Downloads & Free Reading Options - Results

Topics: Expression evaluation and the ways of evaluating. The representation of the environment of expression evaluation. De Bruijn's theory of computation of expression evaluation. Syntactical theory of computation. The kinds of the expression evaluation theories.

Rum is a theory of applicative, side-effect free computations over an algebraic data structure. It goes beyond a theory of functions computed by programs, treating both intensional and extensional aspects of computation. Powerful programming tools such as streams, object-oriented programming, escape mechanisms, and co-routines can be represented. Intensional properties include the number of multiplications executed, the number of context switches, and the maximum stack depth required in a computation. Extensional properties include notions of equality for streams and co-routines and characterization of functionals implementing strategies for searching tree-structured spaces. Precise definitions of informal concepts such as stream and co-routine are given and their mathematical theory is developed. Operations on programs treated include program transformations which introduce functional and control abstractions; a compiling morphism that provides a representation of control abstractions as functional abstractions; and operations that transform intensional properties to extensional properties. The goal is not only to account for programming practice in Lisp, but also to improve practice by providing mathematical tools for developing programs and building programming systems. Rum views computation as a process of generating computation structures - trees for context-independent computations and sequences for context-dependent computations. The recursion theorem gives a fixed-point function that computes computationally minimal fixed points. The context insensitivity theorem says that context-dependent computations are uniformly parameterized by the calling context and that computations in which context dependence is localized can be treated like context-independent computations.

In this report, relevant parts of the scattering theory for magnetic spheres are presented. Mass extinction coefficients, and the lognormal size distribution are defined. The theory and algorithms for integrating scattering parameters over size distributions are developed. The integrations are carried out in terms of dimensionless scattering, and size distribution parameters, which are simply related to the usual mass scattering coefficients. Fortran codes, which implement the algorithmic design, are presented, and examples of code use are given. Code listings are included. (AN)

In this report, relevant parts of the scattering theory for magnetic spheres are presented. Mass extinction coefficients, and the lognormal size distribution are defined. The theory and algorithms for integrating scattering parameters over size distributions are developed. The integrations are carried out in terms of dimensionless scattering, and size distribution parameters, which are simply related to the usual mass scattering coefficients. Fortran codes, which implement the algorithmic design, are presented, and examples of code use are given. Code listings are included. (AN)

390p. ; 24 cm

This paper is in the public domain in USA. Metadata comes from the CrossRef API, see full record in the source URL below.

ksiazka

A viscoelastic model for deformation and stress associated with earthquakes is reported. The model consists of a rectangular dislocation (strike slip fault) in a viscoelastic layer (lithosphere) lying over a viscoelastic half space (asthenosphere). The time dependent surface stresses are analyzed. The model predicts that near the fault a significant fraction of the stress that was reduced during the earthquake is recovered by viscoelastic softening of the lithosphere. By contrast, the strain shows very little change near the fault. The model also predicts that the stress changes associated with asthenospheric flow extend over a broader region than those associated with lithospheric relaxation even though the peak value is less. The dependence of the displacements, stresses on fault parameters studied. Peak values of strain and stress drop increase with increasing fault height and decrease with fault depth. Under many circumstances postseismic strains and stresses show an increase with decreasing depth to the lithosphere-asthenosphere boundary. Values of the strain and stress at distant points from the fault increase with fault area but are relatively insensitive to fault depth.

theory of automata

Molecular Density Functional Theory (MDFT) offers an efficient implicit- solvent method to estimate molecule solvation free-energies whereas conserving a fully molecular representation of the solvent. Even within a second order ap- proximation for the free-energy functional, the so-called homogeneous reference uid approximation, we show that the hydration free-energies computed for a dataset of 500 organic compounds are of similar quality as those obtained from molecular dynamics free-energy perturbation simulations, with a computer cost reduced by two to three orders of magnitude. This requires to introduce the proper partial volume correction to transform the results from the grand canoni- cal to the isobaric-isotherm ensemble that is pertinent to experiments. We show that this correction can be extended to 3D-RISM calculations, giving a sound theoretical justifcation to empirical partial molar volume corrections that have been proposed recently.

