Nonstandard Gaussian quadrature formulae based on operator values

In this paper, we develop the theory of so-called nonstandard Gaussian quadrature formulae based on operator values for a general family of linear operators, acting of the space of algebraic polynomials, such that the degrees of polynomials are preserved. Also, we propose a stable numerical algorithm for constructing such quadrature formulae. In particular, for some special classes of linear operators we obtain interesting explicit results connected with theory of orthogonal polynomials.     

Calculation of coefficients of a cardinal B-spline

It is well known that a cardinal B-spline of order $m,m\in \mathbb{N}$, is a piecewise polynomial function. In this note we propose an effective method for calculating the coefficients of polynomials which constitute a cardinal B-spline.     

Chemical and structural modifications of laser treated WTi surfaces at different ambient conditions

In this work we have studied the influence of laser modification on the composition and structure of tungsten titanium (WTi) thin films, deposited on n-type (100) silicon wafers. After deposition, the samples were multi-pulse laser irradiated in a nitrogen, oxygen, and helium ambient. The composition of the WTi/Si sample was determined by Elastic Recoil Detection Analysis (ERDA). Surface morphology was monitored by Atomic Force Microscopy (AFM). In the experiment, typical laser output parameters were: wavelength 1064 nm, pulse duration 150 ps, and laser pulse energy 30 mJ. Surface concentrations of W and Ti, as well as the concentration of gas components nitrogen and oxygen were determinated before and after the action of laser radiation in different ambient conditions. The contents of W and Ti decreased after irradiation due to adsorbed gases from the surrounding atmosphere. After surface irradiation in the inert ambient (He), the concentrations of the components were not significantly changed. In other cases, oxygen was the dominant component at the surface, probably due to the high affinity of thin film components. Also, the morphological changes occurred at the surface of WTi, as an increase in the surface roughness and formation of the granular structures are a result of laser-induced surface oxidation and recrystallization.     

The Affinity of Some Lewis Bases for Hexafluoroisopropanol as a Reference Lewis Acid: An ITC/DFT Study

To figure out the possible role of 1,1,1,3,3,3-hexafluoropropan-2-ol (HFIP) as well as to provide reference thermochemical data in solution, the formation of Lewis acid-base complexes between HFIP (Lewis acid) and a series of 8 different Lewis bases (3 sulfoxides, 3 Nsp² pyridine derivatives, 1 aromatic amine, 1 cyclic aliphatic ether) was examined by isothermal titration calorimetry (ITC) experiments and static density functional theory augmented with Dispersion (DFT−D) calculations. Measured ITC association enthalpy values (ΔH_a) lie between −9.3 and −14 kcal mol⁻¹. Computations including a PCM implicit solvation model produced similar exothermicity of association of all studied systems compared to the ITC data with ΔH_a values ranging from −8.5 to −12.7 kcal mol⁻¹. An additional set of calculations combining implicit and explicit solvation by chlorobenzene of the reactants, pointed out the relatively low interference of the solvent with the HFIP-base complexation: its main effect is to slightly enhance the Gibbs energy of the HFIP-Lewis base association. It is speculated that the interactions of bulk HFIP with Lewis bases therefore may significantly intervene in catalytic processes not only via the dynamic microstructuring of the medium but also more explicitly by affecting bonds’ polarization at the Lewis bases.     

Fractionalization into merons in quantum dots

We study by exact diagonalization, in the lowest Landau level approximation, the Coulomb interaction problem of N=4 and N=6 quantum dots in the limit of zero Zeeman coupling. We find that meron excitations constitute the lowest lying states of the quantum dots. This is based on a mapping between the excitations of the dot and states of the Haldane-Shastry spin chain.     

