Extremum of second-order directional derivatives

In this paper, the extremum of second-order directional derivatives, i.e. the gradient of first-order derivatives is discussed. Given second-order directional derivatives in three nonparallel directions, or given second-order directional derivatives and mixed directional derivatives in two nonparallel directions, the formulae for the extremum of second-order directional derivatives are derived, and the directions corresponding to maximum and minimum are perpendicular to each other.

Laboratory Implementation of Direct Torque Controller based Speed Loop Pseudo Derivative Feedforward Controller for PMSM Drive

This paper,evaluate the effectiveness of a proposed speed loop pseudo derivative feedforward(PDFF)controller-based direct torque controller(DTC)for a PMSM drive against the performance of existing PI speed controller-based DTC and hysteresis current controller(HCC).The proposed PDFF-based speed regulator effectively reduces oscillation and overshoot associated with rotor angular speed,electromagnetic torque,and stator current.Two case studies,one using forward-to-reverse motoring operation and the other involving reverse-to-forward braking operation,has been validated to show the effectiveness of the proposed control strategy.The proposed controller's superior performance is demonstrated through experimental verification utilizing an FPGA controller for a 1.5 kW PMSM drive laboratory prototype.

Relations of 3D directional derivatives and expressions of typical differential operators

Relations of the 3D multi-directional derivatives are studied in this paper. These relations are applied to a geeral second-order linear elliptical operator and the corresponding expression are obtained. These relations and expressions play important roles in the meshless finite point method.

Image Filter for Removal of Impulse Noise Based on Directional Derivatives

One of the most common image processing tasks involves the removal of noise from images. Noise can be introduced during image capture, during transmission, or during storage. For design purposes, noise sources are frequently approximated by random variables with a known probability distribution. One common noise model corrupts a signal by introducing impulses. And the surface of the image disturbed by impulse noise displays many peaks or vales. According to the characteristic of impulse noise, a novel algorithm is proposed to the detection of impulse noise point from images based on directional derivatives. First, the theory of calculus on directional derivatives is introduced in detail. Then it is applied to the field of image to removing noise with the discrete form derived from its continuous mathematical model. And a number of contrasting simulations illustrate that our algorithm not only can preserve the structure information while removing impulse noise but also can mostly save the gray value of the pixels undisturbed by noise. In addition, the comparisons of the filtering performance for removing impulse noise are analyzed in detail in the case of different noise densities, and also show that the algorithm suggested outperforms the conventional filter algorithms such as mean filter, median filter and so on in speed and impulse noise reduction, especially in random-valued impulse noise reduction. So it is a very good alternative to the existing schemes.

Optimality for Henig Proper Efficiency in Vector Optimization Involving Dini Set-Valued Directional Derivatives

This note studies the optimality conditions of vector optimization problems involving generalized convexity in locally convex spaces. Based upon the concept of Dini set-valued directional derivatives, the necessary and sufficient optimality conditions are established for Henig proper and strong minimal solutions respectively in generalized preinvex vector optimization problems.

Synthesis of Imidazole Derivatives for Their Second-order Nonlinear Optics

The design and the synthesis of two conjugated donor acceptor imidazole derivatives(1, 2) were carried out for second order nonlinear optics. The thermal properties, the transparency and second order nonlinear optical properties of the molecules were investigated. The experimental results indicate that a good nonlinearity transparency thermal stability trade off is achieved for them.

Importance Analysis of a Multi-state System Based on Direct Partial Logic Derivatives and Multi-valued Decision Diagrams

Importance analysis quantifies the critical degree of individual component. Compared with the traditional binary state system,importance analysis of the multi-state system is more aligned with the practice. Because the multi-valued decision diagram( MDD) can reflect the relationship between the components and the system state bilaterally, it was introduced into the reliability calculation of the multi-state system( MSS). The building method,simplified criteria,and path search and probability algorithm of MSS structure function MDD were given,and the reliability of the system was calculated. The computing methods of importance based on MDD and direct partial logic derivatives( DPLD) were presented. The diesel engine fuel supply system was taken as an example to illustrate the proposed method. The results show that not only the probability of the system in each state can be easily obtained,but also the influence degree of each component and its state on the system reliability can be obtained,which is conducive to the condition monitoring and structure optimization of the system.

CONE-DIRECTED CONTINGENT DERIVATIVES AND GENERALIZED PREINVEX SET-VALUED OPTIMIZATION

By using cone-directed contingent derivatives, the unified necessary and sufficient optimality conditions are given for weakly and strongly minimal elements respectively in generalized preinvex set-valued optimization.

