There is no (95, 40, 12, 20) strongly regular graph

We show that there is no (95, 40, 12, 20) strongly regular graph and, consequently, there is no (96, 45, 24, 18) strongly regular graph, no nontrivial regular two‐graph on 96 vertices, and no partial geometry pg(4, 9, 2). The main idea of the result is based on the star complement technique and requires a moderate amount of computation.     

Transmission of macroeconomic shocks to risk parameters: Their uses in stress testing

In this paper, we are interested in evaluating the resilience of financial portfolios under extreme economic conditions. Therefore, we use empirical measures to characterize the transmission process of macroeconomic shocks to risk parameters. We propose the use of an extensive family of models, called General Transfer Function Models, which condense well the characteristics of the transmission described by the impact measures. The procedure for estimating the parameters of these models is described employing the Bayesian approach and using the prior information provided by the impact measures. In addition, we illustrate the use of the estimated models from the credit risk data of a portfolio.     

Potentiometric and Thermodynamic Studies of Some Metal–Cysteine Complexes

A new and simple potentiometric method is developed to determine the stability constants of cysteine complexes with Mn(II), Cu(II), Zn(II), Cd(II), and Ce(III) metal ions using a modified Bjerrum method. Potentiometric titrations were performed in water and water/dioxane mixtures at five different temperatures. The least and highest stable complexes were those of Cu(II) and Zn(II), respectively. Furthermore, by conducting the experiments at temperatures of 15, 20, 25, 35, and 45 °C, the thermodynamic parameters ΔH°, ΔS°, and ΔG° for the pertinent complexes were calculated. The results show that the ΔH° values of the complexes are positive except for Zn(II). Negative values of ΔG° are evidence for the spontaneity of the reactions.     

MNA/PMMA有机薄膜光波导

研究出MNA/PMMA有机薄膜光波导。用棱镜耦合器进行了波导参数的测量,发现薄膜呈现各向异性,有较大的双折射。     

Cayley digraphs and lexicographic product

In this paper, we prove that a Cayley digraph Γ = Cay(G, S) is a nontrivial lexicographical product if and only if there is a nontrivial subgroup H of G such that S∖H is a union of some double cosets of H in G.      

The pure rotational spectrum of ZnS (XΣ)

The pure rotational spectrum of ZnS (X¹Σ⁺) has been measured using direct-absorption millimeter/sub-millimeter techniques in the frequency range 372–471 GHz. This study is the first spectroscopic investigation of this molecule. Spectra originating in four zinc isotopologues (⁶⁴ZnS, ⁶⁶ZnS, ⁶⁸ZnS, and ⁶⁷ZnS) were recorded in natural abundance in the ground vibrational state, and data from the v = 1 state were also measured for the two most abundant zinc species. Spectroscopic constants have been subsequently determined, and equilibrium parameters have been estimated. The equilibrium bond length was calculated to be r_e  2.0464 Å, which agrees well with theoretical predictions. In contrast, the dissociation energy of D_E  3.12 eV calculated for ZnS, assuming a Morse potential, was significantly higher than past experimental and theoretical estimates, suggesting diabatic interaction with other potentials that lower the effective dissociation energy. Although ZnS is isovalent with ZnO, there appear to be subtle differences in bonding between the two species, as suggested by their respective force constants and bond length trends in the 3d series.     

Fitting Height and Character Degree Graphs

Given a group G, Γ(G) is the graph whose vertices are the primes that divide the degree of some irreducible character and two vertices p and q are joined by an edge if pq divides the degree of some irreducible character of G. By a definition of Lewis, a graph Γ has bounded Fitting height if the Fitting height of any solvable group G with Γ(G)=Γ is bounded (in terms of Γ). In this note, we prove that there exists a universal constant C such that if Γ has bounded Fitting height and Γ(G)=Γ then h(G)≤C. This solves a problem raised by Lewis. Research supported by the Spanish Ministerio de Educación y Ciencia, MTM2004-06067-C02-01 and MTM2004-04665, the FEDER and Programa Ramón y Cajal.     

Reducing system of parameters and the Cohen-Macaulay property

Let R be a local ring and let (x ₁, …, x _r) be part of a system of parameters of a finitely generated R-module M, where r < dim_R M. We will show that if (y ₁, …, y _r) is part of a reducing system of parameters of M with (y ₁, …, y _r) M = (x ₁, …, x _r) M then (x ₁, …, x _r) is already reducing. Moreover, there is such a part of a reducing system of parameters of M iff for all primes P ε Supp M ∩ V _R(x ₁, …, x _r) with dim_R R/P = dim_R M − r the localization M _P of M at P is an r-dimensional Cohen-Macaulay module over R _P. Furthermore, we will show that M is a Cohen-Macaulay module iff y _d is a non zero divisor on M/(y ₁, …, y _d−1) M, where (y ₁, …, y _d) is a reducing system of parameters of M (d:= dim_R M).