The Rate of Mixing of Two-dimensional Markov Shifts

The definitions of a two-dimensional Markov shift and the associated Markov measure are given. Then a sufficient condition for the exponential mixing of such shifts is provided. This generalizes the well-known result in the one-dimensional case

Spectral and distributional problems for homogeneous extensions of dynamical systems and the rate of mixing of two-dimensional Markov shifts

This thesis consists of four chapters. Chapters 1 and 2 are somewhat related in the sense that they deal with similar dynamical systems. Each chapter comes complete with its own references and notations. For the convenience of the reader, we provide an introduction and indeed an elongated summary to the whole thesis in Chapter 0. In Chapter 1, we study how closed orbits of a subshift of finite type hits to a finite homogeneous extension. In particular, we obtain an asymptotic formula for the number of closed orbits according to how they lift to the extension space. We apply our findings to the case of finite extensions and also to automorphism extensions of hyperbolic toral automorphisms. Chapter 2 deals with lifting ergodic properties of an arbitrary measure preserving transformation T to homogeneous extensions of T. Our results extends well known theorems already obtained for the case of compact group extensions of measure-preserving transformations. We also give simplified results to the special case when the base transformation is a Markov shift and the skewing-function depends on a finite number of coordinates. In Chapter 3, we look at the rate of mixing of rectangle sets of two dimensional Markov shifts with respect to the natural shift actions. We show that if one of the matrix defining the Markov measure is aperiodic then this rate is exponentially fast. We provide an example to illustrate what could happen in general

Modelling of Marangoni convection using proper orthogonal decomposition

Proper orthogonal decomposition (POD) is applied to Marangoni convection in a horizontal fluid layer heated from below and cooled from above with non-deformable free surface. We investigate two-dimensional Marangoni convection for the case of free-slip bottom in the limit of small Prandtl number. The POD technique is then used to the velocity and temperature data to obtain basis functions for both velocity and temperature fields. When these basis functions are used in a Galerkin procedure, the low-dimensional of Marangoni convection are constructed with the smallest possible degree of freedom. The results based on this low-dimensional model are discussed

Aplikasi model baharu penambahbaikan pendekatan kalut ke atas peramalan siri masa kepekatan ozon

Kajian ini merupakan aplikasi pendekatan kalut ke atas peramalan siri masa bahan pencemar udara ozon di stesen asas Malaysia yang terletak di Jerantut, Pahang. Sebelum model peramalan dibina, siri masa diuji terlebih dahulu sama ada bersifat kalut atau tidak. Melalui plot ruang fasa dan kaedah Cao, siri masa bahan pencemar ozon didapati bersifat kalut bermatra rendah. Oleh itu, model peramalan melalui kaedah penghampiran linear setempat dibina. Sebagai inovasi, model ini ditambah baik. Sebagai perbandingan, model peramalan regresi linear turut dibina. Melalui pengiraan purata ralat mutlak, ralat punca purata kuasa dua dan pekali korelasi, keputusan menunjukkan bahawa model baharu penambahbaikan penghampiran linear setempat adalah lebih baik berbanding model-model yang lain. Maka, penambahbaikan yang dilakukan adalah berbaloi. Dengan itu, pendekatan kalut adalah pendekatan alternatif yang sesuai digunakan bagi membangunkan model peramalan siri masa bahan pencemar ozon. Penemuan model baharu dalam kajian ini diharap dapat membantu memudahkan usaha pihak-pihak berkepentingan dalam menguruskan isu pencemaran udara, khususnya ozon

Modified Baptista type cryptosystem via matrix secret key.

In 1998, M.S. Baptista proposed a chaotic cryptosystem using the ergodicity property of the simple low-dimensional and chaotic logistic equation. Since then, many cryptosystems based on Baptista's work have been proposed. However, over the years research has shown that this cryptosystem is predictable and vulnerable to attacks and is widely discussed. Among the weaknesses are the non-uniform distribution of ciphertexts and succumbing to the one-time pad attack (a type of chosen plaintext attack). In this Letter, our objective is to modify the chaotic cryptographic scheme proposed previously. We use a matrix secret key such that the cryptosystem would no longer succumb to the one-time pad attack

A review of some works in the theory of diskcyclic operators

In this paper, we give a brief review concerning diskcyclic operators and then we provide some further characterizations of diskcyclic operators on separable Hilbert spaces. In particular, we show that if $x\in {\mathcal H}$ has a disk orbit under $T$ that is somewhere dense in ${\mathcal H}$ then the disk orbit of $x$ under $T$ need not be everywhere dense in ${\mathcal H}$. We also show that the inverse and the adjoint of a diskcyclic operator need not be diskcyclic. Moreover, we establish another diskcyclicity criterion and use it to find a necessary and sufficient condition for unilateral backward shifts that are diskcyclic operators. We show that a diskcyclic operator exists on a Hilbert space ${\mathcal H}$ over the field of complex numbers if and only if $\dim({\mathcal H})=1$ or $\dim({\mathcal H})=\infty$ . Finally we give a sufficient condition for the somewhere density disk orbit to be everywhere dense.Comment: To appear in bull. malays. math. sci. so

On Quasi- ω

We introduce a new class of mappings called quasi-ω-confluent maps, and we study the relation between these mappings, and some other forms of confluent maps. Moreover, we prove several results about some operations on quasi-ω-confluent mappings such as: composition, factorization, pullbacks, and products

Numerical Analytic Solution of SIR Model of Dengue Fever Disease in South Sulawesi using Homotopy Perturbation Method and Variational Iteration Method

In this research, the susceptible"“infected"“recovered (SIR) model of dengue fever is considered. We have implemented two analytical techniques, namely the variational iteration method (VIM) and the homotopy perturbation method (HPM) for solving the SIR model. The Lagrange multiplier was investigated for the VIM and He's polynomial approach for the HPM was used. In these schemes, the solution takes the form of a convergent series with easily computable components. The resultsshow thatthe VIM solution is more accurate than the HPM solution for short time intervals, whereasthe HPM is more accurate than the VIM for long time intervalswhencompared with the fourth-orderRunge-Kutta method (RK4).We found that the HPM and the RK4 were in excellent conformance