scholarly journals Upper Bounds for the Isolation Number of a Matrix over Semirings

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 65
Author(s):  
LeRoy B. Beasley ◽  
Seok-Zun Song
Keyword(s):  
Upper Bound ◽  
Upper Bounds ◽  
R Matrix ◽  
The Matrix ◽  
The Given ◽  
Minimal Integer

Let S be an antinegative semiring. The rank of an m × n matrix B over S is the minimal integer r such that B is a product of an m × r matrix and an r × n matrix. The isolation number of B is the maximal number of nonzero entries in the matrix such that no two entries are in the same column, in the same row, and in a submatrix of B of the form b i , j b i , l b k , j b k , l with nonzero entries. We know that the isolation number of B is not greater than the rank of it. Thus, we investigate the upper bound of the rank of B and the rank of its support for the given matrix B with isolation number h over antinegative semirings.

scholarly journals Lower and Upper Bounds for the Discrete Bi-Directional Preemptive Conversion Problem with a Constant Price Interval

Algorithms ◽  
2020 ◽  
Vol 13 (2) ◽  
pp. 42
Author(s):  
Michael Schwarz
Keyword(s):  
Competitive Analysis ◽  
Upper Bound ◽  
Competitive Ratio ◽  
Upper Bounds ◽  
Investment Horizon ◽  
Lower And Upper Bounds ◽  
Single Period ◽  
Price Trends ◽  
The Given ◽  
Period Model

In the conversion problem, wealth has to be distributed between two assets with the objective to maximize the wealth at the end of the investment horizon. The bi-directional preemptive conversion problem with a constant price interval is the only problem, of the four main variants of the conversion problem, that has not yet been optimally solved by competitive analysis. Assuming a given number of monotonous price trends called runs, lower and upper bounds for the competitive ratio are given. In this work, the assumption of a given number of runs is rejected and lower and upper bounds for the bi-directional preemptive conversion problem with a constant price interval are given. Furthermore, an algorithm based on error balancing is given which at minimum achieves the given upper bound. It can also be shown that this algorithm is optimal for the single-period model.

The Convex Polytopes and Homogeneous Coordinate Rings of Bivariate Polynomials

2019 ◽  
Vol 16 (2) ◽  
pp. 1
Author(s):  
Shamsatun Nahar Ahmad ◽  
Nor’Aini Aris ◽  
Azlina Jumadi
Keyword(s):  
Convex Polytopes ◽  
Polynomial Systems ◽  
Matrix Formulation ◽  
Bivariate Polynomials ◽  
Homogeneous Coordinates ◽  
The Matrix ◽  
Projective Vector ◽  
Coordinate Rings ◽  
Resultant Matrix ◽  
The Given

Concepts from algebraic geometry such as cones and fans are related to toric varieties and can be applied to determine the convex polytopes and homogeneous coordinate rings of multivariate polynomial systems. The homogeneous coordinates of a system in its projective vector space can be associated with the entries of the resultant matrix of the system under consideration. This paper presents some conditions for the homogeneous coordinates of a certain system of bivariate polynomials through the construction and implementation of the Sylvester-Bèzout hybrid resultant matrix formulation. This basis of the implementation of the Bèzout block applies a combinatorial approach on a set of linear inequalities, named 5-rule. The inequalities involved the set of exponent vectors of the monomials of the system and the entries of the matrix are determined from the coefficients of facets variable known as brackets. The approach can determine the homogeneous coordinates of the given system and the entries of the Bèzout block. Conditions for determining the homogeneous coordinates are also given and proven.

scholarly journals Integrated Recycling Process of Matrices of Organic Moulding Sands

2013 ◽  
Vol 58 (3) ◽  
pp. 809-812 ◽  
Author(s):  
R. Dańko
Keyword(s):  
Recycling Process ◽  
Conceptual Approach ◽  
Assessment Index ◽  
Experimental Stand ◽  
Synthetic Resins ◽  
The Matrix ◽  
Ignition Loss ◽  
On Line ◽  
The Given ◽  
Reclamation Process

