Some results on solvability of ordinary linear differential equations in locally convex spaces

Let $\Gamma$ be the class of sequentially complete locally convex spaces such that an existence theorem holds for the linear Cauchy problem $\dot x = Ax$, $x(0) = x_0$ with respect to functions $x: R\to E$. It is proved that if $E\in \Gamma$, then $E\times R^A$ is-an-element-of $\Gamma$ for an arbitrary set $A$. It is also proved that a topological product of infinitely many infinite-dimensional Frechet spaces, each not isomorphic to $\omega$, does not belong to $\Gamma$.

Resting energy expenditure in non-ventilated, non-sedated patients recovering from serious traumatic brain injury: Comparison of prediction equations with indirect calorimetry values

Background & aims: Little is known about energy requirements in brain injured (TBI) patients, despite evidence suggesting adequate nutritional support can improve clinical outcomes. The study aim was to compare predicted energy requirements with measured resting energy expenditure (REE) values, in patients recovering from TBI.

Methods: Indirect calorimetry (IC) was used to measure REE in 45 patients with TBI. Predicted energy requirements were determined using FAO/WHO/UNU and Harris–Benedict (HB) equations. Bland– Altman and regression analysis were used for analysis.

Results: One-hundred and sixty-seven successful measurements were recorded in patients with TBI. At an individual level, both equations predicted REE poorly. The mean of the differences of standardised areas of measured REE and FAO/WHO/UNU was near zero (9 kcal) but the variation in both directions was substantial (range 591 to þ573 kcal). Similarly, the differences of areas of measured REE and HB demonstrated a mean of 1.9 kcal and range 568 to þ571 kcal. Glasgow coma score, patient status, weight and body temperature were signi?cant predictors of measured REE (p < 0.001; R²⁼ 0.47).

Conclusions: Clinical equations are poor predictors of measured REE in patients with TBI. The variability in REE is substantial. Clinicians should be aware of the limitations of prediction equations when estimating energy requirements in TBI patients.

Modeling Multivariate Interest Rates Using Time-Varying Copulas and Reducible Nonlinear Stochastic Differential Equations

We propose a new approach for modeling nonlinear multivariate interest rate processes based on time-varying copulas and reducible stochastic differential equations (SDEs). In the modeling of the marginal processes, we consider a class of nonlinear SDEs that are reducible to Ornstein--Uhlenbeck (OU) process or Cox, Ingersoll, and Ross (1985) (CIR) process. The reducibility is achieved via a nonlinear transformation function. The main advantage of this approach is that these SDEs can account for nonlinear features, observed in short-term interest rate series, while at the same time leading to exact discretization and closed-form likelihood functions. Although a rich set of specifications may be entertained, our exposition focuses on a couple of nonlinear constant elasticity volatility (CEV) processes, denoted as OU-CEV and CIR-CEV, respectively. These two processes encompass a number of existing models that have closed-form likelihood functions. The transition density, the conditional distribution function, and the steady-state density function are derived in closed form as well as the conditional and unconditional moments for both processes. In order to obtain a more flexible functional form over time, we allow the transformation function to be time varying. Results from our study of U.S. and UK short-term interest rates suggest that the new models outperform existing parametric models with closed-form likelihood functions. We also find the time-varying effects in the transformation functions statistically significant. To examine the joint behavior of interest rate series, we propose flexible nonlinear multivariate models by joining univariate nonlinear processes via appropriate copulas. We study the conditional dependence structure of the two rates using Patton (2006a) time-varying symmetrized Joe--Clayton copula. We find evidence of asymmetric dependence between the two rates, and that the level of dependence is positively related to the level of the two rates. (JEL: C13, C32, G12) Copyright The Author 2010. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org, Oxford University Press.

Discretization and solution of the inhomogeneous Bogoliubov-de Gennes equations

In the presence of inhomogeneities, defects and currents, the equations describing a Bose-condensed ensemble of alkali atoms have to be solved numerically. By combining both linear and nonlinear equations within a Discrete Variable Representation framework, we describe a computational scheme for the solution of the coupled Bogoliubov-de Gennes (BdG) and nonlinear Schrodinger (NLS) equations for fields in a 3D spheroidal potential. We use the method to calculate the collective excitation spectrum and quasiparticle mode densities for excitations of a Bose condensed gas in a spheroidal trap. The method is compared against finite-difference and spectral methods, and we find the DVR computational scheme to be superior in accuracy and efficiency for the cases we consider. (C) 2004 Elsevier B.V. All rights reserved.

A review of the equations used to predict the velocity distribution within a ship’s propeller jet

Predicting the velocity within the ship’s propeller jet is the initial step to investigate the scouring made by the propeller jet. Albertson et al. (1950) suggested the investigation of a submerged jet can be undertaken through observation of the plain water jet from an orifice. The plain water jet investigation of Albertson et al. (1950) was based on the axial momentum theory. This has been the basis of all subsequent work with propeller jets. In reality, the velocity characteristic of a ship’s propeller jet is more complicated than a plain water jet. Fuehrer and Römisch (1977), Blaauw and van de Kaa (1978), Berger et al. (1981), Verhey (1983) and Hamill (1987) have carried out investigations using physical model. This paper reviews the state-of-art of the equations used to predict the time-averaged axial, tangential and radial components of velocity within the zone of flow establishment and the zone of established flow of a ship’s propeller jet.

