scholarly journals A generalization of the matrix form of the Brunn-Minkowski inequality

2007 ◽  
Vol 83 (1) ◽  
pp. 125-134 ◽  
Author(s):  
Jun Yuan ◽  
Gangsong Lenga
Keyword(s):  
Minkowski Inequality ◽  
Matrix Form ◽  
Subject Classification ◽  
Primary 52A40 ◽  
The Matrix

AbstractIn this paper, we establish an extension of the matrix form of the Brunn-Minkowski inequality. As applications, we give generalizations on the metric addition inequality of Alexander.2000 Mathematics subject classification: primary 52A40.

An Application of Fuzzy Clustering to Customer Portfolio Analysis in Automotive Industry

2016 ◽  
Vol 5 (2) ◽  
pp. 13-25
Author(s):  
Abdulkadir Hiziroglu ◽  
Umit Dursun Senbas
Keyword(s):  
Fuzzy Clustering ◽  
Automotive Industry ◽  
Quantitative Assessment ◽  
Portfolio Analysis ◽  
Matrix Form ◽  
Automotive Supplier ◽  
Qualitative And Quantitative ◽  
Marketing Managers ◽  
The Matrix

Having achieved an optimized customer portfolio has been of significant importance for companies. The literature provides several portfolio models and vast majority of them are in matrix form where several descriptors are used as dimensions of the matrix. These dimensions are characterized in ambiguity and require specific methods to tackle with it. The aim of this paper is to utilize fuzzy clustering in customer portfolio analysis to reduce this uncertainty and to make a comparison with a traditional customer portfolio model. A dataset of 130 customers of an automotive supplier in Turkey is used to perform the analyses and the results are compared with a conventional customer portfolio matrix. By making use of substantiality and balance of portfolio parameters, a qualitative and quantitative assessment of categorization generated by both approaches are evaluated. The use of fuzzy clustering gives more substantial clusters and a more balanced customer portfolio compared to the traditional matrix form of portfolio. Marketing managers can understand their overall customer portfolio better and reduce the effect of descriptive indicators via benefiting the fuzzy clustering results.

Matrix form of interval multivariable gray model and its application

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Sandang Guo ◽  
Yaqian Jing ◽  
Bingjun Li
Keyword(s):  
Three Dimensional ◽  
Original Data ◽  
Upper Bounds ◽  
Matrix Form ◽  
Gray Model ◽  
Interval Numbers ◽  
Content Type ◽  
The Matrix ◽  
Number Sequences ◽  
The Difference

PurposeThe purpose of this paper is to make multivariable gray model to be available for the application on interval gray number sequences directly, the matrix form of interval multivariable gray model (IMGM(1,m,k) model) is constructed to simulate and forecast original interval gray number sequences in this paper.Design/methodology/approachFirstly, the interval gray number is regarded as a three-dimensional column vector, and the parameters of multivariable gray model are expressed in matrix form. Based on the dynamic gray action and optimized background value, the interval multivariable gray model is constructed. Finally, two examples and comparisons are carried out to verify the effectiveness of IMGM(1,m,k) model.FindingsThe model is applied to simulate and predict expert value, foreign direct investment, automobile sales and steel output, respectively. The results show that the proposed model has better simulation and prediction performance than another two models.Practical implicationsDue to the uncertainty information and continuous changing of reality, the interval gray numbers are used to characterize full information of original data. And the IMGM(1,m,k) model not only considers the characteristics of parameters changing with time but also takes into account information on lower, middle and upper bounds of interval gray numbers simultaneously to make better suitable for practical application.Originality/valueThe main contribution of this paper is to propose a new interval multivariable gray model, which considers the interaction between the lower, middle and upper bounds of interval numbers and need not to transform interval gray number sequences into real sequences. According to combining different characteristics of each bound of interval gray numbers, the matrix form of interval multivariable gray model is established to simulate and forecast interval gray numbers. In addition, the model introduces dynamic gray action to reflect the changes of parameters over time. Instead of white equation of classic MGM(1,m), the difference equation is directly used to solve the simulated and predicted values.

Symmetries of the Degeneracy of the Vertebrate Mitochondrial Genetic Code in the Matrix Form

2010 ◽  
pp. 31-49
Author(s):  
Sergey Petoukhov ◽  
Matthew He
Keyword(s):  
Mathematical Modeling ◽  
Genetic Code ◽  
Matrix Form ◽  
Black And White ◽  
Mitochondrial Genetic Code ◽  
The Matrix

Symmetries of the degeneracy of the vertebrate mitochondrial genetic code in the mosaic matrix form of its presentation are described in this chapter. The initial black-and-white genomatrix of this code is reformed into a new mosaic matrix when internal positions in all triplets are permuted simultaneously. It is revealed unexpectedly that for all six variants of positional permutations in triplets (1-2-3, 2-3-1, 3-1-2, 1-3-2, 2-1-3, 3-2-1) the appropriate genetic matrices possess symmetrical mosaics of the code degeneracy. Moreover the six appropriate mosaic matrices in their binary presentation have the general non-trivial property of their “tetra-reproduction,” which can be utilized in particular for mathematical modeling of the phenomenon of the tetra-division of gametal cells in meiosis. Mutual interchanges of the genetic letters A, C, G, U in the genomatrices lead to new mosaic genomatrices, which possess similar symmetrical and tetra-reproduction properties as well.