Abstract The idea and experimental verification of assumptions of the integrated recycling process of matrices of uniform self-hardening moulding sands with synthetic resins, leading to obtaining moulding sands matrix of expected quality - is presented in the hereby paper. The basis of the presented process constitutes a combination of the method of forecasting averaged ignition losses of moulding sands after casting and defining the range of necessary matrix reclamation treatments in order to obtain its full recycling. Simultaneously, the empirically determined dependence of dusts amounts emitted during the reclamation process of the matrix from the given spent sand on the ignition loss values (which is the most proper assessment index of the obtained reclaimed material quality) was taken into account. The special experimental stand for investigations of the matrix recycling process was one of the elements of the conceptual approach and verification of its assumptions. The stand was equipped with the system of current on-line control of the purification degree of matrix grains from organic binder remains. The results of own investigations, allowing to combine ignition loss values of spent moulding sands after casting knocking out with amounts of dusts generated during the mechanical reclamation treatment of such sands, were utilized in the system.

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.

A Yield Criterion of Porous Materials With Anisotropy Caused by Geometry or Distribution of Pores

1991 ◽  
Vol 113 (4) ◽  
pp. 425-429 ◽  
Author(s):  
T. Hisatsune ◽  
T. Tabata ◽  
S. Masaki
Keyword(s):  
Velocity Field ◽  
Porous Materials ◽  
Upper Bound ◽  
Volume Fraction ◽  
Yield Criterion ◽  
Longitudinal Direction ◽  
Axisymmetric Deformation ◽  
The Other ◽  
The Matrix ◽  
Spherical Cells

Axisymmetric deformation of anisotropic porous materials caused by geometry of pores or by distribution of pores is analyzed. Two models of the materials are proposed: one consists of spherical cells each of which has a concentric ellipsoidal pore; and the other consists of ellipsoidal cells each of which has a concentric spherical pore. The velocity field in the matrix is assumed and the upper bound approach is attempted. Yield criteria are expressed as ellipses on the σm σ3 plane which are longer in longitudinal direction with increasing anisotropy and smaller with increasing volume fraction of the pore. Furthermore, the axes rotate about the origin at an angle α from the σm-axis, while the axis for isotropic porous materials is on the σm-axis.

Upper bounds on the energy dissipation in turbulent precession

1996 ◽  
Vol 321 ◽  
pp. 335-370 ◽  
Author(s):  
R. R. Kerswell
Keyword(s):  
Experimental Data ◽  
Energy Dissipation ◽  
Viscous Dissipation ◽  
Upper Bound ◽  
Dissipation Rate ◽  
Oblate Spheroid ◽  
Upper Bounds ◽  
Precession Rate ◽  
Long Cylinder

Rigorous upper bounds on the viscous dissipation rate are identified for two commonly studied precessing fluid-filled configurations: an oblate spheroid and a long cylinder. The latter represents an interesting new application of the upper-bounding techniques developed by Howard and Busse. A novel ‘background’ method recently introduced by Doering & Constantin is also used to deduce in both instances an upper bound which is independent of the fluid's viscosity and the forcing precession rate. Experimental data provide some evidence that the observed viscous dissipation rate mirrors this behaviour at sufficiently high precessional forcing. Implications are then discussed for the Earth's precessional response.

scholarly journals The Essential Dimension of Stacks of Parabolic Vector Bundles over Curves

2012 ◽  
Vol 10 (3) ◽  
pp. 455-488 ◽  
Author(s):  
Indranil Biswas ◽  
Ajneet Dhillon ◽  
Nicole Lemire
Keyword(s):  
Lower Bounds ◽  
Upper Bound ◽  
Vector Bundles ◽  
Upper Bounds ◽  
Essential Dimension ◽  
Parabolic Structure ◽  
Moduli Stack

AbstractWe find upper bounds on the essential dimension of the moduli stack of parabolic vector bundles over a curve. When there is no parabolic structure, we improve the known upper bound on the essential dimension of the usual moduli stack. Our calculations also give lower bounds on the essential dimension of the semistable locus inside the moduli stack of vector bundles of rank r and degree d without parabolic structure.

