scholarly journals Optimized Cramer’s Rule in WZ Factorization and Applications

2020 ◽  
Vol 13 (4) ◽  
pp. 1035-1054
Author(s):  
Olayiwola Babarinsa ◽  
Azfi Zaidi Mohammad Sofi ◽  
Mohd Asrul Hery Ibrahim ◽  
Hailiz Kamarulhaili
Keyword(s):  
Sparse Matrices ◽  
Schur Complement ◽  
Matrix Group ◽  
Lu Factorization ◽  
Triangular Matrices ◽  
Performance Time ◽  
The Matrix ◽  
Cramer’S Rule ◽  
And Performance ◽  
Matrix Norms

In this paper, W Z factorization is optimized with a proposed Cramer’s rule and compared with classical Cramer’s rule to solve the linear systems of the factorization technique. The matrix norms and performance time of WZ factorization together with LU factorization are analyzed using sparse matrices on MATLAB via AMD and Intel processor to deduce that the optimized Cramer’s rule in the factorization algorithm yields accurate results than LU factorization and conventional W Z factorization. In all, the matrix group and Schur complement for every Zsystem (2×2 block triangular matrices from Z-matrix) are established.

Diamond tool wear monitoring by sensory analysis in milling of absolute black granite

2021 ◽  
pp. 095440542110406
Author(s):  
Sandro Turchetta ◽  
Luca Sorrentino ◽  
Gianluca Parodo
Keyword(s):  
Tool Wear ◽  
Cutting Tools ◽  
Depth Of Cut ◽  
Surface Machining ◽  
Diamond Tools ◽  
The Matrix ◽  
Cutting Force Components ◽  
Force Components ◽  
Natural Stones ◽  
And Performance

Diamond tools suitable for machining operations of natural stones can be divided into two groups: cutting tools, including blades, the circular blades and the wires, and the surface machining ones, involving mills and grinders, that can be of different shapes. For the stone sawing process, the most adopted tool type is the diamond mill, whose duration and performance are influenced by various elements such as: the mineralogical characteristics of the material to be machined; the working conditions such as the depth of cut, the feed rate and the spindle speed; the production process of the diamond segment and the characteristics of both the matrix and the diamond, such as the size, the type and the concentration of the diamonds and the metal bond formulation hardness. This work allows to indirectly assess the wear of sintered diamond tools by signal analysis (in time and frequency domain) of the cutting force components acquired in the process. The results obtained represent a fundamental step for the development of a sensory supervision system capable of assessing the tool wear and hence to modify the process parameters in process, in order to optimize cutting performance and tool life.

scholarly journals Rocess Design of Fiber Reinforced Magnesium Matrix Composites

2018 ◽  
Vol 1 (1) ◽  
Author(s):  
Ding Hualun
Keyword(s):  
Composite Materials ◽  
Matrix Composites ◽  
Deposition Method ◽  
Fiber Reinforced ◽  
Casting Method ◽  
Magnesium Matrix ◽  
Preparation Methods ◽  
Magnesium Matrix Composites ◽  
The Matrix ◽  
And Performance

This paper chooses magnesium as the matrix of composite materials, selects carbon fi ber as reinforcement, anddesigns the composite scheme according to the structure and performance of Mg-based composites. The performancecharacteristics and application prospect of fiber-reinforced magnesium matrix composites are introduced. Wait. Inthis paper, the process of preparing carbon fi ber magnesium matrix composites by compression casting method andspray deposition method is designed. The process fl ow chart of these two design schemes is determined by analyzingthe principle of these two kinds of preparation methods, and the specifi c problems of the process are analyzed andsummarized.

Research on Process Optimization and Abrasion Resistance of Plasma Spraying Al2O3-13wt%TiO2 Coating

2013 ◽  
Vol 341-342 ◽  
pp. 92-95
Author(s):  
Li Jun Wang ◽  
Jian Jun Hao ◽  
Yue Jin Ma ◽  
Jian Guo Zhao ◽  
Jian Chang Li
Keyword(s):  
Wear Resistance ◽  
Plasma Spraying ◽  
Friction And Wear ◽  
Performance Test ◽  
Sample Surface ◽  
Coating Performance ◽  
The Matrix ◽  
Average Wear ◽  
And Performance ◽  
Spraying Process