We provide ways to turn ancillas into phase gates (chapter 1), leading to irrational phase gates (chapter 2). We realize all the 2-qubit permutation gates (chapter 3).

In these lectures the authors sketches a theory of functions and relations that are computable and specifiable, uniformly over a class of many sorted algebras. Such a class K of algebras is a mathematical model of the semantics of software module; in particular, a module defining an abstract data type. The theory of computation, specification and verification over K has many applications; those I will describe concern the following subjects: Program specification and verification; logic programming modules and abstract data types; and synchronous concurrent algorithms and their application in hardware design. The author's research on these apparently disparate applications is part of a program based on the algebraic theory of abstract data types, that aims at the formulation and analysis of the many interesting notions of computability, specifiability, and verifiability that exist in different areas of computer science and mathematics. (KR)

We have studied the formation of Hall-qubit (LLL state) in Quantum Hall effect due to the Aharonov-Bhom oscillation of quasiparticles.The spin echo method plays the key role in the topological entanglement of qubits. The proper ratio of fluxes for maximally entangling qubits has also been pointed out. The generation of higher Quantum Hall state may be possible with the help of quantum teleportation.

We have studied the formation of Hall-qubit (LLL state) in Quantum Hall effect due to the Aharonov-Bhom oscillation of quasiparticles.The spin echo method plays the key role in the topological entanglement of qubits. The proper ratio of fluxes for maximally entangling qubits has also been pointed out. The generation of higher Quantum Hall state may be possible with the help of quantum teleportation.

This paper deals with a method of calculating the deviation of the path of an orbiting body from a nominal or reference trajectory. The form in which the solution is cast was motivated by a particular perturbation problem. Stanford University is developing a 'drag-free', or 'dragmakeup', scientific satellite which is designed to follow a purely gravitational orbit. The satellite consists actually of two satellites: an inner sphere or proof mass, and an outer concentric shell. The relative position of the shell with respect to the inner sphere is sensed with a capacitive pickoff. The position signals command an active translation control system which fires jets mounted on the outer shell so that it chases the inner sphere without ever touching it. Thus the proof mass is shielded from gas drag and solar radiation pressure and, except for very small disturbances caused by force interactions with the outer shell, it follows a purely gravitational orbit.

This paper deals with the computation of the rank and of some integer Smith forms of a series of sparse matrices arising in algebraic K-theory. The number of non zero entries in the considered matrices ranges from 8 to 37 millions. The largest rank computation took more than 35 days on 50 processors. We report on the actual algorithms we used to build the matrices, their link to the motivic cohomology and the linear algebra and parallelizations required to perform such huge computations. In particular, these results are part of the first computation of the cohomology of the linear group GL_7(Z).

The aim in this note is to define an algorithm to carry out minimal curvature spherical harmonics interpolation, which is then used to calculate the Laplacian for multi-electrode EEG data analysis. The approach taken is to respect the data. That is, we implement a minimal curvature condition for the interpolating surface subject to the constraints determined from the multi-electrode data. We implement this approach using spherical harmonics interpolation. In this elegant example we show that minimization requirement and constraints complement each other to fix all degrees of freedom automatically, as occurs in gauge theories. That is, the constraints are respected, while only the orthogonal subspace minimization constraints are enforced. As an example, we discuss the application to interpolate control data and calculate the temporal sequence of laplacians from an EEG Mismatch Negativity (MMN) experiment (using an implementation of the algorithm in IDL).

Vagueness is a linguistic phenomenon as well as a property of physical objects. Fuzzy set theory is a mathematical model of vagueness that has been used to define vague models of computation. The prominent model of vague computation is the fuzzy Turing machine. This conceptual computing device gives an idea of what computing under vagueness means, nevertheless, it is not the most natural model. Based on the properties of this and other models of vague computing, it is aimed to formulate a basis for a philosophy of a theory of fuzzy computation.

