http://www.hindawi.comThe latest articles from Hindawi Publishing Corporation© 2012, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/amp/2012/857493/We present a geometric framework to analyze optimal control problems of uncoupled spin 1/2 particles occurring in nuclear magnetic resonance. According to the Pontryagin's maximum principle, the optimal trajectories are solutions of a pseudo-Hamiltonian system. This computation is completed by sufficient optimality conditions based on the concept of conjugate points related to Lagrangian singularities. This approach is applied to analyze two relevant optimal control issues in NMR: the saturation control problem, that is, the problem of steering in minimum time a single spin 1/2 particle from the equilibrium point to the zero magnetization vector, and the contrast imaging problem. The analysis is completed by numerical computations and experimental results.Bernard Bonnard, Steffen J. Glaser, and Dominique SugnyCopyright © 2012 Bernard Bonnard et al. All rights reserved.http://www.hindawi.com/journals/amp/2012/309398/In the semiclassical regime, we obtain a lower bound for the counting function of resonances corresponding to the perturbed periodic Schrödinger operator Ph=-Δ+Vx+W(hx). Here V is a periodic potential, W a decreasing perturbation and h a small positive constant.Mouez DimassiCopyright © 2012 Mouez Dimassi. All rights reserved.http://www.hindawi.com/journals/amp/2011/365085/We apply a special case, the restriction principle (for which we give a definition simpler than the usual one), of a basic result in functional analysis (the polar decomposition of an operator) in order to define Cμ,t, the C-version of the Segal-Bargmann transform, associated with a finite Coxeter group acting in ℝN and a given value t>0 of Planck's constant, where μ is a multiplicity function on the roots defining the Coxeter group. Then we immediately prove that Cμ,t is a unitary isomorphism. To accomplish this we identify the reproducing kernel function of the appropriate Hilbert space of holomorphic functions. As a consequence we prove that the Segal-Bargmann transforms for Versions A, B, and D are also unitary isomorphisms though not by a direct application of the restriction principle. The point is that the C-version is the only version where a restriction principle, in our definition of this method, applies directly. This reinforces the idea that the C-version is the most fundamental, most natural version of the Segal-Bargmann transform.Stephen Bruce SontzCopyright © 2011 Stephen Bruce Sontz. All rights reserved.http://www.hindawi.com/journals/amp/2011/957592/We make explicit in terms of categories a number of statements from the theory of partial inner product spaces (PIP-spaces) and operators on them. In particular, we construct sheaves and cosheaves of operators on certain PIP-spaces of practical interest.Jean-Pierre Antoine, Dominique Lambert, and Camillo TrapaniCopyright © 2011 Jean-Pierre Antoine et al. All rights reserved.http://www.hindawi.com/journals/amp/2011/862186/We consider N point vortices whose positions satisfy a stochastic ordinary differential equation on ℝ2N perturbed by spatially correlated Brownian noise. The associated signed point measure-valued empirical process turns out to be a weak solution to a stochastic Navier-Stokes equation (SNSE) with a state-dependent stochastic term. As the number of vortices tends to infinity, we obtain a smooth solution to the SNSE, and we prove the conservation of total vorticity in this continuum limit.Peter M. Kotelenez and Bradley T. SeadlerCopyright © 2011 Peter M. Kotelenez and Bradley T. Seadler. All rights reserved.http://www.hindawi.com/journals/amp/2011/527434/Bonome et al., 1997, provided an algebraic characterization for an indefinite Sasakian manifold to reduce to a space of constant ϕ-holomorphic sectional curvature. In this present paper, we generalize the same characterization for indefinite g⋅f⋅f-space forms.Jae Won LeeCopyright © 2011 Jae Won Lee. All rights reserved.http://www.hindawi.com/journals/amp/2011/625978/We prove a version of the Jacobs-de Leeuw-Glicksberg splitting theorem for weak* continuous one-parameter semigroups on dual Banach spaces. This result is applied to give sufficient conditions for a quantum dynamical semigroup to display decoherence. The underlying notion of decoherence is that introduced by Blanchard and Olkiewicz (2003). We discuss this notion in some detail.Mario HellmichCopyright © 2011 Mario Hellmich. All rights reserved.http://www.hindawi.com/journals/amp/2011/680367/We