Determinant: Old algorithms, new insights (Extended Abstract)

In this paper we approach the problem of computing the characteristic polynomial of a matrix from the combinatorial viewpoint. We present several combinatorial characterizations of the coefficients of the characteristic polynomial, in terms of walks and closed walks of different kinds in the underlying graph. We develop algorithms based on these characterizations, and show that they tally with well-known algorithms arrived at independently from considerations in linear algebra.

Spinorial relativistic rotator: The transformation from quasi-Newtonian to Minkowski coordinates

There exists a remarkably close relationship between the operator algebra of the Dirac equation and the corresponding operators of the spinorial relativistic rotator (an indecomposable object lying on a mass-spin Regge trajectory). The analog of the Foldy-Wouthuysen transformation (more generally, the transformation between quasi-Newtonian and Minkowski coordinates) is constructed and explicit results are discussed for the spin and position operators. Zitterbewegung is shown to exist for a system having only positive energies.

Formal description, compression and transformation of digital pictures II. Picture algebra and geometry

In an earlier paper (Part I) we described the construction of Hermite code for multiple grey-level pictures using the concepts of vector spaces over Galois Fields. In this paper a new algebra is worked out for Hermite codes to devise algorithms for various transformations such as translation, reflection, rotation, expansion and replication of the original picture. Also other operations such as concatenation, complementation, superposition, Jordan-sum and selective segmentation are considered. It is shown that the Hermite code of a picture is very powerful and serves as a mathematical signature of the picture. The Hermite code will have extensive applications in picture processing, pattern recognition and artificial intelligence.

Four-dimensional current algebra from Chern-Simons theory

We study an abelian Chern-Simons theory on a five-dimensional manifold with boundary. We find it to be equivalent to a higher-derivative generalization of the abelian Wess-Zumino-Witten model on the boundary. It contains a U(1) current algebra with an operational extension.

A denotational semantics for the generalized ER model and a simple ER algebra

The recent spurt of research activities in Entity-Relationship Approach to databases calls for a close scrutiny of the semantics of the underlying Entity-Relationship models, data manipulation languages, data definition languages, etc. For reasons well known, it is very desirable and sometimes imperative to give formal description of the semantics. In this paper, we consider a specific ER model, the generalized Entity-Relationship model (without attributes on relationships) and give denotational semantics for the model as well as a simple ER algebra based on the model. Our formalism is based on the Vienna Development Method—the meta language (VDM). We also discuss the salient features of the given semantics in detail and suggest directions for further work.

Poincaré invariance of anomalous gauge theories

We establish the Poincaré invariance of anomalous gauge theories in two dimensions, for both the Abelian and non-Abelian cases, in the canonical Hamiltonian formalism. It is shown that, despite the noncovariant appearance of the constraints of these theories, Poincaré generators can be constructed which obey the correct algebra and yield the correct transformations in the constrained space.

Variable Elimination in Linear Constraints

Gauss and Fourier have together provided us with the essential techniques for symbolic computation with linear arithmetic constraints over the reals and the rationals. These variable elimination techniques for linear constraints have particular significance in the context of constraint logic programming languages that have been developed in recent years. Variable elimination in linear equations (Guassian Elimination) is a fundamental technique in computational linear algebra and is therefore quite familiar to most of us. Elimination in linear inequalities (Fourier Elimination), on the other hand, is intimately related to polyhedral theory and aspects of linear programming that are not quite as familiar. In addition, the high complexity of elimination in inequalities has forces the consideration of intricate specializations of Fourier's original method. The intent of this survey article is to acquaint the reader with these connections and developments. The latter part of the article dwells on the thesis that variable elimination in linear constraints over the reals extends quite naturally to constraints in certain discrete domains.

ChemInform Abstract: Synthesis of Anion-Deficient Layered Perovskites, ACa2Nb3-xMxO10-x (A: Rb, Cs; M: Al, Fe), Exhibiting Ion-Exchange and Intercalation. Evidence for the Formation of Layered Brownmillerites, ACa2Nb2AlO9 (A: Cs, H)

Anion-deficient layered perovskite oxides of the formula, ACa2Nb3-xMxO10-x (A = Rb, Cs; M = Al, Fe) for 0 < x less-than-or-equal-to 1.0, possessing tetragonal structures similar to the parent ACa2Nb3O10, have been synthesized. The interlayer A cations in these materials are readily exchanged with protons in aqueous HNO3 to give the protonated derivatives, HCa2Nb3-xMxO10-x; the latter are solid Bronsted acids intercalating a number of organic amines including aniline (pK(a) = 4.63). The distribution of acid sites in the interlayer region of HCa2Nb2MO9 inferred from n-alkylamine intercalation suggests that oxygen vacancies and Nb/M atoms are disordered in the ACa2Nb2MO9 samples prepared at 1100-1200-degrees-C. Annealing a disordered sample of CsCa2Nb2AlO9 for a long time at lower temperatures tends to order the Nb/Al atoms and oxygen vacancies to produce octahedral (NbO6/2)-tetrahedral (AlO4/2)-octahedral (NbO6/2) layer sequence reminiscent of the brownmillerite structure.

ChemInform Abstract: Enantioselective Formal Total Synthesis of (-)-Homogynolide-A

ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.

ChemInform Abstract: Simple and Regioselective Reductive Cleavage of Tetrahydropyranyl Ethers to Alcohols

ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.

ChemInform Abstract: Slicing the Perovskite Structure into Layers: Synthesis of Novel Three- Dimensional and Layered Perovskite Oxides, ALaSrNb2M(II)O9 (A: Na, Cs)

ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.

ChemInform Abstract: Sodium Perborate/Acetic Anhydride: A Convenient Reagent for the Conversion of Cyclic Acetals to Esters

A facile oxidative cleavage of cyclic acetals to their respective esters using an inexpensive reagent system, sodium perborate/acetic anhydride is described.

ChemInform Abstract: Synthesis Based on Cyclohexadienes. Part 16. Synthesis of Methyl 2,7-Dimethyltricyclo (5.2.2.01,5)undec-5-ene-6-carboxylates

Synthesis of methyl 2, 7-dimethyltricyclo{5.2.2.0(1,5}undec-5-en-6-carboxylates, the tricyclic skeleton present in (+)-allo-cedrol (1) is described using the Diels-Alder strategy. Thus, Birch reduction of the aromatic acid 8 gives 5, the methyl ester of which is isomerised with DBU to a 1:1 mixture of the dienes 6 and 4. Cycloaddition of this mixture with 2-chloroacrylonitrile followed by hydrolysis yields the ketone 60 having the tricyclo{5.2.2.0(1.5)}undec-5-ene framework. Similar reaction with methyl vinyl ketone affords the regioisomeric adducts 61 and 62.

Uniform algebras generated by holomorphic and close-to-harmonic functions

The initial motivation for this paper is to discuss a more concrete approach to an approximation theorem of Axler and Shields, which says that the uniform algebra on the closed unit disc (D) over bar generated by z and h, where h is a nowhere-holomorphic harmonic function on D that is continuous up to partial derivative D, equals C((D) over bar). The abstract tools used by Axler and Shields make harmonicity of h an essential condition for their result. We use the concepts of plurisubharmonicity and polynomial convexity to show that, in fact, the same conclusion is reached if h is replaced by h + R, where R is a non-harmonic perturbation whose Laplacian is ``small'' in a certain sense.