In this paper we present a new unified theoretical framework that describes the full dynamics of quantum computation. Our formulation allows any questions pertaining to the physical behavior of a quantum computer to be framed, and in principle, answered. We refer to the central organizing principle developed in this paper, on which our theoretical structure is based, as the *Quantum Computer Condition* (QCC), a rigorous mathematical statement that connects the irreversible dynamics of the quantum computing machine, with the reversible operations that comprise the quantum computation intended to be carried out by the quantum computing machine. Armed with the QCC, we derive a powerful result that we call the *Encoding No-Go Theorem*. This theorem gives a precise mathematical statement of the conditions under which fault-tolerant quantum computation becomes impossible in the presence of dissipation and/or decoherence. In connection with this theorem, we explicitly calculate a universal critical damping value for fault-tolerant quantum computation. In addition we show that the recently-discovered approach to quantum error correction known as "operator quantum error-correction" (OQEC) is a special case of our more general formulation. Our approach furnishes what we will refer to as "operator quantum fault-tolerance" (OQFT). In particular, we show how the QCC allows one to derive error thresholds for fault tolerance in a completely general context. We prove the existence of solutions to a class of time-dependent generalizations of the Lindblad equation. Using the QCC, we also show that the seemingly different circuit, graph- (including cluster-) state, and adiabatic paradigms for quantum computing are in fact all manifestations of a single, universal paradigm for all physical quantum computation.

We investigate the exact effect on ion trap quantum computation after field quantization. First an exact expression of failure probability from field quantization after many CNOT operations in Cirac-Zoller scheme is given. It is proportional to operation number and the amplitude of $|1\rangle_x |0\rangle_y$ or $|1\rangle_x |1\rangle_y$ in initial state, and inverse proportional to mean number of photons and amplitude of $|0\rangle_x |0\rangle_y$ or $|0\rangle_x |1\rangle_y$ in initial state. Then we calculate the failure probability when the limitation to mean number of photons in sideband transition is considered. When the initial state is $|1\rangle_x |0\rangle_y$ or $|1\rangle_x |1\rangle_y$, after about $10^2$ times of CNOT operations, failure probability is no less than $10^{-2}$, while $10^{-2}$ is the known maximum threshold in fault-tolerant quantum computation. Then when the initial state is $|1\rangle_x |0\rangle_y$ or $|1\rangle_x |1\rangle_y$, the number of CNOT gates on the same pair of physical qubits should be no more than $10^2$ in one error-correction period, or else the computation cannot be implemented reliably. This conclusion can help to determine the number of CNOT operations between coding and decoding in one error-correction period in fault-tolerant quantum computation.

We describe a new and consistent perturbation theory for solid-state quantum computation with many qubits. The errors in the implementation of simple quantum logic operations caused by non-resonant transitions are estimated. We verify our perturbation approach using exact numerical solution for relatively small (L=10) number of qubits. A preferred range of parameters is found in which the errors in processing quantum information are small. Our results are needed for experimental testing of scalable solid-state quantum computers.

The work shows that it is possible to formalize all properties regularly observed in (deterministic and non-deterministic) algorithms in second-order predicate calculus. Moreover, it is shown that for any given algorithm it suffices to know how to formalize its 'partial correctness' by a second-order formula in order to formalize all other properties by second-order formulas. The result is of special interest since 'partial correctness' has already been formalized in second-order predicate calculus for many classes of algorithms.

This chapter from the upcoming Handbook of Knot Theory (eds. Menasco and Thistlethwaite) shows how to construct hyperbolic structures on link complements and perform hyperbolic Dehn filling. Along with a new elementary exposition of the standard ideas from Thurston's work, the article includes never-before-published explanations of SnapPea's algorithms for triangulating a link complement efficiently and for converging quickly to the hyperbolic structure while avoiding singularities in the parameter space.

