Analysis of the free vibration of rectangular plates with central cut-outs using the discrete Ritz method

We present an analysis of the free vibration of plates with internal discontinuities due to central cut-outs. A numerical formulation for a basic L-shaped element which is divided into appropriate sub-domains that are dependent upon the location of the cut-out is used as the basic building element. Trial functions formed to satisfy certain boundary conditions are employed to define the transverse deflection of each sub-domain. Mathematical treatments in terms of the continuities in displacement, slope, moment, and higher derivatives between the adjacent sub-domains are enforced at the interconnecting edges. The energy functional results, from the proper assembly of the coupled strain and kinetic energy contributions of each sub-domain, are minimized via the Ritz procedure to extract the vibration frequencies and. mode shapes of the plates. The procedures are demonstrated by considering plates with central cut-outs that are subjected to two types of boundary conditions. (C) 2003 Elsevier Ltd. All rights reserved.

On the completion of Latin rectangles to symmetric Latin squares

We find necessary and sufficient conditions for completing an arbitrary 2 by n latin rectangle to an n by n symmetric latin square, for completing an arbitrary 2 by n latin rectangle to an n by n unipotent symmetric latin square, and for completing an arbitrary 1 by n latin rectangle to an n by n idempotent symmetric latin square. Equivalently, we prove necessary and sufficient conditions for the existence of an (n - 1)-edge colouring of K-n (n even), and for an n-edge colouring of K-n (n odd) in which the colours assigned to the edges incident with two vertices are specified in advance.

On decomposition of sub-linearised polynomials

We give a detailed exposition of the theory of decompositions of linearised polynomials, using a well-known connection with skew-polynomial rings with zero derivative. It is known that there is a one-to-one correspondence between decompositions of linearised polynomials and sub-linearised polynomials. This correspondence leads to a formula for the number of indecomposable sub-linearised polynomials of given degree over a finite field. We also show how to extend existing factorisation algorithms over skew-polynomial rings to decompose sub-linearised polynomials without asymptotic cost.

Full S matrix calculation via a single real-symmetric Lanczos recursion: The Lanczos artificial boundary inhomogeneity method

We present an efficient and robust method for the calculation of all S matrix elements (elastic, inelastic, and reactive) over an arbitrary energy range from a single real-symmetric Lanczos recursion. Our new method transforms the fundamental equations associated with Light's artificial boundary inhomogeneity approach [J. Chem. Phys. 102, 3262 (1995)] from the primary representation (original grid or basis representation of the Hamiltonian or its function) into a single tridiagonal Lanczos representation, thereby affording an iterative version of the original algorithm with greatly superior scaling properties. The method has important advantages over existing iterative quantum dynamical scattering methods: (a) the numerically intensive matrix propagation proceeds with real symmetric algebra, which is inherently more stable than its complex symmetric counterpart; (b) no complex absorbing potential or real damping operator is required, saving much of the exterior grid space which is commonly needed to support these operators and also removing the associated parameter dependence. Test calculations are presented for the collinear H+H-2 reaction, revealing excellent performance characteristics. (C) 2004 American Institute of Physics.

Recursive filtering of images with symmetric extension

Recursive filters are widely used in image analysis due to their efficiency and simple implementation. However these filters have an initialisation problem which either produces unusable results near the image boundaries or requires costly approximate solutions such as extending the boundary manually. In this paper, we describe a method for the recursive filtering of symmetrically extended images for filters with symmetric denominator. We begin with an analysis of symmetric extensions and their effect on non-recursive filtering operators. Based on the non-recursive case, we derive a formulation of recursive filtering on symmetric domains as a linear but spatially varying implicit operator. We then give an efficient method for decomposing and solving the linear implicit system, along with a proof that this decomposition always exists. This decomposition needs to be performed only once for each dimension of the image. This yields a filtering which is both stable and consistent with the ideal infinite extension. The filter is efficient, requiring less computation than the standard recursive filtering. We give experimental evidence to verify these claims. (c) 2005 Elsevier B.V. All rights reserved.

Analysis of the error performance of adaptive array antennas for CDMA with noncoherent M-ary orthogonal modulation in Nakagami fading

This letter presents an analytical model for evaluating the Bit Error Rate (BER) of a Direct Sequence Code Division Multiple Access (DS-CDMA) system, with M-ary orthogonal modulation and noncoherent detection, employing an array antenna operating in a Nakagami fading environment. An expression of the Signal to Interference plus Noise Ratio (SINR) at the output of the receiver is derived, which allows the BER to be evaluated using a closed form expression. The analytical model is validated by comparing the obtained results with simulation results.

Dual-symmetric Lagrangians in quantum electrodynamics: I. Conservation laws and multi-polar coupling

By using a complex field with a symmetric combination of electric and magnetic fields, a first-order covariant Lagrangian for Maxwell's equations is obtained, similar to the Lagrangian for the Dirac equation. This leads to a dual-symmetric quantum electrodynamic theory with an infinite set of local conservation laws. The dual symmetry is shown to correspond to a helical phase, conjugate to the conserved helicity. There is also a scaling symmetry, conjugate to the conserved entanglement. The results include a novel form of the photonic wavefunction, with a well-defined helicity number operator conjugate to the chiral phase, related to the fundamental dual symmetry. Interactions with charged particles can also be included. Transformations from minimal coupling to multi-polar or more general forms of coupling are particularly straightforward using this technique. The dual-symmetric version of quantum electrodynamics derived here has potential applications to nonlinear quantum optics and cavity quantum electrodynamics.

Self-condensation of a thiazole-peptide bearing a 21-membered loop into a library of giant macrocycles with multiple orthogonal loops

Tetrapeptide analogue H-[Glu-Ser-Lys(Thz)]-OH, containing a turn-inducing thiazole constraint, was used as a template to produce a 21-membered structurally characterized loop by linking Glu and Lys side chains with a Val-Ile dipeptide. This template was oligomerized in one pot to a library (cyclo-[1](n), n = 2-10) of giant symmetrical macrocycles (up to 120-membered rings), fused to 2-10 appended loops that were carried intact through multiple oligomerization (chain extension) and cyclization (chain terminating) reactions of the template. A three-dimensional solution structure for cyclo-[1](3) shows all three appended loops projecting from the same face of the macrocycle. This is a promising approach to separating pepticle motifs over large distances.

Comparative study of symmetric and asymmetric cylindrical MRI gradient Y-coils in terms of induced eddy currents

We have recently introduced the concept of whole-body asymmetric MRI systems [1]. In this theoretical study, we investigate the PNS characteristics of whole-body asymmetric gradient systems as compared to conventional symmetric systems. Recent experimental evidence [2] supports the hypothesis of transverse gradients being the largest contributor of PNS due to induced electric currents. Asymmetric head gradient coils have demonstrated benefits in the past [3]. The numerical results are based on an anatomically-accurate 2mm-human voxel-phantom NORMAN [4]. The results of this study can facilitate the optimization of whole-body asymmetric gradients in terms of patient comfort/safety (less PNS), while prospering the use of asymmetric MRI systems for in-vivo medical interventions.