Approximation of mild solutions of the linear and nonlinear elliptic equations

In this paper, we investigate the Cauchy problem for both linear and semi-linear elliptic equations. In general, the equations have the form $$\frac{\partial^{2}}{\partial t^{2}}u\left(t\right)=\mathcal{A}u\left(t\right)+f\left(t,u\left(t\right)\right),\quad t\in\left[0,T\right],$$ where $\mathcal{A}$ is a positive-definite, self-adjoint operator with compact inverse. As we know, these problems are well-known to be ill-posed. On account of the orthonormal eigenbasis and the corresponding eigenvalues related to the operator, the method of separation of variables is used to show the solution in series representation. Thereby, we propose a modified method and show error estimations in many accepted cases. For illustration, two numerical examples, a modified Helmholtz equation and an elliptic sine-Gordon equation, are constructed to demonstrate the feasibility and efficiency of the proposed method.Comment: 29 pages, 16 figures, July 201

Síntesis de interpolación de los controladores para un sistema de accionamiento eléctrico multimotor que contiene un elemento enlazado elásticamente

Partial differential equations, integral, differential, or other equations describe multi-motor automatic electric drive systems containing elastic conveyor belts. Because of the elastic and distributive nature of the system parameters, the transfer function describing them is often a complex expression, containing not only the arguments as a linear system but also the inertial and transcendental components. This makes the precise control of tension and speed synchronously much more complicated than the centralized parameter system. A promising numerical solution based on the real interpolation method will simplify the procedure for synthesizing control loops while preserving the characteristic properties of objects with distributed parameters. The objective of the study is to propose a feasible solution for synthesizing the regulators based on the real interpolation method; it allows direct operation with the original transfer function containing the inertial and transcendental components. In this paper, we proposed an approach to synthesize the control system for objects with distributed parameters using the real interpolation method to reduce computational capacity and synthesis error while preserving the properties of this object class. Building an experimental model of the two-motor electric drive system containing an elastic conveyor to verify the effectiveness of the proposed algorithm. The simulation and experimental results indicate that the control system with the received regulators operating stably and meets the required quality criteria. It proves the efficiency of the synthesis algorithm based on the real interpolation method.Introducción: los sistemas de accionamiento eléctrico multimotor que incluyen transportadores elásticos son un ejemplo de sistemas típicos con parámetros distribuidos descritos por ecuaciones complejas. Debido a la naturaleza elástica y distributiva de los parámetros del sistema, la función de transferencia que los describe suele ser una expresión compleja que contiene los componentes inercial y trascendental. Problema: la naturaleza elástica y distributiva de los parámetros del sistema hace que el control preciso de la tensión y la velocidad sincrónicamente sea mucho más complicado que el sistema de parámetros centralizados. Metodología: se propone una solución numérica para sintetizar los reguladores basada en el método de interpolación real para reducir la capacidad computacional y el error de síntesis preservando las propiedades características de los objetos con parámetros distribuidos. Conclusión: la eficacia del algoritmo propuesto se verifica mediante un modelo experimental del sistema de accionamiento eléctrico de dos motores que contiene un transportador elástico. Los resultados de simulación y experimentales indican que el sistema de control con los reguladores recibidos opera de manera estable y cumple con los criterios de calidad requeridos. Originalidad: los resultados de la investigación se pueden aplicar en el desarrollo de sistemas centrales de control y monitoreo para líneas de producción automáticas con sistemas de accionamiento multimotor que incluyen transportadores

Secrecy performance enhancement for underlay cognitive radio networks employing cooperative multi-hop transmission with and without presence of hardware impairments

In this paper, we consider a cooperative multi-hop secured transmission protocol to underlay cognitive radio networks. In the proposed protocol, a secondary source attempts to transmit its data to a secondary destination with the assistance of multiple secondary relays. In addition, there exists a secondary eavesdropper who tries to overhear the source data. Under a maximum interference level required by a primary user, the secondary source and relay nodes must adjust their transmit power. We first formulate effective signal-to-interference-plus-noise ratio (SINR) as well as secrecy capacity under the constraints of the maximum transmit power, the interference threshold and the hardware impairment level. Furthermore, when the hardware impairment level is relaxed, we derive exact and asymptotic expressions of end-to-end secrecy outage probability over Rayleigh fading channels by using the recursive method. The derived expressions were verified by simulations, in which the proposed scheme outperformed the conventional multi-hop direct transmission protocol.Web of Science212art. no. 21