Tissue-protective effects of fullerenol C60(OH)24 and amifostine in irradiated rats

Polyhydroxylated fullerenes, named fullerenols (C(60)(OH)(n); n=12-26) are excellent antioxidants. Harmful effects of ionizing radiation on living organism are mainly mediated by free radical species and fullerenols attract an attention as a potential radioprotectors. Our preliminary investigations on mice and rats subjected to radiation injury show that fullerenol C(60)(OH)(24) provides high survival rate of irradiated small rodents. Radioprotective effect was comparable to that of the standard radioprotector amifostine. The aim of this study was to compare the efficacy of fullerenol C(60)(OH)(24) (10 and 100mg/kg i.p.) and amifostine (300 mg/kg i.p.) in protection of rats against harmful effects of ionizing radiation. The animals were whole-body irradiated by X-rays (8 MV). Both compounds were given 30 min before irradiation. In order to evaluate the general radioprotective efficacy of fullerenol and amifostine rats were irradiated with an absolutely lethal dose of X-rays (8 Gy) and their survival and body mass gain were monitored during the period of 30 days after irradiation. The aim of the second part of the study is to investigate the tissue-protective effects of tested compounds (100 mg/kg i.p. of fullerenol and 300 mg/kg i.p. of amifostine, 30 min before irradiation). It was carried out on rats irradiated with a sublethal dose of X-rays (7 Gy). Influence of ionizing radiation on hematopoesis as well as the radioprotective efficiency of the compounds given were evaluated by determining blood cell count during 28 days after irradiation. For this purpose the blood was taken from tail vein before irradiation and on the 3rd, 7th, 14th, 21st and 28th day after irradiation. In order to estimate the radioprotective effects of fullerenol and amifostine on other rat tissue, the animals were sacrificed on the 7th and 28th day after irradiation and their main organs (lung, heart, liver, kidney, small intestine and spleen) were taken for histopathological analysis. In the experiment in which the general radioprotective efficacy of fullerenol and amifostine was examined, fullerenol given in a dose of 100mg/kg produced better protection than given in a dose of 10mg/kg. This effect was comparable to that of amifostine. The results of hematological investigations showed that fullerenol better than amifostine prevented radiation-induced reduction in the white cell count (granulocytes and lymphocytes), particularly in the first 7 days after irradiation. Pathohistology examinations revealed better radioprotective effects of fullerenol compared to those of amifostine on the spleen, small intestine and lung, while amifostine had better radioprotective effects than fullerenol in protection of the heart, liver and kidney. These results confirm satisfactory radioprotective efficacy of fullerenol and encourage further investigations as a potential radioprotector.     

On the steepest descent approximation method for the zeros of generalized accretive operators

In this paper we present certain characteristic conditions for the convergence of the generalized steepest descent approximation process to a zero of a generalized strongly accretive operator, defined on a uniformly smooth Banach space. Our study is based on an important result of Reich [S. Reich, An iterative procedure for constructing zeros of accretive sets in Banach spaces, Nonlinear Anal. 2 (1978) 85–92] and given results extend and improve some of the earlier results which include the steepest descent approximation method.     

Uniqueness and computation of Gaussian interval quadrature formula for Jacobi weight function

Summary. In this paper we prove the uniqueness of the Gaussian interval quadrature formula for the Jacobi weight function. An algorithm for numerical construction has also investigated and some suitable solutions are proposed. For the special case of Chebyshev weight of the first kind and the special set of lengths we give an analytic solution.Mathematics Subject Classification (2000): 65D32, 65D30, 41A55The authors were supported in part by the Serbian Ministry of Science and Environmental Protection (Project #2002: Applied Orthogonal Systems, Constructive Approximation and Numerical Methods).     

Summation of series and Gaussian quadratures,II

Continuing previous work, we discuss applications of our summation/integration procedure to some classes of complex slowly convergent series. Especially, we consider the series of the form , where 0<v1 andR(s) is a rational function. Such cases were recently studied by Gautschi, using the Laplace transform method. Also, we give an appropriate method for calculating values of the Riemann zeta function , which can be transformed to a weighted integral on (0,+)of the functiont exp (–z/2)log(1- _m ² t ²))cos(z arctan( _m t, _m >=2/((2m+1)),m₀, involving the hyperbolic weightw(t)=1/cosh² t. Numerical results are included to illustrate the method.Dedicated to Luigi Gatteschi on the occasion of his 70th birthday