Angular region: a measure of underdamped behavior

The natural modes of an underdamped dynamical system are given by the characteristic numbers of the quadratic operator pencil

$\text{P(s)=s}{}^2\text{I+sB+A,}$

where the operator A depends on the dissipative and reactive elements of the system, while B depends solely on the reactive elements. The operator P(s) for every applied stimulus vector signal x must satisfy:

$\text{(Bx,x)}{}^2\text{<4(Ax,x).}$

A measure of underdamped behaviour is suggested by predetermining an angular region |φ| containing all natural modes of the system,

$\text{|}\text{tan}\text{φ|?}\text{[4(Ax,x)?(Bx,x)}{}^2\text{]}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(Bx,x)}\text{.}$

When a comparison between positive operators A and B is available, say B²=KA, then

$\text{|}\text{tan}\text{φ|?}\text{√(4?K}{}^2\text{)}\text{K}\text{.}$

The paper is motivated by Duffin-Krein-Gohberg's earlier mathematical contributions.     

Modeling switched circuits based on wavelet decomposition and neural networks

In this paper, switched circuits are modeled based on wavelet decomposition and neural network. Also describes the usage of wavelet decomposition and neural network for modeling and simulation of nonlinear systems. The switched circuits are piecewise-linear circuits. At each position of switch the circuit is linear but when considered all switching positions of the circuit it becomes nonlinear. An important problem which arises in modeling switched circuit is high structural complexity. In this study, wavelet decomposition is used for feature extracting from input signals and neural network is used as an intelligent modeling tool. Two performance measures root-mean-square (RMS) and the coefficient of multiple determinations (R²) are given to compare the predicted and computed values for model validation. The evaluated R² value is 0.9985 and RMS value is 0.0099. All simulations showed that the proposed method is more effective and can be used for analyzing and modeling switched circuits. When we consider obtained performance, we can easily say that the proposed method can be used efficiently for modeling any other nonlinear dynamical systems.     

Two-element type normal n-ports

A new classification of RLC reciprocal n-ports in normal and non-normal systems is proposed. The normal systems exhibit the most natural generalization of the scalar RLC one-ports; they admit canonic synthesis representations.Let R, L and C be open loop parameters of an RLC reciprocal n-port with m = n dynamically linearly independent loops. For a normal system R, L and C must commute pairwise. Alternatively, the Hermitian components of Z(s) shall commute. There exists a complete set of common orthonormal eigenvectors for R, L and C. With respect to this coordinate system the normal n-port admits a canonic structure.A normal n-port can be canonically synthesized by a unit R, L and C and an adequate supply of ideal transformers. Such decoupling is not realizable for non-normal n-ports.     

Fixed point properties of the binomial function

Fixed point properties of the binomial function

are developed. It is shown that for any 1 < L < N, T^L_Nhas a unique fixed point p? in (0, 1), and that for large N, the fixed point is L/N. This has application to signal detection schemes commonly used in communication systems. When detecting the presence or absence of a signal with an initial false alarm probability p_FAand an initial detection probability p_D, then T^L_N(p_FA) < p_FAand T^L_N(p_D) > p_Dif, and only if, p_FA < p? < p_D. When this condition is satisfied, as N → ∞, T^L_N(p_FA) → 0 and T^L_N(p_D → 1.     

An experimental investigation of forced vibrations

The solution of the differential equation y″ + 2Ry′ + n²y = E cos pt is written in a new form which clearly exhibits many important facts thus far overlooked by theoretical and experimental investigators. Writing s = n ? p, and Δn = n ? √n² ? R², it is found: (a) When s ≠ Δn, there are “beats,” and the first “beat” maximum is greater than any later maximum while the first “beat” minimum is less than any later “beat” minimum. The “beat” frequency is $\text{(s ?}\text{Δ}\text{n)}\text{2π}$. (b) When n² ? p² = R², there are no “beats,” and the resultant amplitude grows monotonically from zero to the amplitude of the forced vibration, (c) At resonance, when n = p, we still have maxima which occur with a frequency $\text{Δ}\text{n}\text{2π}$ in a damped system. (d) The absence of “beats” is neither a sufficient nor a necessary condition for resonance in a damped system.In the experimental investigation the upper extremity of a simple pendulum was moved in simple harmonic motion and photographic records obtained of the motion of the pendulum bob. Different degrees of damping were used, ranging from very small to critical.The experimental results are in excellent agreement with theory.     

