomorphic.In particular, we prove that every MV-algebra is isomorphic to the direct product of the fixed point set of Boolean additive derivations and that of their adjoint derivations. Finally we show that every Boolean algebra is isomorphic to the algebra of all Boolean additive(implicative)derivations. These results also give the negative answers to two open problems, which were proposed in [Fuzzy Sets and Systems, 303(2016), 97-113] and [Information Sciences, 178(2008),307-316].

Algebraic Properties for Molecular Structure of Magnesium Iodide

As an inorganic chemical,magnesium iodide has a significant crystalline structure.It is a complex and multifunctional substance that has the potential to be used in a wide range of medical advancements.Molecular graph theory,on the other hand,provides a sufficient and cost-effective method of investigating chemical structures and networks.M-polynomial is a relatively new method for studying chemical networks and structures in molecular graph theory.It displays numerical descriptors in algebraic form and highlights molecular features in the form of a polynomial function.We present a polynomials display of magnesium iodide structure and calculate several M-polynomials in this paper,particularly the M-polynomials of the augmented Zagreb index,inverse sum index,hyper Zagreb index and for the symmetric division index.

Norm-Based Adaptive Coefficient ZNN for Solving the Time-Dependent Algebraic Riccati Equation

Dear Editor, The time-dependent algebraic Riccati equation(TDARE) problem is applied to many optimal control industrial applications. It is susceptible to interference from measurement noises in the virtual environment, which current methods cannot effectively address. A normbased adaptive coefficient zeroing neural network(NACZNN) model to solve the TDARE problem is proposed.

On Boolean elements and derivations in 2-dimension linguistic lattice implication algebras

A 2-dimension linguistic lattice implication algebra(2DL-LIA)can build a bridge between logical algebra and 2-dimension fuzzy linguistic information.In this paper,the notion of a Boolean element is proposed in a 2DL-LIA and some properties of Boolean elements are discussed.Then derivations on 2DL-LIAs are introduced and the related properties of derivations are investigated.Moreover,it proves that the derivations on 2DL-LIAs can be constructed by Boolean elements.

COMPARISON OF HOMOLOGIES AND AUTOMATIC EXTENSIONS OF INVARIANT DISTRIBUTIONS

Let G be a reductive Nash group,acting on a Nash manifold X.Let Z be a G-stable closed Nash submanifold of X and denote by U the complement of Z in X.Letχbe a character of G and denote by g the complexified Lie algebra of G.We give a sufficient condition for the natural linear map H_(k)(g,S(U)×χ)→H_k(g,S(X)×χ)between the Lie algebra homologies of Schwartz functions to be an isomorphism.For k=0,by considering the dual,we obtain the automatic extensions of g-invariant(twisted by-χ)Schwartz distributions.

New Class of Doubt Bipolar Fuzzy Sub Measure Algebra

The ideas of ambiguous bipolar skepticism under algebra and closed skepticism ambiguous bipolar ideals and related features have been developed.The fuzzy measure ideal is described in terms of bipolar ambiguous measure algebra and bipolar skepticism,and the linkages between bipolar fuzzy measure algebra are determined.A bipolar misty ideal’s skepticism is examined.InBCW andBCL-measure algebra,homogeneous ideas and dubious pictures of fuzzy bipolar measure ideas are examined.Also,we gave the relationship between these concepts.Finally,it is given the perfect terms for an occult bipolar doubt to be a measure of ideal fuzzy bipolar closed doubt.

JONES TYPE C^(*)-BASIC CONSTRUCTION IN NON-EQUILIBRIUM HOPF SPIN MODELS

Let H be a finite dimensional Hopf C^(*)-algebra,and let K be a Hopf^(*)-subalgebra of H.Considering that the field algebra■K of a non-equilibrium Hopf spin model carries a D(H,K)-invariant subalgebra ■K,this paper shows that the C^(*)-basic construction for the inclusion ■K×■K can be expressed as the crossed product C^(*)-algebra■KD(H,K).Here,D(H,K)is a bicrossed product of the opposite dual H^(op) and K.Furthermore,the natural action of D(H,K)on D(H,K)gives rise to the iterated crossed product■KD(H,K)×D(H,K),which coincides with the C^(*)-basic construction for the inclusion■K×■KD(H,K).In the end,the Jones type tower of field algebra■Kis obtained,and the new field algebra emerges exactly as the iterated crossed product.

Cascading Delays for the High-Speed Rail Network Under Different Emergencies:A Double Layer Network Approach

High-speed rail(HSR) has formed a networked operational scale in China. Any internal or external disturbance may deviate trains’ operation from the planned schedules, resulting in primary delays or even cascading delays on a network scale. Studying the delay propagation mechanism could help to improve the timetable resilience in the planning stage and realize cooperative rescheduling for dispatchers. To quickly and effectively predict the spatial-temporal range of cascading delays, this paper proposes a max-plus algebra based delay propagation model considering trains’ operation strategy and the systems’ constraints. A double-layer network based breadth-first search algorithm based on the constraint network and the timetable network is further proposed to solve the delay propagation process for different kinds of emergencies. The proposed model could deal with the delay propagation problem when emergencies occur in sections or stations and is suitable for static emergencies and dynamic emergencies. Case studies show that the proposed algorithm can significantly improve the computational efficiency of the large-scale HSR network. Moreover, the real operational data of China HSR is adopted to verify the proposed model, and the results show that the cascading delays can be timely and accurately inferred, and the delay propagation characteristics under three kinds of emergencies are unfolded.