Systematic Construction of Linear Transform Based Full-Diversity, Rate-One Space-Time Frequency Codes

In this paper, we generalize the existing rate-one space frequency (SF) and space-time frequency (STF) code constructions. The objective of this exercise is to provide a systematic design of full-diversity STF codes with high coding gain. Under this generalization, STF codes are formulated as linear transformations of data. Conditions on these linear transforms are then derived so that the resulting STF codes achieve full diversity and high coding gain with a moderate decoding complexity. Many of these conditions involve channel parameters like delay profile (DP) and temporal correlation. When these quantities are not available at the transmitter, design of codes that exploit full diversity on channels with arbitrary DIP and temporal correlation is considered. Complete characterization of a class of such robust codes is provided and their bit error rate (BER) performance is evaluated. On the other hand, when channel DIP and temporal correlation are available at the transmitter, linear transforms are optimized to maximize the coding gain of full-diversity STF codes. BER performance of such optimized codes is shown to be better than those of existing codes.

Linear time geometrical design rule checker based on quadtree representation of VLSI mask layouts

An efficient geometrical design rule checker is proposed, based on operations on quadtrees, which represent VLSI mask layouts. The time complexity of the design rule checker is O(N), where N is the number of polygons in the mask. A pseudoPascal description is provided of all the important algorithms for geometrical design rule verification.

New initiators for the ring-opening thermal polymerization of hexachlorocyclotriphosphazene: synthesis of linear poly(dichlorophosphazene) in high yields

Ring-opening thermal polymerization of hexachlorocyclotriphosphazene (N3P3C&h)a s been investigated at 250 "C and at 1.333-Pa pressure using chlorocyclotriphosphazenes N3P3C15(N=PPh3) and N3P3Cl,.,(NMe2), (n = 2-4), salt hydrates, triphenylphosphine, and benzoic acid as initiators. The linear poly (dich1orophosphazene) products are phenoxylated, and the phenoxy polymers are characterized by gel permeation chromatography and dilute solution viscometry. Among the various initiators investigated, CaS04.2H20b rings about a high conversion (>60%) of N3P3C&to the linear [NPC12], polymer which possesses a high molecular weight (>5 X lo6). The rationale for the choice of the initiators and possible mechanism(s) of polymerization is discussed. Several mixed substituent polymers, [NP(OPh),(OC6H4Me-p)2,1, and [NP(OPh),(OCHzCF3)2,]nh, ave been prepared and their thermal properties evaluated.

Non-linear resonance in strings under narrow band random excitation, part I: Planar response and stability

Non-linear planar response of a string to planar narrow band random excitation is investigated in this paper. A response equation for the mean square deflection σ2 is obtained under a single mode approximation by using the equivalent linearization technique. It is shown that the response is triple valued, as in the case of harmonic excitation, if the centre frequency of excitation Ω lies in a certain specified range. The triple valued response occurs only if the excitation bandwidth β is smaller than a critical value βcrit which is a monotonically increasing function of the intensity of excitation. An approximate method of investigating the almost sure asymptotic stability of the solution is presented and regions of instability in the Ω-σ2 plane have been charted. It is shown that planar response can become unstable either due to an unbounded growth of the in-plane component of motion or due to a spontaneous appearance of an out-of-plane component.

A new algorithm for parallel solution of linear equations

Abstract is not available.

Representation of functional dependencies in relational databases using linear graphs

Functional dependencies in relational databases are investigated. Eight binary relations, viz., (1) dependency relation, (2) equipotence relation, (3) dissidence relation, (4) completion relation, and dual relations of each of them are described. Any one of these eight relations can be used to represent the functional dependencies in a database. Results from linear graph theory are found helpful in obtaining these representations. The dependency relation directly gives the functional dependencies. The equipotence relation specifies the dependencies in terms of attribute sets which functionally determine each other. The dissidence relation specifies the dependencies in terms of saturated sets in a very indirect way. Completion relation represents the functional dependencies as a function, the range of which turns out to be a lattice. Depletion relation which is the dual of the completion relation can also represent functional dependencies and similarly can the duals of dependency, equipotence, and dissidence relations. The class of depleted sets, which is the dual of saturated sets, is defined and used in the study of depletion relations.

Comment: Eigenvalue sensitivity method for optimal stabilisation of linear systems

In a letter RauA proposed a new method for designing statefeedback controllers using eigenvalue sensitivity matrices. However, there appears to be a conceptual mistake in the procedure, or else it is unduly restricted in its applicability. In particular the equation — BR~lBTK = A/.I, in which K is a positive-definite symmetric matrix.

