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"Telah dibangun Lagrangian baru serta dilakukan perhitungan analitik tensor energi-momentum untuk fluida QCD yang mengandung suku viskositas. Suku viskositas ini dibuat dengan asumsi bahwa persamaan gerak yang diperoleh mereproduksi persamaan gerak hidrodinamika relativistik. Suku viskositas mengakibatkan perusakan simetri fluida QCD. Memakai Lagrangian yang telah dibangun, dihitung distribusi jumlah partikel memakai teori kinetik dan resolusi Cooper- Frye. Ditunjukkan bahwa distribusi jumlah partikel memiliki kontur yang samamdengan hasil perhitungan sebelumnya memakai persamaan gerak hidrodinamika relativistik.

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A new Lagrangian and energy momentum tensor for fluid QCD with viscous term have been developed and calculated analytically. The viscous term has been constructed assuming that the generated equation of motion should reproduce the known relativistic hydrodynamics. The viscous term induces symmetry breaking of fluid QCD. Using the Lagrangian, the particle number distribution has been calculated using kinetic theory and Cooper-Frye prescription. It is shown that the distribution has the same contour as previous results calculated using the equation of motion of relativistic hydrodynamics."

"Dikaji masalah massa neutrino berdasarkan model GUT (Grand United Theory) SU(6) 5D setelah mengalami perusakan simetri menjadi SU(3)CSU(3)H U(1)C melalui mekanisme Scherk-Schwarz. Dari level SU(3)CSU(3)H U(1)C ini diperoleh lagrangian massa partikel neutrino yang berasal dari representasi f6g, f15g, f6g, dan f15g untuk diaplikasikan mekanisme seesaw. Lagrangian massa ini yang terdiri atas suku neutrino Dirac dan suku neutrino Majorana dibentuk kembali dalam bentuk matriks massa. Dari matriks massa ini kemudian didapatkan nilai eigen massa (mass eigenvalue) yang merupakan massa efektif neutrino.

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The neutrino mass problem based on GUT (Grand Unified Theory) SU(6) 5D model breaking to SU(3)C SU(3)H U(1)C by Scherk-Schwarz mechanism is discussed. From SU(3)C SU(3)H U(1)C is obtained neutrino mass lagrangian which from f6g, f15g, f6g, and f15g representation for applied seesaw mechanism. This mass lagrangian which consists of Dirac and Majorana neutrino term is formed again into a mass matrix. From this mass matrix we got mass eigenvalues which are the neutrino effective mass."

"Mathematical symmetry and chaos come together to form striking, beautiful color images throughout this impressive work, which addresses how the dynamics of complexity can produce familiar universal patterns.The book, a richly illustrated blend of mathematics and art, was widely hailed in publications as diverse as the New York Review of Books, Scientific American, and Science when first published in 1992. This much-anticipated second edition features many new illustrations and addresses the progress made in the mathematics and science underlying symmetric chaos in recent years; for example, the classifications of attractor symmetries and methods for determining the symmetries of higher dimensional analogues of images in the book. In particular, the concept of patterns on average and their occurrence in the Faraday fluid dynamics experiment is described in a revised introductory chapter."

"Symmetries, coupled with the mathematical concept of group theory, are an essential conceptual backbone in the formulation of quantum field theories capable of describing the world of elementary particles. This primer is an introduction to and survey of the underlying concepts and structures needed in order to understand and handle these powerful tools. Specifically, in Part I of the book the symmetries and related group theoretical structures of the Minkowskian space-time manifold are analyzed, while Part II examines the internal symmetries and their related unitary groups, where the interactions between fundamental particles are encoded as we know them from the present standard model of particle physics. This book, based on several courses given by the authors, addresses advanced graduate students and non-specialist researchers wishing to enter active research in the field, and having a working knowledge of classical field theory and relativistic quantum mechanics. Numerous end-of-chapter problems and their solutions will facilitate the use of this book as self-study guide or as course book for topical lectures."

"This monograph provides the first up-to-date and self-contained presentation of a recently discovered mathematical structure—the Schrödinger-Virasoro algebra. Just as Poincaré invariance or conformal (Virasoro) invariance play a key rôle in understanding, respectively, elementary particles and two-dimensional equilibrium statistical physics, this algebra of non-relativistic conformal symmetries may be expected to apply itself naturally to the study of some models of non-equilibrium statistical physics, or more specifically in the context of recent developments related to the non-relativistic AdS/CFT correspondence.The study of the structure of this infinite-dimensional Lie algebra touches upon topics as various as statistical physics, vertex algebras, Poisson geometry, integrable systems and supergeometry as well as representation theory, the cohomology of infinite-dimensional Lie algebras, and the spectral theory of Schrödinger operators."