Tables of octic fields with a quartic subfield

We describe the computation of extended tables of degree 8 fields with a quartic subfield, using class field theory. In particular we find the minimum discriminants for all signatures and for all the possible Galois groups. We also discuss some phenomena and statistics discovered while making the tables, such as the occurrence of 11 non-isomorphic number fields having the same discriminant, or several pairs of non-isomorphic number fields having the same Dedekind zeta function.

     

Renormalized perturbation theory by the moment method for degenerate states: Anharmonic oscillators

We apply renormalized perturbation theory by the moment method to an anharmonic oscillator in two dimensions with a perturbation that couples unperturbed degenerate states. The method leads to simple recurrence relations for the perturbation corrections to the energy and moments of the eigenfunction. We calculate accurate energy eigenvalues, illustrate the general features of the method, and comment on the application of the approach to other quantum mechanical models. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 261–272, 1998     

Darstellung und spektroskopische Charakterisierung von Kupfer(II)- und Nickel(II)-tricyanmethanid-Komplexen mit Imidazol-Derivaten – Kristallstruktur von [Cu{C(CN)3}2(2-meiz)2]

Synthesis and Spectroscopic Characterization of Copper(II) and Nickel(II) Tricyanomethanide Complexes with Imidazoles – Crystal Structure of [Cu{C(CN)₃}₂(2-meiz)₂] The copper(II) and nickel(II) tricyanomethanide complexes with imidazoles of the type [Cu{C(CN)₃}₂L₄], [L = 2- or 4-methylimidazole (meiz)] and [M{C(CN)₃}₂L₂] [M = Cu, L = imidazole (iz), 2- or 4-meiz; M = Ni, L = iz, 2- or 4-meiz] were prepared and characterized by electronic, infrared, and – some of them – by ESR spectroscopy. The structure [Cu{C(CN)₃}₂(2-meiz)₂], solved by X-ray crystallographic analysis, shows a two-dimensional network with unsymmetric C(CN)₃-bridges between the Cu^II atoms. Polymeric structures with bridging C(CN)₃-groups were identified by means of spectroscopic methods also for the other [M{C(CN)₃}₂L₂] complexes. On the other hand, for the complexes [M{C(CN)₃}₂L₄] follow molecular structures, in which monodentate C(CN)₃ ligands are present. All compounds under investigation show a tetragonal-bipyramidal geometry with various degree of tetragonal distortion.     

Wall boundary conditions for inviscid compressible flows on unstructured meshes

In this paper we revisit the problem of implementing wall boundary conditions for the Euler equations of gas dynamics in the context of unstructured meshes. Both (a) strong formulation, where the zero normal velocity on the wall is enforced explicitly and (b) weak formulation, where the zero normal velocity on the wall is enforced through the flux function are discussed. Taking advantage of both approaches, mixed procedures are defined. The new wall boundary treatments are accurate and can be applied to any approximate Riemann solver. Numerical comparisons for various flow regimes, from subsonic to supersonic, and for various approximate Riemann solvers point out that the mixed boundary procedures drastically improve the accuracy. © 1998 John Wiley & Sons, Ltd.     

Aktivierung von Schwefelkohlenstoff an Trirutheniumclustern: Synthese und Kristallstruktur von [Ru3(CO)4(μ‐PCy2)2(μ‐Ph2PCH2PPh2)(μ3‐S){μ3‐η2‐CSC(S)S}]

Activation of Carbon Disulfide on Triruthenium Clusters: Synthesis and X‐Ray Crystal Structure Analysis of [Ru₃(CO)₄(μ‐PCy₂)₂(μ‐Ph₂PCH₂PPh₂)(μ₃‐S){μ₃‐η²‐CSC(S)S}] [Ru₃(CO)₄(μ‐H)₃(μ‐PCy₂)₃(μ‐dppm)] ( 2 ) (dppm = Ph₂PCH₂PPh₂) reacts with CS₂ at room temperature and yields the open 50 valence electron cluster [Ru₃(CO)₄(μ‐PCy₂)₂(μ‐dppm)(μ₃‐S){μ₃‐η²‐CSC(S)S}] ( 3 ) containing the unusual μ₃‐η²‐C₂S₃ mercaptocarbyne ligand. Compound 3 was characterized by single crystal X‐ray structure analysis.     

