Positive Lower Bound Research Articles

Event-Triggered and Self-Triggered L∞ Control for Markov Jump Stochastic Nonlinear Systems Under DoS Attacks.

This article investigates event-triggered and self-triggered L∞ control problems for the Markov jump stochastic nonlinear systems subject to denial-of-service (DoS) attacks. When attacks prevent system devices from obtaining valid information over networks, a new switched model with unstable subsystems is constructed to characterize the effect of DoS attacks. On the basis of the switched model, a multiple Lyapunov function method is utilized and a set of sufficient conditions incorporating the event-triggering scheme (ETS) and restriction of DoS attacks are provided to preserve L∞ performance. In particular, considering that ETS based on mathematical expectation is difficult to be implemented on a practical platform, a self-triggering scheme (STS) without mathematical expectation is presented. Meanwhile, to avoid the Zeno behavior resulted from general exogenous disturbance, a positive lower bound is fixed in STS in advance. In addition, the exponent parameters are designed in STS to reduce triggering frequency. Based on the STS, the mean-square asymptotical stability and almost sure exponential stability are both discussed when the system is in the absence of exogenous disturbance. Finally, two examples are given to substantiate the effectiveness of the proposed method.

The Existence of Ground State Solutions for Schrödinger-Kirchhoff Equations Involving the Potential without a Positive Lower Bound

In this paper, we study the following Schrödinger-Kirchhoff equation where V(x) ≥ 0 and vanishes on an open set of R2 and f has critical exponential growth. By using a version of Trudinger-Moser inequality and variational methods, we obtain the existence of ground state solutions for this problem.

Fuzzy event-triggered sliding mode depth control of unmanned underwater vehicles

This paper focuses on the problem of depth controller design of unmanned underwater vehicles (UUVs) subject to ocean currents and communication delays via a Takagi–Sugeno (T–S) fuzzy modeling method and an event-triggered integral sliding mode control strategy. An event-triggered scheme is developed to avoid unnecessary redundancy in terms of communication resources and an integral sliding mode control strategy is proposed to strength anti-interference ability of the vehicle in complex ocean currents. Sufficient conditions for the existence of a practical sliding mode and the stability of the sliding motion are established in the form of linear matrix inequalities (LMIs), under which the state trajectory is compelled to a bounded region near the sliding surface and moves along the surface toward the equilibrium point after finite time. Whether inter-execution time intervals have a positive lower bound is also analyzed and the absence of the Zeno effect in the designed event-triggered scheme is corroborated. Finally, simulation results and discussions are provided to verify the effectiveness of the new design techniques.

Many Frobenius complements have even order

The theory of Frobenius groups with Frobenius complements of even order largely reduces to tractable algebraic number theory. If we consider only Frobenius complements with an upper bound s on the number of distinct primes dividing the order of their commutator subgroups, then the proportion of these with odd order is less than A positive lower bound is also given.

In Search of an Appropriate Lower Bound. The Zero Lower Bound vs. the Positive Lower Bound under Discretion and Commitment

Abstract Using a standard New Keynesian model, we show that moderate side effects of zero lower bound (ZLB) policy suffice for positive lower bound (PLB) policy to pay off in terms of welfare, especially when central banks fail to commit. For given side effects of the ZLB, as the shock that makes the ZLB bind becomes larger and more persistent, the dominance of PLB policy over ZLB policy becomes more likely. The findings hold for flexible and rigid economies with both fast and slow potential output growth and low and high inflation targets.

Event-Based Synchronization Control for Memristive Neural Networks With Time-Varying Delay.

In this paper, we investigate the global synchronization control problem for memristive neural networks (MNNs) with time-varying delay. A novel event-triggered controller is introduced with the linear diffusive term and discontinuous sign term. In order to greatly reduce the computation cost of the controller under certain event-triggering condition, two event-based control schemes are proposed with static event-triggering condition and dynamic event-triggering condition. Some sufficient conditions are derived by these control schemes to ensure the response MNN to be synchronized with the driving one. Furthermore, under certain event-triggering conditions, a positive lower bound is achieved for the interexecution time to guarantee that Zeno behavior cannot be executed. Finally, numerical simulations are provided to substantiate the effectiveness of the proposed theoretical results.

Analysis and Design of Synchronization for Heterogeneous Network.

