scholarly journals Homaloidal nets and ideals of fat points II: Subhomaloidal nets

2017 ◽  
Vol 27 (06) ◽  
pp. 677-715 ◽  
Author(s):  
Zaqueu Ramos ◽  
Aron Simis
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Good Deal ◽  
Detailed Examination ◽  
Symbolic Power ◽  
Fat Points ◽  
Higher Dimensional ◽  
General Plane ◽  
Classical Arithmetic ◽  
The Ideal

This work is a natural sequel to a previous paper by the authors in that it tackles problems of the same nature. Here, one aims at the ideal theoretic and homological properties of an ideal of general plane fat points for which the corresponding second symbolic power has virtual multiplicities of a proper homaloidal type. For this purpose, one carries a detailed examination of the underlying linear system at the initial degree, where a good deal of the results depends on the method of the classical arithmetic quadratic transformations of Hudson–Nagata. A subsidiary guide to understand these ideals through their initial linear systems has been supplied by questions of birationality with source [Formula: see text] and target higher dimensional spaces. This leads, in particular, to the retrieval of birational maps studied by Geramita–Gimigliano–Pitteloud, including a few of the celebrated Bordiga–White parameterizations.

scholarly journals Homaloidal nets and ideals of fat points I

2016 ◽  
Vol 19 (1) ◽  
pp. 54-77 ◽  
Author(s):  
Zaqueu Ramos ◽  
Aron Simis
Keyword(s):  
Linear System ◽  
Fat Points ◽  
Base Points ◽  
Algebraic Properties ◽  
The Ideal

We consider plane Cremona maps with proper base points and the base ideal generated by the linear system of forms defining the map. The object of this work is to study the link between the algebraic properties of the base ideal and those of the ideal of these points fattened by the virtual multiplicities arising from the linear system. We reveal conditions which naturally regulate this association, with particular emphasis on the homological side. While most classical numerical inequalities concern the three highest virtual multiplicities, here we emphasize also the role of one single highest multiplicity. In this vein we describe classes of Cremona maps for large and small values of the highest virtual multiplicity. We also deal with the delicate question as to when is the base ideal non-saturated and consider the structure of its saturation.

Abraham Maslow, Utopian Realist

2021 ◽  
pp. 002216782110076
Author(s):  
Nadine Weidman
Keyword(s):  
Linear Systems ◽  
21St Century ◽  
Shared Values ◽  
Important Lesson ◽  
Abraham Maslow ◽  
Human Community ◽  
Community Or ◽  
Non Linear Systems ◽  
American Society ◽  
The Ideal

The ideal human community or “Eupsychia” envisioned by Abraham Maslow was a place inhabited by a thousand “self-actualizing people” who shared a devotion to certain higher values. These values were, for Maslow, universally human and biologically rooted, and they included truth, beauty, justice, and the ability to become the best that one was capable of becoming. In addition to imagining it, Maslow searched for Eupsychia in reality and thought he had found it in three California locations: Non-Linear Systems, a technology company; Synanon, a drug rehab center; and Esalen, a hippie retreat. Despite its dependence on shared values, for Maslow Eupsychia was not a perfect place, either in his imagination or in reality, and he realized that its inhabitants would need ways to confront strife and deal with their differences. I suggest that his utopian realism contains an important lesson for our own highly divided 21st-century American society.

The Linear System Solver of Programs Named CORTH and KYLIN2

2017 ◽  
Author(s):  
Pingzhou Ming ◽  
Junjie Pan ◽  
Xiaolan Tu ◽  
Dong Liu ◽  
Hongxing Yu
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Nuclear Power ◽  
Experimental Results ◽  
Gmres Method ◽  
Thermal Hydraulics ◽  
Lattice Calculation ◽  
Minimal Residual

Sub-channel thermal-hydraulics program named CORTH and assembly lattice calculation program named KYLIN2 have been developed in Nuclear Power Institute of China (NPIC). For the sake of promoting the computing efficiency of these programs and achieving the better description on fined parameters of reactor, the programs’ structure and details are interpreted. Then the characteristics of linear systems of these programs are analyzed. Based on the Generalized Minimal Residual (GMRES) method, different parallel schemes and implementations are considered. The experimental results show that calculation efficiencies of them are improved greatly compared with the serial situation.

scholarly journals (M,β)-Stability of Positive Linear Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Octavian Pastravanu ◽  
Mihaela-Hanako Matcovschi
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Transient Behavior ◽  
Short Term ◽  
Time Dynamics ◽  
The Right ◽  
Long Term Behavior ◽  
Stability Concept

The main purpose of this work is to show that the Perron-Frobenius eigenstructure of a positive linear system is involved not only in the characterization of long-term behavior (for which well-known results are available) but also in the characterization of short-term or transient behavior. We address the analysis of the short-term behavior by the help of the “(M,β)-stability” concept introduced in literature for general classes of dynamics. Our paper exploits this concept relative to Hölder vectorp-norms,1≤p≤∞, adequately weighted by scaling operators, focusing on positive linear systems. Given an asymptotically stable positive linear system, for each1≤p≤∞, we prove the existence of a scaling operator (built from the right and left Perron-Frobenius eigenvectors, with concrete expressions depending onp) that ensures the best possible values for the parametersMandβ, corresponding to an “ideal” short-term (transient) behavior. We provide results that cover both discrete- and continuous-time dynamics. Our analysis also captures the differences between the cases where the system dynamics is defined by matrices irreducible and reducible, respectively. The theoretical developments are applied to the practical study of the short-term behavior for two positive linear systems already discussed in literature by other authors.