Non-linear dynamic analysis of rotors by finite element method

Non-linear natural vibration characteristics and the dynamic response of hingeless and fully articulated rotors of rectangular cross-section are studied by using the finite element method. In the formulation of response problems, the global variables are augmented with appropriate additional variables, facilitating direct determination of sub-harmonic response. Numerical results are given showing the effect of the geometric non-linearity on the first three natural frequencies. Response analysis of typical rotors indicates a possibility of substantial sub-harmonic response especially in the fully articulated rotors widely adopted in helicopters.

A simple, wide-range, linear thermistor-based temperature indicator

A novel thermistor-based temperature indicator using an RC oscillator and an up/down counter has been developed and described. The indicator provides linear performance over a wide dynamic temperature range of 0-100°C. This indicator is free from the error due to lead resistances of the thermistor and gives a maximum error of ±0 · 1°C in the range 0-100°C. Test results are given to support the theory.

On a linear steady-state system of equations in microcontinuum fluid mechanics

Galerkin representations and integral representations are obtained for the linearized system of coupled differential equations governing steady incompressible flow of a micropolar fluid. The special case of 2-dimensional Stokes flows is then examined and further representation formulae as well as asymptotic expressions, are generated for both the microrotation and velocity vectors. With the aid of these formulae, the Stokes Paradox for micropolar fluids is established.

A linear root water uptake model

A model of root water extraction is proposed, in which a linear variation of extraction rate with depth is assumed. Five crops are chosen for simulation studies of the model, and soil moisture depletion under optimal conditions from different layers for each crop is calculated. Similar calculations are also made using the constant extraction rate model. Rooting depth is assumed to vary linearly with potential evapotranspiration for each crop during the vegetative phase. The calculated depletion patterns are compared with measured mean depletion patterns for each crop. It is shown that the constant extraction rate model results in large errors in the prediction of soil moisture depletion, while the proposed linear extraction rate model gives satisfactory results. Hypothetical depletion patterns predicted by the model in combination with a moisture tension-dependent sink term developed elsewhere are indicated.

CSSI-PRO: a method for secondary structure type editing, assignment and estimation in proteins using linear combination of backbone chemical shifts

Estimation of secondary structure in polypeptides is important for studying their structure, folding and dynamics. In NMR spectroscopy, such information is generally obtained after sequence specific resonance assignments are completed. We present here a new methodology for assignment of secondary structure type to spin systems in proteins directly from NMR spectra, without prior knowledge of resonance assignments. The methodology, named Combination of Shifts for Secondary Structure Identification in Proteins (CSSI-PRO), involves detection of specific linear combination of backbone H-1(alpha) and C-13' chemical shifts in a two-dimensional (2D) NMR experiment based on G-matrix Fourier transform (GFT) NMR spectroscopy. Such linear combinations of shifts facilitate editing of residues belonging to alpha-helical/beta-strand regions into distinct spectral regions nearly independent of the amino acid type, thereby allowing the estimation of overall secondary structure content of the protein. Comparison of the predicted secondary structure content with those estimated based on their respective 3D structures and/or the method of Chemical Shift Index for 237 proteins gives a correlation of more than 90% and an overall rmsd of 7.0%, which is comparable to other biophysical techniques used for structural characterization of proteins. Taken together, this methodology has a wide range of applications in NMR spectroscopy such as rapid protein structure determination, monitoring conformational changes in protein-folding/ligand-binding studies and automated resonance assignment.

A conditionally linearized Monte Carlo filter in non-linear structural dynamics

State and parameter estimations of non-linear dynamical systems, based on incomplete and noisy measurements, are considered using Monte Carlo simulations. Given the measurements. the proposed method obtains the marginalized posterior distribution of an appropriately chosen (ideally small) subset of the state vector using a particle filter. Samples (particles) of the marginalized states are then used to construct a family of conditionally linearized system of equations and thus obtain the posterior distribution of the states using a bank of Kalman filters. Discrete process equations for the marginalized states are derived through truncated Ito-Taylor expansions. Increased analyticity and reduced dispersion of weights computed over a smaller sample space of marginalized states are the key features of the filter that help achieve smaller sample variance of the estimates. Numerical illustrations are provided for state/parameter estimations of a Duffing oscillator and a 3-DOF non-linear oscillator. Performance of the filter in parameter estimation is also assessed using measurements obtained through experiments on simple models in the laboratory. Despite an added computational cost, the results verify that the proposed filter generally produces estimates with lower sample variance over the standard sequential importance sampling (SIS) filter.

Non-linear flapping vibrations of rotating blades

The non-linear equations of motion of a rotating blade undergoing extensional and flapwise bending vibration are derived, including non-linearities up to O (ε3). The strain-displacement relationship derived is compared with expressions derived by earlier investigators and the errors and the approximations made in some of those are brought out. The equations of motion are solved under the inextensionality condition to obtain the influence of the amplitude on the fundamental flapwise natural frequency of the rotating blade. It is found that large finite amplitudes have a softening effect on the flapwise frequency and that this influence becomes stronger at higher speeds of rotation.