A Simple Algorithm for Solving the n-Dimensional linear Diophantine Equation

1975 ◽  
Vol 68 (1) ◽  
pp. 56-57
Author(s):  
Aziz Ibrahim ◽  
Edward J. Gucker
Keyword(s):  
General Solution ◽  
Diophantine Equation ◽  
Simple Algorithm ◽  
Euclidean Algorithm ◽  
Transformation Matrix ◽  
Matrix Transformation ◽  
Two Dimensional ◽  
Linear Diophantine Equation ◽  
The Given

In an earlier paper, we showed that the Euclidean algorithm could be written as a matrix transformation to obtain the solution of a two-dimensional Diophantine equation (Ibrahim and Gucker, 1972). In the present paper, we generalize this approach to n-dimensional and also simplify the algorithm that produces the transformation matrix. We also show that the final matrix contains the most general solution of the given Diophantine equation.

A fixed point approach to the stability of sextic Lie *-derivations

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4933-4944
Author(s):  
Dongseung Kang ◽  
Heejeong Koh
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Single Case ◽  
Fixed Point Method ◽  
Point Method ◽  
Fixed Point Approach ◽  
The Stability ◽  
The Given ◽  
Lie Derivations

We obtain a general solution of the sextic functional equation f (ax+by)+ f (ax-by)+ f (bx+ay)+ f (bx-ay) = (ab)2(a2 + b2)[f(x+y)+f(x-y)] + 2(a2-b2)(a4-b4)[f(x)+f(y)] and investigate the stability of sextic Lie *-derivations associated with the given functional equation via fixed point method. Also, we present a counterexample for a single case.

A general solution method for two-dimensional nonplanar oxidation

1983 ◽  
Vol 30 (9) ◽  
pp. 993-998 ◽  
Author(s):  
Daeje Chin ◽  
Soo-Young Oh ◽  
R.W. Dutton
Keyword(s):  
General Solution ◽  
Solution Method ◽  
Two Dimensional

Einführung in eine anorganische Strukturchemie

1986 ◽  
Vol 175 (3-4) ◽  
Author(s):  
E. Hellner
Keyword(s):  
Three Dimensional ◽  
Standard Setting ◽  
Transformation Matrix ◽  
Two Dimensional ◽  
Coordination Polyhedra ◽  
Systematic Description ◽  
Point Configurations ◽  
Inorganic Structure

AbstractA systematic description and classification of inorganic structure types is proposed on the basis of homogeneous or heterogeneous point configurations (Bauverbände) described by invariant lattice complexes and coordination polyhedra; subscripts or matrices explain the transformation of the complexes in respect (M) to their standard setting; the value of the determinant of the transformation matrix defines the order of the complex. The Bauverbände (frameworks) may be described by three-dimensional networks or two-dimensional nets explicitely shown with structures types of the

scholarly journals Selection of Pairings Reaching Evenly Across the Data (SPREAD): A simple algorithm to design maximally informative fully crossed mating experiments

2014 ◽  
Author(s):  
Kolea Zimmerman ◽  
Daniel Levitis ◽  
Ethan Addicott ◽  
Anne Pringle
Keyword(s):  
Nearest Neighbor ◽  
Simple Algorithm ◽  
Two Dimensional ◽  
Neighbor Distance ◽  
Crossing Experiments ◽  
The Mean ◽  
Parameter Values ◽  
Selection Of ◽  
Novel Algorithm ◽  
Trait Space

We present a novel algorithm for the design of crossing experiments. The algorithm identifies a set of individuals (a ?crossing-set?) from a larger pool of potential crossing-sets by maximizing the diversity of traits of interest, for example, maximizing the range of genetic and geographic distances between individuals included in the crossing-set. To calculate diversity, we use the mean nearest neighbor distance of crosses plotted in trait space. We implement our algorithm on a real dataset ofNeurospora crassastrains, using the genetic and geographic distances between potential crosses as a two-dimensional trait space. In simulated mating experiments, crossing-sets selected by our algorithm provide better estimates of underlying parameter values than randomly chosen crossing-sets.

Projection Transformation on 3D Object’s Three Views

2014 ◽  
Vol 1049-1050 ◽  
pp. 1950-1953
Author(s):  
Yu Lei Wang ◽  
Yin Han Gao ◽  
Wei Lei Wang
Keyword(s):  
Transformation Matrix ◽  
Matrix Transformation ◽  
Practical Application ◽  
3D Object ◽  
Transformation Algorithm ◽  
Projection Transformation

We always use projection transformation to display and draw 3D object. With the aid of matrix transformation algorithm, this paper deduces projection transformation matrix of 3D object’s three views, gets these points’planar coordinate, then we can present the three views. It has practical application value.

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