scholarly journals New bounds for the minimum eigenvalue of 𝓜-tensors

2017 ◽  
Vol 15 (1) ◽  
pp. 296-303 ◽  
Author(s):  
Jianxing Zhao ◽  
Caili Sang
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Minimum Eigenvalue ◽  
Numerical Examples ◽  
Theoretical Results

Abstract A new lower bound and a new upper bound for the minimum eigenvalue of an 𝓜-tensor are obtained. It is proved that the new lower and upper bounds improve the corresponding bounds provided by He and Huang (J. Inequal. Appl., 2014, 2014, 114) and Zhao and Sang (J. Inequal. Appl., 2016, 2016, 268). Finally, two numerical examples are given to verify the theoretical results.

scholarly journals A Computational Perspective on Network Coding

2010 ◽  
Vol 2010 ◽  
pp. 1-11
Author(s):  
Qin Guo ◽  
Mingxing Luo ◽  
Lixiang Li ◽  
Yixian Yang
Keyword(s):  
Graph Theory ◽  
Computational Complexity ◽  
Lower Bound ◽  
Network Coding ◽  
Upper Bound ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Multicast Networks ◽  
Computational Perspective ◽  
Source Rate

From the perspectives of graph theory and combinatorics theory we obtain some new upper bounds on the number of encoding nodes, which can characterize the coding complexity of the network coding, both in feasible acyclic and cyclic multicast networks. In contrast to previous work, during our analysis we first investigate the simple multicast network with source rateh=2, and thenh≥2. We find that for feasible acyclic multicast networks our upper bound is exactly the lower bound given by M. Langberg et al. in 2006. So the gap between their lower and upper bounds for feasible acyclic multicast networks does not exist. Based on the new upper bound, we improve the computational complexity given by M. Langberg et al. in 2009. Moreover, these results further support the feasibility of signatures for network coding.

Minimization of Bounded Cable Tensions in Cable-Based Parallel Manipulators

2007 ◽  
Author(s):  
Mahir Hassan ◽  
Amir Khajepour
Keyword(s):  
Lower Bound ◽  
Numerical Method ◽  
Upper Bound ◽  
Task Force ◽  
Parallel Manipulators ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Alternating Projection ◽  
Alternating Projection Method ◽  
Cable Forces

In this work, the application of the Dykstra’s alternating projection method to find the minimum-2-norm solution for actuator forces is discussed in the case when lower and upper bounds are imposed on the actuator forces. The lower bound is due to specified pretension desired in the cables and the upper bound is due to the maximum allowable forces in the cables. This algorithm presents a systematic numerical method to determine whether or not a solution exists to the cable forces within these bounds and, if it does exist, calculate the minimum-2-norm solution for the cable forces for a given task force. This method is applied to an example 2-DOF translational cable-driven manipulator and a geometrical demonstration is presented.

Asymptotic bounds for the fluid queue fed by sub-exponential On/Off sources

2000 ◽  
Vol 32 (01) ◽  
pp. 244-255 ◽  
Author(s):  
V. Dumas ◽  
A. Simonian
Keyword(s):  
Lower Bound ◽  
Finite Number ◽  
Upper Bound ◽  
Content Distribution ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Fluid Queue ◽  
Asymptotic Bounds ◽  
Multiplicative Factor ◽  
Buffer Content

We consider a fluid queue fed by a superposition of a finite number of On/Off sources, the distribution of the On period being subexponential for some of them and exponential for the others. We provide general lower and upper bounds for the tail of the stationary buffer content distribution in terms of the so-called minimal subsets of sources. We then show that this tail decays at exponential or subexponential speed according as a certain parameter is smaller or larger than the ouput rate. If we replace the subexponential tails by regularly varying tails, the upper bound and the lower bound are sharp in that they differ only by a multiplicative factor.

scholarly journals Almost simplicial polytopes: the lower and upper bound theorems

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Eran Nevo ◽  
Guillermo Pineda-Villavicencio ◽  
Julien Ugon ◽  
David Yost
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Upper Bound Theorem ◽  
Simplicial Polytopes ◽  
Full Version ◽  
The Face ◽  
International Audience ◽  
Bound Theorem

International audience this is an extended abstract of the full version. We study n-vertex d-dimensional polytopes with at most one nonsimplex facet with, say, d + s vertices, called almost simplicial polytopes. We provide tight lower and upper bounds for the face numbers of these polytopes as functions of d, n and s, thus generalizing the classical Lower Bound Theorem by Barnette and Upper Bound Theorem by McMullen, which treat the case s = 0. We characterize the minimizers and provide examples of maximizers, for any d.

scholarly journals Iterative estimation of total π-electron energy

2005 ◽  
Vol 70 (10) ◽  
pp. 1193-1197 ◽  
Author(s):  
Lemi Türker ◽  
Ivan Gutman
Keyword(s):  
Lower Bound ◽  
Electron Energy ◽  
Upper Bound ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Benzenoid Hydrocarbons ◽  
Total Electron ◽  
Iterative Estimation ◽  
Total Electron Energy ◽  
Almost All

In this work, the lower and upper bounds for total ?-electron energy (E) was studied. A method is presented, by means of which, starting with a lower bound EL and an upper bound EU for E, a sequence of auxiliary quantities E0 E1, E2,? is computed, such that E0 = EL, E0 < E1 < E2 < ?, and E = EU. Therefore, an integer k exists, such that Ek E < Ek+1. If the estimates EL and EU are of the McClelland type, then k is called the McClelland number. For almost all benzenoid hydrocarbons, k = 3.

