(4aR, 8aS, 9aR, 10aS)-8a, 9a-Difluoro-1,4,4a, 5,8,8a, 9,9a, 10,10a-decahydroanthracene-4a, 10a-diol hemihydrate

The title compound, C(14)H(18)F(2)O(2)center dot 0.5H(2)O, a hemihydrate of a C(s)-symmetric unsaturated difluorodiol, crystallizes in the centrosymmetric space group P2/m (Z = 4). The asymmetric unit contains two crystallographically independent difluorodiol half-molecules, occupying the mirror planes at (x, 0, z) and (x, 1/2, z), and half a molecule of water, lying on the twofold axis at (0, y, 0). Four difluorodiol molecules self-assemble around each solvent water molecule via O-H center dot center dot center dot O hydrogen bonds in a near tetrahedral symmetry to generate a cylindrical column-like architecture.

From the Icosahedron to Natural Triangulations of CP(2) and S(2) x S(2)

We present two constructions in this paper: (a) a 10-vertex triangulation CP(10)(2) of the complex projective plane CP(2) as a subcomplex of the join of the standard sphere (S(4)(2)) and the standard real projective plane (RP(6)(2), the decahedron), its automorphism group is A(4); (b) a 12-vertex triangulation (S(2) x S(2))(12) of S(2) x S(2) with automorphism group 2S(5), the Schur double cover of the symmetric group S(5). It is obtained by generalized bistellar moves from a simplicial subdivision of the standard cell structure of S(2) x S(2). Both constructions have surprising and intimate relationships with the icosahedron. It is well known that CP(2) has S(2) x S(2) as a two-fold branched cover; we construct the triangulation CP(10)(2) of CP(2) by presenting a simplicial realization of this covering map S(2) x S(2) -> CP(2). The domain of this simplicial map is a simplicial subdivision of the standard cell structure of S(2) x S(2), different from the triangulation alluded to in (b). This gives a new proof that Kuhnel's CP(9)(2) triangulates CP(2). It is also shown that CP(10)(2) and (S(2) x S(2))(12) induce the standard piecewise linear structure on CP(2) and S(2) x S(2) respectively.

Linear Filtering in MDCT domain

In this paper, expressions for convolution multiplication properties of MDCT are derived starting from the equivalent DFT representations. Using these expressions, methods for implementing linear filtering through block convolution in the MDCT domain are presented. The implementation is exact for symmetric filters and approximate for non-symmetric filters in the case of rectangular window based MDCT. For a general MDCT window function, the filtering is done on the windowed segments and hence the convolution is approximate for symmetric as well as non-symmetric filters. This approximation error is shown to be perceptually insignificant for symmetric impulse response filters. Moreover, the inherent $50 \%$ overlap between adjacent frames used in MDCT computation does reduce this approximation error similar to smoothing of other block processing errors. The presented techniques are useful for compressed domain processing of audio signals.

Volume Change behaviour in Calcitic Soil influenced with Sulphuric Acid using Artificial Neural Networks

This paper elucidates the methodology of applying artificial neural network model (ANNM) to predict the percent swell of calcitic soil in sulphuric acid solutions, a complex phenomenon involving many parameters. Swell data required for modelling is experimentally obtained using conventional oedometer tests under nominal surcharge. The phases in ANN include optimal design of architecture, operation and training of architecture. The designed optimal neural model (3-5-1) is a fully connected three layer feed forward network with symmetric sigmoid activation function and trained by the back propagation algorithm to minimize a quadratic error criterion.The used model requires parameters such as duration of interaction, calcite mineral content and acid concentration for prediction of swell. The observed strong correlation coefficient (R2 = 0.9979) between the values determined by the experiment and predicted using the developed model demonstrates that the network can provide answers to complex problems in geotechnical engineering.

