On connected sub-tree of Cayley tree of order 2 with fixed nodes by Mukhamedov, Farrukh, Pah, Chin Hee, Saburov, Mansoor

“…We found an exact formulation for a finite sub-tree counting problem. Solution to two extremal cases are Catalan Triangle introduced by Shapiro and ballot Catalan triangles. …”
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On quantum Markov chains on Cayley tree II: phase transitions for the associated chain with XY -Model on the Cayley tree of order tree by Accardi, Luigi, Mukhamedov, Farrukh, Saburov, Mansoor

“…In the present paper, we study forward quantum Markov chains (QMC) defined on a Cayley tree. Using the tree structure of graphs, we give a construction of quantum Markov chains on a Cayley tree. …”
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Lattice models with interactions on Caylay tree by Mukhamedov, Farrukh

“…We consider an Ising competitive model defined over a triangular Husimi tree where loops, responsible for an explicit frustration, are even allowed. …”
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On Quantum Markov Chains on Cayley tree I: uniqueness of the associated chain with XY-model on the Cayley tree of order two by Accardi, Luigi, Mukhamedov, Farrukh, Saburov, Mansoor

“…In the present paper we study forward Quantum Markov Chains (QMC) defined on Cayley tree. A construction of such QMC is provided, namely we construct states on finite volumes with boundary conditions, and define QMC as a weak limit of those states which depends on the boundary conditions. …”
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Quantum Markov chains on a Caylay tree by Mukhamedov, Farrukh

“…In the present paper we provide a construction of Quantum Markov chain on a Cayley tree. Moreover, we give a concrete example of such chains, which is shift invariant and has the clustering property.…”
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On pricing futures options on random binomial tree by Ganikhodjaev, Nasir, Bayram, Kamola

“…The discrete-time approach to real option valuation has typically been implemented in the finance literature using a binomial tree framework. Instead we develop a new model by randomizing the environment and call such model a random binomial tree. …”
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Quantum Markov chains on a Cayley tree by Mukhamedov, Farrukh

“…In the present paper we provode a construction of Quantum Markov chain on a Cayley tree. Moreover, we give a more concrete example of such chains, which is shift invariant and has clustering property. …”
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On phase transitions in Quantum Markov Chains on Cayley tree by Accardi, Luigi, Mukhamedov, Farrukh, Saburov, Mansoor

“…On Quantum Markov chains on Cayley tree and associated chains with XY-model arxiv: 1004.3623] we provided a construction of forward and backward Quantum Markov Chains (QMC) defined on the Cayley tree, and established uniqueness of QMC associated with XY-model on a Cayley tree order 2. …”
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Generalized quantum Markov chains on a Cayley tree by Mukhamedov, Farrukh

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On Ising model with four competing interactions on Cayley tree by Ganikhodjaev, Nasir, Rozikov, Utkir Abdulloevich

“…In the paper we consider an Ising model with four competing interactions (external field, nearest neighbor, second neighbors and triples of neighbors) on the Cayley tree of order two.We show that for some parameter values of the model there is a phase transition. …”
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Single Polygon Counting on Cayley Tree of Order 3 by Pah, Chin Hee

“…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. …”
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Two potts models on Cayley Tree of arbitrary order by Ganikhodjaev, Nasir, Nawi, Ashraf Mohamed, Mohd Rodzhan, Mohd Hirzie

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Minimal spanning tree for 100 companies in Bursa Malaysia by Bahaludin, Hafizah, Abdullah, Mimi Hafizah, Mat Salleh, Supian

“…This paper investigates the stock market network among the stocks traded in Bursa Malaysia by using minimal spanning tree (MST) techniques. The daily closing prices from 2011 until 2013 of 100 companies based on market capitalization are chosen to construct the network. …”
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An Ising model with three competing interactions on a Cayley tree by Ganikhodjaev, Nasir, Pah, Chin Hee, Wahiddin, Mohamed Ridza

“…In this paper we consider an Ising model with three competing restricted interactions on the Cay ley tree J2(J3). The translation invariant and periodic Gibbs measures for these models are investigated and the problem of the phase transition in these classes is solved. © 2004 American Institute of Physics.…”
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Strange attractors in the Vannimenus model on an arbitrary order cayley tree by Ganikhodjaev, Nasir, Akin, Hasan, Temir, Seyit, Uguz, Selman, Nawi, Ashraf Mohamed

“…We consider the Vannimenus model on a Cayley tree of arbitrary order k with competing nearest-neighbour interactions J1 and next-nearest-neighbour interactions J2 and J3 in the presence of an external magnetic field h. …”
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The p-adic potts model on the cayley tree of order three by Mukhamedov, Farrukh, Akin, Hasan

“…We study a phase transition problem for the q-state p-adic Potts model on the Cayley tree of order three. We find certain conditions for the existence of p-adic Gibbs measures and then establish the existence of a phase transition.…”
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Zero skew clock routing for fast clock tree generation by Reaz, Mamun Ibn, Amin, Nowshad, Ibrahimy, Muhammad Ibn, Mohamad-Yasin, F., Mohammad, A.

“…The methodology has been tested using a real design database and resulting in a significant improvement in the through put time required to complete the clock tree generation. This improvement is attributed to the ability to generate clock tree on much smaller portions of clock nets that supports of speeding up the clock tree generation process in IC design. …”
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On p-adic ising model with competing interactions on the cayley tree by Mukhamedov, Farrukh, Akin, Hasan, Dogan, Mutlay

“…Namely, we consider p-adic Ising model with competing next-nearest-neighbor interactions on the Cayley tree of order two. Note that usual p-adic Ising model on the tree was earlier studied by the �rst author. …”
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On quantum Markov chains on Cayley tree III: Ising model by Accardi, Luigi, Mukhamedov, Farrukh, Saburov, Mansoor

“…In this paper, we consider the classical Ising model on the Cayley tree of order k (k ≥ 2), and show the existence of the phase transition in the following sense: there exists two quantum Markov states which are not quasi-equivalent. …”
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A tree-based QoS multicast routing protocol for MANETs by Qabajeh, Mohammad M., Hassan Abdalla Hashim, Aisha, Khalifa, Othman Omran, Qabajeh, Liana K.

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