Contents -- Preface -- A Generalization of Grover's Algorithm -- ABSTRACT -- 1 Unitary operators which increase the probability of the

2. SIMPLE QUANTUM STOCHASTIC PRODUCT INTEGRALS WITH A SYSTEM ALGEBRA. -- 3. THE FUBINI THEOREM FOR SYMMETRISED DOUBLE QUANTUM STOCHASTIC PRODUCT INTEGRALS. -- 4. A SIMPLE PROOF OF THE MULTIPLICATION RULE FOR DOUBLE PRODUCT INTEGRALS IN THE COMMUTATIVE CASE. -- 5. REFERENCES -- Growth Functions for Generalized Functions on White Noise Space -- 1. INTRODUCTION -- 2. SPACES OF TEST AND GENERALIZED FUNCTIONS -- 3. GROWTH FUNCTIONS FOR GENERALIZED FUNCTIONS -- REFERENCES -- Some Properties of a Random Field Derived by Variational Calculus -- 1 Introduction -- 2 Background -- 3 Basic Concepts and Variational Calculus -- 4 Main Results -- References -- A Stochastic Expression of a Semi-Group Generated by the Lévy Laplacian -- 1 Introduction -- 2 Preliminaries -- 3 A semigroup generated by the Lévy Laplacian -- 4 A stochastic process generated by the Lévy Laplacian -- Concluding Remark -- References -- On the Design of Efficient Quantum Algorithms -- 1 Introduction -- 2 Quantum Turing Machines -- 3 The Shortest Vector in Lattice Problem -- 4 The Collision Problem -- References -- Phylogenetic Relation of HIV-1 in the V3 Region by Information Measure -- Abstract -- 1 Introduction -- 2 Material and methods -- 3 Results -- 4 Discussion -- References -- Quantum Logical Gate Based on Electron Spin Resonance -- 1 Quantum channel for NOT gate based on ESR -- 2 Quantum channel for CNOT gate based on ESR -- References -- Current Fluctuations in Nonequilibrium Steady States for a One-Dimensional Lattice Conductor -- 1 Introduction -- 2 Model and Nonequilibrium Steady States -- 3 Current Fluctuations and Their Symmetry -- 4 N ->∞ Limit of the Correlation Functions -- 5 Kubo Formula and Current Fluctuations -- 6 Conclusions -- Appendix -- References.

Representations and Transformations of Gaussian Random Fields -- 1 Introduction -- 2 Background -- 3 Kernel criterion for canonical representation of Gaussian random field -- 4 Representations and transformations of Gaussian random fields -- References -- Time Reversal Symmetry of Fluctuation in Equilibrium and Nonequilibrium States -- 1 Introduction -- 2 Definition of Time-Reversibility -- 3 Fluctuation in equilibrium state -- 4 Fluctuation in nonequilibrium state -- References -- Stochastic Convergence of Superdiffusion in a Superdiffusive Medium -- 1 Introduction and Main Results -- 2 Notation and Preliminaries -- 3 Superdiffusion in a Superdiffusive Medium -- 4 Longtime Asymptotic Behaviors -- References.