Design of Geocell Reinforcement for Supporting Embankments on Soft Ground

The methods of design available for geocell-supported embankments are very few. Two of the earlier methods are considered in this paper and a third method is proposed and compared with them. The first method is the slip line method proposed by earlier researchers. The second method is based on slope stability analysis proposed by this author earlier and the new method proposed is based on the finite element analyses. In the first method, plastic bearing failure of the soil was assumed and the additional resistance due to geocell layer is calculated using a non-symmetric slip line field in the soft foundation soil. In the second method, generalpurpose slope stability program was used to design the geocell mattress of required strength for embankment using a composite model to represent the shear strength of geocell layer. In the third method proposed in this paper, geocell reinforcement is designed based on the plane strain finite element analysis of embankments. The geocell layer is modelled as an equivalent composite layer with modified strength and stiffness values. The strength and dimensions of geocell layer is estimated for the required bearing capacity or permissible deformations. These three design methods are compared through a design example.

Displacement Amplifying Compliant Mechanisms for Two-axis High-resolution Monolithic Inertial Sensors

Novel designs for two-axis, high-resolution, monolithic inertial sensors are presented in this paper. Monolithic, i.e., joint-less single-piece compliant designs are already common in micromachined inertial sensors such as accelerometers and gyroscopes. Here, compliant mechanisms are used not only to achieve de-coupling between motions along two orthogonal axes but also to amplify the displacements of the proof-mass. Sensitivity and resolution capabilities are enhanced because the amplified motion is used for sensing the measurand. A particular symmetric arrangement of displacement-amplifying compliant mechanisms (DaCMs) leads to de-coupled and amplified motion. An existing DaCM and a new topology-optimized DaCM are presented as a building block in the new arrangement. A spring-mass-lever model is presented as a lumped abstraction of the new arrangement. This model is useful for arriving at the optimal parameters of the DaCM and for performing system-level simulation. The new designs improved the performance by a factor of two or more.

{C}^0$ penalty methods for the fully nonlinear Monge-Ampère equation

In this paper, we develop and analyze C(0) penalty methods for the fully nonlinear Monge-Ampere equation det(D(2)u) = f in two dimensions. The key idea in designing our methods is to build discretizations such that the resulting discrete linearizations are symmetric, stable, and consistent with the continuous linearization. We are then able to show the well-posedness of the penalty method as well as quasi-optimal error estimates using the Banach fixed-point theorem as our main tool. Numerical experiments are presented which support the theoretical results.

High-rate analysis of channel-optimized vector quantization

High-rate analysis of channel-optimized vector quantizationThis paper considers the high-rate performance of channel optimized source coding for noisy discrete symmetric channels with random index assignment. Specifically, with mean squared error (MSE) as the performance metric, an upper bound on the asymptotic (i.e., high-rate) distortion is derived by assuming a general structure on the codebook. This structure enables extension of the analysis of the channel optimized source quantizer to one with a singular point density: for channels with small errors, the point density that minimizes the upper bound is continuous, while as the error rate increases, the point density becomes singular. The extent of the singularity is also characterized. The accuracy of the expressions obtained are verified through Monte Carlo simulations.

Classical screw theory: A fresh look using dual eigenvalue approach

This paper presents a novel algebraic formulation of the central problem of screw theory, namely the determination of the principal screws of a given system. Using the algebra of dual numbers, it shows that the principal screws can be determined via the solution of a generalised eigenproblem of two real, symmetric matrices. This approach allows the study of the principal screws of the general screw systems associated with a manipulator of arbitrary geometry in terms of closed-form expressions of its architecture and configuration parameters. The formulation is illustrated with examples of practical manipulators.

Modeling of active fiber composite for delamination sensing

In order to demonstrate the feasibility of Active Fiber Composites (AFC) as sensors for detecting damage, a pretwisted strip made of AFC with symmetric free-edge delamination is considered in this paper. The strain developed on the top/bottom of the strip is measured to detect and assess delamination. Variational Asymptotic Method (VAM) is used in the development of a non-classical non-linear cross sectional model of the strip. The original three dimensional (3D) problem is simplified by the decomposition into two simpler problems: a two-dimensional (2D) problem, which provides in a compact form the cross-sectional properties using VAM, and a non-linear one-dimensional (1D) problem along the length of the beam. This procedure gives the non-linear stiffnesses, which are very sensitive to damage, at any given cross-section of the strip. The developed model is used to study a special case of cantilevered laminated strip with antisymmetric layup, loaded only by an axial force at the tip. The charge generated in the AFC lamina is derived in closed form in terms of the 1D strain measures. It is observed that delamination length and location have a definite influence on the charge developed in the AFC lamina. Also, sensor voltage output distribution along the length of the beam is obtained using evenly distributed electrode strip. These data could in turn be used to detect the presence of damage.

