Effect of curve crossing on absorption and resonance Raman spectra: analytical treatment for delta-function coupling in parabolic potentials

We propose an exactly solvable model for the two-state curve-crossing problem. Our model assumes the coupling to be a delta function. It is used to calculate the effect of curve crossing on the electronic absorption spectrum and the resonance Raman excitation profile.

An algebraic theory of functional and multivalued dependencies in relational databases

Computation of the dependency basis is the fundamental step in solving the membership problem for functional dependencies (FDs) and multivalued dependencies (MVDs) in relational database theory. We examine this problem from an algebraic perspective. We introduce the notion of the inference basis of a set M of MVDs and show that it contains the maximum information about the logical consequences of M. We propose the notion of a dependency-lattice and develop an algebraic characterization of inference basis using simple notions from lattice theory. We also establish several interesting properties of dependency-lattices related to the implication problem. Founded on our characterization, we synthesize efficient algorithms for (a): computing the inference basis of a given set M of MVDs; (b): computing the dependency basis of a given attribute set w.r.t. M; and (c): solving the membership problem for MVDs. We also show that our results naturally extend to incorporate FDs also in a way that enables the solution of the membership problem for both FDs and MVDs put together. We finally show that our algorithms are more efficient than existing ones, when used to solve what we term the ‘generalized membership problem’.

Algebraic and geometric intersection numbers for free groups

We show that the algebraic intersection number of Scott and Swarup for splittings of free groups Coincides With the geometric intersection number for the sphere complex of the connected sum of copies of S-2 x S-1. (C) 2009 Elsevier B.V. All rights reserved.

Algebraic characterization of decentralized fixed modes

An input-output, frequency-domain characterization of decentralized fixed modes is given in this paper, using only standard block-diagram algebra, well-known determinantal expansions and the Binet-Cauchy formula.

Algebraic design techniques for reliable stabilization

In this paper we study two problems in feedback stabilization. The first is the simultaneous stabilization problem, which can be stated as follows. Given plantsG_{0}, G_{1},..., G_{l}, does there exist a single compensatorCthat stabilizes all of them? The second is that of stabilization by a stable compensator, or more generally, a "least unstable" compensator. Given a plantG, we would like to know whether or not there exists a stable compensatorCthat stabilizesG; if not, what is the smallest number of right half-place poles (counted according to their McMillan degree) that any stabilizing compensator must have? We show that the two problems are equivalent in the following sense. The problem of simultaneously stabilizingl + 1plants can be reduced to the problem of simultaneously stabilizinglplants using a stable compensator, which in turn can be stated as the following purely algebraic problem. Given2lmatricesA_{1}, ..., A_{l}, B_{1}, ..., B_{l}, whereA_{i}, B_{i}are right-coprime for alli, does there exist a matrixMsuch thatA_{i} + MB_{i}, is unimodular for alli?Conversely, the problem of simultaneously stabilizinglplants using a stable compensator can be formulated as one of simultaneously stabilizingl + 1plants. The problem of determining whether or not there exists anMsuch thatA + BMis unimodular, given a right-coprime pair (A, B), turns out to be a special case of a question concerning a matrix division algorithm in a proper Euclidean domain. We give an answer to this question, and we believe this result might be of some independent interest. We show that, given twon times mplantsG_{0} and G_{1}we can generically stabilize them simultaneously provided eithernormis greater than one. In contrast, simultaneous stabilizability, of two single-input-single-output plants, g0and g1, is not generic.

High-resolution melt-curve analysis of random-amplified-polymorphic-DNA markers, for the characterisation of pathogenic Leptospira.

A new test for pathogenic Leptospira isolates, based on RAPD-PCR and high-resolution melt (HRM) analysis (which measures the melting temperature of amplicons in real time, using a fluorescent DNA-binding dye), has recently been developed. A characteristic profile of the amplicons can be used to define serovars or detect genotypes. Ten serovars, of leptospires from the species Leptospira interrogans (serovars Australis, Robinsoni, Hardjo, Pomona, Zanoni, Copenhageni and Szwajizak), L. borgpetersenii (serovar Arborea), L. kirschneri (serovar Cynopteri) and L. weilii (serovar Celledoni), were typed against 13 previously published RAPD primers, using a real-time cycler (the Corbett Life Science RotorGene 6000) and the optimised reagents from a commercial kit (Quantace SensiMix). RAPD-HRM at specific temperatures generated defining amplicon melt profiles for each of the tested serovars. These profiles were evaluated as difference-curve graphs generated using the RotorGene software package, with a cut-off of at least 8 'U' (plus or minus). The results demonstrated that RAPD-HRM can be used to measure serovar diversity and establish identity, with a high degree of stability. The characterisation of Leptospira serotypes using a DNA-based methodology is now possible. As an objective and relatively inexpensive and rapid method of serovar identification, at least for cultured isolates, RAPD-HRM assays show convincing potentia.

High-resolution melt-curve analysis of random amplified polymorphic DNA (RAPD-HRM) for the characterisation of pathogenic leptospires: intra-serovar divergence, interserovar convergence, and evidence of attenuation in Leptospira reference collections.

