scholarly journals Observations on the Computation of Eigenvalue and Eigenvector Jacobians

Algorithms ◽  
2019 ◽  
Vol 12 (12) ◽  
pp. 245 ◽  
Author(s):  
Andrew J. Liounis ◽  
John A. Christian ◽  
Shane B. Robinson
Keyword(s):  
Complex Case ◽  
Extensive Literature ◽  
Jacobian Matrices ◽  
Special Cases ◽  
The Matrix ◽  
General Complex ◽  
Analytic Expressions ◽  
And Performance ◽  
Eigenvector Derivatives ◽  
Eigenvalue And Eigenvector

Many scientific and engineering problems benefit from analytic expressions for eigenvalue and eigenvector derivatives with respect to the elements of the parent matrix. While there exists extensive literature on the calculation of these derivatives, which take the form of Jacobian matrices, there are a variety of deficiencies that have yet to be addressed—including the need for both left and right eigenvectors, limitations on the matrix structure, and issues with complex eigenvalues and eigenvectors. This work addresses these deficiencies by proposing a new analytic solution for the eigenvalue and eigenvector derivatives. The resulting analytic Jacobian matrices are numerically efficient to compute and are valid for the general complex case. It is further shown that this new general result collapses to previously known relations for the special cases of real symmetric matrices and real diagonal matrices. Finally, the new Jacobian expressions are validated using forward finite differencing and performance is compared with another technique.

Improving x-ray map resolution with image restoration techniques

1996 ◽  
Vol 54 ◽  
pp. 598-599
Author(s):  
Richard B. Mott ◽  
John J. Friel ◽  
Charles G. Waldman
Keyword(s):  
Image Restoration ◽  
Hubble Space Telescope ◽  
Extensive Literature ◽  
Small Object ◽  
X Rays ◽  
X Ray ◽  
Mapping Parameters ◽  
The Matrix ◽  
The 1960S ◽  
Map Resolution

X-rays are emitted from a relatively large volume in bulk samples, limiting the smallest features which are visible in X-ray maps. Beam spreading also hampers attempts to make geometric measurements of features based on their boundaries in X-ray maps. This has prompted recent interest in using low voltages, and consequently mapping L or M lines, in order to minimize the blurring of the maps.An alternative strategy draws on the extensive work in image restoration (deblurring) developed in space science and astronomy since the 1960s. A recent example is the restoration of images from the Hubble Space Telescope prior to its new optics. Extensive literature exists on the theory of image restoration. The simplest case and its correspondence with X-ray mapping parameters is shown in Figures 1 and 2.Using pixels much smaller than the X-ray volume, a small object of differing composition from the matrix generates a broad, low response. This shape corresponds to the point spread function (PSF). The observed X-ray map can be modeled as an “ideal” map, with an X-ray volume of zero, convolved with the PSF. Figure 2a shows the 1-dimensional case of a line profile across a thin layer. Figure 2b shows an idealized noise-free profile which is then convolved with the PSF to give the blurred profile of Figure 2c.

A general inverse matrix series relation and associated polynomials – II

2021 ◽  
Vol 71 (2) ◽  
pp. 301-316
Author(s):  
Reshma Sanjhira
Keyword(s):  
Matrix Polynomial ◽  
Combinatorial Identities ◽  
Inverse Matrix ◽  
Matrix Polynomials ◽  
Special Cases ◽  
Series Representations ◽  
The Matrix ◽  
Associated Polynomials ◽  
Matrix Pair ◽  
Matrix Series

Abstract We propose a matrix analogue of a general inverse series relation with an objective to introduce the generalized Humbert matrix polynomial, Wilson matrix polynomial, and the Rach matrix polynomial together with their inverse series representations. The matrix polynomials of Kiney, Pincherle, Gegenbauer, Hahn, Meixner-Pollaczek etc. occur as the special cases. It is also shown that the general inverse matrix pair provides the extension to several inverse pairs due to John Riordan [An Introduction to Combinatorial Identities, Wiley, 1968].

scholarly journals Inversion of Tridiagonal Matrices Using the Dunford-Taylor’s Integral

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 870
Author(s):  
Diego Caratelli ◽  
Paolo Emilio Ricci
Keyword(s):  
Functional Analysis ◽  
Computer Algebra ◽  
Toeplitz Matrices ◽  
Test Cases ◽  
Recursive Procedure ◽  
Tridiagonal Matrices ◽  
Special Cases ◽  
The Matrix ◽  
Matrix Eigenvalues ◽  
Complex Valued

We show that using Dunford-Taylor’s integral, a classical tool of functional analysis, it is possible to derive an expression for the inverse of a general non-singular complex-valued tridiagonal matrix. The special cases of Jacobi’s symmetric and Toeplitz (in particular symmetric Toeplitz) matrices are included. The proposed method does not require the knowledge of the matrix eigenvalues and relies only on the relevant invariants which are determined, in a computationally effective way, by means of a dedicated recursive procedure. The considered technique has been validated through several test cases with the aid of the computer algebra program Mathematica©.

scholarly journals In vivo evidence for the unique kinetics of evoked dopamine release in the patch and matrix compartments of the striatum