Symmetry in Scalar Field Topology

Study of symmetric or repeating patterns in scalar fields is important in scientific data analysis because it gives deep insights into the properties of the underlying phenomenon. Though geometric symmetry has been well studied within areas like shape processing, identifying symmetry in scalar fields has remained largely unexplored due to the high computational cost of the associated algorithms. We propose a computationally efficient algorithm for detecting symmetric patterns in a scalar field distribution by analysing the topology of level sets of the scalar field. Our algorithm computes the contour tree of a given scalar field and identifies subtrees that are similar. We define a robust similarity measure for comparing subtrees of the contour tree and use it to group similar subtrees together. Regions of the domain corresponding to subtrees that belong to a common group are extracted and reported to be symmetric. Identifying symmetry in scalar fields finds applications in visualization, data exploration, and feature detection. We describe two applications in detail: symmetry-aware transfer function design and symmetry-aware isosurface extraction.

Single Cavity Trapped Vortex Combustor Simulations

The present work describes steady and unsteady computation of reacting flow in a Trapped Vortex Combustor. The primary motivation of this study is to develop this concept into a working combustor in modern gas turbines. The present work is an effort towards development of an experimental model test rig for further understanding dynamics of a single cavity trapped vortex combustor. The steady computations with and without combustion have been done for L/D of 0.8, 1 and 1.2; also unsteady non-reacting flow simulation has been done for L/D of 1. Fuel used for the present study is methane and Eddy-Dissipation model has been used for combustion-turbulence interactions. For L/D of 0.8, combustion efficiency is maximum and pattern factor is minimum. Also, primary vortex in the cavity is more stable and symmetric for L/D of 0.8. From unsteady non-reacting flow simulations, it is found that there is no vortex shedding from the cavity but there are oscillations in the span-wise direction of the combustor.

High-Rate Vector Quantization for Noisy Channels With Applications to Wideband Speech Spectrum Compression

This paper considers the high-rate performance of source coding for noisy discrete symmetric channels with random index assignment (IA). Accurate analytical models are developed to characterize the expected distortion performance of vector quantization (VQ) for a large class of distortion measures. It is shown that when the point density is continuous, the distortion can be approximated as the sum of the source quantization distortion and the channel-error induced distortion. Expressions are also derived for the continuous point density that minimizes the expected distortion. Next, for the case of mean squared error distortion, a more accurate analytical model for the distortion is derived by allowing the point density to have a singular component. The extent of the singularity is also characterized. These results provide analytical models for the expected distortion performance of both conventional VQ as well as for channel-optimized VQ. As a practical example, compression of the linear predictive coding parameters in the wideband speech spectrum is considered, with the log spectral distortion as performance metric. The theory is able to correctly predict the channel error rate that is permissible for operation at a particular level of distortion.

Coding for High-Density Recording on a 1-D Granular Magnetic Medium

In terabit-density magnetic recording, several bits of data can be replaced by the values of their neighbors in the storage medium. As a result, errors in the medium are dependent on each other and also on the data written. We consider a simple 1-D combinatorial model of this medium. In our model, we assume a setting where binary data is sequentially written on the medium and a bit can erroneously change to the immediately preceding value. We derive several properties of codes that correct this type of errors, focusing on bounds on their cardinality. We also define a probabilistic finite-state channel model of the storage medium, and derive lower and upper estimates of its capacity. A lower bound is derived by evaluating the symmetric capacity of the channel, i.e., the maximum transmission rate under the assumption of the uniform input distribution of the channel. An upper bound is found by showing that the original channel is a stochastic degradation of another, related channel model whose capacity we can compute explicitly.

Constant weight codes based on ideals of commutative rings

We present a construction of constant weight codes based on the prime ideals of a Noetherian commutative ring. The coding scheme is based on the uniqueness of the primary decomposition of ideals in Noetherian rings. The source alphabet consists of a set of radical ideals constructed from a chosen subset of the prime spectrum of the ring. The distance function between two radical ideals is taken to be the Hamming metric based on the symmetric distance between sets. As an application we construct codes for random networks employing SAF routing.