Gauge theory of a group of diffeomorphisms. II. The conformal and de Sitter groups

The extension of Hehl's Poincaré gauge theory to more general groups that include space-time diffeomorphisms is worked out for two particular examples, one corresponding to the action of the conformal group on Minkowski space, and the other to the action of the de Sitter group on de Sitter space, and the effect of these groups on physical fields.

Velocity and acceleration analysis of complex mechanisms by graphical iteration

A simple graphical method is presented for velocity and acceleration analysis of complex mechanisms possessing low or high degree of complexity. The method is iterative in character and generally yields the solution within a few iterations. Several examples have been worked out to illustrate the method.

Paraxial Maxwell beams: transformation by general linear optical systems

Extending the work of earlier papers on the relativistic-front description of paraxial optics and the formulation of Fourier optics for vector waves consistent with the Maxwell equations, we generalize the Jones calculus of axial plane waves to describe the action of the most general linear optical system on paraxial Maxwell fields. Several examples are worked out, and in each case it is shown that the formalism leads to physically correct results. The importance of retaining the small components of the field vectors along the axis of the system for a consistent description is emphasized.

Some Generalisations of the Time Minimising Assignment Problem

The time minimising assignment problem is the problem of finding an assignment of n jobs to n facilities, one to each, which minimises the total time for completing all the jobs. The usual assumption made in these problems is that all the jobs are commenced simultaneously. In this paper two generalisations of this assumption are considered, and algorithms are presented to solve these general problems. Numerical examples are worked out illustrating the algorithms.

Magnetic behaviour in metal-organic frameworks-Some recent examples

The article describes the synthesis, structure and magnetic investigations of a series of metal-organic framework compounds formed with Mn+2 and Ni+2 ions. The structures, determined using the single crystal X-ray diffraction, indicated that the structures possess two- and three-dimensional structures with magnetically active dimers, tetramers, chains, two-dimensional layers connected by polycarboxylic acids. These compounds provide good examples for the investigations of magnetic behaviour. Magnetic studies have been carried out using SQUID magnetometer in the range of 2-300 K and the behaviour indicates a predominant anti-ferromagnetic interactions, which appears to differ based on the M-O-C-O-M and/or the M-O-M (M = metal ions) linkages. Thus, compounds with carboxylate (Mn-O-C-O-Mn) connected ones, [C3N2H [Mn(H2O)''C6H3(COO)(3)''], I, [''Mn(H2O (3)''aEuroeC(12)H(8)O(COO)(2)'']center dot H2O, II, [''Mn(H2O)''aEuroeC(12)H(8)O(COO)(2)''], III, show simple anti-ferromagnetic behaviour. The compounds with Mn-O/OH-Mn connected dimer and tetramer units in [NaMn''C6H3(COO)(3)''], IV, [Mn-2(A mu(3)-OH) (H2O)(2)''C6H3(COO)(3)'']center dot 2H(2)O, V, show canted-antiferromagnetic and anti-ferromagnetic behaviour, respectively. The presence of infinite one-dimensional -Ni-OH-Ni- chains in the compound, [Ni-2(H2O)(A mu(3)-OH)(2)(C8H5NO4], VI, gives rise to ferromagnet-like behaviour at low temperatures. The compounds, [Mn-3''C6H3(COO)(3)''(2)], VII and [''Mn(OH)''(2)''C12H8O(COO)(2)''], VIII, have two-dimensional infinite -Mn-O/OH-Mn- layers with triangular magnetic lattices, which resemble the Kagome and brucite-like layer. The magnetic studies indicated canted-antiferromagnetic behaviour in both the cases. Variable temperature EPR and theoretical magnetic modelling studies have been carried out on selected compounds to probe the nature of the magnetic species and their interactions with them.

The 31p nmr Spectra of Isomeric Diaminohexa-hlorocyclotetraphosphazatetraenes; Examples of a2b2 and aa'bb' spin Systems

The 31P nmr spectra of 2,4- and 2,6-diamino-derivatives of octachlorocyclotetraphosphazatetraene, N4P4Cl6(NR1R2)2 (R1 = H, R2 = But; R1 = H, R2 = CH2Ph; R1 = Me, R2 = Ph), have been measured. The 2,4- and 2,6-isomers were analysed as AA'BB' and A2B2 spin systems respectively. In the 2,4-isomers the spin-spin couplings 2J(PNP) and 4J(PNPNP) were of opposite sign.

Effect of grain size and texture on the mechanical properties of warm worked cadmium-1.5 Pct zinc alloy

The structural changes occurring during warm working of Cd-1.5 pct Zn alloy and their effect on the subsequent mechanical properties are studied. It is observed that changes in grain size and preferred orientation are important to a large extent in controlling the mechanical strength. The Hall-Petch slope,R decreases in the warm worked material while the friction stress, σo increases. The lowerR values are attributed to the development of a (101l) texture and the higher σo values are interpreted on the basis of changes in the basal texture.

A method for estimation of the radius of elastic-plastic boundary around cold-worked holes

The radius of an elastic-plastic boundary was measured by the strain gage method around the cold-worked region in L72-aluminum alloy. The relative radial expansion was varied from 2.5 to 6.5 percent during the cold-working process using mandrel and split sleeve. The existing theoretical studies in this area are reviewed. The experimental results are compared with existing experimental data of various investigators and with various theoretical formulations. A model is developed to predict the radius of elastic-plastic boundary, and the model is assessed by comparing with the present experiments.