present the relativistic particle model without Grassmann variables which, being canonically quantized, leads to the Dirac equation. Classical dynamics of the model is in correspondence with the dynamics of mean values of the corresponding operators in the Dirac theory. Classical equations for the spin tensor are the same as those of the Barut-Zanghi model of spinning particle.A. A. DeriglazovCopyright © 2011 A. A. Deriglazov. All rights reserved.http://www.hindawi.com/journals/amp/2011/259089/We explain how the representation theory associated with supersymmetry in diverse dimensions is encoded within the representation theory of supersymmetry in one time-like dimension. This is enabled by algebraic criteria, derived, exhibited, and utilized in this paper, which indicate which subset of one-dimensional supersymmetric models describes “shadows” of higher-dimensional models. This formalism delineates that minority of one-dimensional supersymmetric models which can “enhance” to accommodate extra dimensions. As a consistency test, we use our formalism to reproduce well-known conclusions about supersymmetric field theories using one-dimensional reasoning exclusively. And we introduce the notion of “phantoms” which usefully accommodate higher-dimensional gauge invariance in the context of shadow multiplets in supersymmetric quantum mechanics.M. G. Faux, K. M. Iga, and G. D. LandweberCopyright © 2011 M. G. Faux et al. All rights reserved.http://www.hindawi.com/journals/amp/2011/252186/We study the Jacobian Poisson structures in any dimension invariant with respect to the discrete Heisenberg group. The classification problem is related to the discrete volume of suitable solids. Particular attention is given to dimension 3 whose simplest example is the Artin-Schelter-Tate Poisson tensors.G. Ortenzi, V. Rubtsov, and S. R. Tagne PelapCopyright © 2011 G. Ortenzi et al. All rights reserved.http://www.hindawi.com/journals/amp/2011/870613/We prove that the Lie superalgebra of regular differential operators on the superspace ℂM|N[t,t−1] has an essentially unique non-trivial central extension.Carina Boyallian and Jose I. LiberatiCopyright © 2011 Carina Boyallian and Jose I. Liberati. All rights reserved.http://www.hindawi.com/journals/amp/2011/420608/we propose a new high-order approximation for the solution of two-space-dimensional quasilinear hyperbolic partial differential equation of the form utt=A(x,y,t,u)uxx+B(x,y,t,u)uyy+g(x,y,t,u,ux,uy,ut), 0<x, y<1, t>0 subject to appropriate initial and Dirichlet boundary conditions , where k>0 and h>0 are mesh sizes in time and space directions, respectively. We use only five evaluations of the function g as compared to seven evaluations of the same function discussed by (Mohanty et al., 1996 and 2001). We describe the derivation procedure in details and also discuss how our formulation is able to handle the wave equation in polar coordinates. The proposed method when applied to a linear hyperbolic equation is also shown to be unconditionally stable. Some examples and their numerical results are provided to justify the usefulness of the proposed method.R. K. Mohanty and Suruchi SinghCopyright © 2011 R. K. Mohanty and Suruchi Singh. All rights reserved.http://www.hindawi.com/journals/amp/2011/983678/J. C. Maxwell derived formulae for the calculation of current density and current in a cylindrical conductor supplied with variable current. In the 1950s K. Simonyi published a method for calculating current density in a cylindrical conductor made up of two conductors, cylindrical and tubular, of different resistivities. The present paper proves that Simonyi's result is incorrect. The main attention is devoted to the method of calculating current density in a tubular conductor made up of tubular conductors of different resistivities.Oldřich CoufalCopyright © 2011 Oldřich Coufal. All rights reserved.http://www.hindawi.com/journals/amp/2011/546058/Following Linchenko and Montgomery's arguments we show that the smash product of an involutive weak Hopf algebra and a semiprime module algebra, satisfying a polynomial identity, is semiprime.Inês Borges and Christian LompCopyright © 2011 Inês Borges and Christian Lomp. All rights reserved.http://www.hindawi.com/journals/amp/2011/456784/We prove that any potential symmetry of a system of evolution equations reduces to a Lie symmetry through a nonlocal transformation of variables. This fact is in the core of our approach to computation of potential and more general nonlocal symmetries of systems of