A nonfactorial algorithm for testing isomorphism of two graphs

An algorithm is constructed for checking two graphs for isomorphism. It is proved that the worst case running time of the algorithm is O(exp(n)) where n is the size of a graph. This is the first substantial improvement on naive n! algorithms.     

Time reversal for obstacle location in elastodynamics from acoustic recording

The Note is concerned with a feasibility study of time reversal in a non-homogeneous elastic medium, from data recorded in an acoustic medium. Our aim here is to determine the presence and some physical properties of elastic “inclusions” (unknown, not observable solid objects, characterized by their elastic properties) from partial observations of acoustic waves scattered by these inclusions. A finite element numerical method, based on a variational acousto-elastodynamics formulation, is derived and used to solve the forward, and then, the time-reversed problem. A criterion, derived from the reverse time migration framework, is introduced, to help construct images of the inclusions to be determined. Numerical illustrations on configurations that mimic the breast cancer configuration are proposed, and show that one can differentiate between two inclusions, even with different properties.     

New Era of Resonance Reaction Studies

Physics of Atomic Nuclei - The article presents a review of resonance reaction studies made by TTIK method.     

Determination of Economic Packaging Set-up Frequency of Jointly Replenished Items

This paper deals with the problem of determining the economic operating policy for inventory items which are manufactured jointly but packaged individually. The proposed new approach is very simple and efficient. An extensive simulation study is presented so that the results of several heuristics (based on a wide range of data, measuring the number of optimal solutions, average error and maximum error) can be compared.     

The isomorphism problem for some universal operator algebras

This paper addresses the isomorphism problem for the universal (non-self-adjoint) operator algebras generated by a row contraction subject to homogeneous polynomial relations. We find that two such algebras are isometrically isomorphic if and only if the defining polynomial relations are the same up to a unitary change of variables, and that this happens if and only if the associated subproduct systems are isomorphic. The proof makes use of the complex analytic structure of the character space, together with some recent results on subproduct systems. Restricting attention to commutative operator algebras defined by a radical ideal of relations yields strong resemblances with classical algebraic geometry. These commutative operator algebras turn out to be algebras of analytic functions on algebraic varieties. We prove a projective Nullstellensatz connecting closed ideals and their zero sets. Under some technical assumptions, we find that two such algebras are isomorphic as algebras if and only if they are similar, and we obtain a clear geometrical picture of when this happens. This result is obtained with tools from algebraic geometry, reproducing kernel Hilbert spaces, and some new complex-geometric rigidity results of independent interest. The C^?-envelopes of these algebras are also determined. The Banach-algebraic and the algebraic classification results are shown to hold for the wot-closures of these algebras as well.     

Linear response in the strong field domain

We show that, while it is well-known that first-order perturbation theory leads to linear response (of, e.g., a material system to an external field), the reverse is not true: linear response does not necessarily imply the validity of first-order perturbation theory, nor does it follow from it that the external perturbation is weak. We do so by analyzing the intensity dependence in the photoexcitation followed by dissociation or isomerization of a bound molecular system by a shaped broadband laser pulse. We show that, in certain cases where strong field effects are definitely present, the observed photoexcitation yield as a function of intensity may exhibit linear dependence over a wide range of intensities. The behavior is shown to coexist with a rather extensive range of coherent control over the branching ratios, an effect that was shown in the past to be impossible in the single precursor state (e.g., in the first-order perturbation theory) domain. For example, we demonstrate computationally that when (flat continuum-mediated) Raman transitions are present, appropriate pulse shaping can lead to a linear yield with intensity over a wide range of intensities, while coherent control over the branching ratio is significant. Thus, it is not necessary to invoke external bath effects (as is currently being done) to explain present-day experiments where coherent control is observed in the linear response regime.     

Predicting solute adsorption on activated carbon: phenol

Activated carbon (AC), the most widely used adsorbent in water and in wastewater treatment, comprises a high surface area of very small, convoluted and interconnected pores. Despite the wide use of AC, there is little fundamental atomic-level understanding of its adsorption capacity and selectivity as well as its pore structure. The purpose of this work is to suggest the methodology for calculation of equilibrium adsorption capacity of common water organic pollutants and use it for phenol as a model. The effects of various functional groups, pore size, and coverage on thermodynamics of phenol adsorption from the gas phase and from water media are calculated using molecular mechanics (MM) and density functional theory (DFT) approaches.     

Living polymerization and block copolymerization of alpha-olefins by an amine bis(phenolate) titanium catalyst

An amine bis(phenolate) dibenzyl titanium complex having a methoxy donor on a side arm leads, upon activation with tris(pentafluorophenyl)borane, to unique living properties in alpha-olefin polymerization: exceptionally high molecular weight poly(1-hexene) is obtained in a living fashion at room temperature, living polymerization of 1-hexene is obtained above room temperature, and block copolymerization of 1-hexene and 1-octene at room temperature is described as well.