scholarly journals Rigid Linkages and Partial Zero Forcing

10.37236/8097 ◽  
2019 ◽  
Vol 26 (2) ◽  
Author(s):  
Daniela Ferrero ◽  
Mary Flagg ◽  
H. Tracy Hall ◽  
Leslie Hogben ◽  
Jephian C.-H. Lin ◽  
...  
Keyword(s):  
Upper Bound ◽  
Special Kind ◽  
Symmetric Matrices ◽  
Zero Forcing ◽  
The Real ◽  
Related Notion ◽  
Maximum Multiplicity ◽  
Multiplicity Of An Eigenvalue

Connections between vital linkages and zero forcing are established. Specifically, the notion of a rigid linkage is introduced as a special kind of unique linkage and it is shown that spanning forcing paths of a zero forcing process form a spanning rigid linkage and thus a vital linkage. A related generalization of zero forcing that produces a rigid linkage via a coloring process is developed. One of the motivations for introducing zero forcing is to provide an upper bound on the maximum multiplicity of an eigenvalue among the real symmetric matrices described by a graph. Rigid linkages and a related notion of rigid shortest linkages are utilized to obtain bounds on the multiplicities of eigenvalues of this family of matrices.

The Inverse Eigenvalue Problem for Symmetric Doubly Arrow Matrices

2013 ◽  
Vol 444-445 ◽  
pp. 625-627
Author(s):  
Kan Ming Wang ◽  
Zhi Bing Liu ◽  
Xu Yun Fei
Keyword(s):  
Eigenvalue Problem ◽  
Special Kind ◽  
Inverse Eigenvalue Problem ◽  
Symmetric Matrices ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
The Real ◽  
Inverse Eigenvalue ◽  
Necessary And Sufficient

In this paper we present a special kind of real symmetric matrices: the real symmetric doubly arrow matrices. That is, matrices which look like two arrow matrices, forward and backward, with heads against each other at the station, . We study a kind of inverse eigenvalue problem and give a necessary and sufficient condition for the existence of such matrices.

scholarly journals A Viable Approach to Mitigating Irreproducibility

Stats ◽  
2021 ◽  
Vol 4 (1) ◽  
pp. 205-215
Author(s):  
David Trafimow ◽  
Tonghui Wang ◽  
Cong Wang
Keyword(s):  
Upper Bound ◽  
Recent Article ◽  
Practical Problem ◽  
The Real ◽  
Viable Approach ◽  
Real Universe ◽  
The Ideal

In a recent article, Trafimow suggested the usefulness of imagining an ideal universe where the only difference between original and replication experiments is the operation of randomness. This contrasts with replication in the real universe where systematicity, as well as randomness, creates differences between original and replication experiments. Although Trafimow showed (a) that the probability of replication in the ideal universe places an upper bound on the probability of replication in the real universe, and (b) how to calculate the probability of replication in the ideal universe, the conception is afflicted with an important practical problem. Too many participants are needed to render the approach palatable to most researchers. The present aim is to address this problem. Embracing skewness is an important part of the solution.

scholarly journals The location of classified edges due to the change in the geometric multiplicity of an eigenvalue in a tree

2019 ◽  
Vol 7 (1) ◽  
pp. 257-262
Author(s):  
Kenji Toyonaga
Keyword(s):  
Symmetric Matrix ◽  
Symmetric Matrices ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Geometric Multiplicity ◽  
Necessary And Sufficient ◽  
Multiplicity Of An Eigenvalue

Abstract Given a combinatorially symmetric matrix A whose graph is a tree T and its eigenvalues, edges in T can be classified in four categories, based upon the change in geometric multiplicity of a particular eigenvalue, when the edge is removed. We investigate a necessary and sufficient condition for each classification of edges. We have similar results as the case for real symmetric matrices whose graph is a tree. We show that a g-2-Parter edge, a g-Parter edge and a g-downer edge are located separately from each other in a tree, and there is a g-neutral edge between them. Furthermore, we show that the distance between a g-downer edge and a g-2-Parter edge or a g-Parter edge is at least 2 in a tree. Lastly we give a combinatorially symmetric matrix whose graph contains all types of edges.

scholarly journals Matrix Games with Interval-Valued 2-Tuple Linguistic Information

Games ◽  
2018 ◽  
Vol 9 (3) ◽  
pp. 62 ◽  
Author(s):  
Anjali Singh ◽  
Anjana Gupta
Keyword(s):  
Linear Programming ◽  
Lower Bound ◽  
Real World ◽  
Upper Bound ◽  
Duality Theorem ◽  
Matrix Game ◽  
Matrix Games ◽  
Linguistic Information ◽  
The Real ◽  
Interval Valued

