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5 results on '"Chin Hee Pah"'

1. λ-model with Competing Potts Interactions on Cayley Tree of Order 2.

Author

Mukhamedov, Farrukh, Chin Hee Pah, and Jamil, Hakim

Subjects
*CAYLEY graphs, *NEAREST neighbor analysis (Statistics), *POTTS model, *STATISTICAL mechanics, *STATISTICAL research
Abstract

In this paper, we consider the λ-model on Cayley tree for order two with Potts competing nearest-neighbor and prolonged next-nearest neighbor interactions. We described the construction of the Gibbs measure for the considered model. We proved the existence of the translation-invariant limiting Gibbs measures for the model. [ABSTRACT FROM AUTHOR]

Published
2018
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2. Pitchfork Bifurcation of a Class of Discrete Dynamical Systems.

Author

Chin Hee Pah

Subjects
*BIFURCATION theory, *DYNAMICAL systems, *MATHEMATICS, *APPLIED mathematics, *DIFFERENTIAL equations
Abstract

A class of discrete dynamical systems is introduced to unify various dynamical systems that appeared in the study of phase transition phenomenon of Ising model on the Cayley tree. We give an alternative method to study the stable fixed points of these dynamical systems. The regions of non-uniqueness of stable fixed point and single stable fixed point are immediately obtained. All the previous results could be derived using this criterion. [ABSTRACT FROM AUTHOR]

Published
2017
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3. Exact Solution for an Ising Model on the Cayley Tree of Order 5.

Author

Jamil, Hakim and Chin Hee Pah

Subjects
*ISING model, *CAYLEY graphs, *TREE graphs, *MEASURE theory, *PHASE transitions, *NEAREST neighbor analysis (Statistics)
Abstract

We investigate an Ising model with two restricted competing interactions (nearest neighbors, and one-level neighbors) on the Cayley tree of order 5. The translation Gibbs measures is considered for this model. Our result of the critical curve shows that the phase transition occurs in this model, further it confirms a particular case of a conjecture. [ABSTRACT FROM AUTHOR]

Published
2016
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4. On Connected Sub-Tree with Fixed Nodes in Cayley Tree of Order 2.

Author

Mukhamedov, Farrukh, Chin Hee Pah, and Saburov, Mansoor

Subjects
*CAYLEY algebras, *CATALAN numbers, *COMBINATORICS, *LINEAR equations, *MATHEMATICAL analysis
Abstract

In this paper we found an exact formula for a finite sub-tree counting problem. Note that the formulas, which correspond to two extremal cases, are Catalan Triangle introduced by Shapiro and ballot Catalan triangles. The general formula could be expressed as a linear combination of these Catalan triangles. [ABSTRACT FROM AUTHOR]

Published
2017

5. Single Polygon Counting on Cayley Tree of Order 3.

Author

Chin Hee Pah

Subjects
*CATALAN numbers, *GAMMA functions, *TRANSCENDENTAL functions, *POLYGONS, *POINT mappings (Mathematics)
Abstract

We showed that one form of generalized Catalan numbers is the solution to the problem of finding different connected component with finite vertices containing a fixed root for the semi-infinite Cayley tree of order 3. We give the formula for the full graph, Cayley tree of order 3 which is derived from the generalized Catalan numbers. Using ratios of Gamma functions, two upper bounds are given for problem defined on semi-infinite Cayley tree of order 3 as well as the full graph. [ABSTRACT FROM AUTHOR]

Published
2010
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