N. B. Pleshchinskii

Abstract: The microstrip antennas with symmetrical comb-shaped radiator are considered. The influence of depth of the cuts on main electrical characteristics of four- and eight-comb antennas is researched. The resonance frequency, the bandwidth and reflection coefficient are chosen as characteristics. The graphs of unknown dependencies are constructed for the two basic frequencies.

Abstract: The over-determined Cauchy problems for the Maxwell equations set in semi-spaces are investigated in the space of distributions by Fourier integral transform method. The relations between traces of the tangential components of the electric and magnetic fields are obtained. The solution of auxiliary jump problem on the plane is constructed in the closed form. The different variants of the reducing the electromagnetic wave diffraction problem on the metallic screens to integral equations are proposed.

Abstract: The solvability conditions of the over-determined boundary value problems for PDE with constant coefficients in the form of connection between Fourier transforms of boundary functions are obtained. The jump problem on the hyperplane for PDE is formulated and investigated. Two-dimensional Helmholtz equation is considered as an example. It is proved that the mixed type conjugation problem for Helmholtz equation, to which the diffraction problem of the electromagnetic wave on thin conducting ribbons is reduced, is equivalent to one-sided mixed type boundary value problem. The uniqueness theorem is proved for this problem.

Abstract: The problem of plane electromagnetic harmonic wave difiraction on a graded- refractive-index layer of some thickness is considered. It is assumed that refractive index of a layer monotonically increases and then monotonically decreases. Cases of the linear, parabolic, sinusoidal, exponential and logarithmic refractive index proflles of the layer are investigated. The difiraction problem is reduced to an ordinary difierential equation with appropriate boundary conditions. The problem for the linear proflle is solved analytically; for the other proflles it is investigated numerically. The method of approximating an integral identity is applied to increase accuracy of the grid solution of the boundary value problem. Emphasis is given to the cases, in which wave energy, either re∞ected or transited, reaches maxima. 1. INTRODUCTION Refractive index gradients in the direction of light propagation have been theoretically studied for quite a long time. Physical implementation of this concept for using in antire∞ective applications has also been investigated based on evaporation of very thin alternating high/low index fllms that create an efiective index gradient by varying the thickness ratios in these stacks (1,2). Applications for a thin fllm include dye-sensitized solar cells (3), optical waveguides (4), dis- tributed Bragg re∞ectors, light-emitting diodes, and as potential replacements for SiO2 in advanced gate stacks on metaloxide semiconductor fleld efiect transistors. TiO2 and SiO2 have a high re- fractive index (n … 2:5) and a low refractive index (n … 1:5), respectively, and both are optically transparent in the visible and the near-IR region. Varying compositions of TiO2 and SiO2 can help to form thin fllms of any refractive index between those of TiO2 and SiO2. The volume ratio of TiO2 and SiO2 in a deposited dielectric fllm, deflned as x in (TiO2)x(SiO2)1ix, determines the refractive index of the composite material (5). Deposition of thin dielectric layers of difierent materials forms a stack of graded-refractive-index layers, which have been used as antire∞ection coatings for applications such as solar cells (6) and optical interference fllters. In this article, the difiraction problem is reduced to an ordinary difierential equation with appropriate boundary conditions. These conditions are formed by elimination of two semi-inflnite domains from the waveguide structure. We consider the case in which refractive index (wave number) of a layer monotonically increases and then monotonically decreases. As refractive index varies from one layer to another unissentially, we neglected a graded structure of the layer and adopted a continuous function for the refractive index distribution. Furthermore, we assume that the refractive index is independent of wave frequency !. We studied the cases of the linear, parabolic, sinusoidal, exponential and logarithmic refractive index proflles of the layer. The characteristic resemblance and peculiarities of in∞uence of each of the proflles on wave propagation through the graded-index layer are presented. The problem of difiraction on the layer for the linear proflle is solved analytically; for the other proflles it is investigated numerically. The method of approximating a n integral identity is applied to increase the accuracy of the grid solution of the boundary value problem. In the case of elastic waves, the problem of wave propagation through a non-homogeneous layer can be considered by the same method but this case is more complicated for performing calculations. 2. PROBLEM STATEMENT Let the plane electromagnetic harmonic wave of type u0(x) = A0e iik

Abstract: In this article general solution to the Maxwell equations in spherical coordinates is constructed. The method of expansion of unknown functions into series of spherical harmonics is used. It is shown that the exterior boundary value problems for the Maxwell equations have the unique oriented solutions, and the interior boundary value problems have non-trivial solutions in the case of resonance. Necessary and sufficient solvability conditions of over-determined boundary value problems for the Maxwell equations are found.

