1,721,154 research outputs found
International Conference on Advancement in Science and Technology 2012 (iCAST): Contemporary Mathematics, Mathematical Physics and their Applications
No full textThe 4th International Conference on the Advancement of Science and Technology 2012 (iCAST 2012), with theme 'Contemporary Mathematics, Mathematical Physics and their Applications', took place in Kuantan, Malaysia, from Wednesday 7 to Friday 9 November 2012. The conference was attended by more than 100 participants, and hosted about 160 oral and poster papers by more than 140 pre-registered authors. The key topics of the 4th iCAST 2012 include Pure Mathematics, Applied Mathematics, Theoretical/Mathematical Physics, Dynamical Systems, Statistics and Financial Mathematics. The scientific program was rather full since after the Keynote and Invited Talks in the morning, four parallel sessions ran every day. However, according to all attendees, the program was excellent with a high level of talks and the scientific environment was fruitful; thus all attendees had a creative time.
The conference aimed to promote the knowledge and development of high-quality research in mathematical fields concerned with the application of other scientific fields as well as modern technological trends in physics, chemistry, biology, medicine, economics, sociology and environmental sciences.
We would like to thank the Keynote and the Invited Speakers for their significant contributions to 4th iCAST 2012. We would also like to thank the members of the International Scientific Committee and the members of the Organizing Committee. We cannot end without expressing our many thanks to International Islamic University Malaysia and our sponsors for their financial support .
This volume presents selected papers which have been peer-reviewed. The editors hope that it may be useful and fruitful for scholars, researchers, and advanced technical members of the industrial laboratory facilities for developing new tools and products
Lattice models with interactions on Caylay tree
Full text linkWe consider an Ising competitive model defined over a triangular Husimi tree where loops,
responsible for an explicit frustration, are even allowed. We first analyze the phase diagram of the model
with fixed couplings in which a “gas of noninteracting dimmers (or spin liquid) — ferro or
antiferromagnetic ordered state” zero temperature transition is recognized in the frustrated regions. Then
we introduce the disorder for studying the spin glass version of the model: the triangular ±J model. We
find out that, for any finite value of the averaged couplings, the model exhibits always a finite temperature
phase transition even in the frustrated regions, where the transition turns out to be a glassy transition. On
the other hand, In this investigation we studied one-dimensional countable state p-adic Potts model. We
prove the existence of generalized p-adic Gibbs measures for the given model. It is also shown that under
the condition there may occur a phase transition
On ? a -Quadratic Stochastic operators on 2-D Simplex
No full textA quadratic stochastic operator (Qso) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. The general problem in the nonlinear operator theory is to study the behavior of operators. This problem was not fully finished even for quadratic stochastic operators which are the simplest nonlinear operators. To study this problem, several classes of QSO were investigated. In this paper, we study the fri)-Qso defined on 2D simplex. We first classify 4-(a)-QS0 into 2 non-conjugate classes. Further, we investigate the dynamics of these classes of such operators
Recent achievements in dynamical systems: proceedings od Department of Computational and Theoretical Sciences, Faculty of Science, IIUM. Vol. 2
Full text linkQuantum Markov chains on a Cayley tree
No full textIn 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
On L (1)-weak ergodicity of nonhomogeneous discrete Markov processes and its applications
No full textIn the present paper we investigate the L1-weak ergodicity of nonhomogeneous
discrete Markov processes with general state spaces. Note that the L1-weak ergodicity
is weaker than well-known weak ergodicity.We provide a necessary and sufficient
condition for such processes to satisfy the L1-weak ergodicity. Moreover, we
apply the obtained results to establish L1-weak ergodicity of discrete time quadratic
stochastic processes. As an application of the main result, certain concrete examples
are also provided
On dynamical systems and phase transitions for q + 1-state p-adic Potts model on the Cayley tree
No full textIn the present paper, we study a new kind of p-adic measures for
q + 1-state Potts model, called p-adic quasi Gibbs measure. For such a model,
we derive a recursive relations with respect to boundary conditions. Note that
we consider twomode of interactions: ferromagnetic and antiferromagnetic. In
both cases, we investigate a phase transition phenomena from the associated
dynamical system point of view. Namely, using the derived recursive relations
we define a fractional p-adic dynamical system. In ferromagnetic case, we
establish that if q is divisible by p, then such a dynamical system has two
repelling and one attractive fixed points. We find basin of attraction of the
fixed point. This allows us to describe all solutions of the nonlinear recursive
equations. Moreover, in that case there exists the strong phase transition. If
q is not divisible by p, then the fixed points are neutral, and this yields that
the existence of the quasi phase transition. In antiferromagnetic case, there
are two attractive fixed points, and we find basins of attraction of both fixed
points, and describe solutions of the nonlinear recursive equation. In this case,
we prove the existence of a quasi phase transition
On the existence of generalized Gibbs measures for the one-dimensional p-adic countable state Potts model
No full textWe consider the one-dimensional countable state p-adic Potts model. A construction of generalized p-adic Gibbs measures depending on weights λ is given, and an investigation of such measures is reduced to the examination of a p-adic dynamical system. This dynamical
system has a form of series of rational functions. Studying such a dynamical system, under some condition concerning weights, we prove the existence of generalized p-adic Gibbs measures. Note that the condition found does not depend on the values of the prime p, and therefore an analogous fact is not true when the number of states is finite. It is also shown that under the condition there may occur a phase transition
On the existence of phase transition for one dimensional P-adic countable state Potts model
Full text linkIn the present paper we shall consider countable state p -adic Potts model on Z . A main aim is to establish the existence of the phase transition for the model. In our
study, we essentially use one dimensionality of the model. To establish the phase transition we investigation of an infinite-dimensional nonlinear equation. We find a condition on weights to show that the derived equation has two solutions, which yields the existence of the phase transition. Note that it turns out that the finding condition does not depend on values of the prime p , and therefore, an analogous fact is not true when the number of spins is finite
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