Properties of a Subclass of Avakumović Functions and Their Generalized Inverses

We study properties of a subclass of ORV functions introduced by Avakumovi and provide their applications for the strong law of large numbers for renewal processes.     

Peer methods for the one-dimensional shallow-water equations with CWENO space discretization

For many practical problems an efficient solution of the one-dimensional shallow-water equations (Saint–Venant equations) is important, especially when large networks of rivers, channels or pipes are considered. In order to test and develop numerical methods four test problems are formulated. These tests include the well-known dam break and hydraulic jump problems and two steady state problems with varying channel bottom, channel width and friction.The space discretization of the partial differential equations is based on a finite volume approach with central WENO interpolation and local Lax–Friedrich fluxes (Kurganov and Levy, 2000) [7]. For time-integration new linearly-implicit two-step peer methods of orders three and four are developed. These methods are especially adapted to the usage within the method of lines framework. They show a good performance compared to the well-established methods like ode15s, radau5 or rodasp.     

Limit theorems for record counts and times in the F α -scheme

We determine the almost sure and central limiting behaviour of the number of records and record times for the F ^α -scheme. Elementary methods are used to obtain general results. The basic results are extended to a random environments model.     

Extreme Value Asymptotics for Multivariate Renewal Processes

For a sequence of partial sums ofd-dimensional independent identically distributed random vectors a corresponding multivariate renewal process is defined componentwise. Via strong invariance together with an extreme value limit theorem for Rayleigh processes, a number of weak asymptotic results are established for thed-dimensional renewal process. Similar theorems for the estimated version of this process are also derived. These results are suggested to serve as simultaneous asymptotic testing devices for detecting changes in the multivariate setting.     

On Chung's Lil and Csáki's Law for Renewal Processes

In this paper, Chung's law of the iterated logarithm (LIL) for partial sums, Csáki's law (a generalization of Chung's LIL), and Hirsch's law are extended to renewal processes.     

On general versions of Erdős-Rényi laws

Summary Rather general versions of the Erds-Rényi [6] new law of large numbers have recently been given by S. Csörg [5] for sequences of rv's which have stationary and independent increments and satisfy a first order large deviation theorem. It is shown that Csörg's results can be extended to cover also situations of stochastic processes where stationarity and independence of increments are not generally available, but for randomly chosen subsequences of the process. Examples demonstrate that the main result can be applied, for instance, to waiting-times in G/G/1 queuing models or cumulative processes in renewal theory, where Erds-Rényi type laws cannot be derived from Csörg's theorems.     

Darstellung und spektroskopische Charakterisierung der Nona-halogenodiiridate(III), [Ir2X9]3−, X = Cl,Br

Preparation and Spectroscopic Characterization of Nonahalogenodiiridates(III), [Ir₂X₉]^3?, X = Cl, Br The pure nonahalogenodiiridates(III), A₃[Ir₂X₉] (A = K, Cs, tetraalkylammonium; X = Cl, Br) have been prepared. They are formed from the monomer hexahalogenoiridates(III) which are bridged to confacial bioctahedral complexes by ligand abstraction in less polar organic solvents. The IR and Raman spectra exhibit bands in three characteristic regions; at high wavenumbers stretching vibrations with terminal ligands ν(Ir?Cl_t): 360?300, ν(Ir?Br_t): 250?220; in a middle region with bridging ligands ν(Ir?Cl_b): 290?235, ν(Ir?Br_b): 205?190 cm^?1; the deformation bands are observed at distinct lower frequencies. The distance between ν(Ir?X_t) and ν(Ir?X_b) increases with decreasing size of the cations. The electronic spectra measured at thin films of the pure complex salts at 10 K show some intensive charge transfer transitions in the UV and one or two weak d? d bands in the visible region.     

PRV property and the <Emphasis Type="Italic">ϕ</Emphasis>-asymptotic behavior of solutions of stochastic differential equations

In this paper, we investigate the a.s. asymptotic behavior of the solution of the stochastic differential equation dX(t) = g(X(t)) dt + σ(X(t))dW(t), X(0) ≢ 1, where g(·) and σ(·) are positive continuous functions, and W(·) is a standard Wiener process. By means of the theory of PRV functions we find conditions on g(·), σ(·), and ϕ(·) under which ϕ(X(·)) may be approximated a.s. by ϕ(μ(·)) on {X(t) → ∞}, where μ(·) is the solution of the ordinary differential equation dμ(t) = g(μ(t)) dt with μ(0) = 1. Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 4, pp. 445–465, October–December, 2007.     

The application of Rosenbrock-Wanner type methods with stepsize control in differential-algebraic equations

Summary Two Rosenbrock-Wanner type methods for the numerical treatment of differential-algebraic equations are presented. Both methods possess a stepsize control and an index-1 monitor. The first method DAE34 is of order (3)4 and uses a full semi-implicit Rosenbrock-Wanner scheme. The second method RKF4DA is derived from the Runge-Kutta-Fehlberg 4(5)-pair, where a semi-implicit Rosenbrock-Wanner method is embedded, in order to solve the nonlinear equations. The performance of both methods is discussed in artificial test problems and in technical applications.