Inline Interdigital Pseudo-Elliptic Helical Resonator Filters

A new inline coupling topology for narrowband helical resonator filters is proposed that allows to introduce selectively located transmission zeros (TZs) in the stopband. We show that a pair of helical resonators arranged in an interdigital configuration can realize a large range of in-band coupling coefficient values and also selectively position a TZ in the stopband. The proposed technique dispenses the need for auxiliary elements, so that the size, complexity, power handling and insertion loss of the filter are not compromised. A second order prototype filter with dimensions of the order of 0.05 lambda, power handling capability up to 90 W, measured insertion loss of 0.18 dB and improved selectivity is presented.

Critical assessment of two-qubit post-Markovian master equations

A post-Markovian master equation has been recently proposed as a tool to describe the evolution of a system coupled to a memory-keeping environment [A. Shabani and D. A. Lidar, Phys. Rev. A 71, 020101 ( R) ( 2005)]. For a single qubit affected by appropriately chosen environmental conditions, the corresponding dynamics is always legitimate and physical. Here we extend such a situation to the case of two qubits, only one of which experiences the environmental effects. We show how, despite the innocence of such an extension, the introduction of the second qubit should be done cum grano salis to avoid consequences such as the breaking of the positivity of the associated dynamical map. This hints at the necessity of using care when adopting phenomenologically derived models for evolutions occurring outside the Markovian framework.

Cold-formed steel sections with web openings subjected to web crippling under two-flange loading conditions - Part II: Parametric study and proposed design equations

A parametric study of cold-formed steel sections with web openings subjected to web crippling was undertaken using finite element analysis, to investigate the effects of web holes and cross-section sizes on the web crippling strengths of channel sections subjected to web crippling under both interior-two-flange (ITF) and end-two-flange (ETF) loading conditions. In both loading conditions, the hole was centred beneath the bearing plate. It was demonstrated that the main factors influencing the web crippling strength are the ratio of the hole depth to the flat depth of the web, and the ratio of the length of bearing plates to the flat depth of the web. In this paper, design recommendations in the form of web crippling strength reduction factors are proposed, that are conservative to both the experimental and finite element results.

R-matrix-Floquet theory of multiphoton processes:VIII. A linear equations method

A new linear equations method for calculating the R-matrix, which arises in the R-matrix-Floquet theory of multiphoton processes, is introduced. This method replaces the diagonalization of the Floquet Hamiltonian matrix by the solution of a set of linear simultaneous equations which are solved, in the present work, by the conjugate gradient method. This approach uses considerably less computer memory and can be readily ported onto parallel computers. It will thus enable much larger problems of current interest to be treated. This new method is tested by applying it to three-photon ionization of helium at frequencies where double resonances with a bound state and autoionizing states are important. Finally, an alternative linear equations method, which avoids the explicit calculation of the R-matrix by incorporating the boundary conditions directly, is described in an appendix.

Hardware elliptic curve cryptographic processor over GF(p)

A novel hardware architecture for elliptic curve cryptography (ECC) over GF(p) is introduced. This can perform the main prime field arithmetic functions needed in these cryptosystems including modular inversion and multiplication. This is based on a new unified modular inversion algorithm that offers considerable improvement over previous ECC techniques that use Fermat's Little Theorem for this operation. The processor described uses a full-word multiplier which requires much fewer clock cycles than previous methods, while still maintaining a competitive critical path delay. The benefits of the approach have been demonstrated by utilizing these techniques to create a field-programmable gate array (FPGA) design. This can perform a 256-bit prime field scalar point multiplication in 3.86 ms, the fastest FPGA time reported to date. The ECC architecture described can also perform four different types of modular inversion, making it suitable for use in many different ECC applications. © 2006 IEEE.

Sound Synthesis for Contact-Driven Musical Instruments via Discretisation of Hamilton's Equations

Physical modelling of musical instruments involves studying nonlinear interactions between parts of the instrument. These can pose several difficulties concerning the accuracy and stability of numerical algorithms. In particular, when the underlying forces are non-analytic functions of the phase-space variables, a stability proof can only be obtained in limited cases. An approach has been recently presented by the authors, leading to unconditionally stable simulations for lumped collision models. In that study, discretisation of Hamilton’s equations instead of the usual Newton’s equation of motion yields a numerical scheme that can be proven to be energy conserving. In this paper, the above approach is extended to collisions of distributed objects. Namely, the interaction of an ideal string with a flat barrier is considered. The problem is formulated within the Hamiltonian framework and subsequently discretised. The resulting nonlinearmatrix equation can be shown to possess a unique solution, that enables the update of the algorithm. Energy conservation and thus numerical stability follows in a way similar to the lumped collision model. The existence of an analytic description of this interaction allows the validation of the model’s accuracy. The proposed methodology can be used in sound synthesis applications involving musical instruments where collisions occur either in a confined (e.g. hammer-string interaction, mallet impact) or in a distributed region (e.g. string-bridge or reed-mouthpiece interaction).