Computing automorphisms of abelian number fields

Let be an abelian number field of degree . Most algorithms for computing the lattice of subfields of require the computation of all the conjugates of . This is usually achieved by factoring the minimal polynomial of over . In practice, the existing algorithms for factoring polynomials over algebraic number fields can handle only problems of moderate size. In this paper we describe a fast probabilistic algorithm for computing the conjugates of , which is based on -adic techniques. Given and a rational prime which does not divide the discriminant of , the algorithm computes the Frobenius automorphism of in time polynomial in the size of and in the size of . By repeatedly applying the algorithm to randomly chosen primes it is possible to compute all the conjugates of .

     

Solubility of Mannitol in Aqueous Sodium Chloride by the Isopiestic Method

Using a method for determination of solubilities of nonelectrolytes in electrolyte solutions based on isopiestic equilibration and precise chemical analyses, we have measured and report the solubilities of mannitol in sodium chloride solutions. Our results are, in general, in good agreement with the data of Kelly et al. The method is described and its advantages discussed.     

Zur Reaktion eines Bis(amino)germylens mit Germaniumaziden: Abfangreaktionen von instabilen Germa-Iminen

Reaction of a Cyclic Bis(amino)germylene with Germaniumazides: Trapping-Reactions of Unstable Germa-Imines . The cyclic bis(amino)germylene 1 reacts with different germaniumazides of the type Me₂Si(NtBu)₂Ge(R)N₃ (R = Me ( 2 ), tBu ( 3 ), N(SiMe₃)₂ ( 4 ), R = N₃ ( 5 )). With the exception of 4 all azides lose dinitrogen when treated with 1 and the Ge^II center coordinates the α-nitrogen of the azide group. It seems to be reasonable to assume a transient germaimine (nitride) which is trapped by further reaction with the azide molecules 2 and 5 or by reaction with the solvent pyridine ( 3 ). In the case of 2 the germatetrazole [Me₂Si(NtBu)₂]GeN₄[Ge(NtBu)₂SiMe₂]₂ ( 6 ) is formed, the tetrazole nitrogens being exclusively substituted by germanium atoms (point symmetry of the molecule C_s(m)). When 1 is treated with 5 a tris(germa)amine [Me₂Si(NtBu)₂Ge(N₃)]₃N ( 8 ) is formed, which has an azide group attached to each Ge-atom. X-ray analysis reveals that the nine nitrogen atoms of the azide groups are coplanar with the trigonal planar Ge₃N moiety (crystallographic symmetry: 3/m). The reaction of 1 with 3 is very surprising: the pyridine in the product Me₂Si(NtBu)₂Ge(C₅H₄N)? N(H)Ge(tBu)(NtBu)₂SiMe₂ ( 7 ) is bonded via an α-carbon atom while the remaining hydrogen has added to the nitride-nitrogen. 6 crystallizes in the monoclinic system space group C2/m, a = 24.306(9), b = 10.933(6), c = 19.420(9) Å, β = 91.81(2)° and Z = 4. 7 crystallizes in the hexagonal system space group P6₃/m with a = b = 16.73(1), c = 11.006(8) Å, γ = 120° and Z = 2, and 8 crystallizes in the monoclinic system space group P2₁/n, a = 11.341(6), b = 26.086(9), c = 13.244(7) Å, β = 98. I2(2)° mit Z = 4.     

Computational experience with the Chow—Yorke algorithm

The Chow—Yorke algorithm is a nonsimplicial homotopy type method for computing Brouwer fixed points that is globally convergent. It is efficient and accurate for fixed point problems. L.T. Watson, T.Y. Li, and C.Y. Wang have adapted the method for zero finding problems, the nonlinear complementarity problem, and nonlinear two-point boundary value problems. Here theoretical justification is given for applying the method to some mathematical programming problems, and computational results are presented.This work was partially supported by NSF Grant MCS 7821337.     

Optimal numerical method for simulating dynamic flow of gas in pipelines

Finite difference methods for solving the linear model describing unsteady state flow in pipelines are considered in the present paper. These methods are compared with each other in order to determine the best one, which meets the criteria of accuracy and relatively small computation time.     

Optimal accumulation of Jacobian matrices by elimination methods on the dual computational graph

The accumulation of the Jacobian matrix F of a vector function can be regarded as a transformation of its linearized computational graph into a subgraph of the directed complete bipartite graph K_n,m. This transformation can be performed by applying different elimination techniques that may lead to varying costs for computing F. This paper introduces face elimination as the basic technique for accumulating Jacobian matrices by using a minimal number of arithmetic operations. Its superiority over both edge and vertex elimination methods is shown. The intention is to establish the conceptual basis for the ongoing development of algorithms for optimizing the computation of Jacobian matrices.     