On-chip microfluidic systems for determination of L-glutamate based on enzymatic recycling of substrate

Two microfluidic systems have been developed for specific analysis of L-glutamate in food based on substrate recycling fluorescence detection. L-glutamate dehydrogenase and a novel enzyme, D-phenylglycine aminotransferase, were covalently immobilized on (i) the surface of silicon microchips containing 32 porous flow channels of 235 μm depth and 25 μm width and (ii) polystyrene Poros™ beads with a particle size of 20 μm. The immobilized enzymes recycle L-glutamate by oxidation to 2-oxoglutarate followed by the transfer of an amino group from D-4-hydroxyphenylglycine to 2-oxoglutarate. The reaction was accompanied by reduction of nicotinamide adenine dinucleotide (NAD⁺) to NADH, which was monitored by fluorescence detection (ε_ex=340 nm, ε_em=460 nm). First, the microchip-based system, L-glutamate was detected within a range of 3.1–50.0 mM. Second, to be automatically determined, sequential injection analysis (SIA) with the bead-based system was investigated. The bead-based system was evaluated by both flow injection analysis and SIA modes, where good reproducibility for L-glutamate calibrations was obtained (relative standard deviation of 3.3% and 6.6%, respectively). In the case of SIA, the beads were introduced and removed from the microchip automatically. The immobilized beads could be stored in a 20% glycerol and 0.5 mM ethylenediaminetetraacetic acid solution maintained at a pH of 7.0 using a phosphate buffer for at least 15 days with 72% of the activity remaining. The bead-based system demonstrated high selectivity, where L-glutamate recoveries were between 91% and 108% in the presence of six other L-amino acids tested.     

Kernel size and weight affected by three plant bioregulators applied at bloom to Non Pareil and Carmel almond cultivars

BackgroundThe yield of almonds [Prunus dulcis (Mill.) D.A. Webb] could be low due to climatic problems and any factor improving kernel size and weight, such as the use of plant bioregulators (PBRs), should be beneficial.ResultsThree plant bioregulators: 24-epibrassinolide (BL), gibberellic acid (GA₃) and kinetin (KN) were applied at three spray concentrations to Non Pareil and Carmel cultivars, at two phenological stages during bloom, in the 2014 and 2015 seasons. The results showed significant differences (P < 0.0001). For total dry weight of Non Pareil, the best treatment was BL (30 mg·L^-1), with an average of 1.45 g, while the control was 1.30 g, at pink button during 2015. For Carmel, the best dry weight was 1.23 g, achieved with BL (30 mg·L^-1) at fallen petals in both seasons. The average dry weight of the controls varied between 1.13 and 1.18 g. The greatest almond lengths and widths in Non Pareil were 24.98 mm and 15.05 mm, achieved with BL (30 mg·L^-1) and KN (50 μL·L^-1) treatments, respectively, applied at pink button in 2015. In Carmel, the greatest length and width were 24.38 and 13.44 mm, obtained with BL (30 mg·L^-1) applied at the stages of pink button and fallen petals, respectively, in 2015. The control reached lengths between 22.33 and 23.38 mm, and widths between 11.99 and 12.93 mm.ConclusionsThe use of the bioregulators showed significant favorable effects on dry weight, length and width of kernels at harvest, in both cultivars.     

Stability and L2-gain analysis of switched input delay systems with unstable modes under asynchronous switching

We consider the stability and L₂-gain analysis problem for a class of switched linear systems. We study the effects of the presences of input delay and switched delay in the feedback channels of the switched linear systems with an external disturbance. By contrast with the most of the contributions available in literatures, we do not require that all the modes of the switched system are stable when input delay appears in the feedback input. By reaching a compromise among the matched-stable period, the matched-unstable period, and the unmatched period and permitting the increasing of the multiple Lyapunov functionals on all the switching times, the solvable conditions of exponential stability and weighted L₂-gain are developed for the switched system under mode-dependent average dwell time scheme (MDADT). Finally, numerical examples are given to illustrate the effectiveness of the proposed theory.     

