Periodic solutions for a fourth-order p-Laplacian neutral functional differential equation

By means of Mawhin's continuation theorem, we study a kind of fourth-order p-Laplacian neutral functional differential equation with a deviating argument in the form:

(φ_p(x(t)−cx(t−δ))^″)^″=f(x(t))x^′(t)+g(t,x(t−τ(t,|x|_∞)))+e(t).     

Generalization of all stabilizing compensators for finite-dimensional linear systems

For finite-dimensional linear systems, the Youla-Kucera parameterization (YKP) with a Q parameter over RH_∞ is assumed to satisfy the Diophantine identity. However, the stability is guaranteed if the Diophantine equation is the “U(RH_∞)“ equality, but not if it is the “identity” equality. However, Vidyasagar's structure with an H parameter over U(RH_∞) is an observer-controller configuration that satisfies the Diophantine equation. This study discusses the deficiency of the Diophantine identity; expands the YKP using an H parameter over U(RH_∞), and expands the Vidyasagar's structure using a Q_v parameter over RH_∞ so that both of the expanded parameterizations satisfy the Diophantine equation and are equivalent for all stabilizing compensators. Moreover, an equation that relates to Q, Q_v, and H will be introduced to establish relationships among the YKP, Vidyasagar's structure and both expanded parameterizations.     

Periodic solutions for a kind of Rayleigh equation with two deviating arguments

In this paper, we use the coincidence degree theory to establish new results on the existence of T-periodic solutions for the Rayleigh equation with two deviating arguments of the form

x^″+f(x^′(t))+g₁(t,x(t-τ₁(t)))+g₂(t,x(t-τ₂(t)))=p(t).     

A test for robust Hurwitz stability of convex combinations of complex polynomials

In this paper we present a method for testing the Hurwitz property of a segment of polynomials (1−λ)p₀(s)+λp₁(s), where λ∈[0,1] and p₀(s) and p₁(s) are nth-degree polynomials with complex coefficients. The method consists in constructing a parametric Routh-like array with polynomial entries and generating Sturm sequences for checking the absence of zeros of two real λ-polynomials of degrees 2 and 2n in the interval (0,1). The presented method is easy to implement. Moreover, it accomplishes the test in a finite number of arithmetic operations because it does not invoke any numerical root-finding procedure.     

Large-scale multiferroic complex oxide epitaxy with magnetically switched polarization enabled by solution processing

Complex oxides with tunable structures have many fascinating properties, though high-quality complex oxide epitaxy with precisely controlled composition is still out of reach. Here we have successfully developed solution-based single-crystalline epitaxy for multiferroic (1-x)BiTi_(1-y)/2Fe_yMg_(1-y)/2O₃–(x)CaTiO₃ (BTFM–CTO) solid solution in large area, confirming its ferroelectricity at the atomic scale with strong spontaneous polarization. Careful compositional tuning leads to a bulk magnetization of 0.07 ± 0.035 μ_B/Fe at room temperature, enabling magnetically induced polarization switching exhibiting a large magnetoelectric coefficient of 2.7–3.0 × 10⁻⁷ s/m. This work demonstrates the great potential of solution processing in large-scale complex oxide epitaxy and establishes novel room-temperature magnetoelectric coupling in epitaxial BTFM–CTO film, making it possible to explore a much wider space of composition, phase, and structure that can be easily scaled up for industrial applications.     

Periodic solutions for p-Laplacian neutral Liénard equation with a sign-variable coefficient

Using Lu's continuation theorem, the extension one of Manásevich-Mawhin, we study the existence of periodic solutions for p-Laplacian neutral Liénard equation of the form

(?_p(x(t)-cx(t-σ))^′)^′+f(x(t))x^′(t)+β(t)g(x(t-τ(t))=e(t).     

Fractional multiple birth-death processes with birth probabilities λi(Δt)+o((Δt))

The usual model for (Poissonian) linear birth-death processes is extended to multiple birth-death processes with fractional birth probabilities in the form λ_i(Δt)^α+o((Δt)^α, 0<α<1. The probability generating function for the time dependent population size is provided by a fractional partial differential equation. The solution of the latter is obtained and comparison with the usual model is made. The probability of ultimate extinction is obtained. One considers the special case of fractional Poissonian processes with individual arrivals only, and then one outlines basic results for continuous processes defined by fractional Poissonian noises. The key is the Taylor’s series of fractional order f(x+h)=E_α(h^αD_x^α)f(x), where E_α(·) is the Mittag-Leffler function, and D_x^α is the modified Riemann-Liouville fractional derivative, as previously introduced by the author.     

