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"The main aim of this volume is to offer a unified, self-contained introduction to the interplay of these three main areas of research, ergodic theory, hyperbolic dynamics, and dimension theory. Furthermore, it includes an introduction to the thermodynamic formalism, which is an important tool in dimension theory."

"We explore full-duplex technique in wireless communication particularly for relay networks. We consider the relay to operate in full-duplex, which transmission and reception are conducted in the same channel. We investigate potential benefits of full-duplex technique in relay networks, which uses multiple antennas for transmission and reception combined with Amplify-Forward (AF) scenario. We study the effects of multiple antennas in terms of relay capacity. We derive an ergodic capacity expression using Tracy-Widom distribution. Using Singular Value Decomposition (SVD) and perfect Channel State Information (CSI), we investigate three scenarios: First, we consider the relay to have antenna larger than that of both source and destination. Second, we consider both relay and destination to have antenna larger than that of source. Third, we consider both relay and source to have antenna larger than that of destination. We show the results that the capacity of relay with full-duplex technique is almost twice the capacity of half-duplex. We show that increasing the number of destination antennas is not help much when one of source antennas is small. Moreover, the capacity decreases due to channel hardening effect, when the number of destination antennas is larger than that of source."

"This book gives a unified presentation in an abstract setting of the main theorems in bifurcation theory, as well as more recent and lesser known results. It covers both the local and global theory of one-parameter bifurcations for operators acting in infinite-dimensional Banach spaces, and shows how to apply the theory to problems involving partial differential equations. In addition to existence, qualitative properties such as stability and nodal structure of bifurcating solutions are treated in depth. "

"Dynamical systems arise in all fields of applied mathematics. The author focuses on the description of numerical methods for the detection, computation, and continuation of equilibria and bifurcation points of equilibria of dynamical systems. This subfield has the particular attraction of having links with the geometric theory of differential equations, numerical analysis, and linear algebra.Several features make this book unique. The first is the systematic use of bordered matrix methods in the numerical computation and continuation of various bifurcations. The second is a detailed treatment of bialternate matrix products and their Jordan structure. Govaerts discusses their use in the numerical methods for Hopf and related bifurcations. A third feature is a unified treatment of singularity theory, with and without a distinguished bifurcation parameter, from a numerical point of view. Finally, numerical methods for symmetry-breaking bifurcations are discussed in detail, up to the fundamental cases covered by the equivariant branching lemma."

"This is a collection of contributed papers which focus on recent results in areas of differential equations, function spaces, operator theory and interpolation theory. In particular, it covers current work on measures of non-compactness and real interpolation, sharp Hardy-Littlewood-Sobolev inequalites, the HELP inequality, error estimates and spectral theory of elliptic operators, pseudo differential operators with discontinuous symbols, variable exponent spaces and entropy numbers. "

"ABSTRAKSistem terkorelasi kuat adalah sistem dimana skala energi untuk interaksi antar partikel tidak lagi dapat diabaikan. Dynamical Mean Field Theory(DMFT) menjadi salah satu metode yang banyak dikenal sebagaimetode ampuh untuk menjelaskan fisika dari sistem terkorelasi kuat. Disini kami mempelajari metodepenyelesaian impuritas yang tersedia di DMFT untuk model Hubbard, model paling sederhana dalam sistemterkorelasi kuat. Dengan melihat berbagai keterbatasan metode penyelesaian impuritas dengan sumberdayanumerik yang murah, kami mengembangkan metode penyelesaian impuritas dengan numerik yang murahlainnya yang dikembangkan dari metode medan rata-rata dengan melibatkan fluktuasi okupasi sebagai kuantitasnumerik. Dengan melihat efek fluktuasi, kami membandingkan hasil tersebut dengan metode penyelesaianimpuritas lainnya, yakni medan rata-rata dan iterasi perturbasi teori yang dipelajari pada keadaan paramagnetikdan antiferomagnetik. Kami simpulkan bahwa fluktuasi okupasi belum sepenuhnya mampu menjadi metodepenyelesaian impuritas yang baik, namun memberikan hasil yang menarik untuk digunakan sebagai koreksi dariiterasi perturbasi teori.

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ABSTRACT

Strongly correlated system is physical system where the interaction among particle cannot be neglected.

Dynamical Mean Field Theory(DMFT) becomes one of the established method to explain and calculate physical

observable of strongly correlated system. Here we study the impurity solver in DMFT for Hubbard model, the

simplest model for strongly correlated system. We realizing that exact impurity solver gives high numerical cost,

where approximate impurity solver gives relative low numerical cost. Here we develop another low numerical

cost to aim more exact result than approximate method, where we developed it from mean-field method where is the occupation fluctuation is taking into account in the semi-classical sense. We compare this method by another lower numerical impurity solver, i.e mean-field and iterated perturbation theory, where they are studied in restricted case of paramagnetic and unrestricted case of magnetic ordering. We concluded that occupation fluctuation not really giving exact result if we compared to mean-field and iterated perturbation theory, but becomes interesting if we implement occupation fluctuation as iterated perturbation theory correction.

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