High-resolution melt-curve analysis of random amplified polymorphic DNA (RAPD-HRM) is a novel technology that has emerged as a possible method to characterise leptospires to serovar level. RAPD-HRM has recently been used to measure intra-serovar convergence between strains of the same serovar as well as inter-serovar divergence between strains of different serovars. The results indicate that intra-serovar heterogeneity and inter-serovar homogeneity may limit the application of RAPD-HRM in routine diagnostics. They also indicate that genetic attenuation of aged, high-passage-number isolates could undermine the use of RAPD-HRM or any other molecular technology. Such genetic attenuation may account for a general decrease seen in titres of rabbit hyperimmune antibodies over time. Before RAPD-HRM can be further advanced as a routine diagnostic tool, strains more representative of the wild-type serovars of a given region need to be identified. Further, RAPD-HRM analysis of reference strains indicates that the routine renewal of reference collections, with new isolates, may be needed to maintain the genetic integrity of the collections.

Coexistence curve of acetonitrile and cyclohexane liquid system

The paper reports a detailed determination of the coexistence curve for the binary liquid system acetonitrile+cyclohexane, which have very closely matched densities and the data points get affected by gravity only for t=(Tc−T)/ Tc[approximately-equal-to]10−6. About 100 samples were measured over the range 10−6curve appear symmetric in the new variables is pointed out. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

A novel approach to assessing road-curve crash severity

Curves are a common feature of road infrastructure; however crashes on road curves are associated with increased risk of injury and fatality to vehicle occupants. Countermeasures require the identification of contributing factors. However, current approaches to identifying contributors use traditional statistical methods and have not used self-reported narrative claim to identify factors related to the driver, vehicle and environment in a systemic way. Text mining of 3434 road-curve crash claim records filed between 1 January 2003 and 31 December 2005 at a major insurer in Queensland, Australia, was undertaken to identify risk levels and contributing factors. Rough set analysis was used on insurance claim narratives to identify significant contributing factors to crashes and their associated severity. New contributing factors unique to curve crashes were identified (e.g., tree, phone, over-steer) in addition to those previously identified via traditional statistical analysis of Police and licensing authority records. Text mining is a novel methodology to improve knowledge related to risk and contributing factors to road-curve crash severity. Future road-curve crash countermeasures should more fully consider the interrelationships between environment, the road, the driver and the vehicle, and education campaigns in particular could highlight the increased risk of crash on road-curves.

An algebraic algorithm for the design and analysis of linear dynamical systems

In an earlier paper [1], it has been shown that velocity ratio, defined with reference to the analogous circuit, is a basic parameter in the complete analysis of a linear one-dimensional dynamical system. In this paper it is shown that the terms constituting velocity ratio can be readily determined by means of an algebraic algorithm developed from a heuristic study of the process of transfer matrix multiplication. The algorithm permits the set of most significant terms at a particular frequency of interest to be identified from a knowledge of the relative magnitudes of the impedances of the constituent elements of a proposed configuration. This feature makes the algorithm a potential tool in a first approach to a rational design of a complex dynamical filter. This algorithm is particularly suited for the desk analysis of a medium size system with lumped as well as distributed elements.

On Random Planar Curves and Their Scaling Limits

Planar curves arise naturally as interfaces between two regions of the plane. An important part of statistical physics is the study of lattice models. This thesis is about the interfaces of 2D lattice models. The scaling limit is an infinite system limit which is taken by letting the lattice mesh decrease to zero. At criticality, the scaling limit of an interface is one of the SLE curves (Schramm-Loewner evolution), introduced by Oded Schramm. This family of random curves is parametrized by a real variable, which determines the universality class of the model. The first and the second paper of this thesis study properties of SLEs. They contain two different methods to study the whole SLE curve, which is, in fact, the most interesting object from the statistical physics point of view. These methods are applied to study two symmetries of SLE: reversibility and duality. The first paper uses an algebraic method and a representation of the Virasoro algebra to find common martingales to different processes, and that way, to confirm the symmetries for polynomial expected values of natural SLE data. In the second paper, a recursion is obtained for the same kind of expected values. The recursion is based on stationarity of the law of the whole SLE curve under a SLE induced flow. The third paper deals with one of the most central questions of the field and provides a framework of estimates for describing 2D scaling limits by SLE curves. In particular, it is shown that a weak estimate on the probability of an annulus crossing implies that a random curve arising from a statistical physics model will have scaling limits and those will be well-described by Loewner evolutions with random driving forces.

An algebraic approach to the restoration of images

Two different matrix algorithms are described for the restoration of blurred pictures. These are illustrated by numerical examples.

Liquid-liquid critical phenomena. The coexistence curve of n-heptane-acetic anhydride

The coexistence curve of the binary liquid mixture n-heptane-acetic anhydride has been determined by the observation of the transition temperatures of 76 samples over the range of compositions. The functional form of the difference in order parameter, in terms of either the mole fraction or the volume fraction, is consistent with theoretical predictions invoking the concept of universality at critical points. The average value of the order parameter, the diameter of the coexistence curve, shows an anomaly which can be described by either an exponent 1 - a, as predicted by various theories (where a is the critical exponent of the specific heat), or by an exponent 20 (where P is the coexistence curve exponent), as expected when the order parameter used is not the one the diameter of which diverges asymptotically as 1 - a.