Defining the antigenic structure of human GM-CSF and its implications for receptor interaction and therapeutic treatments

Three epitopes of human Granulocyte-Macrophage Colony-Stimulating Factor (hGM-CSF) recognised by neutralising and non-neutralising monoclonal antibodies (mAbs) were characterised using competitive binding assays, dissociation constant measurements with glycosylated and non-glycosylated rhGM-CSF, bioactivity inhibition studies, and synthetic peptide arrays. Based on the first approach, two different binding sites were identified: an area referred to as A, recognised by mAbs M1B8 and CC5B5, and an area referred to as B, recognised by mAbs CC1H7 and CC3C12. These binding sites on hGM-CSF were accurately delineated using cytokine-derived overlapping peptide scans and combinatorial hexapeptide libraries prepared by SPOT synthesis on cellulose membranes. We assigned the identical linear epitope A₁P₂A₃R₄ to both non-neutralising mAbs CC1H7 and CC3C12. The conformational epitopes A₁₈E₂₁R₂₃R₂₄F₁₁₉ and R₂₃E₂₁N₁₇W₁₃ recognised by mAb CC5B5, and P₁₁₈F₁₁₉EW₁₃E₁₄ recognised by mAb M1B8, were delineated by dual-positional scanning and subsequent iterative searches with two interrogating positions. Competitive binding assays with mAbs M1B8 and CC5B5 revealed the overlapping nature of the cytokine recognition. However, peptide library screening confirmed their binding to different epitopes of which the essential amino acids were found very closely located on the native protein surface. Inhibition of hGM-CSF biological activity by these mAbs demonstrated that these epitopes are located within or very near the receptor binding site of hGM-CSF. Finally, this work supports the importance of residues from helix A and residues from the C-terminal region of the cytokine, composing a common area that is indispensable for the cytokine's biological activity.     

A computational study of cation-π interactions in polycyclic systems: exploring the dependence on the curvature and electronic factors

Density functional theory (B3LYP) calculations with double and triple-ζ quality basis sets were performed on the Li⁺ and Na⁺ π-complexes of corannulene 2, sumanene 3CH₂, heterosumanenes 3X, triphenylene 4 and heterotrindenes 5X. The metal ions bind to both convex and concave faces of buckybowls, with a consistent preference to bind to the convex surface by about 1-4 kcal/mol. The metal ion complexation with the π-framework of the central six-membered ring span wider range compared to benzene, indicating the control of size, curvature and electronic perturbations over the strength of cation-π interactions. Computations show that the bowl-to-bowl inversion barriers are only slightly altered upon metal complexation, indicating the continuity of bowl-to-bowl inversion despite metal complexation. We have calculated the binding energies of model systems, triphenylene (4) and heterotrindenes (5X), which indicate that the interaction energies are controlled by electronic factors. While the inversion barrier is dependent mainly on the size of the heteroatom, the extent of binding is independent of the size of the atom or the bowl depth.     

High order accurate,one-sided finite-difference approximations to concentration gradients at the boundaries,for the simulation of electrochemical reaction-diffusion problems in one-dimensional space geometry

Accurate calculation of concentration gradients at the boundaries is crucial in electrochemical kinetic simulations, owing to the frequent occurrence of gradient-dependent boundary conditions, and the importance of the gradient-dependent electric current. By using the information about higher spatial derivatives of the concentrations, contained in the time-dependent, kinetic reaction-diffusion partial differential equation(s) in one-dimensional space geometry, under appropriate assumptions it is possible to increase the accuracy orders of the conventional, one-sided n-point finite-difference formulae for the concentration gradients at the boundaries, without increasing n. In this way a new class of high order accurate gradient approximations is derived, and tested in simulations of potential-step chronoamperometric and current-step chronopotentiometric transients for the Reinert-Berg system. The new formulae possess advantages over the conventional gradient approximations. For example, they allow one to obtain a third order accuracy by using two space points only, or fourth order accuracy by using three points, and yet they yield smaller errors than the conventional four-point, or five-point formulae, respectively. Needing fewer points, for approximating the gradients with a given accuracy, simplifies also the solution of the linear algebraic equations arising from the application of implicit time integration schemes.