Reliability Analysis of Truss Structures by Using Matrix Method

1980 ◽  
Vol 102 (4) ◽  
pp. 749-756 ◽  
Author(s):  
Y. Murotsu ◽  
H. Okada ◽  
K. Niwa ◽  
S. Miwa
Keyword(s):  
Lower Bound ◽  
Failure Probability ◽  
Matrix Method ◽  
Failure Criteria ◽  
Upper Bounds ◽  
Truss Structures ◽  
Lower And Upper Bounds ◽  
Numerical Examples ◽  
Modes Of Failure ◽  
Complete Failure

This paper proposes a method of systematically generating the failure criteria of truss structures by using Matrix Method. The resulting criterion for a statically determinate truss is simple and its failure probability is easily evaluated. In case of a statically indeterminate truss, however, there are many possible modes or paths to complete failure of the structure and it is impossible in practice to generate all of them. Hence, the failure probability is estimated by evaluating its lower and upper bounds. The lower bound is evaluated by selecting the dominant modes of failure and calculating their probabilities. The upper bound is evaluated by assuming that the redundant truss behaves itself like a statically determinate truss, i.e., the structure fails if any one member is subject to failure. Numerical examples are provided to demonstrate the applicability of the propsed methods.

scholarly journals Some Bounds on Eigenvalues of the Hadamard Product and the Fan Product of Matrices

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 147
Author(s):  
Qianping Guo ◽  
Jinsong Leng ◽  
Houbiao Li ◽  
Carlo Cattani
Keyword(s):  
Lower Bound ◽  
Spectral Radius ◽  
Upper Bound ◽  
Hadamard Product ◽  
Simple Type ◽  
Nonnegative Matrices ◽  
Minimum Eigenvalue ◽  
Numerical Examples ◽  
Product Of Matrices

In this paper, an upper bound on the spectral radius ρ ( A ∘ B ) for the Hadamard product of two nonnegative matrices (A and B) and the minimum eigenvalue τ ( C ★ D ) of the Fan product of two M-matrices (C and D) are researched. These bounds complement some corresponding results on the simple type bounds. In addition, a new lower bound on the minimum eigenvalue of the Fan product of several M-matrices is also presented. These results and numerical examples show that the new bounds improve some existing results.

BOUNDS ON THE MINIMAL SUMSET SIZE FUNCTION IN GROUPS

2007 ◽  
Vol 03 (04) ◽  
pp. 503-511 ◽  
Author(s):  
SHALOM ELIAHOU ◽  
MICHEL KERVAIRE
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Solvable Groups ◽  
Upper Bounds ◽  
Minimal Size ◽  
Lower And Upper Bounds ◽  
Numerical Function ◽  
Size Function

In this paper, we give lower and upper bounds for the minimal size μG(r,s) of the sumset (or product set) of two finite subsets of given cardinalities r,s in a group G. Our upper bound holds for solvable groups, our lower bound for arbitrary groups. The results are expressed in terms of variants of the numerical function κG(r,s), a generalization of the Hopf–Stiefel function that, as shown in [6], exactly models μG(r,s) for G abelian.

scholarly journals On the Number of Maximal Bipartite Subgraphs of a Graph

2002 ◽  
Vol 9 (17) ◽  
Author(s):  
Bolette Ammitzbøll Madsen ◽  
Jesper Makholm Byskov ◽  
Bjarke Skjernaa
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Infinite Family ◽  
Upper Bounds ◽  
Lower And Upper Bounds

We show new lower and upper bounds on the number of maximal induced bipartite subgraphs of graphs with n vertices. We present an infinite family of graphs having 105^{n/10} ~= 1.5926^n such subgraphs, which improves an earlier lower bound by Schiermeyer (1996). We show an upper bound of n . 12^{n/4} ~= n . 1.8613^n and give an algorithm that lists all maximal induced bipartite subgraphs in time proportional to this bound. This is used in an algorithm for checking 4-colourability of a graph running within the same time bound.

NUMBER OF SOLUTIONS FOR QUARTIC SIMPLE THUE EQUATIONS

2012 ◽  
Vol 08 (06) ◽  
pp. 1367-1386 ◽  
Author(s):  
ISAO WAKABAYASHI
Keyword(s):  
Lower Bound ◽  
Approximation Method ◽  
Upper Bound ◽  
Continued Fraction ◽  
Padé Approximation ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Number Of Solutions ◽  
Partial Quotients ◽  
Thue Equation

Let F(X, Y) = bX4 - aX3Y - 6bX2Y2 + aXY3 + bY4 ∈ Z[X, Y]. We show that the number of solutions for the Thue equation F(x, y) = ±1 is 0 or 4 except for a few already known cases. To obtain an upper bound for the size of solutions, we use Padé approximation method. To obtain a lower bound for the size of solutions, we construct a continued fraction with positive or negative rational partial quotients. This construction is carried out carefully by using special properties of the form F. Combining these lower and upper bounds, we obtain the result.

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