The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

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.

Guest paper: Failure trends in a large disk drive population

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.

Design of Miniaturized Antenna Using Corrugated Microstrip

The problem of fast designing of a well-matched symmetrical four-tooth-shaped microstrip antenna at frequency of 2.44 GHz is considered. To solve the problem, we use regression models for wavelength, resistance and bandwidth. The optimization problem for finding the geometrical parameters of the antenna radiator is formulated by using these models. In the first step of approximation, the antenna is obtained as a solution to the optimization problem. In the next step, the geometry of the radiator is refined so as the base frequency of the antenna is closer to 2.44 GHz.

Fast method for designing a well-matched symmetrical four-tooth-shaped microstrip antenna for Wi-Fi applications

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.

http://www.helix.dnares.in/wp-content/uploads/2017/12/2275-2283.879.pdf

Bandwidth Enhancement of Symmetrical Fourth-Teeth-Shaped Microstrip Antenna

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.

On electrical characteristics of comb-shaped microstrip antennas

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.

Over-determined boundary value problems for PDE and their application in the wave propagation theory

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.

The Over-Determined Cauchy Problems for the Maxwell Equations Set and Electromagnetic Waves Diffraction on the Metallic Screens

The rectangular waveguide is attached to a hole in a wall of rectangular resonator and the corresponding to the hole part of the waveguide boundary is cross-section of the waveguide. The problem of excitation of the resonator by an eigen wave of the waveguide is investigated. The condition on a hole is obtained from the condition defining the wave in the waveguide, outgoing from cross-section. The initial diffraction problem is reduced to some infinite set of linear algebraic equations. Numerical experiment shows that the dependence of expansion coefficients of the field in the resonator on frequency of exciting wave has resonant nature. We propose to use the real values of the resonance frequencies of the running on the hole wave as the initial approximations for eigen frequencies of the resonator with a hole in the wall.

On the Eigen Frequencies of Rectangular Resonator with a Hole in the Wall

The problem of designing a symmetrical eight-tooth-shaped microstrip dual-band Wi-Fi antenna (2.4 GHz and 5 GHz) is considered. At the first stage of antenna design, numerical experiments are performed to determine the dependence of values of the first two resonance frequencies of the antenna and the corresponding bandwidths on the geometric parameters of the radiator. A regression analysis is carried out and regression models for resonance frequencies are obtained. The absolute and relative errors for the models are calculated. A family of Wi-Fi dual-band antennas with a certain ratio of length to depth of rectangular cutouts of the radiator is selected by analyzing the models. Further analysis of the matching and of the bandwidth for the antennas from the obtained family allows determining the best matched Wi-Fi antennas.

N. B. Pleshchinskii

Papers

On electrical characteristics of comb-shaped microstrip antennas

Over-determined boundary value problems for PDE and their application in the wave propagation theory

The Over-Determined Cauchy Problems for the Maxwell Equations Set and Electromagnetic Waves Diffraction on the Metallic Screens

On the Eigen Frequencies of Rectangular Resonator with a Hole in the Wall

Designing the Symmetrical Eight-Tooth-Shaped Microstrip Antenna for Wi-Fi Applications