A generalization of the semiclassical cubic spline known in the literature as the exponential spline is discussed. In actuality, the exponential spline represents a continuum of interpolants ranging from the cubic spline to the linear spline. A particular member of this family is uniquely specified by the choice of certain tension parameters. The theoretical underpinnings of the exponential spline are outlined. This development roughly parallels the existing theory for cubic splines. The primary extension lies in the ability of the exponential spline to preserve convexity and monotonicity present in the data. Next, the numerical computation of the exponential spline is discussed. A variety of numerical devices are employed to produce a stable and robust algorithm. An algorithm for the selection of tension parameters that will produce a shape preserving approximant is developed. A sequence of selected curve-fitting examples are presented which clearly demonstrate the advantages of exponential splines over cubic splines.

In this paper we describe the numerical analysis underlying our efforts to develop an accurate and reliable code for simulating flame propagation using complex physical and chemical models. We discuss our spatial and temporal discretization schemes, which in our current implementations range in order from two to six. In space we use staggered meshes to define discrete divergence and gradient operators, allowing us to approximate complex diffusion operators while maintaining ellipticity. Our temporal discretization is based on the use of preconditioning to produce a highly efficient linearly implicit method with good stability properties. High order for time accurate simulations is obtained through the use of extrapolation or deferred correction procedures. We also discuss our techniques for computing stationary flames. The primary issue here is the automatic generation of initial approximations for the application of Newton's method. We use a novel time-stepping procedure, which allows the dynamic updating of the flame speed and forces the flame front towards a specified location. Numerical experiments are presented, primarily for the stationary flame problem. These illustrate the reliability of our techniques, and the dependence of the results on various code parameters.

In this paper we describe the numerical analysis underlying our efforts to develop an accurate and reliable code for simulating flame propagation using complex physical and chemical models. We discuss our spatial and temporal discretization schemes, which in our current implementations range in order from two to six. In space we use staggered meshes to define discrete divergence and gradient operators, allowing us to approximate complex diffusion operators while maintaining ellipticity. Our temporal discretization is based on the use of preconditioning to produce a highly efficient linearly implicit method with good stability properties. High order for time accurate simulations is obtained through the use of extrapolation or deferred correction procedures. We also discuss our techniques for computing stationary flames. The primary issue here is the automatic generation of initial approximations for the application of Newton's method. We use a novel time-stepping procedure, which allows the dynamic updating of the flame speed and forces the flame front towards a specified location. Numerical experiments are presented, primarily for the stationary flame problem. These illustrate the reliability of our techniques, and the dependence of the results on various code parameters.

Privacy is a growing concern in the digital world as more information becomes digital every day. Often the implications of how this information could be exploited for nefarious purposes are not explored until after the fact. The public is becoming more concerned about this. This dissertation introduces a new paradigm for tackling the problem, namely, transferable multiparty computation (T-MPC). T-MPC builds upon existing multiparty computation work yet allows some additional exibility in the set of participants. T-MPC is orders of magnitude more efficient for certain applications. This greatly increases the scalability of the sizes of networks supported for privacy-preserving computation.

The theory of finite Fourier transforms is developed from the definitions of infinite transforms and applied to the computation of convolutions, correlations, and power spectra. Detailed procedures for these computations are given, including listings and writeups of FORTRAN subroutines.

The theory of finite Fourier transforms is developed from the definitions of infinite transforms and applied to the computation of convolutions, correlations, and power spectra. Detailed procedures for these computations are given, including listings and writeups of FORTRAN subroutines.

We present a combination method based on orignal version of Davidson algorithm for extracting few of the lowest eigenvalues and eigenvectors of a sparse symmetric Hamiltonian matrix and the simplest version of Lanczos technique for obtaining a tridiagonal representation of the Hamiltonian to compute the continued fraction expansion of the Green's function at a very low temperature. We compare the Davidson$+$Lanczos method with the full diagonalization on a one-band Hubbard model on a Bethe lattice of infinite-coordination using dynamical mean field theory.

We present a combination method based on orignal version of Davidson algorithm for extracting few of the lowest eigenvalues and eigenvectors of a sparse symmetric Hamiltonian matrix and the simplest version of Lanczos technique for obtaining a tridiagonal representation of the Hamiltonian to compute the continued fraction expansion of the Green's function at a very low temperature. We compare the Davidson$+$Lanczos method with the full diagonalization on a one-band Hubbard model on a Bethe lattice of infinite-coordination using dynamical mean field theory.