2021 ◽  
Author(s):  
Andrea Jaquins-Gerstl ◽  
Kathryn M. Nesbitt ◽  
Adrian C. Michael
Keyword(s):  
Dopamine Release ◽  
Spatial Organization ◽  
Dorsal Striatum ◽  
Immunohistochemical Analysis ◽  
Extensive Literature ◽  
Fast Scan Cyclic Voltammetry ◽  
Medial Dorsal ◽  
The Matrix ◽  
Slow Kinetic

AbstractThe neurochemical transmitter dopamine (DA) is implicated in a number of diseases states, including Parkinson’s disease, schizophrenia, and drug abuse. DA terminal fields in the dorsal striatum and core region of the nucleus accumbens in the rat brain are organized as heterogeneous domains exhibiting fast and slow kinetic of DA release. The rates of dopamine release are significantly and substantially faster in the fast domains relative to the slow domains. The striatum is composed of a mosaic of spatial compartments known as the striosomes (patches) and the matrix. Extensive literature exists on the spatial organization of the patch and matrix compartments and their functions. However, little is known about these compartments as they relate to fast and slow kinetic DA domains observed by fast scan cyclic voltammetry (FSCV). Thus, we combined high spatial resolution of FSCV with detailed immunohistochemical analysis of these architectural compartments (patch and matrix) using fluorescence microscopy. Our findings demonstrated a direct correlation between patch compartments with fast domain DA kinetics and matrix compartments to slow domain DA kinetics. We also investigated the kinetic domains in two very distinct sub-regions in the striatum, the lateral dorsal striatum (LDS) and the medial dorsal striatum (MDS). The lateral dorsal striatum as opposed to the medial dorsal striatum is mainly governed by fast kinetic DA domains. These finding are highly relevant as they may hold key promise in unraveling the fast and slow kinetic DA domains and their physiological significance. Graphical abstract

scholarly journals The Algebraic Degree of Phase-Type Distributions

2010 ◽  
Vol 47 (03) ◽  
pp. 611-629
Author(s):  
Mark Fackrell ◽  
Qi-Ming He ◽  
Peter Taylor ◽  
Hanqin Zhang
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Polynomial Algorithm ◽  
Algebraic Degree ◽  
Nonnegative Matrices ◽  
Stieltjes Transform ◽  
Special Cases ◽  
Phase Type ◽  
Phase Type Distributions ◽  
The Matrix

This paper is concerned with properties of the algebraic degree of the Laplace-Stieltjes transform of phase-type (PH) distributions. The main problem of interest is: given a PH generator, how do we find the maximum and the minimum algebraic degrees of all irreducible PH representations with that PH generator? Based on the matrix exponential (ME) order of ME distributions and the spectral polynomial algorithm, a method for computing the algebraic degree of a PH distribution is developed. The maximum algebraic degree is identified explicitly. Using Perron-Frobenius theory of nonnegative matrices, a lower bound and an upper bound on the minimum algebraic degree are found, subject to some conditions. Explicit results are obtained for special cases.

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 Thermodynamic and Elastic Properties of Interstitial Alloy FeC with BCC Structure at Zero Pressure

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Bui Duc Tinh ◽  
Nguyen Quang Hoc ◽  
Dinh Quang Vinh ◽  
Tran Dinh Cuong ◽  
Nguyen Duc Hien
Keyword(s):  
Nearest Neighbor ◽  
Young Modulus ◽  
Thermodynamic Quantities ◽  
Atom Concentration ◽  
Main Metal ◽  
Special Cases ◽  
Analytic Expressions ◽  
Rigidity Modulus ◽  
Bcc Structure ◽  
The Mean

The analytic expressions for the thermodynamic and elastic quantities such as the mean nearest neighbor distance, the free energy, the isothermal compressibility, the thermal expansion coefficient, the heat capacities at constant volume and at constant pressure, the Young modulus, the bulk modulus, the rigidity modulus, and the elastic constants of binary interstitial alloy with body-centered cubic (BCC) structure, and the small concentration of interstitial atoms (below 5%) are derived by the statistical moment method. The theoretical results are applied to interstitial alloy FeC in the interval of temperature from 100 to 1000 K and in the interval of interstitial atom concentration from 0 to 5%. In special cases, we obtain the thermodynamic quantities of main metal Fe with BCC structure. Our calculated results for some thermodynamic and elastic quantities of main metal Fe and alloy FeC are compared with experiments.

scholarly journals Workspace Delineation of Cable-Actuated Parallel Manipulators

2004 ◽  
Author(s):  
Ethan Stump ◽  
Vijay Kumar
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Extensive Literature ◽  
Reachable Workspace ◽  
Planar Parallel Manipulator ◽  
Analytic Expressions

While there is extensive literature available on parallel manipulators in general, there has been much less attention given to cable-driven parallel manipulators. In this paper, we address the problem of analyzing the reachable workspace using the tools of semi-definite programming. We build on earlier work [1, 2] done using similar techniques by deriving limiting conditions that allow us to compute analytic expressions for the boundary of the reachable workspace. We illustrate this computation for a planar parallel manipulator with four actuators.

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.

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