ances and covariances obtained from REML are normally distributed with expectation vector and variance-covariance matrix equal to the fol-low  ing, r  espectiv    ely,   When σˆ > 0.04, let νˆ = δˆ + σˆ + σˆ − 2ωˆ + σˆ − (1 + c (7.6) be an estimate for the (7.3) reference-scaled metric in accordance with FDA Guidance (2001) and using a REML UN model. Then (Patter-son, 2003; Patterson and Jones, 2002b), this estimate is asymptotically normally distributed and unbiased with E[νˆ ] = δ +σ − (1 + c and Var[νˆ ] = 4σ + l + 4l + (1 + c ) (l )+ 2l −2(1+c − 2(1+c +4(1+c −2(1+c . Similarly, for the constant-scaled metric, when σˆ ≤ 0.04, νˆ = δˆ + σˆ + σˆ − 2ωˆ + σˆ − σˆ − 0.04(c ) (7.7) E[νˆ ] = δ +σ − 0.04(c ) Var[νˆ ] = 4σ + l + 4l + 2l − 2l − 4l + 4l − 2l . The required asymptotic upper bound √ of the 90% confidence interval can √ then be calculated as νˆ + 1.645× V̂ ar[νˆ ] or νˆ + 1.645× V̂ ar[νˆ ], where the variances are obtained by ‘plugging in’ the estimated values of the variances and covariances obtained from SAS proc mixed into the formulae for Var[νˆ ] or Var[νˆ ]. The necessary SAS code to do this is given in Appendix B. The output reveals that σˆ = 0.0714 and the upper bound is−0.060 for log(AUC). For log(Cmax), σˆ = 0.1060 and the upper bound is −0.055. As both of these upper bounds are below zero, IBE can be claimed.

2003 ◽  
pp. 367-367
Keyword(s):  
Confidence Interval ◽  
Covariance Matrix ◽  
Upper Bound ◽  
Upper Bounds ◽  
Fda Guidance ◽  
Asymptotic Upper Bound ◽  
Variance Covariance Matrix ◽  
Normally Distributed

scholarly journals State estimation for bilinear impulsive control systems under uncertainties

2018 ◽  
pp. 35-41 ◽  
Author(s):  
Oxana G. Matviychuk
Keyword(s):  
Differential Equations ◽  
State Estimation ◽  
Control Systems ◽  
Uncertain Systems ◽  
Impulsive Control ◽  
Compact Set ◽  
The Matrix ◽  
Initial States ◽  
Impulsive Control Systems ◽  
The Given

The state estimation problem for uncertain impulsive control systems with a special structure is considered. The initial states are taken to be unknown but bounded with given bounds. We assume here that the coefficients of the matrix included in the differential equations are not exactly known, but belong to the given compact set in the corresponding space. We present here algorithms that allow to find the external ellipsoidal estimates of reachable sets for such bilinear impulsive uncertain systems.

scholarly journals Transformation of land use pattern in the East Borsod coal basin from the beginning of minig industry to the political changes

2016 ◽  
Vol 10 (3-4) ◽  
pp. 223-231
Author(s):  
László Sütő ◽  
Erika Homoki ◽  
Zoltán Dobány ◽  
Péter Rózsa
Keyword(s):  
Land Cover ◽  
Human Disturbance ◽  
The Political ◽  
Early 20Th Century ◽  
Late Period ◽  
Topographic Map ◽  
Coal Basin ◽  
Land Use Pattern ◽  
The Matrix ◽  
The Given

Historical geographic studies on land cover may support the understanding of the recent state. Focusing on coal mining, this process was followed and analyzed in the case of the East Borsod Coal Basin from the early 20th century to the political change. The contemporaneous maps and manuscripts concerning the mining were evaluated using geoinformatic techniques. Moreover, digitalized topographic map coming from the early and late period of mining (1924 and 1989, respectively) were analyzed. To determine the degree of human disturbance hemerobic relations and changes of the given land cover patches were quantified on the basis of the maps of the three military surveys, too. It can be stated that montanogenic subtype of an industrialagricultural landscape has been formed in the Bükkhát area. Beside the concentrated artificial surfaces, however, relative dominance of forest forming the matrix of the landscape remained.

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