The auction algorithm for the transportation problem

The auction algorithm is a parallel relaxation method for solving the classical assignment problem. It resembles a competitive bidding process whereby unassigned persons bid simultaneously for objects, thereby raising their prices. Once all bids are in, objects are awarded to the highest bidder. This paper generalizes the auction algorithm to solve linear transportation problems. The idea is to convert the transportation problem into an assignment problem, and then to modify the auction algorithm to exploit the special structure of this problem. Computational results show that this modified version of the auction algorithm is very efficient for certain types of transportation problems.     

Universality at the edge of the spectrum for unitary,orthogonal, and symplectic ensembles of random matrices

We prove universality at the edge of the spectrum for unitary (β = 2), orthogonal (β = 1), and symplectic (β = 4) ensembles of random matrices in the scaling limit for a class of weights w(x) = e^?V(x) where V is a polynomial, V(x) = κ_2mx^2m + · · ·, κ_2m > 0. The precise statement of our results is given in Theorem 1.1 and Corollaries 1.2 and 1.4 below. For the same class of weights, a proof of universality in the bulk of the spectrum is given in [12] for the unitary ensembles and in [9] for the orthogonal and symplectic ensembles. Our starting point in the unitary case is [12], and for the orthogonal and symplectic cases we rely on our recent work [9], which in turn depends on the earlier work of Widom [46] and Tracy and Widom [42]. As in [9], the uniform Plancherel‐Rotach‐type asymptotics for the orthogonal polynomials found in [12] plays a central role. The formulae in [46] express the correlation kernels for β = 1, 4 as a sum of a Christoffel‐Darboux (CD) term, as in the case β = 2, together with a correction term. In the bulk scaling limit [9], the correction term is of lower order and does not contribute to the limiting form of the correlation kernel. By contrast, in the edge scaling limit considered here, the CD term and the correction term contribute to the same order: this leads to additional technical difficulties over and above [49]. © 2006 Wiley Periodicals, Inc.     

Asymmetry in the Multiprotein Systems of Molecular Biology

Signaling in living systems needs to achieve high specificity, to be reversible, and to achieve high signal to noise. Signaling mediated by multiprotein systems has evolved that avoids the requirement for high-affinity binary complexes that would be difficult to reverse and which, in the overcrowded cell, would lead to excessive noise in the system. Symmetrical structures are only occasionally formed. When they are, it is principally to colocate components, for example, the tyrosyl kinases of growth factors, where dimers form. Symmetry is, however, often broken, presumably to create more sensitivity and specificity in the signaling system by assembling other components, into higher-order multiprotein systems. The binding of a single heparin to two 1:1 FGF:FGFR complexes is an example, as is the binding of a single ligase to the Xrcc4 dimer, perhaps so creating a further DNA-binding site.     

The Residually Weakly Primitive Geometries of M 22

We announce the classification of all firm and residually connected geometries satisfying the conditions (I P)₂ and (2T)₁ and on which the Mathieu group M ₂₂ acts flag-transitively and residually weakly primitively. The complete list of geometries is available as a supplement to this note [6].     

Constructions of rank five geometries for the Mathieu group M 22

We construct nine rank five incidence geometries that are firm and residually connected and on which the Mathieu group M²² acts flag-transitively. The constructions use mainly objects arising from the Steiner systemS(3, 6, 22). One of these geometries was constructed by Meixner and Pasini in [10]. Three of them are obtained from the geometry of Meixner and Pasini using doubling (see [8] or [12]) or similar constructions. The remaining five are new and four of them have a star diagram. These latter four geometries are constructed using special partitions of the 22 points of the Steiner system S(3, 6, 22).     

Bisindoles. 14. Electrophilic substitution reactions in the di(5-indolyl) oxide series

Chemistry of Heterocyclic Compounds - Some electrophilic substitution reactions in the di(5-indolyl) oxide series were studied. The Vilsmeier and Mannich reactions and diazo coupling and...     

A new scheme for the mechanism of Fischer indolization of arylhydrazones

A new scheme for the mechanism of Fischer indolization of arylhydrazones has been suggested based on quantum-chemical calculations by the MNDO AM1 method.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 961–962, May, 1994.     

A quantum-chemical study of regioselectivity of indolization of some unsymmetrical ketone phenylhydrazones

The heat of formation (H _f) of unsymmetrical ketone phenylhydrazones and their enehydrazine tautomers was calculated by the semi-empirical quantum-chemical AM1 method. It is concluded that from H _f values it is possible to judge the regioselectivity of indolization of unsymmetrical ketone phenylhydrazones.Translated fromIzvestiya Akademii Nauk, Seriya Khimicheskaya, No. 1, pp. 220–221, January, 1993.