evolution equations having nontrivial Lie symmetry. Several examples are considered.Renat ZhdanovCopyright © 2011 Renat Zhdanov. All rights reserved.http://www.hindawi.com/journals/amp/2011/606757/We study a hyperbolic (telegrapher's equation) free boundary problem describing the pressure-driven channel flow of a Bingham-type fluid whose constitutive model was derived in the work of Fusi and Farina (2011). The free boundary is the surface that separates the inner core (where the velocity is uniform) from the external layer where the fluid behaves as an upper convected Maxwell fluid. We present a procedure to obtain an explicit representation formula for the solution. We then exploit such a representation to write the free boundary equation in terms of the initial and boundary data only. We also perform an asymptotic expansion in terms of a parameter tied to the rheological properties of the Maxwell fluid. Explicit formulas of the solutions for the various order of approximation are provided.Lorenzo Fusi and Angiolo FarinaCopyright © 2011 Lorenzo Fusi and Angiolo Farina. All rights reserved.http://www.hindawi.com/journals/amp/2011/138358/The quantum Langevin equation has been studied for dissipative system using the approach of Ford et al. Here, we have considered the inverted harmonic oscillator potential and calculated the effect of dissipation on tunneling time, group delay, and the self-interference term. A critical value of the friction coefficient has been determined for which the self-interference term vanishes. This approach sheds new light on understanding the ion transport at nanoscale.Samyadeb Bhattacharya and Sisir RoyCopyright © 2011 Samyadeb Bhattacharya and Sisir Roy. All rights reserved.http://www.hindawi.com/journals/amp/2011/189801/The homological Kähler-de Rham differential mechanism models the dynamical behavior of physical fields by purely algebraic means and independently of any background manifold substratum. This is of particular importance for the formulation of dynamics in the quantum regime, where the adherence to such a fixed substratum is problematic. In this context, we show that the functorial formulation of the Kähler-de Rham differential mechanism in categories of sheaves of commutative algebras, instantiating generalized localization environments of physical observables, induces a consistent functorial framework of dynamics in the quantum regime.Anastasios Mallios and Elias ZafirisCopyright © 2011 Anastasios Mallios and Elias Zafiris. All rights reserved.http://www.hindawi.com/journals/amp/2011/126108/We will show that a two-parameter extended entropy function is characterized by a functional equation. As a corollary of this result, we obtain that Tsallis entropy function is characterized by a functional equation, which is a different form that used by Suyari and Tsukada, 2009, that is, in a proposition 2.1 in the present paper. We give an interpretation of the functional equation in our main theorem.Shigeru FuruichiCopyright © 2011 Shigeru Furuichi. All rights reserved.http://www.hindawi.com/journals/amp/2011/652126/We show that a “dynamical” interaction for arbitrary spin can be constructed in a straightforward way if gauge and Lorentz transformations are placed on the same foundation. As Lorentz transformations act on space-time coordinates, gauge transformations are applied to the gauge field. Placing these two transformations on the same ground means that all quantized field like spin-1/2 and spin-3/2 spinors are functions not only of the coordinates but also of the gauge field components. As a consequence, on this stage the (electromagnetic) gauge field has to be considered as classical field. Therefore, standard quantum field theory cannot be applied. Despite this inconvenience, such a common ground is consistent with an old dream of physicists almost a century ago. Our approach, therefore, indicates a straightforward way to realize this dream.Rein Saar, Stefan Groote, Hannes Liivat, and Ilmar OtsCopyright © 2011 Rein Saar et al. All rights reserved.http://www.hindawi.com/journals/amp/2011/471314/This paper is devoted to the study of the chaotic properties of some specific backward shift unbounded operators Hp=A*pAP+1; p=0,1,… realized as differential operators in Bargmann space, where A and A* are the standard Bose annihilation and creation operators such that [A,A*]=I.Abdelkader IntissarCopyright © 2011 Abdelkader Intissar. All rights reserved.http://www.hindawi.com/journals/amp/2011/257916/Through the systematic use of the Minlos theorem on