We use a single site lattice in four dimensions to study the scaling of large N Yang-Mills field coupled to a single massless Dirac fermion in the adjoint representation. We use the location of the strong to weak coupling transition defined through the eigenvalues of the folded Wilson loop operator to set a scale. We do not observe perturbative scaling in the region studied in this paper. Instead, we observe that the scale changes very slowly with the bare coupling. The lowest eigenvalue of the overlap Dirac operator is another scale that shows similar behavior as a function of the lattice coupling. We speculate that this behavior is due to the beta function appoaching close to a zero.

The first author introduced a relative symplectic capacity $C$ for a symplectic manifold $(N,\omega_N)$ and its subset $X$ which measures the existence of non-contractible periodic trajectories of Hamiltonian isotopies on the product of $N$ with the annulus $A_R=(R,R)\times\mathbb{R}/\mathbb{Z}$. In the present paper, we give an exact computation of the capacity $C$ of the $2n$-torus $\mathbb{T}^{2n}$ relative to a Lagrangian submanifold $\mathbb{T}^n$ which implies the existence of non-contractible Hamiltonian periodic trajectories on $A_R\times\mathbb{T}^{2n}$. Moreover, we give a lower bound on the number of such trajectories.

Besides the traditional circuit-based model of quantum computation, several quantum algorithms based on a continuous-time Hamiltonian evolution have recently been introduced, including for instance continuous-time quantum walk algorithms as well as adiabatic quantum algorithms. Unfortunately, very little is known today on the behavior of these Hamiltonian algorithms in the presence of noise. Here, we perform a fully analytical study of the resistance to noise of these algorithms using perturbation theory combined with a theoretical noise model based on random matrices drawn from the Gaussian Orthogonal Ensemble, whose elements vary in time and form a stationary random process.

We compute the Schroedinger functional (SF) for the case of pure SU(3) gauge theory at two-loop order in lattice perturbation theory. This allows us to extract the three-loop beta-function in the SF-scheme. These results are required to compute the running coupling, the Lambda-parameter and quark masses by finite size techniques with negligible systematic errors. In addition, we can now implement two-loop O(a) improvement in simulations and extend and study series in alternative ("tadpole-improved") bare couplings.

We compute the Schroedinger functional (SF) for the case of pure SU(3) gauge theory at two-loop order in lattice perturbation theory. This allows us to extract the three-loop beta-function in the SF-scheme. These results are required to compute the running coupling, the Lambda-parameter and quark masses by finite size techniques with negligible systematic errors. In addition, we can now implement two-loop O(a) improvement in simulations and extend and study series in alternative ("tadpole-improved") bare couplings.

This report presents two numerical methods considered for the computation of fuel-optimal, low-thrust orbit transfers in large numbers of burns. The origins of these methods are observations made with the extremal solutions of transfers in small numbers of burns; there seems to exist a trend such that the longer the time allowed to perform an optimal transfer the less fuel that is used. These longer transfers are obviously of interest since they require a motor of low thrust; however, we also find a trend that the longer the time allowed to perform the optimal transfer the more burns are required to satisfy optimality. Unfortunately, this usually increases the difficulty of computation. Both of the methods described use small-numbered burn solutions to determine solutions in large numbers of burns. One method is a homotopy method that corrects for problems that arise when a solution requires a new burn or coast arc for optimality. The other method is to simply patch together long transfers from smaller ones. An orbit correction problem is solved to develop this method. This method may also lead to a good guidance law for transfer orbits with long transfer times.