Input-to-state stability of switched stochastic delayed systems with Lévy noise

This paper focuses on input-to-state stability of a class of switched stochastic delayed systems which are drived by Lévy noise. By multiple Lyapunov function and average dwell time approach, the sufficient conditions of the ψ^λ(t)-weighted input-to-state stability can be obtained if all the subsystems are input-to-state stable. Then utilizing comparison principle and the method of constant variation, the sufficient criteria of the e^λt-weighted input-to-state stability of the switched stochastic delayed systems containing both input-to-state stable subsystems and non-input-to-state stable subsystems can also be derived. Finally, an example is given to illustrate the effectiveness of the proposed results.     

Delay-dependent stability criteria for systems with asymmetric bounds on delay derivative

This paper discretizes the states, a method introduced in [18] for constant delayed systems, not only in constructing the Lyapunov-Krasovskii (L-K) functional but also in designing the integral inequality technique [17] and [19] for time-varying delayed systems, which increase the order of uncorrelated augmentation [5], [21] and [22]. Based on the discretized state, [10] and [27]'s piecewise analysis method is applied to confirm the system stability in whole delay bound. Asymmetric variation of the delay derivative is assumed so that direct extension to all constraints of the delay derivative can be achieved. Examples show the resulting criteria improve the allowable delay bounds over all existing ones in the literature.     

Towards the minimum-cost control of target nodes in directed networks with linear dynamics

Determining an input matrix, i.e., locating predefined number of nodes (named “key nodes”) connected to external control sources that provide control signals, so as to minimize the cost of controlling a preselected subset of nodes (named “target nodes”) in directed networks is an outstanding issue. This problem arises especially in large natural and technological networks. To address this issue, we focus on directed networks with linear dynamics and propose an iterative method, termed as “L₀-norm constraint based projected gradient method” (LPGM) in which the input matrix B is involved as a matrix variable. By introducing a chain rule for matrix differentiation, the gradient of the cost function with respect to B can be derived. This allows us to search B by applying probabilistic projection operator between two spaces, i.e., a real valued matrix space R^N?×?M and a L₀ norm matrix space $R_{L_0}^{N\times M}$ by restricting the L₀ norm of B as a fixed value of M. Then, the nodes that correspond to the M nonzero elements of the obtained input matrix (denoted as $B^{L_0}$) are selected as M key nodes, and each external control source is connected to a single key node. Simulation examples in real-life networks are presented to verify the potential of the proposed method. An interesting phenomenon we uncovered is that generally the control cost of scale free (SF) networks is higher than Erdos-Renyi (ER) networks using the same number of external control sources to control the same size of target nodes of networks with the same network size and mean degree. This work will deepen the understanding of optimal target control problems and provide new insights to locate key nodes for achieving minimum-cost control of target nodes in directed networks.     

Generalized filtering of one-sided Lipschitz nonlinear systems under measurement delays

This paper addresses the filtering problem for the one-sided Lipschitz nonlinear systems under measurement delays and disturbances using a generalized observer. A generalized architecture for filtering of the one-sided Lipschitz nonlinear systems with output delays is explored, which exhibits diverging manifolds, namely, the conventional static-gain filter and the dynamical filter, and can be employed to render robust stability of the filtering error dynamics. A matrix inequality based framework is obtained by employing a Lyapunov?Krasovskii (LK) functional, whose derivative is exploited through Jensen's inequality, one-sided Lipschitz condition, quadratic inner-boundedness inequality and range of the measurement delay, resulting into L₂ stability for the filtering error system. Generalized filter design for the Lipschitz nonlinear systems with delayed outputs and specific results for the delay-dependent and delay-rate-independent filtering schemes for the one-sided Lipschitz nonlinear systems are deduced from the proposed approach. Convex optimization techniques are employed to achieve a solution for the nonlinear constraints through linear matrix inequalities by employing cone complementary linearization approach. Illustrative numerical examples to demonstrate the effectiveness of proposed method are provided.     