In this paper, we investigate the synchronization for heterogeneous network subject to event-triggering communication. The designed controller for each node includes reference generator (RG) and regulator. The predicted value of relative information between intermittent communication can significantly reduce the transmitted information. Based on the event triggering strategy and time-dependent threshold, all RGs can exponentially track the target trajectory. Then by the action of regulator, each node synchronizes with its RG. Meanwhile, a positive lower bound is obtained for the interevent intervals. Numerical example is given to demonstrate the effectiveness of the proposed event triggering strategy.

Decentralized Integral-Based Event-Triggered Stabilization for Linear Plant with Actuator Saturation and Output Feedback

This paper studies the integral-based event-triggered asymptotic stabilization for a continuous-time linear plant. Both actuator saturation and observer-based output feedback are considered. The sensors and actuators are implemented in a decentralized manner and a type of Zeno-free decentralized integral-based event condition is designed to guarantee the asymptotic stability of the closed-loop systems. The positive lower bound of inter-event times is guaranteed by enforcing the event conditions not to be triggered until some fixed intervals. A linear optimization problem is introduced to find the largest stability region. Moreover, the co-design of the parameters in event conditions and the controller gain matrices is proposed in terms of linear matrix inequalities. Finally, two numerical examples are given to illustrate the efficiency and the feasibility of the proposed results.

Noncompact 4-manifolds with uniformly positive isotropic curvature

In this paper, we study Ricci flow on noncompact 4-manifolds with uniformly positive isotropic curvature and with no essential imcompressible space form. That means there is positive lower bound of isotropic curvature and bounded geometry. Then by Perelman’s technique, we can analyze the structures of such manifolds.

Multiple Comparisons with the Best for Supplier Selection

Evaluating and selecting suppliers are essential tasks in managing supply chains. Quality is one of the most important factors for supplier selection among various criteria. To compare the quality of k (k ≥ 2) suppliers, this paper proposes a multiple comparisons with the best method based on the yield index, Spk. Other than the existing work that provides a subset containing the best supplier, the proposed method further gives the upper and lower bounds for each difference in Spk from the unknown best supplier at a confidence level of at least 1‐α. The supplier having a zero lower bound is identified as the best supplier with the highest yield, whereas having a positive lower bound is inferior with a lower yield. The power analysis shows that proposed method would be more and more powerful than the existing work when k gets large. The required sample sizes for certain power levels are provided. An application to comparing three suppliers of the IC drivers of the light‐emitting diode module is presented to show the effectiveness of the proposed method to a real‐world problem. Copyright © 2013 John Wiley & Sons, Ltd.

Two-Stage Fixed-Width Confidence Intervals for a Normal Mean in the Presence of Suspect Outliers

We revisit fixed-width (= 2d) confidence interval procedures with a preassigned confidence coefficient (≥1 − α) for the mean μ of a normal distribution when its variance σ2 is unknown. Had σ been known, the required optimal fixed sample size would be C ≡ a 2σ2/d 2 where a ≡ a α is the upper 50α% point of N(0, 1). In his fundamental two-stage procedure, Stein (1945, 1949) estimated C by replacing σ2 with a sample variance from pilot data of size m(≥2) and a with t m−1, α/2. Mukhopadhyay (1982) opened the possibility of incorporating less traditional estimators of σ2. We focus on estimating σ2 by a statistic defined via Gini's mean difference (GMD), mean absolute deviation (MAD), and range. Such modifications are warranted especially when we suspect one or more outliers but normality of the data may not be questioned by a standard test for normality assumption. Obviously, then, t m−1, α/2 must be replaced by the upper 50α% point corresponding to a pivotal distribution of the sample mean standardized appropriately by U m . This way, we explore the role of Mukhopadhyay (1982) two-stage confidence interval procedure when the requisite sample size is determined through GMD, MAD, or range. Associated exact and some asymptotic first-order properties are developed first. Next, we revisit Mukhopadhyay and Duggan (1997) updated two-stage methodology that was proposed when a known positive lower bound was available for σ2 in the present light. We highlight associated (i) first-order efficiency properties for all proposed fixed-width confidence interval procedures and (ii) second-order efficiency property of the GMD-based procedure. These are accompanied with extensive data analyses via simulations as well as real data.

Global convergence of some modified PRP nonlinear conjugate gradient methods

Recently, similar to Hager and Zhang (SIAM J Optim 16:170–192, 2005), Yu (Nonlinear self-scaling conjugate gradient methods for large-scale optimization problems. Thesis of Doctors Degree, Sun Yat-Sen University, 2007) and Yuan (Optim Lett 3:11–21, 2009) proposed modified PRP conjugate gradient methods which generate sufficient descent directions without any line searches. In order to obtain the global convergence of their algorithms, they need the assumption that the stepsize is bounded away from zero. In this paper, we take a little modification to these methods such that the modified methods retain sufficient descent property. Without requirement of the positive lower bound of the stepsize, we prove that the proposed methods are globally convergent. Some numerical results are also reported.