Abstract: It is estimated that over 90% of all new information produced in the world is being stored on magnetic media, most of it on hard disk drives. Despite their importance, there is relatively little published work on the failure patterns of disk drives, and the key factors that affect their lifetime. Most available data are either based on extrapolation from accelerated aging experiments or from relatively modest sized field studies. Moreover, larger population studies rarely have the infrastructure in place to collect health signals from components in operation, which is critical information for detailed failure analysis. We present data collected from detailed observations of a large disk drive population in a production Internet services deployment. The population observed is many times larger than that of previous studies. In addition to presenting failure statistics, we analyze the correlation between failures and several parameters generally believed to impact longevity. Our analysis identifies several parameters from the drive's self monitoring facility (SMART) that correlate highly with failures. Despite this high correlation, we conclude that models based on SMART parameters alone are unlikely to be useful for predicting individual drive failures. Surprisingly, we found that temperature and activity levels were much less correlated with drive failures than previously reported.

Abstract: The over-determined boundary value problems in the partial domains are proposed to be used as the auxiliary problems to investigate the wave processes in the complex structures. The necessary and su-cient conditions of solvability of the over-determined problem are the dependencies between the boundary functions. These dependencies can be obtained in terms of the Fourier transforms or Fourier coe-cients of the boundary functions. The difiraction problems for the electromagnetic waves on the conducting screens in the space and in the waveguides with metallic walls are considered as the examples. The method of partial domains is widely used in the electromagnetic wave propagation and difirac- tion theory to solve the conjugation problems and boundary value problems with mixed boundary conditions. In the case when the integral or summatorial representations of the fleld to be found are obtained in some parts of the waveguide structure it is possible to get the integral or summatorial equations equivalent to the initial problem. It is convenient to consider the over-determined boundary value problems in the partial domains as the auxiliary problems. By this we are to consider more boundary conditions on some pieces of the domains boundaries than it is necessary to choose the unique solution. The review of articles devoted to over-determined boundary value problem method for the partial difierential equations is given in the paper (1). The necessary and su-cient conditions of solvability of the over-determined problems have the form of the supplementary connections between the auxiliary boundary functions. These con- nections together with the initial boundary conditions and the conjunction conditions form the complete set of equations to determine the electromagnetic fleld. In many cases the conditions at the inflnity for the unbounded domains (the radiation conditions) can be formulated also as the auxiliary conditions for the boundary functions in the over-determined problem.

Abstract: The microstrip antenna with a symmetrical rectangular radiator and four teeth is described. The influence of the base geometric parameters of the antenna on the bandwidth at the base frequency was studied. The following geometric parameters of the antenna are selected: the length and the width of the radiator, the depth of cuts, the thickness of the substrate, the length of the ground plane and the width of the feed line. The regression analysis was carried out and the mathematical model describing the dependence of the bandwidth on the length and the width of the radiator and the depth of the cuts was developed. The rootmean-square error and the relative absolute error of the model were calculated. The graphs of the bandwidth dependences on the geometric parameters are presented. It was established that the decrease of the bandwidth values is associated with an increase of the radiator width and the substrate thickness. It was shown that a slight influence on the bandwidth are made by the changes of the radiator length and the depths of the cuts only in the case when the radiator width is much smaller than its length. The proposed formula describing the relationship of the bandwidth with the geometric parameters of the antenna can be used to design a four-tooth antenna with wide bandwidth.

Abstract: We present a new method to design miniaturized antennas using a corrugated microstrip (CM) line, which shows good slow wave characteristic in the required frequency band. To achieve good radiating behavior and low profile simultaneously, CM is employed as the resonating part of the antenna. The impact of the CM propagation constant on the antenna is discussed in detail. The miniaturized antenna is designed and measured to verify the feasibility of the design method. The measured results show that the proposed antenna can achieve a beamwidth of 70° in E-plane and 75° in H-plane with a gain tolerance of 3 dB, and the realized peak gain level at the central frequency is 5.15 dBi, which have good agreements to the expected designs. Such results indicate that the proposed antenna exhibits excellent radiation characteristics at the resonant mode. The effective size of the proposed miniaturized antenna is $0.16\lambda _{0}\times 0.16 \lambda _{0}\times 0.04 \lambda _{0}$ at 9 GHz, in which $\lambda _{0}$ is the wavelength of the central frequency.