scholarly journals A Modification of Minimal Residual Iterative Method to Solve Linear Systems

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
Xingping Sheng ◽  
Youfeng Su ◽  
Guoliang Chen
Keyword(s):  
Linear System ◽  
Iterative Method ◽  
Linear Systems ◽  
Residual Error ◽  
Projection Technique ◽  
Numerical Example ◽  
Minimal Residual

We give a modification of minimal residual iteration (MR), which is 1V-DSMR to solve the linear systemAx=b. By analyzing, we find the modifiable iteration to be a projection technique; moreover, the modification of which gives a better (at least the same) reduction of the residual error than MR. In the end, a numerical example is given to demonstrate the reduction of the residual error between the 1V-DSMR and MR.

The Gray World of Practical Data Analysis: An Introduction to Part 2

2011 ◽  
Author(s):  
Gidon Eshel
Keyword(s):  
Data Analysis ◽  
Linear System ◽  
Linear Algebra ◽  
Actual Data ◽  
Distinguishing Characteristic ◽  
Real Numbers ◽  
Ideal World ◽  
Main Distinguishing Characteristic ◽  
Realistic Data ◽  
The Ideal

This chapter provides an overview of the second part of the book. This part is the crux of the matter: how to analyze actual data. While this part builds on Part 1, especially on linear algebra fundamentals covered in Part 1, the two are not redundant. The main distinguishing characteristic of Part 2 is its nuanced grayness. In the ideal world of algebra (and thus in most of part 1), things are black or white: two vectors are either mutually orthogonal or not, real numbers are either zero or not, a vector either solves a linear system or does not. By contrast, realistic data analysis, the province of Part 2, is always gray, always involves subjective decisions.

Quantum CFD Simulations for Heat Transfer Applications

2020 ◽  
Author(s):  
Chao Lu ◽  
Zhao Hu ◽  
Bei Xie ◽  
Ning Zhang
Keyword(s):  
Heat Transfer ◽  
Quantum Computing ◽  
Linear System ◽  
Linear Equation ◽  
Linear Systems ◽  
Quantum Algorithm ◽  
Quantum Circuit ◽  
Quantum Phase ◽  
Cfd Simulations ◽  
Analytical Result

Abstract In this paper, computational heat transfer (CHT) equations were solved using the state-of-art quantum computing (QC) technology. The CHT equations can be discretized into a linear equation set, which can be possibly solved by a QC system. The linear system can be characterized by Ax = b. The A matrix in this linear system is a Hermitian matrix. The linear system is then solved by using the HHL algorithm, which is a quantum algorithm to solve a linear system. The quantum circuit requires an Ancilla qubit, clock qubits, qubits for b and a classical bit to record the result. The process of the HHL algorithm can be described as follows. Firstly, the qubit for b is initialized into the phase as desire. Secondly, the quantum phase estimation (QPE) is used to determine the eigenvalues of A and the eigenvalues are stored in clock qubits. Thirdly, a Rotation gate is used to rotate the inversion of eigenvalues and information is passed to the Ancilla bit to do Pauli Y-rotation operation. Fourthly, revert the whole processes to untangle qubits and measure all of the qubits to output the final results for x. From the existing literature, a few 2 × 2 matrices were successfully solved with QC technology, proving the possibility of QC on linear systems [1]. In this paper, a quantum circuit is designed to solve a CHT problem. A simple 2 by 2 linear equation is modeled for the CHT problem and is solved by using the quantum computing. The result is compared with the analytical result. This result could initiate future studies on determining the quantum phase parameters for more complicated QC linear systems for CHT applications.

A Note About Linear Systems on Curves

1984 ◽  
Vol 27 (3) ◽  
pp. 371-374
Author(s):  
Allen Tannenbaum
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Minimal Degree ◽  
Maximal Dimension ◽  
Degree Relative ◽  
Irreducible Curve ◽  
The Given

AbstractInverting the Castelnuovo bound in two ways, we show that for given integers p ≥ 0, d > 1, n > 1, we can find a smooth irreducible curve of genus p which contains a linear system of degree d and of maximal dimension relative to the given data p and d, and a smooth irreducible curve of genus p which contains a linear system of dimension n and of minimal degree relative to the data p and n.

Multiple Harmonic Balance Method for Aperiodic Vibration of a Piecewise-Linear System

1998 ◽  
Vol 120 (1) ◽  
pp. 181-187 ◽  
Author(s):  
Y. B. Kim
Keyword(s):  
Linear System ◽  
Harmonic Balance ◽  
Piecewise Linear ◽  
Harmonic Balance Method ◽  
Steady State Solution ◽  
Balance Method ◽  
Piecewise Linear System ◽  
Higher Dimensional ◽  
Computational Procedures ◽  
The Stability

A multiple harmonic balance method is presented in this paper for obtaining the aperiodic steady-state solution of a piecewise-linear system. As the method utilizes general and systematic computational procedures, it can be applied to analyze the multi-tone or combination-tone responses for the higher dimensional nonlinear systems such as rotors. Moreover, it is capable of informing the stability of the obtained solution using Floquet theory. To demonstrate the systematic approach of the new method, the almost periodic forced vibration of an articulated loading platform (ALP) with a piecewise-linear stiffness is computed as an example.

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