In this paper, a two-player constant-sum interval-valued 2-tuple linguistic matrix game is construed. The value of a linguistic matrix game is proven as a non-decreasing function of the linguistic values in the payoffs, and, hence, a pair of auxiliary linguistic linear programming (LLP) problems is formulated to obtain the linguistic lower bound and the linguistic upper bound of the interval-valued linguistic value of such class of games. The duality theorem of LLP is also adopted to establish the equality of values of the interval linguistic matrix game for players I and II. A flowchart to summarize the proposed algorithm is also given. The methodology is then illustrated via a hypothetical example to demonstrate the applicability of the proposed theory in the real world. The designed algorithm demonstrates acceptable results in the two-player constant-sum game problems with interval-valued 2-tuple linguistic payoffs.

VERONESE ARRANGEMENTS OF HYPERPLANES IN REAL PROJECTIVE SPACES

2012 ◽  
Vol 23 (05) ◽  
pp. 1250061 ◽  
Author(s):  
KOJI CHO ◽  
MASAAKI YOSHIDA
Keyword(s):  
General Position ◽  
Special Kind ◽  
Projective Spaces ◽  
Hyperplane Arrangements ◽  
The Real ◽  
Arrangements Of Hyperplanes

This paper studies chambers cut out by a special kind of hyperplane arrangements in general position, the Veronese arrangements, in the real projective spaces.

LOWER BOUNDS FOR STREETS AND GENERALIZED STREETS

2001 ◽  
Vol 11 (04) ◽  
pp. 401-421 ◽  
Author(s):  
ALEJANDRO LÓPEZ-ORTIZ ◽  
SVEN SCHUIERER
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Real Line ◽  
Upper Bound ◽  
Competitive Ratio ◽  
Search Strategy ◽  
The Real ◽  
Simple Polygons ◽  
On Line ◽  
Special Classes

We present lower bounds for on-line searching problems in two special classes of simple polygons called streets and generalized streets. In streets we assume that the location of the target is known to the robot in advance and prove a lower bound of [Formula: see text] on the competitive ratio of any deterministic search strategy—which can be shown to be tight. For generalized streets we show that if the location of the target is not known, then there is a class of orthogonal generalized streets for which the competitive ratio of any search strategy is at least [Formula: see text] in the L2-metric—again matching the competitive ratio of the best known algorithm. We also show that if the location of the target is known, then the competitive ratio for searching in generalized streets in the L1-metric is at least 9 which is tight as well. The former result is based on a lower bound on the average competitive ratio of searching on the real line if an upper bound of D to the target is given. We show that in this case the average competitive ratio is at least 9-O(1/ log D).

scholarly journals APPROXIMATE SOLUTION OF ONE PROBLEM ON ELECTRICAL OSCILLATIONS IN WIRES WITH THE USE OF POLYLOGARITHMS

2017 ◽  
Vol 60 (4) ◽  
pp. 334-340 ◽  
Author(s):  
P. G. Lasy ◽  
I. N. Meleshko
Keyword(s):  
Approximate Solution ◽  
Initial Conditions ◽  
Fourier Method ◽  
Special Kind ◽  
Elementary Functions ◽  
The Real ◽  
First Order ◽  
Homogeneous Wave ◽  
Transcendental Functions ◽  
Current Flows

The article considers a mixed problem with homogeneous boundary conditions for onedimensional homogeneous wave equation. Such a problem can arise, for example, when studying oscillations of current and voltage in the conductor through which electric current flows, while the line is free from distortion. The solution can be found with the use of the Fourier method in the form of trigonometric series. This representation is of purely theoretical interest, because the real calculation should be, first, to find a large number of coefficients of the integrals, which in itself is not a trivial task and, second, it is almost impossible to assess the error of the calculations. An alternative way of solving this problem based on the use of transcendental functions i. e. polylogarithms that represent complex power series of a special kind. The exact solution of the problem is expressed through the imaginary part of a polylogarithm of the first order on the single circle and the approximate one – via the real part of the dilogarithm. In addition, if the initial conditions in the problem are elementary functions, then the solution is also computed using elementary functions. A simple and effective error estimate of the approximate solution has been found. It does not depend on time and it has the first-order of accuracy regarding the step of a partitioning segment of the numerical axis on which the problem is considered. This valuation is uniform with respect to the variables of the problem – both spatial and temporal. 

Sign in / Sign up

Export Citation Format

Share Document