Consensus control for multi-agent systems with distributed parameter models via iterative learning algorithm

This paper deals with the problem of iterative learning control algorithm for a class of multi-agent systems with distributed parameter models. And the considered distributed parameter models are governed by the parabolic or hyperbolic partial differential equations. Based on the framework of network topologies, a consensus-based iterative learning control protocol is proposed by using the nearest neighbor knowledge. When the iterative learning control law is applied to the systems, the consensus errors between any two agents on L² space are bounded, and furthermore, the consensus errors on L² space can converge to zero as the iteration index tends to infinity in the absence of initial errors. Simulation examples illustrate the effectiveness of the proposed method.     

Direct transformation of dinitrogen: synthesis of N-containing organic compounds via N−C bond formation

N-containing organic compounds are of vital importance to lives. Practical synthesis of valuable N-containing organic compounds directly from dinitrogen (N₂), not through ammonia (NH₃), is a holy-grail in chemistry and chemical industry. An essential step for this transformation is the functionalization of the activated N₂ units/ligands to generate N−C bonds. Pioneering works of transition metal-mediated direct conversion of N₂ into organic compounds via N−C bond formation at metal-dinitrogen [N₂-M] complexes have generated diversified coordination modes and laid the foundation of understanding for the N−C bond formation mechanism. This review summarizes those major achievements and is organized by the coordination modes of the [N₂-M] complexes (end-on, side-on, end-on-side-on, etc.) that are involved in the N−C bond formation steps, and each part is arranged in terms of reaction types (N-alkylation, N-acylation, cycloaddition, insertion, etc.) between [N₂-M] complexes and carbon-based substrates. Additionally, earlier works on one-pot synthesis of organic compounds from N₂ via ill-defined intermediates are also briefed. Although almost all of the syntheses of N-containing organic compounds via direct transformation of N₂ so far in the literature are realized in homogeneous stoichiometric thermochemical reaction systems and are discussed here in detail, the sporadically reported syntheses involving photochemical, electrochemical, heterogeneous thermo-catalytic reactions, if any, are also mentioned. This review aims to provide readers with an in-depth understanding of the state-of-the-art and perspectives of future research particularly in direct catalytic and efficient conversion of N₂ into N-containing organic compounds under mild conditions, and to stimulate more research efforts to tackle this long-standing and grand scientific challenge.     

Silylamido supported dinitrogen heterobimetallic complexes: syntheses and their catalytic ability

Molybdenum dinitrogen complexes supported by monodentate arylsilylamido ligand, [Ar(Me₃Si)N]₃MoN₂Mg(THF)₂[N(SiMe₃)Ar] (5) and [Ar(Me₃Si)N]₃MoN₂SiMe₃ (6) (Ar = 3,5-Me₂C₆H₃) were synthesized and structurally characterized, and proved to be effective catalysts for the disproportionation of cyclohexadienes and isomerization of terminal alkenes. The ¹H NMR spectrum suggested that the bridging nitrogen ligand remains intact during the catalytic reaction, indicating possible catalytic ability of the Mo-N=N motif.     

Some properties of a class of biased regression estimators

For the linear statistical model y = Xb + e, X of full column rank estimates of b of the form (C + X′X)⁺X′y are studied, where C commutes with X′X and Q⁺ is the Moore-Penrose inverse of Q. Such estimators may have smaller mean square error, component by component than does the least squares estimator. It is shown that this class of estimators is equivalent to two apparently different classes considered by other authors. It is also shown that there is no C such that (C + X′X)⁺X′Y = My, in which My has the smallest mean square error, component by component. Two criteria, other than tmse, are suggested for selecting C. Each leads to an estimator independent of the unknown b and σ². Subsequently, comparisons are made between estimators in which the C matrices are functions of a parameter k. Finally, it is shown for the no intercept model that standardizing, using a biased estimate for the transformed parameter vector, and retransforming to the original units yields an estimator with larger tmse than the least squares estimator.     

Finite-size scaling of O(n) systems at the upper critical dimensionality

Logarithmic finite-size scaling of the O(n) universality class at the upper critical dimensionality (d_c = 4) has a fundamental role in statistical and condensed-matter physics and important applications in various experimental systems. Here, we address this long-standing problem in the context of the n-vector model (n = 1, 2, 3) on periodic four-dimensional hypercubic lattices. We establish an explicit scaling form for the free-energy density, which simultaneously consists of a scaling term for the Gaussian fixed point and another term with multiplicative logarithmic corrections. In particular, we conjecture that the critical two-point correlation g(r, L), with L the linear size, exhibits a two-length behavior: follows governed by the Gaussian fixed point at shorter distances and enters a plateau at larger distances whose height decays as with a logarithmic correction exponent. Using extensive Monte Carlo simulations, we provide complementary evidence for the predictions through the finite-size scaling of observables, including the two-point correlation, the magnetic fluctuations at zero and nonzero Fourier modes and the Binder cumulant. Our work sheds light on the formulation of logarithmic finite-size scaling and has practical applications in experimental systems.     

