Dynamical analysis,control,boundedness,and prediction for a fractional-order financial risk system

This paper delves into the dynamical analysis,chaos control,Mittag–Leffler boundedness(MLB),and forecasting a fractional-order financial risk(FOFR)system through an absolute function term.To this end,the FOFR system is first proposed,and the adomian decomposition method(ADM)is employed to resolve this fractional-order system.The stability of equilibrium points and the corresponding control schemes are assessed,and several classical tools such as Lyapunov exponents(LE),bifurcation diagrams,complexity analysis(CA),and 0–1 test are further extended to analyze the dynamical behaviors of FOFR.Then the global Mittag–Leffler attractive set(MLAS)and Mittag–Leffler positive invariant set(MLPIS)for the proposed financial risk(FR)system are discussed.Finally,a proficient reservoir-computing(RC)method is applied to forecast the temporal evolution of the complex dynamics for the proposed system,and some simulations are carried out to show the effectiveness and feasibility of the present scheme.

THE BOUNDEDNESS OF OPERATORS ON WEIGHTED MULTI-PARAMETER LOCAL HARDY SPACES

Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.

BOUNDEDNESS OF A CHEMOTAXIS-CONVECTION MODEL DESCRIBING TUMOR-INDUCED ANGIOGENESIS

This paper is concerned with the parabolic-parabolic-elliptic system■in a bounded domainΩ?Rnwith a smooth boundary,where the parametersχ,ζ1,ζ2are positive constants and m≥1.Based on the coupled energy estimates,the boundedness of the global classical solution is established in any dimensions(n≥1)provided that m>1.

Boundedness and liveness enforcement for labeled Petri nets using transition priority

This paper deals with the supervisory control problem of discrete event systems modeled by labeled Petri nets. The system is originally unbounded. First, the solvability of the problem is confirmed. A necessary condition is given and proven for the existence of a feasible priority-based controller based on the notions of liveness and transition invariants. Next, a cyclic behavior graph is constructed, which shows the reachable markings that guarantee the maximum liveness of the system within a given bound vector. Finally, an on-line control strategy is proposed to enforce boundedness and liveness to the given system by appending priority relations to transitions. The dynamic priority relation changes flexibly according to the current state of the system and enforces the system evolving in a bounded and live manner. In addition, numerical examples are studied to verify the validity of the proposed approach that remains the structure of the plant net and is efficient for on-line control.

Boundedness Types of Perturbations on the Growth of Semigroups

We study types of boundedness of a semigroup on a Banach space in terms of the Cesáro-average and the behavior of the resolvent at the origin and also exhibit a characterization of type Hille-Yosida for the generators of ϕj-bounded strongly continuous semigroups. Furthermore, these results are used to investigate the effect of the Perturbation on the type of the growth of sequences.

MINIMIZERS OF L^(2)-SUBCRITICAL VARIATIONAL PROBLEMS WITH SPATIALLY DECAYING NONLINEARITIES IN BOUNDED DOMAINS

This paper is concerned with the minimizers of L^(2)-subcritical constraint variar tional problems with spatially decaying nonlinearities in a bounded domain Ω of R~N(N≥1).We prove that the problem admits minimizers for any M> 0.Moreover,the limiting behavior of minimizers as M→∞ is also analyzed rigorously.

Boundedness of Solutions of A Class of Certain Integro-Differential Equations

本文研究了积分-微分方程解的有界性质。给出了方程(A)所有解有界的判別准则,同时也研究了方程(A)解的渐近性质。给出了方程(A)所有解当t→∞时趋向于有穷极限的充分条件。

ON BOUNDEDNESS OF SOLUTIONS OFIMPULSIVE INTEGRO-DIFFERENTIAL SYSTEMSWITH FIXED MOMENTS OF IMPULSE EFFECTS

Several boundedness criteria for the impulsive integro-differential systems with fixed moments of impulse effects are established, employing the method of Lyapunov functions and Razumikhin technique.

The Boundedness of Singular Integral Operator along an Open Curve

It is well known that, the singular integral operatorS defined as: ifL is a closed smooth contour in the complex plane C, thenS is a bounded linear operator fromH μ(L) intoH μ(L): ifL is an open smooth curve, thenS is just a linear operator fromH * intoH *. In this paper, we define a Banach space , and prove that is a bounded linear operator, then verify the boundedness of other kinds of singular integral operators.

EXISTENCE, BOUNDEDNESS AND UNIQUENESS OF WEAK SOLUTION FOR THE THERMISTOR PROBLEM WITH MIXED BOUNDARV CONDITIONS

The thermistor problem is a coupled system of nonlinear PDEs with mixed boundary conditions. The goal of this paper is to study the existence, boundedness and uniqueness of the weak solution for this problem.

L^p BOUNDEDNESS OF COMMUTATOR OPERATOR ASSOCIATED WITH SCHRDINGER OPERATORS ON HEISENBERG GROUP

Let L = -△Hn ＋ V be a SchrSdinger operator on Heisenberg group Hn, where AHn is the sublaplacian and the nonnegative potential V belongs to the reverse HSlder class BQ/2 where Q is the homogeneous dimension of Hn. Let T1 = （--△Hn ＋V）-1V, T2 = （-△Hn ＋V）-1/2V1/2, and T3 = （--AHn ＋V）-I/2△Hn, then we verify that [b, Ti], i = 1, 2, 3 are bounded on some LP（Hn）, where b ∈ BMO（Hn）. Note that the kernel of Ti, i = 1, 2, 3 has no smoothness.