This report presents two numerical methods considered for the computation of fuel-optimal, low-thrust orbit transfers in large numbers of burns. The origins of these methods are observations made with the extremal solutions of transfers in small numbers of burns; there seems to exist a trend such that the longer the time allowed to perform an optimal transfer the less fuel that is used. These longer transfers are obviously of interest since they require a motor of low thrust; however, we also find a trend that the longer the time allowed to perform the optimal transfer the more burns are required to satisfy optimality. Unfortunately, this usually increases the difficulty of computation. Both of the methods described use small-numbered burn solutions to determine solutions in large numbers of burns. One method is a homotopy method that corrects for problems that arise when a solution requires a new burn or coast arc for optimality. The other method is to simply patch together long transfers from smaller ones. An orbit correction problem is solved to develop this method. This method may also lead to a good guidance law for transfer orbits with long transfer times.

The theory of finite Fourier transforms is developed from the definitions of infinite transforms and applied to the computation of convolutions, correlations, and power spectra. Detailed procedures for these computations are given, including listings and writeups of FORTRAN subroutines.

By perturbing properly a linear program to a separable quadratic program it is possible to solve the latter in its dual variable space by iterative techniques such as sparsity-preserving SOR (successive overrelaxation) algorithms. The main result of this paper gives an effective computational criterion to check whether the solutions of the perturbed quadratic programs provide the least 2-norm solution of the original linear program. (Author)

This report presents new theoretical results which lead to new algorithms for the computation of fuel-optimal multiple-burn orbit transfers of low and medium thrust. Theoretical results introduced herein show how to add burns to an optimal trajectory and show that the traditional set of necessary conditions may be replaced with a much simpler set of equations. Numerical results are presented to demonstrate the utility of the theoretical results and the new algorithms. Two indirect methods from the literature are shown to be effective for the optimal orbit transfer problem with relatively small numbers of burns. These methods are the Minimizing Boundary Condition Method (MBCM) and BOUNDSCO. Both of these methods make use of the first-order necessary conditions exactly as derived by optimal control theory. Perturbations due to Earth's oblateness and atmospheric drag are considered. These perturbations are of greatest interest for transfers that take place between low Earth orbit altitudes and geosynchronous orbit altitudes. Example extremal solutions including these effects and computed by the aforementioned methods are presented. An investigation is also made into a suboptimal multiple-burn guidance scheme. The FORTRAN code developed for this study has been collected together in a package named ORBPACK. ORBPACK's user manual is provided as an appendix to this report.

Agostic interactions are covalent intramolecular interactions between an electron deficient metal and a sigma-bond in close geometrical proximity to the metal atom. While the classic cases involve CH sigma-bonds close to early transition metals like titanium, many more agostic systems have been proposed which contain CH, SiH, BH, CC and SiC sigma-bonds coordinated to a wide range of metal atoms. Recent computational studies of a multitude of agostic interactions are reviewed in this contribution. It is highlighted how several difficulties with the theoretical description of the phenomenon arise because of the relative weakness of this interaction. The methodology used to compute and interpret agostic interactions is presented and different approaches such as atoms in molecules (AIM), natural bonding orbitals (NBO) or the electron localization function (ELF) are compared and put into context. A brief overview of the history and terminology of agostic interactions is given in the introduction and fundamental differences between alpha, beta; and other agostic interactions are explained.

We discuss a number of issues arising when computing non-perturbative effects systematically across the string theory landscape. In particular, we cast the study of fairly generic physical properties into the language of computability/number theory and show that this amounts to solving systems of diophantine equations. In analogy to the negative solution to Hilbert's 10th problem, we argue that in such systematic studies there may be no algorithm by which one can determine all physical effects. We take large volume type IIB compactifications as an example, with the physical property of interest being the low-energy non-perturbative F-terms of a generic compactification. A similar analysis is expected to hold for other kinds of string vacua, and we discuss in particular the extension of our ideas to F-theory. While these results imply that it may not be possible to answer systematically certain physical questions about generic type IIB compactifications, we identify particular Calabi-Yau manifolds in which the diophantine equations become linear, and thus can be systematically solved. As part of the study of the required systematics of F-terms, we develop technology for computing Z_2 equivariant line bundle cohomology on toric varieties, which determines the presence of particular instanton zero modes via the Koszul complex. This is of general interest for realistic IIB model building on complete intersections in toric ambient spaces.