Hierarchical structural complexity in atomically precise nanocluster frameworks

The supramolecular chemistry of nanoclusters is a flourishing area of nano-research; however, the controllable assembly of cluster nano-building blocks in different arrays remains challenging. In this work, we report the hierarchical structural complexity of atomically precise nanoclusters in micrometric linear chains (1D array), grid networks (2D array) and superstructures (3D array). In the crystal lattice, the Ag₂₉(SSR)₁₂(PPh₃)₄ nanoclusters can be viewed as unassembled cluster dots (Ag₂₉–0D). In the presence of Cs⁺ cations, the Ag₂₉(SSR)₁₂ nano-building blocks are selectively assembled into distinct arrays with different oxygen-carrying solvent molecules―Cs@Ag₂₉(SSR)₁₂(DMF)_x as 1D linear chains (Ag₂₉–1D), Cs@Ag₂₉(SSR)₁₂(NMP)_x as 2D grid networks (Ag₂₉–2D), and Cs@Ag₂₉(SSR)₁₂(TMS)_x as 3D superstructures (Ag₂₉–3D). Such self-assemblies of these Ag₂₉(SSR)₁₂ units have not only been observed in their crystalline state, but also in their amorphous state. Due to the diverse surface structures and crystalline packing modes, these Ag₂₉-based assemblies manifest distinguishable optical absorptions and emissions in both solutions and crystallized films. Furthermore, the surface areas of the nanocluster crystals are evaluated, the maximum value of which occurs when the cluster nano-building blocks are assembled into 2D arrays (i.e. Ag₂₉–2D). Overall, this work presents an exciting example of the hierarchical assembly of atomically precise nanoclusters by simply controlling the adsorbed molecules on the cluster surface.     

Nonlinear H∞ robust control applied to F-16 aircraft with mass uncertainty using control surface inverse algorithm

In this paper, an analytic solution of nonlinear H_∞ robust controller is first proposed and used in a complete six degree-of-freedom nonlinear equations of motion of flight vehicle system with mass and moment inertia uncertainties. A special Lyapunov function with mass and moment inertia uncertainties is considered to solve the associated Hamilton-Jacobi partial differential inequality (HJPDI). The HJPDI is solved analytically, resulting in a nonlinear H_∞ robust controller with simple proportional feedback structure. Next, the control surface inverse algorithm (CSIA) is introduced to determine the angles of control surface deflection from the nonlinear H_∞ control command. The ranges of prefilter and loss ratio that guarantee stability and robustness of nonlinear H_∞ flight control system implemented by CSIA are derived. Real aerodynamic data, engine data and actuator system of F-16 aircraft are carried out in numerical simulations to verify the proposed scheme. The results show that the responses still keep good convergence for large initial perturbation and the robust stability with mass and moment inertia uncertainties in the permissible ranges of the prefilter and loss ratio for which this design guarantees stability give same conclusion.     

Pragmatic agency in technology standards setting: The case of Ethernet

Technology standards refer to the specifications that provide users and vendors with a common platform and ensure compatibility between components of a technological system. These technical “rules of the game” are being increasingly set in standards development organizations (SDOs). In this paper, I ask the question: how do actors operating in these venues address the challenges posed by the anticipatory and collective nature of the specifications they are establishing? Through an in-depth analytic narrative of the Ethernet LAN (local area network) standard, I indicate how actors engage in an ongoing process of extension generation, ratification and incorporation. In imagining alterations to a specification, approving timely modifications and crafting an identity for a rule even as it changes, they manifest “pragmatic agency” in these contexts. In exercising such agency, SDO's substantially increase the functionality of an existing standard as well as boost its long-term competitive viability.     

Stable denominators for the simplification of z-Transfer Functions

A well-known discrete stability test is used to derive from the denominator D(z) of a given stable high-order transfer function G(z), the denominator of a low-order approximant of G(z). The proposed method, based on the truncation and inversion of a continued fraction formed with the coefficients of D(z), yields a reduced denominator d(z) of degree, say m, which is always stable. Furthermore, depending on the neglected parts of the continued fraction, d(z) approximates m₁ and m₂ = m−m₁ zeros of D(z), located very near the points z=1 and z=-1, respectively. In the special case m₁=m, d(z) is identical to the polynomial obtained by applying to D(z) the indirect technique, which combines the bilinear transformation with the Routh or the Schwarz approximation method.     

Filter design for Markovian jump repeated scalar nonlinear systems

This paper is concerned with the _?2−_?∞${?}_2-{?}_{\infty }$ filtering problem for discrete-time Markovian jump repeated scalar nonlinear systems. Our attention is focused on the design of full- and reduced-order filters that guarantee the filtering error system to be stochastically stable with a prescribed weighted _?2−_?∞${?}_2-{?}_{\infty }$ performance. By employing both the mode dependent Lyapunov function approach and the positive definite diagonally dominant Lyapunov function technique, a sufficient condition is firstly established, which guarantees the Markovian jump repeated scalar nonlinear system to be stochastically stable with an induced _?2−_?∞${?}_2-{?}_{\infty }$ disturbance attenuation performance. The corresponding full-order filter design is cast into a convex optimization problem, which can be efficiently handled by using standard numerical algorithms. Finally, a numerical example is presented to show the effectiveness of the proposed methods.     