Using plasma spraying equipment to prepare Al2O3-13wt%TiO2 coating on Q235 substrate. Study of its organization and performance, test the performance of coating microhardness and the resistance of friction and wear resistance then optimize the spraying process parameters. The surface of the coating performance was studied by SEM. The results show that, Coating microhardness can be as high as 1132HV, Far more than the matrix microhardness. The minimum average wear weightlessness of Sample surface is 0.95mg. Greatly improve the wear resistance

scholarly journals The Effect of Dietary Nitrate Supplementation on Physiology and Performance in Trained Cyclists

2017 ◽  
Vol 12 (5) ◽  
pp. 684-689 ◽  
Author(s):  
Joseph A. McQuillan ◽  
Deborah K. Dulson ◽  
Paul B. Laursen ◽  
Andrew E. Kilding
Keyword(s):  
Time Trial ◽  
Crossover Design ◽  
Moderate Intensity ◽  
Beetroot Juice ◽  
Double Blind ◽  
Dietary Nitrate ◽  
Performance Time ◽  
Exercise Economy ◽  
Nitrate Supplementation ◽  
And Performance

Purpose:To determine the effect of dietary nitrate (NO3 –) supplementation on physiology and performance in well-trained cyclists after 6–8 d of NO3 – supplementation.Methods:Eight competitive male cyclists (mean ± SD age 26 ± 8 y, body mass 76.7 ± 6.9 kg, VO2peak 63 ± 4 mL · kg–1 · min–1) participated in a double-blind, placebo-controlled, crossover-design study in which participants ingested 70 mL of beetroot juice containing ~4 mmol NO3 – (NIT) or a NO3 –-depleted placebo (PLA), each for 8 d. Replicating pretreatment measures, participants undertook an incremental ramp assessment to determine VO2peak and first (VT1) and second (VT2) ventilatory thresholds on d 6 (NIT6 and PLA6), moderate-intensity cycling economy on d 7 (NIT7 and PLA7), and a 4-km time trial (TT) on d 8 (NIT8 and PLA8).Results:Relative to PLA, 6 d of NIT supplementation produced unclear effects for VO2peak (mean ± 95% confidence limit: 1.8% ± 5.5%) and VT1 (3.7% ± 12.3%) and trivial effects for both VT2 (–1.0% ± 3.0%) and exercise economy on d 7 (–1.0% ± 1.6%). However, effects for TT performance time (–0.7% ± 0.9%) and power (2.4% ± 2.5%) on d 8 were likely beneficial.Conclusions:Despite mostly unclear outcomes for standard physiological determinants of performance, 8 d of NO3 – supplementation resulted in likely beneficial improvements to 4-km TT performance in well-trained male endurance cyclists.

Solving Systems of Linear Algebraic Equations with the Use of an Selective Regularization

2021 ◽  
pp. 11-15
Author(s):  
Vladimir N. Lutay
Keyword(s):  
Diagonal Element ◽  
Decomposition Process ◽  
Algebraic Equations ◽  
Original Matrix ◽  
Triangular Matrices ◽  
First Case ◽  
Linear Algebraic Equations ◽  
The Matrix ◽  
Gauss Method ◽  
Scalar Products

The solution of systems of linear algebraic equations, which matrices can be poorly conditioned or singular is considered. As a solution method, the original matrix is decomposed into triangular components by Gauss or Chole-sky with an additional operation, which consists in increasing the small or zero diagonal terms of triangular matrices during the decomposition process. In the first case, the scalar products calculated during decomposition are divided into two positive numbers such that the first is greater than the second, and their sum is equal to the original one. In further operations, the first number replaces the scalar product, as a result of which the value of the diagonal term increases, and the second number is stored and used after the decomposition process is completed to correct the result of calculations. This operation increases the diagonal elements of triangular matrices and prevents the appearance of very small numbers in the Gauss method and a negative root expression in the Cholesky method. If the matrix is singular, then the calculated diagonal element is zero, and an arbitrary positive number is added to it. This allows you to complete the decomposition process and calculate the pseudo-inverse matrix using the Greville method. The results of computational experiments are presented.