We present the first measurement of the vortex free-energy order parameter at weak coupling for SU(2) in simulations employing multihistogram methods. The result shows that the excitation probability for a sufficiently thick vortex in the vacuum tends to unity. This is rigorously known to provide a necessary and sufficient condition for maintaining confinement at weak coupling in SU(N) gauge theories.

Green's function of the problem describing steady forward motion of bodies in an open ocean in the framework of the linear surface wave theory (the function is often referred to as Kelvin's wave source potential) is considered. Methods for numerical evaluation of the so-called `single integral' (or, in other words, `wavelike') term, dominating in the representation of Green's function in the far field, are developed. The difficulty in the numerical evaluation is due to integration over infinite interval of the function containing two differently oscillating factors and the presence of stationary points. This work suggests two methods to approximate the integral and its derivatives. First of the methods is based on the idea suggested by D.Levin in 1982 --- evaluation of the integral is converted to finding a particular slowly oscillating solution of an ordinary differential equation. To overcome well-known numerical instability of Levin's collocation method, an alternative type of collocation is used; it is based on a barycentric Lagrange interpolation with a clustered set of nodes. The second method for evaluation of the wavelike term involves application of the steepest descent method and Clenshaw--Curtis quadrature. The methods are numerically tested and compared for a wide variety of parameters.

Recently, Dil and Boyadzhiev \cite{AD2015} proved an explicit formula for the sum of multiple harmonic numbers whose indices are the sequence $\left( {{{\left\{ 0 \right\}}_r},1} \right)$. In this paper we show that the sums of multiple harmonic numbers whose indices are the sequence $\left( {{{\left\{ 0 \right\}}_r,1};{{\left\{ 1 \right\}}_{k-1}}} \right)$ can be expressed in terms of (multiple) zeta values, multiple harmonic numbers and Stirling numbers of the first kind, and give an explicit formula.

Recently de La Torre et al. [1] reconstructed Quantum Theory from its local structure on the basis of local discriminability and the existence of a one-parameter group of bipartite transformations containing an entangling gate. This result relies on universality of an entangling gate for quantum computation. Here we prove universality of C-NOT with local gates for Real Quantum Theory (RQT), showing that such universality would not be sufficient for the result, whereas local discriminability and the qubit structure play a crucial role. For reversible computation, generally an extra rebit is needed for RQT. As a byproduct we also provide a short proof of universality of C-NOT for CQT.

We present a lattice computation of the effective potential for O(2)-invariant $(\lambda\Phi^4)_4$ theory in the region of bare parameters corresponding to a classically scale-invariant theory. As expected from ``triviality'' and as in the one-component theory, we find very good agreement with the one-loop prediction, while a perturbative leading-log improvement of the effective potential fails to reproduce the Monte Carlo data. The mass $m_h$ of the free shifted radial field is related to the renormalized vacuum expectation value $v_R$ through the same relation $m^2_h=8\pi^2 v^2_R$ as in the one-component case. This confirms the prediction of a weakly interacting 2.2 TeV Higgs particle in the standard model.

A computational study of morphological instabilities of a two-dimensional nematic front under directional growth was performed using a Landau-de Gennes type quadrupolar tensor order parameter model for the first-order isotropic/nematic transition of 5CB (pentyl-cyanobiphenyl). A previously derived energy balance, taking anisotropy into account, was utilized to account for latent heat and an imposed morphological gradient in the time-dependent model. Simulations were performed using an initially homeotropic isotropic/nematic interface. Thermal instabilities in both the linear and non-linear regimes were observed and compared to past experimental and theoretical observations. A sharp-interface model for the study of linear morphological instabilities, taking into account additional complexity resulting from liquid crystalline order, was derived. Results from the sharp-interface model were compared to those from full two-dimensional simulation identifying the specific limitations of simplified sharp-interface models for this liquid crystal system. In the nonlinear regime, secondary instabilities were observed to result in the formation of defects, interfacial heterogeneities, and bulk texture dynamics.