Elongation cutoff technique armed with quantum fast multipole method for linear scaling

A linear‐scaling implementation of the elongation cutoff technique (ELG/C) that speeds up Hartree‐Fock (HF) self‐consistent field calculations is presented. The cutoff method avoids the known bottleneck of the conventional HF scheme, that is, diagonalization, because it operates within the low dimension subspace of the whole atomic orbital space. The efficiency of ELG/C is illustrated for two model systems. The obtained results indicate that the ELG/C is a very efficient sparse matrix algebra scheme. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Diels-Alder reaction with cyclopentadiene and electronic structures of (η5-cyclopentadienyl)M(CO)x(η1-N-maleimidato) (M = Fe,Mo, W,x = 2 or 3)

Diels-Alder reaction of (η⁵-cyclopentadienyl)M(CO)_x(η¹-N-maleimidato) complexes (M = Fe, Mo, W, x = 2 or 3) with cyclopentadiene has been studied. The observed order of reactivity was: N-ethylmaleimide > W complex > Mo complex > Fe complex. The X-ray structures of the adducts have been determined for M = W and Fe. DFT calculations on the starting complexes have been performed to explain the observed reactivity order.     

Local surrounding of Mn in LaMn1−xCoxO3 compounds by means of EXAFS on Mn–K

A systematic study of LaMn_1?xCo_xO₃ perovskite series by means of X-ray absorption spectroscopy in the extended X-ray absorption fine structure (EXAFS) range of the K-absorption edge of Mn is reported. The Mn–K edge absorption measurements in the EXAFS region were performed to study the local surrounding of Mn ions. Polycrystalline powder samples of LaMn_1?xCo_xO₃ (x=0, 0.02; 0.2; 0.4; 0.5; 0.6; 0.8) prepared by solid-state reaction were used. The EXAFS spectra were analyzed with the FEFF8 computer program. The Mn–O distances of Mn to the nearest oxygen surroundings were evaluated for the samples in the series and compared with the Co–O distances obtained by EXAFS in V. Procházka et al., JMMM 310 (2007) 197 and with results of X-ray powder diffraction in C. Autret, J. Phys. Condens. Matter 17 (2005) 1601.     

Graphs with few total dominating sets

We give a lower bound for the number of total dominating sets of a graph together with a characterization of the extremal graphs, for trees as well as arbitrary connected graphs of given order. Moreover, we obtain a sharp lower bound involving both the order and the total domination number, and characterize the extremal graphs as well.     

Multiplier theorem for Hankel transform on Hardy spaces

The aim of this paper is to prove a multiplier theorem for the Hankel transform on the atomic Hardy space H ¹(X), where X = ((0, ∞), x ^α dx) is the space of homogeneous type in the sense of Coifman–Weiss. The main tool is a maximal function characterization of H ¹(X).     

Multiplier theorem for Hankel transform on Hardy spaces

The aim of this paper is to prove a multiplier theorem for the Hankel transform on the atomic Hardy space H ¹(X), where X = ((0, ∞), x ^α dx) is the space of homogeneous type in the sense of Coifman–Weiss. The main tool is a maximal function characterization of H ¹(X).     

Stochastic evolution of 2D crystals

We study a crystalline version of the modified Stefan problem in the plane. The feature of our approach is that, we consider a model with stochastic perturbations and assume the interfacial curve to be a polygon. The existence of solution to our stochastic system is established. Galerkin’s method is one of the main tools used in the proof of our assertion.     

Generalizations of Arnold’s version of Euler’s theorem for matrices

A recent result, conjectured by Arnold and proved by Zarelua, states that for a prime number p, a positive integer k, and a square matrix A with integral entries one has ${\textrm tr}(A^{p^k}) \equiv {\textrm tr}(A^{p^{k-1}}) ({\textrm mod}{p^k})${\textrm tr}(A^{p^k}) \equiv {\textrm tr}(A^{p^{k-1}}) ({\textrm mod}{p^k}). We give a short proof of a more general result, which states that if the characteristic polynomials of two integral matrices A,  B are congruent modulo p ^k then the characteristic polynomials of A ^p and B ^p are congruent modulo p ^k+1, and then we show that Arnold’s conjecture follows from it easily. Using this result, we prove the following generalization of Euler’s theorem for any 2 × 2 integral matrix A: the characteristic polynomials of A ^Φ(n) and A ^Φ(n)-ϕ(n) are congruent modulo n. Here ϕ is the Euler function, ?_i=1^l p_i^a_i\prod_{i=1}^{l} p_i^{\alpha_i} is a prime factorization of n and $\Phi(n)=(\phi(n)+\prod_{i=1}^{l} p_i^{\alpha_i-1}(p_i+1))/2$\Phi(n)=(\phi(n)+\prod_{i=1}^{l} p_i^{\alpha_i-1}(p_i+1))/2.     

On some fixed-point theorems for generalized contractions and their perturbations

The aim of this paper is to prove a collection of fixed-point theorems for mappings which can be roughly called generalized contractions or their perturbations. In particular, we are going to consider operators (single-valued or multi-valued) in Banach spaces with a quasimodulus, in hyperconvex subsets of normed spaces, or finally in non-Archimedean spaces. A particular attention will be paid to Krasnoselskii-type fixed-point theorems as well as to a Schaefer-type fixed-point theorem. Some applications to nonlinear functional-integral equations will be given. Our results extend and complement some commonly known theorems.     

Spectroscopic and Theoretical Studies of Fluorescence Effects in 2-Methylamino-5-(2,4-dihydroxyphenyl)-1,3,4-thiadiazole Induced by Molecular Aggregation

The article presents the results of fluorescence analyses of 2-methylamino-5-(2,4-dihydroxyphenyl)-1,3,4-thiadiazole (MDFT) in an aqueous environment. MDFT dissolved in aqueous solutions with a pH value in the range from 1 to 4.5 yielded an interesting effect of two clearly separated fluorescence emissions. In turn, a single fluorescence was observed in MDFT dissolved in water solutions with a pH value from 4.5 to 12. As it was suggested in the previous investigations of other 1,3,4-thiadiazole compounds, these effects may be associated with conformational changes in the structure of the analysed molecule accompanied by aggregation effects. Crystallographic data showed that the effect of the two separated fluorescence emissions occurred in a conformation with the –OH group in the resorcyl ring bound on the side of the sulphur atom from the 1,3,4-thiadiazole ring. The hypothesis of aggregation as the mechanism involved in the change in the spectral properties at low pH is supported by the results of (Time-Dependent) Density Functional Theory calculations. The possibility of rapid analysis of conformational changes with the fluorescence spectroscopy technique may be rather important outcome obtained from the spectroscopic studies presented in this article. Additionally, the presented results seem to be highly important as they can be easily observed in solutions and biologically important samples.