Transition from Convective to Absolute Instability in a Porous Layer with Either Horizontal or Vertical Solutal and Inclined Thermal Gradients,and Horizontal Throughflow

Recently, in Diaz and Brevdo (J Fluid Mech 681: 567–596, 2011), further in the text referred to as D&B, we found an absolute/convective instability dichotomy at the onset of convection in a flow in a saturated porous layer with either horizontal or vertical solutal and inclined thermal gradients, and horizontal throughflow. The control parameter in D&B triggering the destabilization is the vertical thermal Rayleigh number, R _v. In this article, we treat the parameter cases considered in D&B in which the onset of convection has the character of convective instability and occurs through longitudinal modes. By increasing the vertical thermal Rayleigh number starting from its critical value, R _vc, we determine the value R _vt of R _v at which the transition from convective to absolute instability takes place and compute the physical characteristics of the emerging absolutely unstable wave packet. In some cases, the value of the transitional vertical thermal Rayleigh number, R _vt, is only slightly greater than the critical value, R _vc, meaning that at the onset of convection the base convectively unstable state can be viewed as marginally absolutely unstable. However, in several cases considered, the value of R _vt is significantly greater than the critical value, R _vc, implying that the base state is not marginally but essentially absolutely stable at the point of destabilization.     

A Novel Experimental Approach for Calculating Stress Intensity Factors from Isochromatic Data

In the current paper a new method for calculating the stress intensity factor from isochromatic data is proposed. The method is based on the calculation of a map of the retardation using only the light- and dark-field images of a crack from a circular polariscope. The experimental retardation is compared with the theoretical one predicted by Westergaard’s model using between 700 and 800 data points in an array around the crack tip region. In this way, the necessity of unwrapping and calibrating the isochromatic fringe order distribution is avoided and a large potential source of error is eliminated. Subsequently, K_I, K_II and σ_ox are inferred by minimizing an error function. To show the potential and efficacy of the method, K values have been obtained from photoelastic images captured during fatigue tests conducted in a polycarbonate Center-Cracked-Tension (CCT) specimen. Results show an excellent level of agreement with those predicted from theory, highlighting the potential of the proposed methodology.     

The numerical solution of linear ordinary differential equations by feedforward neural networks

It is demonstrated, through theory and examples, how it is possible to construct directly and noniteratively a feedforward neural network to approximate arbitrary linear ordinary differential equations. The method, using the hard limit transfer function, is linear in storage and processing time, and the L₂ norm of the network approximation error decreases quadratically with the increasing number of hidden layer neurons. The construction requires imposing certain constraints on the values of the input, bias, and output weights, and the attribution of certain roles to each of these parameters.

All results presented used the hard limit transfer function. However, the noniterative approach should also be applicable to the use of hyperbolic tangents, sigmoids, and radial basis functions.     

Principles of melting in hybrid organic–inorganic perovskite and polymorphic ABX3 structures

Four novel dicyanamide-containing hybrid organic–inorganic ABX₃ structures are reported, and the thermal behaviour of a series of nine perovskite and non-perovskite [AB(N(CN)₂)₃] (A = (C₃H₇)₄N, (C₄H₉)₄N, (C₅H₁₁)₄N; B = Co, Fe, Mn) is analyzed. Structure–property relationships are investigated by varying both A-site organic and B-site transition metal cations. In particular, increasing the size of the A-site cation from (C₃H₇)₄N → (C₄H₉)₄N → (C₅H₁₁)₄N was observed to result in a decrease in T_m through an increase in ΔS_f. Consistent trends in T_m with metal replacement are observed with each A-site cation, with Co < Fe < Mn. The majority of the melts formed were found to recrystallise partially upon cooling, though glasses could be formed through a small degree of organic linker decomposition. Total scattering methods are used to provide a greater understanding of the melting mechanism.

Increasing the size of the A-site cation from (C₃H₇)₄N → (C₄H₉)₄N → (C₅H₁₁)₄N in hybrid organic–inorganic ABX₃ structures was observed to result in a decrease in T_m, through an increase in ΔS_f.