TABLE OF CONTENTS -- PREFACE -- Formal Aspects -- Noncommutative Geometry: Fuzzy Spaces, the Groenwald-Moyal Plane A.P. Balachandran* and B.A. Qureshi -- 1. Introduction -- 2. History -- 3. What is Noncommutative Geometry -- 4. Fuzzy Physics -- 4.1. What is fuzzy physics? -- 4.2. Why is this space fuzzy -- 4.3. Field theory on fuzzy sphere -- 4.3.1. Dirac operator -- 4.3.2. Supersymmetry -- 4.3.3. Strings10 -- 5. The Groenwald-Moyal Plane -- 5.1. Quantum gravity and spacetime noncommutativity: heuristics -- 5.1.1. Space-space noncommutativity -- 5.1.2. Time-space noncommutativity -- 5.2. What is the Groenwald-Moyal plane? -- 5.3. How the G-M plane emerges from quantum Hall eflect and strings -- 5.3.1. Quantum Hall effect (the Landau problem) -- 5.3.2. Strings -- 5.4. Prehistory (before 2004/2005) -- 5.5. Modern era -- 6. Acknowledgments -- References -- S-Dualities in Noncommutative and Non-anticommutative Field Theories O.F. Dayi, L. T. Kelleyane, K. Ulker and B. Yapigkan -- 1. Introduction -- 2. Parent actions -- 3. Equivalence of partition functions -- References -- New Casimir Energy Calculations H. Ahmedov and I.H. Durn -- 1. Introduction -- 2. New Casimir Energy Results in Some 3-dimensional Cavities -- 3. Some Known Casimir Energy Results for 3-dimens~nal Cavities -- 4. Discussion -- Acknowledgements -- References -- Quaternionic and Octonionic Structures of the Exceptional Lie Algebras M. Koca -- 1. Introduction -- 2. Octonionic Roots of Es -- 3. Quaternions and Polyhedra -- References -- On Critical Dimensions of String Theories D. Leites and C. Sachse -- 1. Introduction -- 2. Stringy superalgebras and modules over them -- 2.1. Vectorial Lie superalgebras with polynomial or formal coefficients. -- 2.2. Tensor fields. -- 2.3. Modules over stringy superalgebras. -- 3. The spinor and oscillator representations in super setting.

3.1. The Lie superalgebra bei(2nlm). -- 3.1.1. The big and small Weyl superalgebras. -- 3.2. Spinor (Clifford-Weil-wedge-. . . ) and oscillator representations. -- 3.3. The values c and h of the highest weight of the tL(lIN)- and tM (1IN)-module Spin(Fx -- p). -- 3.4. The choice of the cocycle. -- 3.5. Theorem -- Acknowledgements. -- References -- Transition Amplitudes for Time-dependent Linear Harmonic Oscillator with Linear Time-dependent Terms Added to the Hamiltonian M. A. Rashid -- 1. Introduction -- 2. The Transformed Operators z-J-, p -- 3. Calculation of the transformed creation and annihilation operators -- 4. Recursion relation for the transition amplitudes amn ( t ) = (mIU (t)l n) -- 5. Calculation of the transition amplitude -- References -- Entropy Solutions to a Genuinely Nonlinear Ultraparabolic Kolmogorov-type Equation S. A. Sazhenkov -- 1. Introduction -- 2. Notion of entropy solutions -- 3. Formulation of the main results -- 4. Method of justification of Theorems 3.1 and 3.2 -- Acknowledgment -- References -- Fokker-Planck-Kolmogorov Equation for fBm: Derivation and Analytical Solutions G. Unar -- 1. Introduction -- 1.1. Derivation of the FPK equation for fBm -- 2. Generalized Liouville theorem -- 3. Analytical solutions to the modified FPK equation -- Acknowledgments -- References -- Particle Physics and String Theory -- Holography and de Sitter Space M. Ahhahiha* -- 1. Holographic principle and AdS/CFT correspondence -- 2. Holography for de Sitter space -- 2.1. What is de Sitter space? -- 2.2. Why de Sitter space? -- 2.3. dS/CFT correspondence -- 2.4. dS/dS correspondence -- 3. Conclusions -- References -- Brane Cosmology with String Antisymmetric Field F. Ardalan -- References -- Bosonization of a Finite Number of Non-relativistic Fermions and Application A. DhaV -- 1. Introduction -- 2. Exact Operator Bosonization.

3. Applications -- 3.1. Half-BPS sector of h/ = 4 SYM and LLM geometries -- 3.2. Free fermions on a circle -- 3.3. 2 0 Yang-Mills on a cylinder -- References -- Recent Applications of the Weyl Anomaly M. J. Duf -- 1. Thirty three years of the Weyl anomaly -- 2. The holographic Weyl anomaly, 1998 -- 3. The Weyl anomaly and corrections to Newton's law, 2000 -- 4. Weyl anomaly driven inflation, 2000 -- 5. The Weyl anomaly and the graviton mass, 2002 -- 6. Conclusions -- 7. Acknowledgements -- References -- Higher Dimensional Perspective on N = 2 Black Holes A. Fayyazuddin* -- 1. Introduction -- 2. 11-dimensional solutions for 4-d black holes -- 3. The near-horizon regime and geometrical transitions -- 4. Acknowledgments -- References -- pstrings vs Strings D. Ghoshal -- Acknowledgments -- References -- Detecting Two-photon Exchange Effects in Hard Scattering from Nucleon Targets P. Hood bhoy* -- References -- BPS M-brane Geometries T. Z. Husain -- 1. Introduction -- 2. D = l l Supergravity -- 3. The Geometry of BPS M-branes -- 4. How BPS M-branes deform Calabi-Yaw -- 5. Conclusions -- Acknowledgments: -- References -- Ward Identities and Radiative Rare Leptonic B-decays M.J. Aslam, A.H.S. Gilani, M.S. Khan and Riazuddin -- 1. Introduction -- 2. Decay kinematics and current matrix elements -- 3. Dispersion Relations -- 4. Asymptotic Behavior -- 5 . Ward Identities Constraints -- References -- Calculation of NLO QCD Corrections to Polarization Effects in Top Quark Decays A . Kadeer -- 1. Introduction -- 2. Born term results -- 3. Virtual corrections -- 4. Tree graph contributions -- References -- Selected Topics in Top Quark Physics J. G. Korner* -- 1. Introduction -- 2. NNLO description of heavy top quark production -- 3. Decays of unpolarized and polarized top quarks -- 4. Polarized top quark decays -- 5. Summary and conclusions -- Acknowledgements:.

