Approximation of infinite delay and Volterra type equations

Summary We consider a class of infinite delay equations of neutral type which includes Volterrra type integral und integrodifferential equations. Using abstract approximation results (cf. Trotter-Kato-type) for strongly continuous semigroups we develop an approximation scheme which is based on approximation of the system state by Laguerre (and Legendre) polynomials. Numerical examples demonstrate the feasibility of the scheme and show infinite order convergence for smooth data.Supported in part by the Air Force Office of Scientific Research under Contracts AFORS-84-0398 and AFORS-85-0303 and the National Aeronautics and Space Administration under NASA Grant NAG-1-517 and by NSF under Grant UINT-8521208Supported in part by the Air Force Office of Scientific Research under Contract AFORS-84-0398 and in part by the Fonds zur Förderung der wissenschaftlichen Forschung, Austria, under project No. S3206     

An improved approach for hydrogen analysis in metal samples using single laser-induced gas plasma and target plasma at helium atmospheric pressure

We report in this paper the results of an experimental study on hydrogen analysis of solid samples in high pressure helium ambient gas employing the basic scheme of laser induced breakdown spectroscopy (LIBS). It is shown that the metastable excited state of helium atom can be utilized to induce delayed excitation of the ablated hydrogen atoms, and thereby avoid the Stark broadening effect as well as overcoming the undesirable mismatch effect, which are responsible for inefficient excitation respectively. It is further demonstrated that for samples of high boiling-point materials such as zircaloy, successful hydrogen analysis can be achieved by a newly introduced double excitation technique employing single laser realized in a modified configuration of the conventional LIBS method. PACS 51-52     

Measurements of theg-factor ratio of the first 3− and 5− states in40Ca and the lifetime of the 5− state

[Theg-factor ratio of the first excited 3^? and 5^? states in⁴⁰Ca was measured to beg ₃/g ₅=1.01(10) employing the implantation perturbed angular correlation technique. The static hyperfine fields (SF) in Fe and Gd hosts were used. In addition the lifetime of the 5^? state was measured to be τ=426(7)ps. The values of the SF in Gd and Fe hosts were deduced and compared with systematics in this element region.     

New methods for determining the volumetric flow rate in the column and the retention time of the unretained substance in gas chromatography

New methods for calculating the mean volumetric flow rate of the carrier gas and the retention time of the unretained substance in the column under conditions of gas chromatography were proposed. The methods are based on preliminary isothermal calibrations of the flow rate and holdup time for a packed column. A theoretical substantiation of the methods was given. Procedures of plotting calibration dependences for determining the indicated quantities at a desired temperature were described. The calculation results were compared to experimental data obtained by traditional methods. It was demonstrated that the use of calculation methods substantially simplifies the determination of the specific retention volume over a wide temperature range.     

Generalized green operator for an impulsive boundary-value problem with switchings

We establish constructive existence conditions and construct a generalized Green operator for the construction of solutions of a Noetherian linear boundary-value problem for a system of ordinary differential equations with switchings and pulse action in critical and noncritical cases. __________ Translated from Neliniini Kolyvannya, Vol. 10, No. 1, pp. 51–65, January–March, 2007.     

Products of residue currents of Cauchy–Fantappiè–Leray type

With a given holomorphic section of a Hermitian vector bundle, one can associate a residue current by means of Cauchy–Fantappiè–Leray type formulas. In this paper we define products of such residue currents. We prove that, in the case of a complete intersection, the product of the residue currents of a tuple of sections coincides with the residue current of the direct sum of the sections.     

An Implicit Iteration Process with Errors for a Finite Family of r-strictly Asymptotically Pseudocontractive Mappings

In this paper,we will establish several strong convergence theorems for the approximation ofcommon fixed points of r-strictly asymptotically pseudocontractive mappings in uniformly convex Banachspaces using the modiied implicit iteration sequence with errors,and prove the necessary and sufficient conditionsfor the convergence of the sequence.Our results generalize,extend and improve the recent work,in thistopic.