Growth dynamics of citations of cumulative papers of individual authors according to progressive nucleation mechanism: Concept of citation acceleration

Using data generated by progressive nucleation mechanism on the cumulative fraction of citations of individual papers published successively by a hypothetical author, an expression for the time dependence of the cumulative number L_sum(t) of citations of progressively published papers is proposed. It was found that, for all nonzero values of constant publication rate ΔN, the cumulative citations L_sum(t) of the cumulative N papers published by an author in his/her entire publication career spanning over T years may be represented in distinct regions: (1) in the region 0 < t < Θ₀ (where Θ₀ ≈ T/3), L_sum(t) slowly increases proportionally to the square of the citation time t, and (2) in the region t > Θ₀, L_sum(t) approaches a constant L_sum(max) at T. In the former region, the time dependence of L_sum(t) of an author is associated with three parameters, viz. the citability parameter λ₀, the publication rate ΔN and his/her publication career t. Based on the predicted dependence of L_sum(t) on t, a useful scientometric age-independent measure, defined as citation acceleration a = L_sum(t)/t², is suggested to analyze and compare the scientific activities of different authors. Confrontation of the time dependence of cumulative number L_sum(t) of citations of papers with the theoretical equation reveals one or more citation periods during the publication careers of different authors.     

Non-iterative pole placement technique: A step further

This paper comes back to the hard problem of pole placement by static output feedback: let a triplet of matrices {A;B;C}∈R^n×n×R^n×m×R^p×n be given, find a matrix K∈R^m×p such that the spectrum of A+BKC equals a specified set. More precisely, this article focuses on the derivation of non-iterative techniques, based upon the notion of eigenstructure assignment, to solve the problem, especially when Kimura's condition does not hold. Some solutions can sometimes be found.     

Label-free viscosity measurement of complex fluids using reversal flow switching manipulation in a microfluidic channel

The accurate viscosity measurement of complex fluids is essential for characterizing fluidic behaviors in blood vessels and in microfluidic channels of lab-on-a-chip devices. A microfluidic platform that accurately identifies biophysical properties of blood can be used as a promising tool for the early detections of cardiovascular and microcirculation diseases. In this study, a flow-switching phenomenon depending on hydrodynamic balancing in a microfluidic channel was adopted to conduct viscosity measurement of complex fluids with label-free operation. A microfluidic device for demonstrating this proposed method was designed to have two inlets for supplying the test and reference fluids, two side channels in parallel, and a junction channel connected to the midpoint of the two side channels. According to this proposed method, viscosities of various fluids with different phases (aqueous, oil, and blood) in relation to that of reference fluid were accurately determined by measuring the switching flow-rate ratio between the test and reference fluids, when a reverse flow of the test or reference fluid occurs in the junction channel. An analytical viscosity formula was derived to measure the viscosity of a test fluid in relation to that of the corresponding reference fluid using a discrete circuit model for the microfluidic device. The experimental analysis for evaluating the effects of various parameters on the performance of the proposed method revealed that the fluidic resistance ratio (R_JL/R_L, fluidic resistance in the junction channel (R_JL) to fluidic resistance in the side channel (R_L)) strongly affects the measurement accuracy. The microfluidic device with smaller R_JL/R_L values is helpful to measure accurately the viscosity of the test fluid. The proposed method accurately measured the viscosities of various fluids, including single-phase (Glycerin and plasma) and oil-water phase (oil vs. deionized water) fluids, compared with conventional methods. The proposed method was also successfully applied to measure viscosities of blood with varying hematocrits, chemically fixed RBC_S, and channel sizes. Based on these experimental results, the proposed method can be effectively used to measure the viscosities of various fluids easily, without any fluorescent labeling and tedious calibration procedures.