Dynamical robust H∞ filtering for nonlinear uncertain systems: An LMI approach

In this paper, a new approach to robust H_∞ filtering for a class of nonlinear systems with time-varying uncertainties is proposed in the LMI framework based on a general dynamical observer structure. The nonlinearities under consideration are assumed to satisfy local Lipschitz conditions and appear in both state and measured output equations. The admissible Lipschitz constants of the nonlinear functions are maximized through LMI optimization. The resulting H_∞ observer guarantees asymptotic stability of the estimation error dynamics with prespecified disturbance attenuation level and is robust against time-varying parametric uncertainties as well as Lipschitz nonlinear additive uncertainty.     

On some n-normed linear space valued difference sequences

The main aim of this article is to extend the notion of strongly Cesàro summable and strongly lacunary summable real sequences to n-normed linear space valued (n-nls valued) difference sequences. Consequently we introduce the spaces |σ₁|(X,?) and N_θ(X,?), respectively, where X is an n-normed space and ? is a difference operator. We investigate these spaces for completeness as well as for the relationship between these spaces.     

Periodic solutions to systems of reaction-diffusion equations

In this paper, necessary and sufficient conditions are derived for the existence of temporally periodic “dissipative structure” solutions in cases of weak diffusion with the reaction rate terms dominant in a generic system of reaction-diffusion equations ?c_i/?t = D_i?²c_i+Q_i(c), where the enumerator index i runs 1 to n, c_i = c_i(x, t) denotes the concentration or density of the ith participating molecular or biological species, D_i is the diffusivity constant for the ith species and Q_i(c), an algebraic function of the n-tuple c = (c₁,\3., c_n), expresses the local rate of production of the ith species due to chemical reactions or biological interactions.     

Sampled-data H∞ filtering of Takagi–Sugeno fuzzy systems with interval time-varying delays

The sampled-data _H∞$H_{\infty }$ filtering for a continuous-time Takagi–Sugeno fuzzy system with an interval time-varying state delay is investigated, where the measurement outputs from the plant to the filter are assumed to be sampled at discrete instants with a variable period. Firstly, by means of a newly proposed inequality bounding technique and a new Lyapunov–Krasovskii functional, the fuzzy sampled-data _H∞$H_{\infty }$ filtering performance analysis is carried out such that the resultant filter error system is asymptotically stable with a prescribed _H∞$H_{\infty }$ attenuation performance index. Secondly, sufficient conditions on the existence of fuzzy sampled-data _H∞$H_{\infty }$ filters are derived in the simultaneous presence of the time-varying state delay and the variable sampling period. The proposed bounding inequality lies in its more tightness and alleviates the enlargement of some inverse “coefficients” resulting from the utilization of the well-known Jensen integral inequality  . Compared with some existing Lyapunov–Krasovskii functionals, more information about the relationship among the current state and its delayed state is considered. The upper bound of the derivative of the time-varying state delay is not required to be less than one. Different from some existing results in the literature, by applying the proposed results, each different value of such an upper bound (greater than one) leads to a different _H∞$H_{\infty }$ disturbance attenuation level. Finally, a numerical example and a modified continuous stirred tank reactor system are given to show the effectiveness of the proposed results.     

Periodic solutions for third order p-Laplacian equation with a deviating argument

By means of Mawhin's continuation theorem, we study a third-order p-Laplacian differential equation

(?_p(u^″(t)))^′+f(t,u^′(t),u^″(t))+g(t,u(t-τ(t)))=e(t).     

Central suboptimal H∞ filtering for nonlinear polynomial systems with multiplicative noise

This paper presents the central finite-dimensional H_∞ filter for nonlinear polynomial systems with multiplicative noise, that is suboptimal for a given threshold γ with respect to a modified Bolza-Meyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the previously obtained results, the paper reduces the original H_∞ filtering problem to the corresponding optimal H₂ filtering problem, using the technique proposed in [1]. The paper presents the central suboptimal H_∞ filter for the general case of nonlinear polynomial systems with multiplicative noise, based on the optimal H₂ filter given in [31]. The central suboptimal H_∞ filter is also derived in a closed finite-dimensional form for third (and less) degree polynomial system states. Numerical simulations are conducted to verify performance of the designed central suboptimal filter for nonlinear polynomial systems against the central suboptimal H_∞ filters available for polynomial systems with state-independent noise and the corresponding linearized system.