Harvesting of a phytoplankton–zooplankton model

Considering that some phytoplankton and zooplankton are harvested for food, a phytoplankton–zooplankton model with harvesting is proposed and investigated. First, stability conditions of equilibria and existence conditions of a Hopf-bifurcation are established. Our results indicate that over exploitation would result in the extinction of the population and an appropriate harvesting strategy should ensure the sustainability of the population which is in line with reality. Furthermore, the existence of bionomic equilibria and the optimal harvesting policy are discussed. The present value of revenues is maximized by using Pontryagin’s maximum principle subject to the state equations and the control constraints. We discussed the case of optimal equilibrium solution. It is found that the shadow prices remain constant over time in optimal equilibrium when they satisfy the transversality condition. It is established that the zero discounting leads to the maximization of economic revenue and that an infinite discount rate leads to complete dissipation of economic rent. Finally, some numerical simulations are given to illustrate our results.     

Global optimal solutions to a class of quadrinomial minimization problems with one quadratic constraint

This paper studies the canonical duality theory for solving a class of quadrinomial minimization problems subject to one general quadratic constraint. It is shown that the nonconvex primal problem in \mathbb Rⁿ{\mathbb {R}^n} can be converted into a concave maximization dual problem over a convex set in \mathbb R²{\mathbb {R}^2}, such that the problem can be solved more efficiently. The existence and uniqueness theorems of global minimizers are provided using the triality theory. Examples are given to illustrate the results obtained.     

Simulation and optimization of reflection optical module design for single LED

Illuminance uniformity and illuminating efficiency are always the key problems of light emitting diode (LED) lighting system design. Based on the new design of the reflection optical module, illuminance uniformity and illuminating efficiency are investigated simultaneously in this paper. At the first stage, a reflector with various profile designs is installed to improve the uniformity and efficiency of irradiances collected through the receiver. Using the macro commands, an effective process is presented through the optimal design of the reflector geometries, and the merit function is used as the optical quality objective to find the optimal design value of $K2$ K 2 and $R2$ R 2 parameters of the reflector. At the second stage, based on the optimal design result, the displacement between LED source and reflector is further adjusted automatically by the macro commands too. The results from the ray tracing simulation indicate that the optimal design can be achieved through the compromise of Illuminance uniformity and illuminating efficiency. Finally, we obtain the merit function value of $1.81$ 1.81 with $K2=-1.09, R2=1.11\,\hbox {mm}$ K 2 = - 1.09 , R 2 = 1.11 mm , and the source position $Z1= 1.68\,\hbox {mm}$ Z 1 = 1.68 mm . The results shown in this paper could be beneficial for machine vision systems which are heavily demanded in the light source applications for the uniform and efficient illuminance.     

Fault Diagnosis of Rolling Bearings Based on WPE by Wavelet Decomposition and ELM

The fault diagnosis classification method based on wavelet decomposition and weighted permutation entropy (WPE) by the extreme learning machine (ELM) is proposed to address the complexity and non-smoothness of rolling bearing vibration signals. The wavelet decomposition based on ‘db3’ is used to decompose the signal into four layers and extract the approximate and detailed components, respectively. Then, the WPE values of the approximate (CA) and detailed (CD) components of each layer are calculated and composed to be the feature vectors, which are finally fed into the extreme learning machine with optimal parameters for classification. The comparative study of the simulations based on WPE and permutation entropy (PE) shows that the classification method of seven kinds of signals of normal bearing signals and six types of fault states (7 mils and 14 mils) based on WPE (CA, CD) with the number of nodes in the hidden layers of ELM determined by the five-fold cross-validation has the best performances, the training accuracy can reach 100%, and the testing accuracy can reach 98.57% with 37 nodes of the hidden layer by ELM. The proposed method using WPE (CA, CD) by ELM provides guidance for the multi-classification of normal bearing signals.     

On the Upper Bound of Second Eigenvalues for Uniformly Elliptic Operators of any Orders

Abstract Let Ω R~m(m≥1)be a bounded domain with piecewise smooth boundary Ω.Let t and r bepositive integers with t>r+1. We consider the eigenvalue problems(1.1)and(12),and obtain Theorem 1and Theorem 2, which generalize the results in[1,2.5].     

Two-level injection in fiber-delay line based oscillator

Two-level injection-locked opto-electronic oscillator is proposed for low phase noise. Dielectric resonator oscillator (DRO) is used as the first injection source, injection locking a long-fiber loop based opto-electronic oscillator, then its output is injection locking another long-fiber opto-electronic oscillator for getting a lower-phase noise output carrier. After the first injection, the single side band (SSB) phase noise at 10 kHz offset frequency decreases from −123 dBc/Hz to −135 dBc/Hz, then through the second injection the SSB phase noise drops down to −146 dBc/Hz.     

The p-Harmonic Heat Flow with Potential into Homogeneous Spaces

In this paper we prove the existence of global weak solutions of the p-harmonic flow with potential between Riemannian manifolds M and N for arbitrary initial data having finite p-energy in the case when the target N is a homogeneous space with a left invariant metric. Received March 17, 1999, Revised September 22, 1999, Accepted October 15, 1999     

Study on LiFe<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>Sm<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>PO<Subscript>4</Subscript>/C used as cathode materials for lithium-ion batteries with low Sm component

LiFe_1???x Sm _x PO₄/C cathode materials were synthesized though a facile hydrothermal method. Compared with high-temperature solid-phase sintering, the method can allow for the fabrication of low Sm content (2 %), a scarce and expensive rare earth element, while the presence of an optimized carbon coating with large amount of sp²-type carbon sharply increases the material’s electrochemical performance. The high-rate dischargeability at 5 C, as well as the exchange current density, can be increased by 21 and 86 %, respectively, which were attributed to the fine size and the large cell parameter a/c as much. It should be pointed out that the a/c value will be increased for the LiFePO₄ Sm-doped papered by both of the two methods, while the mechanism is different: The value c is increased for the front and the value a is decreased for the latter, respectively.     

Carbon Dioxide Measurement Based on Multimode Diode Laser Correlation Spectroscopy Employing Wavelength Modulation Techniques

The use of a tunable multimode diode laser system based on correlation spectroscopy and wavelength modulation spectroscopy to measure the concentration of the carbon dioxide in ambient air through the 2 υ₁ + 2υ₂ + υ₃ absorption lines around 1570 nm is reported. The carbon dioxide concentrations are derived from the relationship between the normalized second-harmonic signal peak heights of the measurement and reference signals. The validation of the system is conducted by a set of experiments with controlled carbon dioxide and nitrogen mixtures. The correlation and standard deviation between the measured and actual carbon dioxide concentrations are 0.9973 and 4.03%, respectively, over the tested range. A detection limit of 340 ppm m was achieved using 30 successive measurements during 30 min. All these results demonstrated potential utility of the system for carbon dioxide sensing.