Cayley kinematics and the Cayley form of dynamic equations

2005 ◽  
Vol 461 (2055) ◽  
pp. 761-781 ◽  
Author(s):  
Andrew J. Sinclair ◽  
John E. Hurtado
Keyword(s):  
Euler Equations ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Rigid Bodies ◽  
Matrix Form ◽  
Dynamic Equations ◽  
Cayley Transform ◽  
Higher Dimensional ◽  
The Matrix ◽  
General Motion

The Cayley transform and the Cayley–transform kinematic relationships are an important and fascinating set of results that have relevance in N –dimensional orientations and rotations. In this paper these results are used in two significant ways. First, they are used in a new derivation of the matrix form of the generalized Euler equations of motion for N –dimensional rigid bodies. Second, they are used to intimately relate the motion of general mechanical systems to the motion of higher–dimensional rigid bodies. This approach can be used to describe an enormous variety of systems, one example being the representation of general motion of an N –dimensional body as pure rotations of an ( N + 1)–dimensional body.

Legendre Collocation Method to Solve the Riccati Equations with Functional Arguments

2020 ◽  
Vol 17 (10) ◽  
pp. 2050011
Author(s):  
Şuayip Yüzbaşı ◽  
Gamze Yıldırım
Keyword(s):  
Approximate Solutions ◽  
Coefficient Matrix ◽  
Numerical Results ◽  
Matrix Form ◽  
Algebraic Equations ◽  
Mixed Condition ◽  
Collocation Points ◽  
Nonlinear Algebraic Equations ◽  
The Matrix ◽  
Legendre Collocation Method

In this study, a method for numerically solving Riccatti type differential equations with functional arguments under the mixed condition is presented. For the method, Legendre polynomials, the solution forms and the required expressions are written in the matrix form and the collocation points are defined. Then, by using the obtained matrix relations and the collocation points, the Riccati problem is reduced to a system of nonlinear algebraic equations. The condition in the problem is written in the matrix form and a new system of the nonlinear algebraic equations is found with the aid of the obtained matrix relation. This system is solved and thus the coefficient matrix is detected. This coefficient matrix is written in the solution form and hence approximate solution is obtained. In addition, by defining the residual function, an error problem is established and approximate solutions which give better numerical results are obtained. To demonstrate that the method is trustworthy and convenient, the presented method and error estimation technique are explicated by numerical examples. Consequently, the numerical results are shown more clearly with the aid of the tables and graphs and also the results are compared with the results of other methods.

scholarly journals A characterization of the semigroup of matrix units

1980 ◽  
Vol 29 (3) ◽  
pp. 291-296
Author(s):  
Bernard R. Gelbaum ◽  
Stephen Schanuel
Keyword(s):  
Subject Classification ◽  
M 10 ◽  
20 M 10 ◽  
The Matrix ◽  
Matrix Units

AbstractLet I be a set and let (I) denote the set consisting of the 0 matrix over I × I and the matrix units over I × I. Then for x, z in (I) and x≠0≠z, xyz≠0 has precisely one solution y. This and several other statements are shown to be equivalent characterizations of (I) regarded as a semigroup with zero.1980 Mathematics subject classification (Amer. Math. Soc.): 20 M 10.

A Way of Detecting Local Muon-Flux Anisotropies with the Matrix-Form Data of the URAGAN Hodoscope

2019 ◽  
Vol 83 (5) ◽  
pp. 647-649 ◽  
Author(s):  
M. N. Dobrovolsky ◽  
I. I. Astapov ◽  
N. S. Barbashina ◽  
A. D. Gvishiani ◽  
V. G. Getmanov ◽  
...  
Keyword(s):  
Muon Flux ◽  
Matrix Form ◽  
The Matrix

Approximate Solution Of The System Of Non-Linear Volterra Integro-Differential Equations

2008 ◽  
Vol 8 (1) ◽  
pp. 77-85 ◽  
Author(s):  
A. KHANI ◽  
M.M. MOGHADAM ◽  
S. SHAHMORAD
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Numerical Solution ◽  
Matrix Form ◽  
New Method ◽  
Numerical Computations ◽  
Non Linear ◽  
The Matrix ◽  
Computational Aspects

Abstract In this paper we develop a new method to find a numerical solution for the system of non-linear Volterra integro-differential equations (SNVE). To this end, we present our method based on the matrix form of SNVE. The corresponding unknown coefficients of our method have been determined by using the computational aspects of matrices. Finally the accuracy of the method has been verified by presenting some numerical computations.

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