holds as T → ∞. The basic tools of them are the approximate functional equations for ζ(s) and ζ(s). Therefore, one might think that we can obtain the asymptotic formula for the higher moments (sixth moment, eighth moment, etc· · · ) of ζ(s) on the critical line Re(s) = 12 by using the approximate functional equations for ζ(s) (k ≥ 3). However, although these approximate functional equations are...

A linear kinetic equation for heat transfer is solved by means of the method of moments. The moment equations are solved with Maxwelltype boundary conditions for steady state energy transport. The results exhibit marked Knudsen boundary layers. The accuracy of the description is examined, and it is shown that already a relatively small number of moments can give satisfactory resolution of Knuds...

In this paper, we study the dividend payments prior to absolute ruin in a Markov-dependent risk process in which the claim occurrence and the claim amount are regulated by an external discrete time Markov chain. A system of integrodifferential equations with boundary conditions satisfied by the moment-generating function, the nth moment of the discounted dividend payments prior to absolute ruin...

This paper studies an alternative bias correction for the M-estimator, which is obtained by correcting the moment equations in the spirit of Firth (1993). In particular, this paper compares the stochastic expansions of the analytically-bias-corrected estimator and the alternative estimator and finds that the third-order stochastic expansions of these two estimators are identical. This implies t...

A derivation and approximate solution of renormalized mode coupling equations describing the turbulent drift wave spectrum is presented. Arguments are given which indicate that a weak turbulence formulation of the spectrum equations fails for a system with negative dissipation. The inadequacy of the weak turbulence theory is circumvented by utilizing a renormalized formulation. An analytic mome...

In this paper at first introduced constituent equations for piezoelectric and then by the help of this equations, internal energy of hinged-hinged piezoelectric multilayer beam was computed. Then by the principle of minimum potential energy and Rayleigh -Ritz method the bending curvature equation of hinged-hinged piezoelectric multilayer beam under concentrated moment, concentrated force, unifo...

A moment equations method was performed to study the Reversible chain Transfer Catalyzed Polymerization (RTCP) of styrene in 80°C. To do this, a kinetic scheme containing conventional free radical polymerization reactions and equilibrium reactions of RTCP was assumed. After obtaining mass balance equations, three moment equations were defined for free and dormant radicals and dead chains. M...

Solid tumors are heterogeneous in composition. Cancer stem cells (CSCs) are a highly tumorigenic cell type found in developmentally diverse tumors that are believed to be resistant to standard chemotherapeutic drugs and responsible for tumor recurrence. Thus understanding the tumor growth kinetics is critical for development of novel strategies for cancer treatment. In this paper, the moment st...

Aalto University, P.O. Box 11000, FI-00076 Aalto www.aalto.fi Author Zheng Liu Name of the doctoral dissertation MODELING OF MASS TRANSFER AND REACTIONS WITH THE MOMENT METHOD Publisher School of Chemical Technology Unit Department of Biotechnology and Chemical Technology Series Aalto University publication series DOCTORAL DISSERTATIONS 5/2015 Field of research Chemical Engineering Manuscript s...

We present an enhanced moment-closure approximation to the finiteextensiblenonlinear-elastic (FENE) models of polymeric fluids. This new moment-closure method involves the perturbation of the equilibrium probability distribution function (PDF), which takes into account of the drastic split into two spikes and centralized behavior under the large macroscopic flow effects. The resulting macroscop...