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"Inverse limits provide a powerful tool for constructing complicated spaces from simple ones. They also turn the study of a dynamical system consisting of a space and a self-map into a study of a (likely more complicated) space and a self-homeomorphism. In four chapters along with an appendix containing background material the authors develop the theory of inverse limits. The book begins with an introduction through inverse limits on [0,1] before moving to a general treatment of the subject. Special topics in continuum theory complete the book. Although it is not a book on dynamics, the influence of dynamics can be seen throughout; for instance, it includes studies of inverse limits with maps from families of maps that are of interest to dynamicists such as the logistic and the tent families."

"This book shows how to apply theoretical mathematical models to unravel the mechanisms involved in processes found in mathematical physics and the biosciences. It is a unique collection of abstract methods that deploy nonlinear partial differential equations. "

"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."

"Penelitian ini bertujuan untuk meiakukan antisipasi perilaku migrasi kualitas kredit (credit quality migration) dan probabilitas default dan kebangkrutan (bankruptcy) dalam matriks transisi markov chains. Antisipasi ini disebut sistem peringatan dini untuk periode waktu ke depan, yaitu t, t3, t4, t5, sampai dengan jangka panjang, Untuk mencapai tujuan tersebut, pertama-tama, dilakukan evaluasi atas peringkat kredit eksternal (external credit ratings) atau the basic standarized model yang dikeluarkan oleh dua agen pemeringkat, yaitu Pefindo (berafiliasi strategis dengan Standard & Poor's) dan Kasnic (bagian dari jaringan Fitch). Kedua, mengingat masih sedikitnya populasi peringkat kredit eksternal yang diperingkat secara kontinu, disusuniah peringkat kredit internal (internal ratings-based) yang mengacu ke definisi Pefindo. Ketiga, dengan memperhacikan kondisi ekonomi dan perusahaan di Indonesia di tahun 2000 dan 2001. ditambahkan satu peringkat untuk perusahaan-perusahaan yang tengalarni kebangkrutan (bubar, pailit, dimerger, diiikuidasi, perseroan kosong) atau disebut absorbing state.Akhirnya, untuk mencapai matriks transisi markov chains yang regular dan ergoclic, peringkat AA dan AAA digabung menjadi AA* dan absorbing state dikeluarkan dari sistem. Jadi, komposisi jumiah peringkat kredit perusahaan pada keadaan tetap AA*, A, BBB, BB, 13, CCC, SD, dan D berikut ini:[3 i 64 141 34 10 13 34 9 ]Sementara itu, probabilitas pada keadaan sekarang (current state) atau tt berikut ini:[16 47 125 34 15 33 22 44 ]"

"ABSTRAKIt is proved that any random sequence can be exhibited as the output of a stochastic dynamical system driven by white noise. Further refinements are obtained for Markov, stationary, and ergodic sequences. This settles some open problems in stochastic realization theory posed by Willems and Van Schuppen."

"Inverse limits with set-valued functions are quickly becoming a popular topic of research due to their potential applications in dynamical systems and economics. This brief provides a concise introduction dedicated specifically to such inverse limits. The theory is presented along with detailed examples which form the distinguishing feature of this work. The major differences between the theory of inverse limits with mappings and the theory with set-valued functions are featured prominently in this book in a positive light. "

"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. "

"This book introduces the recent developments in the field and provides major advances in fundamental theory of limit cycles. It considers near Hamiltonian systems using Melnikov function as the main mathematical tool. Split into two parts, the first focuses on the study of limit cycles bifurcating from Hopf singularity using normal form theory with later application to Hilbert’s 16th problem, while the second considers near Hamiltonian systems using Melnikov function as the main mathematical tool. Classic topics with new results are presented in a clear and concise manner and are accompanied by the liberal use of illustrations throughout. Containing a wealth of examples and structured algorithms that are treated in detail."

"This book presents recent developments and results found by participants of the Third International Conference on the Dynamics of Information Systems, which took place at the University of Florida, Gainesville FL, USA on February 16-18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and universities to exchange knowledge and results in a broad range of topics relevant to the theory and practice of the dynamics of information systems."