Accelerated cosmological expansion due to a scalar field whose potential has a positive lower bound

In many cases a nonlinear scalar field with potential V can lead to accelerated expansion in cosmological models. This paper contains mathematical results on this subject for homogeneous spacetimes. It is shown that, under the assumption that V has a strictly positive minimum, Wald's theorem on spacetimes with positive cosmological constant can be generalized to a wide class of potentials. In some cases, detailed information on late-time asymptotics is obtained. Results on the behaviour in the past time direction are also presented.

Pointwise lower bounds on the heat kernels of higher order elliptic operators

Suppose that H=H*[ges ]0 on L2(X, dx) and that e−Ht has an integral kernel K(t, x, y) which is a continuous function of all three variables. It follows from the fact that e−Ht is a non-negative self-adjoint operator that K(t, x, x)[ges ]0 for all t>0 and x∈X. Our main abstract results, Theorems 2 and 3, provide a positive lower bound on K(t, x, x) under suitable general hypotheses. As an application we obtain a explicit positive lower bound on K(t, x, y) when x is close enough to y and H is a higher order uniformly elliptic operator in divergence form acting in L2(RN, dx); see Theorem 6.We emphasize that our results are not applicable to second order elliptic operators (except in one space dimension). For such operators much stronger lower bounds can be obtained by an application of the Harnack inequality. For higher order operators, however, we believe that our result is the first of its type which does not impose any continuity conditions on the highest order coefficients of the operators.

Pair creation in the adiabatic limit: a solvable example

A strictly positive lower bound is derived for the average number of chiral fermion/antifermion pairs which are created from the two-dimensional Minkowski space vacuum by an infinitely differentiable external potential of compact support in the adiabatic limit.

Hyperspherical Rindler space, dimensional reduction, and de Sitter-space scalar field theory.

Field theory in de Sitter space is related to flat-spacetime theory via dimensional reduction. de Sitter space can be embedded in Minkowski space of one higher dimension as a hyperboloid of one sheet. This paper examines the field theory imposed on de Sitter space by a free, massless, real scalar field in the embedding space. This corresponds to a collection of massive de Sitter-space scalars, of all masses above a positive lower bound: Half of the field normal modes in hyperspherical Rindler coordinates specialize to such fields on an embedded de Sitter space, while the other half vanish there. Dimensional reduction simply eliminates those noncontributing modes. The quantized field theory in hyperspherical Rindler space, hence, in de Sitter space, is treated here using both canonical operator expansions and the functional Schr\"odinger formalism. Transformations between field operators and state wave functionals in the Rindler--de Sitter theory and those in the Minkowski-space formulation are calculated explicitly. The Minkowski vacuum state corresponds to the Chernikov-Tagirov or Euclidean vacuum of the de Sitter-space fields. The Rindler--de Sitter `` particle'' content of this state, for various simple mode choices, can be time dependent, even nonmonotonic; it can also exhibit ``thermal'' features recalling those of rectangular Rindler-space theory or of Euclidean field theory in de Sitter space.

The application of dissipative operators to nonlinear diffusion equations

with U(L, ~1) positive, smooth for z > 0 and other technical conditions. The initial value problem with o(u, u,) = a(u), o(O) = 0 and g continuous has been previously studied by a different approach; see [8]. In Section 2 we prove that, under the appropriate conditions, A, the closure of Au = (a(~, u,)u,)~, may be regarded as a dissipative operator in Lp which generates a contraction semigroup there. Burnell McKissick proved this for the case a(u, u,) = u(u) in L’ (private communication). Conditions are given, in Section 3, for the existence of a positive lower bound of u(& X) = e”g. g E D(A), in sets of f > 0, --co < x < co. In such a region it is shown, in Section 4, that u(t. x) is a classical solution. The advance over (81 is that, for u(u) independent of u,, u(O) = co is allowed if

Regular solution of 't Hooft's magnetic monopole model in curved space

A regular solution of 't Hooft's magnetic monopole model in curved space is presented. As in flat space, an analytical solution seems impossible, but by using the Einstein equations to eliminate the gravitational degrees of freedom, a positive-definite energy functional is constructed, which at its minimum gives both the required solution and the energy of the system. To first order in the gravitational constant $G$, the energy can be expressed in terms of the flat-space solutions only, whereas for general $G$ a positive lower bound is derived.