Two-mode quantum systems: Invariant classification of squeezing transformations and squeezed states

A general analysis of squeezing transformations for two-mode systems is given based on the four-dimensional real symplectic group Sp(4, R). Within the framework of the unitary (metaplectic) representation of this group, a distinction between compact photon-number-conserving and noncompact photon-number-nonconserving squeezing transformations is made. We exploit the U(2) invariant squeezing criterion to divide the set of all squeezing transformations into a two-parameter family of distinct equivalence classes with representative elements chosen for each class. Familiar two-mode squeezing transformations in the literature are recognized in our framework and seen to form a set of measure zero. Examples of squeezed coherent and thermal states are worked out. The need to extend the heterodyne detection scheme to encompass all of U(2) is emphasized, and known experimental situations where all U(2) elements can be reproduced are briefly described.

The fatigue crack growth rate in L-72 Al-alloy plate specimens with cold worked holes

A fatigue crack growth rate study has been carried out on L-72 aluminium alloy plate specimens with and without cold worked holes. The cold worked specimens showed significantly increased fatigue life compared to unworked specimens. Computer software is developed to evaluate the stress intensity factor for non-uniform stress distributions using Green's function approach. The exponents for the Paris equation in the stable crack growth region for cold worked and unworked specimens are 1.26 and 3.15 respectively. The reduction in exponent value indicates the retardation in crack growth rate. An SEM study indicates more plastic deformation at the edge of the hole for unworked samples as compared to the worked samples during the crack initiation period.

Coherent states on Hilbert modules

We generalize the concept of coherent states, traditionally defined as special families of vectors on Hilbert spaces, to Hilbert modules. We show that Hilbert modules over C*-algebras are the natural settings for a generalization of coherent states defined on Hilbert spaces. We consider those Hilbert C*-modules which have a natural left action from another C*-algebra, say A. The coherent states are well defined in this case and they behave well with respect to the left action by A. Certain classical objects like the Cuntz algebra are related to specific examples of coherent states. Finally we show that coherent states on modules give rise to a completely positive definite kernel between two C*-algebras, in complete analogy to the Hilbert space situation. Related to this, there is a dilation result for positive operator-valued measures, in the sense of Naimark. A number of examples are worked out to illustrate the theory. Some possible physical applications are also mentioned.

Synthesis of workspaces of planar manipulators with arbitrary topology using shape representation and simulated annealing

This paper presents a general methodology for the synthesis of the external boundary of the workspaces of a planar manipulator with arbitrary topology. Both the desired workspace and the manipulator workspaces are identified by their boundaries and are treated as simple closed polygons. The paper introduces the concept of best match configuration and shows that the corresponding transformation can be obtained by using the concept of shape normalization available in image processing literature. Introduction of the concept of shape in workspace synthesis allows highly accurate synthesis with fewer numbers of design variables. This paper uses a new global property based vector representation for the shape of the workspaces which is computationally efficient because six out of the seven elements of this vector are obtained as a by-product of the shape normalization procedure. The synthesis of workspaces is formulated as an optimization problem where the distance between the shape vector of the desired workspace and that of the workspace of the manipulator at hand are minimized by changing the dimensional parameters of the manipulator. In view of the irregular nature of the error manifold, the statistical optimization procedure of simulated annealing has been used. A number of worked-out examples illustrate the generality and efficiency of the present method. (C) 1998 Elsevier Science Ltd. All rights reserved.

Phase-plane techniques for the solution of transient-stability problems

The paper presents a graphical-numerical method for determining the transient stability limits of a two-machine system under the usual assumptions of constant input, no damping and constant voltage behind transient reactance. The method presented is based on the phase-plane criterion,1, 2 in contrast to the usual step-by-step and equal-area methods. For the transient stability limit of a two-machine system, under the assumptions stated, the sum of the kinetic energy and the potential energy, at the instant of fault clearing, should just be equal to the maximum value of the potential energy which the machines can accommodate with the fault cleared. The assumption of constant voltage behind transient reactance is then discarded in favour of the more accurate assumption of constant field flux linkages. Finally, the method is extended to include the effect of field decrement and damping. A number of examples corresponding to each case are worked out, and the results obtained by the proposed method are compared with those obtained by the usual methods.

Learning from positive and unlabelled examples using maximum margin clustering

Learning from Positive and Unlabelled examples (LPU) has emerged as an important problem in data mining and information retrieval applications. Existing techniques are not ideally suited for real world scenarios where the datasets are linearly inseparable, as they either build linear classifiers or the non-linear classifiers fail to achieve the desired performance. In this work, we propose to extend maximum margin clustering ideas and present an iterative procedure to design a non-linear classifier for LPU. In particular, we build a least squares support vector classifier, suitable for handling this problem due to symmetry of its loss function. Further, we present techniques for appropriately initializing the labels of unlabelled examples and for enforcing the ratio of positive to negative examples while obtaining these labels. Experiments on real-world datasets demonstrate that the non-linear classifier designed using the proposed approach gives significantly better generalization performance than the existing relevant approaches for LPU.