BOUNDEDNESS OF RIESZ POTENTIALS IN NONHOMOGENEOUS SPACES

For a class of linear operators including Riesz potentials on R^d with a nonnegative Radon measure μ, which only satisfies some growth condition, the authors prove that their boundedness in Lebesgue spaces is equivalent to their boundedness in the Hardy space or certain weak type endpoint estimates, respectively. As an application, the authors obtain several new end estimates.

Boundedness and convergence of perturbed corrections for helium-like ions in ground states

Applying the improved Rayleigh SchrSdinger perturbation theory based on an integral equation to helium-like ions in ground states and treating electron correlations as perturbations, we obtain the second-order corrections to wavefunctions consisting of a few terms and the third-order corrections to energicity. It is demonstrated that the corrected wavefunctions are bounded and quadratically integrable, and the corresponding perturbation series is convergent. The results clear off the previous distrust for the convergence in the quantum perturbation theory and show a reciprocal development on the quantum perturbation problem of the ground state helium-like systems.

BOUNDEDNESS OF THE HIGHER-DIMENSIONAL QUASILINEAR CHEMOTAXIS SYSTEM WITH GENERALIZED LOGISTIC SOURCE

This article considers the following higher-dimensional quasilinear parabolic-parabolic-ODE chemotaxis system with generalized Logistic source and homogeneous Neumann boundary conditions{ut=∇⋅(D(u)∇u)−∇⋅(S(u)∇v)+f(u),x∈Ω,t>0 vt=Δv+w−v,x∈Ω,t>0,wt=u−w,x∈Ω,t>0,in a bounded domainΩ⊂R^n(n≥2)with smooth boundary ∂Ω,where the diffusion coefficient D(u)and the chemotactic sensitivity function S(u)are supposed to satisfy D(u)≥M1(u+1)^−αand S(u)≤M2(u+1)^β,respectively,where M1,M2>0 and α,β∈R.Moreover,the logistic source f(u)is supposed to satisfy f(u)≤a−μu^γ with μ>0,γ≥1,and a≥0.Asα+2β<γ−1+2γ/n,we show that the solution of the above chemotaxis system with sufficiently smooth nonnegative initial data is uniformly bounded.

BOUNDEDNESS AND CONVERGENCE FOR THE NON-LINARD TYPE DIFFERENTIAL EQUATION

In this article, the author studies the boundedness and convergence for the non-Liénard type differential equation {^·x=a（y）-f（x）,^·y=b（y）β（x）-g（x）＋e（t）,where a（y）, b（y）, f（x）, g（x）,β（x） are real continuous functions in y ∈ R or x ∈ R, β（x） ≥ 0 for all x and e（t） is a real continuous function on R^＋ = {t ： t ≥ 0} such that the equation has a unique solution for the initial value problem. The necessary and sufficient conditions are obtained and some of the results in the literatures are improved and extended.

ON THE BOUNDEDNESS OF SPHERES IN F-SPACES

In this paper, some results concerning the relationship between the bounded-ness of some spheres and the local boundedness of the .F*-space are presented. Moreover, some results about the compactness are also given.

Uniformly ultimate boundedness for discontinuous systems with time-delay

The uniformly ultimate boundedness of discontinuous systems with time-delay in the sense of Filippov solutions is discussed.Based on the Lyapunov-Krasovskii functional,the Lyapunov theorem for the globally strongly uniformly ultimate boundedness of retarded discontinuous systems is presented.Furthermore,the result is applied to a class of mechanical systems with a retarded discontinuous friction item.

ON THE BOUNDEDNESS AND THE STABILITY PROPERTIES OF SOLUTION OF CERTAIN FOURTH ORDER DIFFERENTIAL EQUATIONS

This paper investigates equation (1) in twocases:(i)P=0, (ii)P satisfies|P (i,x,y,z,w)<(A+|y|+|z|+|w|)q(t).whereq(t) is a nonnegative function of t. For case (i) the asymptotic stability in the large of the trivial solution x=0 is investigated and for case (ii) the boundedness result is obtained for solutions of equation (1). These results improve and include several well-known results.

ON THE BOUNDEDNESS AND THE STABILITY RESULTS FOR THE SOLUTION OF CERTAIN FOURTH ORDER DIFFERENTIAL EQUATIONS VIA THE INTRINSIC METHOD

In this paper, we first present constructing a Lyapunov function for (1. 1) and then we show the asymptotic stability in the large of the trivial solution x=0 for case p≡ 0,and the boundedness result of the solutions of (1 .1 ) for case p≠0. These results improve sveral well-known results.

BOUNDEDNESS PROPERTIES OF SOLUTIONS OF DOUBLY NONLINEAR PARABOLIC EQUATIONS

Consider a doubly nonlinear parabolic equation and prove the boundedness of its generalized solutions.