Bounded consensus tracking of second-order multi-agent systems with sampling delay under directed networks

The bounded consensus tracking problems of second-order multi-agent systems under directed networks with sam- pling delay are addressed in this paper. When the sampling delay is more than a sampling period, new protocols based on sampled-data control are proposed so that each agent can track the time-varying reference state of the virtual leader. By using the delay decomposition approach, the augmented matrix method, and the frequency domain analysis, necessary and sufficient conditions are obtained, which guarantee that the bounded consensus tracking is realized. Furthermore, some numerical simulations are presented to demonstrate the effectiveness of the theoretical results.

The inflammatory response of the pulp after direct capping with platelet-rich plasma and enamel matrix derivative:A controlled animal study

Aims: To evaluate the inflammatory response of the exposed pulp of incisor teeth in rats after direct pulp capping, using platelet rich plasma (PRP), enamel matrix derivate (EMD), mineral trioxide aggregate (MTA) and calcium hydroxide (Ca(OH)2). Methods: The study was conducted on 36 Wistar albino rats with a total of 144 incisor teeth. The pulps of 96 teeth of the rats were perforated and capped with different agents. Serving as the positive control group, the pulps of 24 teeth were only perforated and capped without capping agents, whereas the pulps of 24 teeth were used as the negative control group without being perforated (without any process). The research was ended with the extracting of the teeth on the 7th day-28th day. The teeth were taken to the routine and histological follows;cross sections were prepared and painted with hematoxylen & eosin. All of the sections were evaluated in terms of inflammatory reaction by histologic analysis taken by light microscope. Statistical analysis was used. The normal distribution of all data was tested with the Mann Whitney U and the differences between the groups were analyze dusing Kruskal Wallis test at 0.05 level. Results: There are no statistically significant differences in terms of inflammation type and necrosis among the treatment groups on 7 days’ post capping. However, improved inflammatory cell accumulation, hyperemia and lowest necrosis were observed from the samples treated with PRP (p < 0.05). Conversely, the EMD group indicated that the criteria of inflammation scores and hyper- emia were higher in the 28th day (p < 0.05). Conclusions: Most of cells accumulating in the PRP group and most necrosis were seen in the EMD group. These new PRP materials might serve as pulp capping biomaterials to induce initial healing response in the future.

Direct Perturbation Method for Derivative Nonlinear Schrdinger Equation

We extend Lou＇s direct perturbation method for solving the nonlinear Schrodinger equation to the case of the derivative nonlinear Schrodinger equation （DNLSE）. By applying this method, different types of perturbation solutions are obtained. Based on these approximate solutions, the analytical forms of soliton parameters, such as the velocity, the width and the initial position, are carried out and the effects of perturbation on solitons are analyzed at the same time. A numerical simulation of perturbed DNLSE finally verifies the results of the perturbation method.

DIRECT DETERMINATION OF NEODYMIUM AND ERBIUM IN RARE EARTH MIXTURE BY DERIVATIVE SPECTROPHOTOMETRY

The absorption spectra of 4f electron transitions of the complexes of neodymium and erbium with 8-hydroxyquinoline-5-sulphonic acid in the presence of diethylamine and ethanol have been measured by normal and third-derivative spectrophotometry. Their molar absorptivities are 70.7 l.mol^(-1).cm^(-1) for Nd and 62.5 l.mol^(-1).cm^(-1) for Er. They are 7.6 times and 14.9 times greater than those of corresponding chlorides, respectively. Use of the third-derivative spectra both eliminates the interference of Ce(Ⅳ) and increases the sensitivity for Nd and Er. Beer,s Law was obeyed from 0-10 ug/ml of Nd and Er. The method has been applied to the determination of neodymium and erbium in rare earth mixtures.

BrCo (dmgh)_2Py/Zn Promoted Addition of BrCF_2CF_2CH=CHCH_2X to Alkynes: Direct Synthesis of 4,4,5,5-Tetrafluorocyclopentene Derivatives

BrCF2CF2CH=CHCH2X(x=Cl, OAc, OH) reacted smoothly with alkynes in the presence of BrCo(dmgh)2Py/Zn, giving 4,4,5,5-tetrafluorocyclopentene derivatives in moderate yields.

Two parametric approaches for eigenstructure assignment in second-order linear systems

This paper considers eigenstructure assignment in second-order linear systems via proportional plus derivative feedback. It is shown that the problem is closely related to a type of so-called second-order Sylvester matrix equations. Through establishing two general parametric solutions to this type of matrix equations, two complete parametric methods for the proposed eigenstructure assignment problem are presented. Both methods give simple complete parametric expressions for the feedback gains and the closed-loop eigenvector matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the right factorization of the system, and allows the closed-loop eigenvalues to be set undetermined and sought via certain optimization procedures. An example shows the effectiveness of the proposed approaches. Keywords Second-order linear systems - Eigenstructure assignment - Proportional plus derivative feedback - Parametric solution - Singular value decompoition - Right factorization This work was supported in part by the Chinese Outstanding Youth Foundation (No.69504002).