References -- Moduli Stabilization using Open String Fluxes A. Kumar -- 1. Introduction -- 2. Supersymmetry -- 2.1. D9 on T0 -- 3. Fixing Complex Structure Moduli -- 4. RR Tadpoles -- References -- Topological Strings and Special Holonomy Manifolds J. de Boer, A. Naqvi and A. Shomer -- 1. Introduction -- 2. Ga sigma models -- 3. Tri-Critical Ising Model -- 3.1. Chiral Primary States -- 4. Topological Twist -- 5 . The BRST Operator -- 6. Topological Ga Strings -- 7. Conclusions -- Acknowledgement -- References -- Vacua in N = 4 Gauged Supersymmetry S. Panda -- Acknowledgments -- References -- Neutrino Physics Riazuddin* -- 1. Introduction -- 2. The Spectrum Scale of v-mass from Present to Projected Goal2 -- 3. Origin of Neutrino Mass -- 4. Majorana Neutrinos -- 5. Neutrino Mass Models -- 6 . Leptogenesis -- 7. Conclusions -- References -- What String Theory has Taught Us about the Quantum Structure of Space-time M. M. Sheikh- Jabbari* -- 1. Introduction and Motivation -- 2. D-branes, the key objects -- 2.1. The Gauge Theory Picture -- 2.2. The Gravity Picture -- 3. The Tiny Graviton Matrix Theory -- 3.1. Half BPS configurations of TGMT -- 3.2. Relation to LLM geometries -- 4. Summary and Outlook -- References -- Gauge Theory Description of the Fate of the Small Schwarzschild Blackhole S.R. Wadia* -- 1. Blackholes and string theory -- 2. Small 10-dim. Schwarzschild blackhole in Ads5 x S5 -- 3. Gauge theory and effective action -- 4. Effective action and multi-trace unitary matrix model -- 5. A lemma in matrix theory -- 6. Critical behavior in the matrix model -- 6.1. Critical surface of the large N phase transition -- 7. Saddle point equations at large N -- 8. Double scaled partition function at crossover -- 8.1. Condensation of winding modes at the crossover -- 9. Applications to the small blackhole-string transition.

10. Density of states and the singularity of the Lorentzian blackhole -- 11. Acknowledgment -- References -- Plasma Physics -- Zonal Flow Generation by Magnetized Rossby Waves in Ionospheric E-layer T.D. Kaladze, D. J. Wu, O.A. Pokhotelov, R.Z. Sagdeev, L. StenfEo and P.K. Shukla -- 1. Introduction -- 2. Linear magnetized Rossby waves in the ionospheric E-layer -- 3. Nonlinear interactions of magnetized Rossby waves and zonal flows in the E-layer -- 4. Discussion and Conclusions -- Acknowledgments -- References -- Quiescent and Catastrophic Events in Stellar Atmospheres S.M. Mahajan* and N.L. Shatashvili -- 1. Introduction -- 2. Solar Corona - Observations - Inferences -- 2.1. How does the Solar Corona get to be so hot? -- 2.2. The Solar Wind (SW) - History -- 2.3. Present State of Art -- 2.4. Towards a General Unifying Model -- 3. Magneto-fluid Coupling -- 3.1. Construction of a Typical Coronal structure -- 3.2. Curl Curl Equation - Double-Beltrami states -- 3.3. Double Beltrami States -- 3.4. An Example of structural richness -- 4. Acceleration of Plasma Flows -- 4.1. Eruptive and Explosive events, Flaring -- 4.2. Non-uniform density case -- 4.3. Where do the flows come from? Reverse Dynamo - Flow generation -- 4.4. Reverse Dynamo relationship - Theory -- 4.5. Choice of Initial Fields -- 4.6. A Nonlinear Solution in Linear Clothing -- 4.6.1. Analytical Results - An Almost straight dynamo -- 4.6.2. Analytical Results - An Almost Reverse dynamo -- 4.7. A Simulation of Dynamical Acceleration -- 5. Conclusions -- References -- Zero-dimensional MHD Modelling of Two Gas-puff Staged Pinch Plasma with Finite-P Effect A.M. Mirza, F. Deeba, K. Ahmed and M.Q. Haseeb -- 1. Introduction -- 2. Staged pinch dynamics -- 3. Numerical results and discussion -- Acknowledgments -- References -- Does Quasi-neutrality Remain Valid in Pair-ion Plasmas? H. Saleem*.

1. Introduction.