Applications

2004 ◽  
Author(s):  
Wesley Petersen ◽  
Peter Arbenz
Keyword(s):  
Linear Algebra ◽  
Sparse Matrix ◽  
Sparse Matrices ◽  
Simple Procedure ◽  
Complex Numbers ◽  
Multiprocessor Computer ◽  
Basic Linear Algebra Subprograms ◽  
The Matrix ◽  
Shared Memory Multiprocessor ◽  
Real Complex

Linear algebra is often the kernel of most numerical computations. It deals with vectors and matrices and simple operations like addition and multiplication on these objects. Vectors are one-dimensional arrays of say n real or complex numbers x0, x1, . . . , xn−1. We denote such a vector by x and think of it as a column vector, On a sequential computer, these numbers occupy n consecutive memory locations. This is also true, at least conceptually, on a shared memory multiprocessor computer. On distributed memory multicomputers, the primary issue is how to distribute vectors on the memory of the processors involved in the computation. Matrices are two-dimensional arrays of the form The n · m real (complex) matrix elements aij are stored in n · m (respectively 2 · n ·m if complex datatype is available) consecutive memory locations. This is achieved by either stacking the columns on top of each other or by appending row after row. The former is called column-major, the latter row-major order. The actual procedure depends on the programming language. In Fortran, matrices are stored in column-major order, in C in row-major order. There is no principal difference, but for writing efficient programs one has to respect how matrices are laid out. To be consistent with the libraries that we will use that are mostly written in Fortran, we will explicitly program in column-major order. Thus, the matrix element aij of the m×n matrix A is located i+j · m memory locations after a00. Therefore, in our C codes we will write a[i+j*m]. Notice that there is no such simple procedure for determining the memory location of an element of a sparse matrix. In Section 2.3, we outline data descriptors to handle sparse matrices. In this and later chapters we deal with one of the simplest operations one wants to do with vectors and matrices: the so-called saxpy operation (2.3). In Tables 2.1 and 2.2 are listed some of the acronyms and conventions for the basic linear algebra subprograms discussed in this book.

THE VALUE OF TREADMILL EXERCISE TEST PARAMETERS TO PREDICT THE MARATHON PERFORMANCE OF YOUNG AND MIDDLE-AGED RECREATIONAL ATHLETES IN CHINA

2020 ◽  
Vol 20 (08) ◽  
pp. 2050057
Author(s):  
SONG-CUI SHEN ◽  
YING-JIA XU ◽  
WEN-XIA FU ◽  
YAN-JIE LI ◽  
JING-JUAN HUANG ◽  
...  
Keyword(s):  
Exercise Test ◽  
Treadmill Exercise ◽  
Treadmill Exercise Test ◽  
Exercise Time ◽  
Recreational Athletes ◽  
Performance Time ◽  
Total Exercise Time ◽  
And Performance ◽  
Performance Times ◽  
Marathon Performance

Objectives: This study will evaluate the results of parameters measured during a treadmill exercise test to predict marathon performances. Methods: We studied 171 Chinese recreational athletes who participated in marathons or half-marathons (42.2[Formula: see text]k or 21.1[Formula: see text]k, respectively) between October 2016 and December 2017. The participants completed a survey that included questions about demographics and training, and they underwent a treadmill exercise test according to the Bruce protocol. The number of years in training, mean weekly hours of training, mean weekly training volume, and performance time in subsequent marathon events were recorded and analyzed in this study. Results: The total exercise times achieved on the treadmill test were significantly longer for men compared to women ([Formula: see text]). The performance times in the half-marathons were significantly shorter for men compared to women ([Formula: see text]). Training volume was the only independent predictor of total exercise time on the treadmill and performance time in marathons and half-marathons (all [Formula: see text]). The value of the total exercise time on the treadmill to predict performance times in half-marathons ([Formula: see text]) was superior to full marathons ([Formula: see text]) and significantly better in study subjects aged 30–39 years ([Formula: see text], [Formula: see text]) and 40–49 years ([Formula: see text], [Formula: see text]) compared to study subjects aged 20–29 years and 50–59 years. The percentage of decrease in the maximal heart rate (MHR) at the end of one minute of recovery time was negatively correlated with performance times in marathons. Conclusions: The total exercise time achieved during an exhaustive treadmill exercise test and percentage of decrease in the MHR at the end of one minute of recovery time are accessible parameters that can help athletes manage their expectations and adjust their training plans. A large study that includes additional countries is needed to confirm the value of treadmill exercise test results for predicting marathon performance.

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