Comparison of sensory characteristics of green tea in Thai Nguyen and Phu Tho, Vietnam

Green tea is a popular consumption product in Vietnam. Especially, tea which origins from Tan Cuong, Thai Nguyen has been known for long by its better quality than those coming from other regions on the country. The study aims at comparing and finding out if the difference between tea in Thai Nguyen and Phu Tho can be figured by sensory tasting. Two products picked from Tan Cuong, Thai Nguyen province and two others from Phu Ho district, Phu Tho are were evaluated by a panel of twelve judges (eleven women and one man) who was set from a group of thirty eight peoples, had completed a general training and sensory tasting on tea. The experiment on dry tea (eleven descriptors) was carried out separately of the experiment on brewed tea (twenty-one descriptors) and brewed leaf (five descriptors). All attributes are made notes on the sensory unstructured intensity scale. Statistic analyses have shown typical differences by region among all of trees groups of attributes: dry leaf (10/11 attributes), liquor (6/21 attributes) and brewed leaf (5/5 attributes)

Synthesis of gelatin stabilized gold nanoparticles with seed particles enlargement by gamma Co-60 irradiation

Gold nanoparticles (AuNPs) with size from 13 to ~36 nm were synthesized by γ-irradiation method using gelatin as stabilizer. The AuNPs with controllable size were prepared using various concentration of Au3+ from 0.5 to 2 mM and seed particle enlargement with different ratios of [Au3+]/[Auo] up to 50. Maximum absorption wavelength (λmax) was measured by UV-Vis spectroscopy, and particle size was determined from TEM images. Results showed that the size of AuNPs increased with the Au3+ concentration. The seed enlargement approach is efficient to control the size of AuNPs. The value of λmax shifted from 527.5 nm (seed particles) to 537.5 nm, and the size of AuNPs increased from 13 nm (seed particles) to ~36 nm for concentration ratio of [Au3+]/[Auo] up to 40. Thus, γ-irradiation method is favorable for production of AuNPs with controllable size and high purity. The AuNPs/gelatin synthesized by γ-irradiation with the advantages of environmental friendly and mass production process may be potentially promising for applications in medicines, cosmetics and in other fields as well. Keywords. Gold, Nanoparticles, Gelatin, γ-irradiation

SYNTHESIS OF SILVER NANOPARTICLES DOPED IN THE ZEOLITE FRAMEWORK BY CHEMICAL REDUCTION METHOD

ABSTRACT Silver ions (Ag+) were introduced at first into the porous zeolite 4A lattice by an ion-exchange route. And then silver nanoparticles (AgNPs) were synthesized in the zeolite framework by chemical reduction method using hydrazine hydrate (N2H4. H2O) as reducing agent. The synthesized AgNPs/zeolite product was characterized by ultraviolet-visible spectroscopy (UV-vis), X-ray diffraction (XRD), transmission electron microscopy (TEM) and energy dispersive X-ray spectroscopy (EDX). The results showed the maximum absorption wavelength (lmax) of AgNPs/zeolite at 427 nm and the average size of the metallic AgNPs doped in the zeolite of about 30 nm. The synthesis process has been considered as suitable one to prepare AgNPs/zeolite with AgNPs content in zeolite of about 1.2% on large scale. The obtained AgNPs/zeolite product has been used for production of porous ceramic water filters with efficiently bacterial disinfection effect for treatment of drinking water

Magnetic Properties of FePt Nanoparticles Prepared by Sonoelectrodeposition

Sonoelectrodeposition is a useful technique to make metallic nanoparticles, using ultrasound during electrodeposition to remove nanoparticles as they grow on the cathode surface. This paper reports some structural and magnetic properties of FePt nanoparticles prepared by this method. The as-prepared Fe45Pt55 nanoparticles were ferromagnetic at room temperature. Upon annealing at 700°C for 1 h under H2 atmosphere, the saturation magnetization and the coercivity of the nanoparticles were improved significantly. The annealed nanoparticles showed a high coercivity of 13.5 kOe at 2 K and of 9 kOe at room temperature. Sonoelectrodeposition is a promising technique to make large quantity of FePt nanoparticles