Distributed Containment Control of Networked Nonlinear Second-order Systems With Unknown Parameters

In this paper, we study the containment control problem for nonlinear second-order systems with unknown parameters and multiple stationary/dynamic leaders. The topologies that characterize the interaction among the leaders and the followers are directed graphs. Necessary and sufficient criteria which guarantee the control objectives are established for both stationary leaders(regulation case) and dynamic leaders(dynamic tracking case) based protocols. The final states of all the followers are exclusively determined by the initial values of the leaders and the topology structures. In the regulation case, all the followers converge into the convex hull spanned by the leaders,while in the dynamic tracking case, not only the positions of the followers converge into the convex hull but also the velocities of the followers converge into the velocity convex hull of the leaders.Finally, all the theoretical results are illustrated by numerical simulations.

Reference model based consensus control of second-order multi-agent systems

This paper deals with the consensus problem of multi-agent systems with second-order dynamics. The objective is to design algorithms such that all agents will have same positions and velocities. First, a reference model based consensus algorithm is proposed. It is proved that the consensus can be achieved if the communication graph has a spanning tree. Different from most of the consensus algorithms proposed in the literature, the parameters of the control laws are different among agents. Therefore, each agent can design its control law independently. Secondly, it gives a consensus algorithm for the case that the velocities of the agents are not available. Thirdly, the effectiveness of the input delay and the communication delay is considered. It shows that consensus can be achieved if the input delay of every agent is smaller than a bound related to parameters in its control law. Finally, some numerical examples are given to illustrate the proposed results.

Directional Source Localization Based on RSS-AOA Combined Measurements

Source localization plays an indispensable role in many applications.This paper addresses the directional source localization problem in a three-dimensional(3D)wireless sensor network using hybrid received-signal-strength(RSS)and angle-of-arrival(AOA)measurements.Both the position and transmission orientation of the source are to be estimated.In the considered positioning scenario,the angle and range measurements are respectively corresponding to the AOA model and RSS model that integrates the Gaussian-shaped radiation pattern.Given that the localization problem is non-convex and the unknown parameters therein are coupled together,this paper adopts the second-order cone relaxation and alternating optimization techniques in the proposed estimation algorithm.Moreover,to provide a performance benchmark for any localization method,the corresponding Cramer-Rao lower bounds(CRLB)of estimating the unknown position and transmission orientation of the source are derived.Numerical and simulation results demonstrate that the presented algorithm effectively resolves the problem,and its estimation performance is close to the CRLB for the localization with the hybrid measurements.

On Second-order Sufficient Conditions in Constrained Nonsmooth Optimization

In this paper, we establish a second-order sufficient condition for constrained optimization problems of a class of so called t-stable functions in terms of the first-order and the second-order Dini type directional derivatives. The result extends the corresponding result of [D. Bednarik and K. Pastor, Math. Program. Ser. A, 113（2008）, 283-298] to constrained optimization problems.

New optically active poly(amide-imide)s derived from N,N'-(4,4-diphthaloyl)-bis-L-leucine and hydantoin derivatives:Synthesis and properties

Six new optically active poly（amide-imide）s （5a-f） were synthesized through the direct polycondensation reaction of N,N′-（4,4′- diphthaloyl）-bis-L-leucine （3） with six hydantoin derivatives （4a-f）. Tripbenyl phosphite （TPP）/pyridine in the presence of calcium chloride （CaCl2） and N-methyl-2-pyrrolidone （NMP） were successfully applied for direct polycondensation. The polycondensation reactions produce a series of new poly（amide-imide）s （5a-f） in high yields, and inherent viscosity between 0.42 and 0,55 dL/g. The resulting poly（amide-imide）s （5a-f） were characterized by elemental analysis, viscosity measurements, thermal gravimetric analysis （TGA and DTG）, solubility test and FT-IR spectroscopy.

ZINDO-SOS Studies on Second-order Nonlinear Optical Properties of Thiophene S,S-Dioxide Chromophores

The second-order nonlinear optical properties of thiophene S,S -dioxides derivatives were studied by using the ZINDO-SOS method. The computed results show that the thiophene S,S -dioxide derivatives exhibit larger second-order polarizabilities than their thiophene precursors. In order to clarify the origin of the different NLO responses among these chromophores, their electron properties and frontier orbital properties were investigated as well. These thiophene S,S -dioxides derivatives are good candidates for their application in electro-optical device due to their high nonlinearities, good thermal and photo stabilities.