the support of cylindrical measures on R∞, we produce several mathematically rigorous finite-volume euclidean path integrals in interacting euclidean quantum fields with Gaussian free measures defined by generalized powers of finite-volume Laplacian operator.Luiz C. L. BotelhoCopyright © 2011 Luiz C. L. Botelho. All rights reserved.http://www.hindawi.com/journals/amp/2011/519178/Logarithmic gaps have been used in order to find a periodic component of the sequence of prime numbers, hidden by a random noise (stochastic or chaotic). It is shown that multiplicative nature of the noise is the main reason for the successful application of the logarithmic gaps transforming the multiplicative noise into an additive one. A relation of this phenomenon to spontaneous neuron activity and to chaotic brain computations has been discussed.A. BershadskiiCopyright © 2011 A. Bershadskii. All rights reserved.http://www.hindawi.com/journals/amp/2011/393417/A family of generalized binomial probability distributions attached to Landau levels on the Riemann sphere is introduced by constructing a kind of generalized coherent states. Their main statistical parameters are obtained explicitly. As an application, photon number statistics related to coherent states under consideration are discussed.A. Ghanmi, A. Hafoud, and Z. MouaynCopyright © 2011 A. Ghanmi et al. All rights reserved.http://www.hindawi.com/journals/amp/2011/750168/We study the generalized quantum isotonic oscillator Hamiltonian given by H=−d2/dr2+l(l+1)/r2+w2r2+2g(r2−a2)/(r2+a2)2, g>0. Two approaches are explored. A method for finding the quasipolynomial solutions is presented, and explicit expressions for these polynomials are given, along with the conditions on the potential parameters. By using the asymptotic iteration method, we show how the eigenvalues of this Hamiltonian for arbitrary values of the parameters g, w, and a may be found to high accuracy.Nasser Saad, Richard L. Hall, Hakan Çiftçi, and Özlem YeşiltaşCopyright © 2011 Nasser Saad et al. All rights reserved.http://www.hindawi.com/journals/amp/2011/635790/We present an explicit construction of a unitary representation of the commutator algebra satisfied by position and momentum operators on the Moyal plane.J. M. Isidro, P. Fernández de Córdoba, J. M. Rivera-Rebolledo, and J. L. G. SantanderCopyright © 2011 J. M. Isidro et al. All rights reserved.http://www.hindawi.com/journals/amp/2011/983069/We study mixed geodesic GCR-lightlike submanifolds of indefinite Sasakian manifolds and obtain some necessary and sufficient conditions for a GCR-lightlike submanifold to be a GCR-lightlike product.Rakesh Kumar, Varun Jain, and R. K. NagaichCopyright © 2011 Rakesh Kumar et al. All rights reserved.http://www.hindawi.com/journals/amp/2011/191083/The mechanism of differential geometric calculus is based on the fundamental notion of a connection on a module over a commutative and unital algebra of scalars defined together with the associated de Rham complex. In this communication, we demonstrate that the dynamical mechanism of physical fields can be formulated by purely algebraic means, in terms of the homological Kähler-De Rham differential schema, constructed by connection inducing functors and their associated curvatures, independently of any background substratum. In this context, we show explicitly that the application of this mechanism in General Relativity, instantiating the case of gravitational dynamics, is related with the absolute representability of the theory in the field of real numbers, a byproduct of which is the fixed background manifold construct of this theory. Furthermore, the background independence of the homological differential mechanism is of particular importance for the formulation of dynamics in quantum theory, where the adherence to a fixed manifold substratum is problematic due to singularities or other topological defects.Anastasios Mallios and Elias ZafirisCopyright © 2011 Anastasios Mallios and Elias Zafiris. All rights reserved.http://www.hindawi.com/journals/amp/2011/854719/It is the purpose of this paper to give a simple proof of the fact that solutions of the KdV equation can be approximated via solutions of the NLS equation. The proof is based on an elimination of the quadratic terms of the KdV equation via the Miura transformation.Guido SchneiderCopyright © 2011 Guido Schneider. All rights reserved.http://www.hindawi.com/journals/amp/2011/272703/Jean-Pierre Antoine and Camillo TrapaniCopyright © 2011 Jean-Pierre Antoine and Camillo Trapani. All rights reserved.