Types Of Linear Systems Research Articles

A seven-year climatology of the initiation, decay and morphology of severe convective storms during the warm season over North China

AbstractThe present work established a 7-year climatology of the initiation, decay, and morphology of severe convective storms (SCSs) during the warm seasons (May–September) of 2011–2018 (except 2014) over North China. This was achieved by using severe weather reports, precipitation observations, and composite Doppler radar reflectivity data. A total of 371 SCSs were identified. SCSs primarily initiated around noon with the highest frequency over the high terrain of Mount Taihang, and they mostly decayed over the plains at night. The storm morphologies were classified into three types of cellular storms (individual cells, clusters of cells, and broken lines), six types of linear systems (convective lines with no stratiform, with trailing stratiform, leading stratiform, parallel stratiform, embedded lines, and bow echoes), and nonlinear systems. Three types of severe convective weather, namely, short-duration heavy rainfall, hail, and thunderstorm high winds associated with these morphologies were investigated. Nonlinear systems were the most frequent morphology, followed by clusters of cells. Convective lines with trailing stratiform were the most frequent linear morphology. A total of 1,429 morphology samples from the 371 SCSs were found to be responsible for 15,966 severe convective weather reports. Linear (nonlinear) systems produced the most short-duration heavy rainfall (hail and thunderstorm high wind) reports. Bow echos were most efficient in producing both short-duration heavy rainfall and thunderstorm high wind reports whereas broken lines had the highest efficiency for hail production. The results in the present study are helpful for local forecasters to better anticipate the storm types and associated hazardous weather.

Dynamic Linear Solver Selection for Transient Simulations Using Multi-label Classifiers

Many transient simulations spend a significant portion of the overall runtime solving a linear system. A wide variety of preconditioned linear solvers have been developed to quickly and accurately solve different types of linear systems, each having options to customize the preconditioned solver for a given linear system. Transient simulations may produce significantly different linear systems as the simulation progresses due to special events occurring that make the linear systems more difficult to solve or move the model closer to a state of equilibrium with easier to solve linear systems.Machine learning algorithms provide the ability to dynamically select the preconditioned linear solver for each linear system produced by a simulation. We test both single-label and multi-label classifiers, demonstrating that multi-label classifiers achieve the best performance due to associating multiplefast linear solvers with each tested linear system. For more difficult simulations, these classifiers produce significant speedups, while for less diffcult simulations these classifiers achieve performance similar to thefastest single preconditioned linear solvers. We test classifiers generated using limited attribute sets, demonstrating that we can minimize overhead while still obtaining fast, accurate simulations.

Quantitative criterion of conditioning for systems of linear algebraic equations

Conventional conditioning criteria are shown to be invalid for estimating the accuracy of a numerical calculation for systems of linear algebraic equations. A new conditioning criterion is proposed, quantitatively describing the actual loss of decimal digits in calculations. The adequacy of this criterion is confirmed by examples of numerical calculations. Conditioning criteria have been obtained for some types of linear systems arising in important applied problems, in particular, in the difference solution of differential or integral equations.

Linear System Of Equations With Trapezoidal Fuzzy Numbers

A general fuzzy linear system of equations is investigated using embedding approach. In the literature of fuzzy systems two types of linear systems are more important: 1) Fuzzy Linear Systems, 2) Fully Fuzzy Linear Systems. In both class of these systems usually the authors considered triangular type of fuzzy numbers. In this paper, we introduce a linear system of equations with trapezoidal fuzzy numbers as an extension of the fuzzy linear systems which was first introduced by Friedman et al. [6]. Conditions for the existence of a trapezoidal fuzzy solution to n×n linear system are derived and a numerical procedure for calculating the solution is illustrated with some examples.

Equivalence of Linear Systems of Two Second-Order Ordinary Differential Equations

An equivalence problem is solved completely for a linear system of two second-order ordinary differential equations. Using Lie's infinitesimal method we construct the basis of differential invariants for this class of equations and provide the operators of invariant differentiation. Certain types of linear systems are described in terms of their invariants. Some examples are given to illustrate our results. Key Words: Linear Equation; System of Second-Order Ordinary Differential Equations; Equivalence Problem; Differential Invariant

Spring and Summer Severe Weather Reports over the Midwest as a Function of Convective Mode: A Preliminary Study

Abstract Radar data during the period 1 April–31 August 2002 were used to classify all convective storms occurring in a 10-state region of the central United States into nine predominant morphologies, and the severe weather reports associated with each morphology were then analyzed. The morphologies included three types of cellular convection (individual cells, clusters of cells, and broken squall lines), five types of linear systems (bow echoes, squall lines with trailing stratiform rain, lines with leading stratiform rain, lines with parallel stratiform rain, and lines with no stratiform rain), and nonlinear systems. Because linear systems with leading and line-parallel stratiform rainfall were relatively rare in the 2002 sample of 925 events, 24 additional cases of these morphologies from 1996 and 1997 identified by Parker and Johnson were included in the sample. All morphologies were found to pose some risk of severe weather, but substantial differences existed between the number and types of severe weather reports and the different morphologies. Normalizing results per event, nonlinear systems produced the fewest reports of hail, and were relatively inactive for all types of severe weather compared to the other morphologies. Linear systems generated large numbers of reports from all categories of severe weather. Among linear systems, the hail and tornado threat was particularly enhanced in systems having leading and line-parallel stratiform rain. Bow echoes were found to produce far more severe wind reports than any other morphology. The flooding threat was largest in broken lines and linear systems having trailing and line-parallel stratiform rain. Cellular storms, despite much smaller areal coverage, also were abundant producers of severe hail and tornadoes, particularly in broken squall lines.

Boundary-Value Problems for Linear Systems

For several types of linear systems, we consider the problem of the existence of a solution of a two-point boundary-value problem and present asymptotic formulas for this solution.

Identifying dynamic systems with delay

The application of a method of test signals proposed earlier by the authors to determination of the delay parameters of one of the types of linear systems is examined. Identification of systems is a special case of the measurement of their parameters.

Stabilizability of Linear Systems Over a Commutative Normed Algebra with Applications to Spatially-Distributed and Parameter-Dependent Systems

The problem of achieving stabilization by using state feedback is considered for linear systems given by a pair of matrices whose entries belong to a real or complex commutative normed algebra. This framework is applicable to various types of linear systems, including spatially-distributed systems, systems depending on parameters, and infinite-dimensional systems. Necessary and sufficient conditions for stabilizability are derived in terms of solutions to an associated Riccati equation defined in the Gelfand-transform domain. Necessary and sufficient conditions for stabilizability are also given in terms of a local rank criterion involving the Gelfand transform of the system coefficients. The results are applied to the problem of positioning a long seismic cable.