Computation of solutions to linear difference and differential equations with a prescribed asymptotic behavior

Linear differential equations usually arise from mathematical modeling of physical experiments and real-world problems. In most applications these equations are linked to initial or boundary conditions. But sometimes the solution under consideration is characterized by its asymptotic behavior, which leads to the question how to infer from the asymptotic growth of a solution to its initial values. In this paper we show that under some mild conditions the initial values of the desired solution can be computed by means of a continuous-time analogue of a modified matrix continued fraction. For numerical applications we develop forward and backward algorithms which behave well in most situations. The topic is closely related to the theory of special functions and its extension to higher-dimensional problems. Our investigations result in a powerful tool for solving some classical mathematical problems. To demonstrate the efficiency of our method we apply it to Poincaré type and Kneser’s differential equation.

Effect of a Dc Oblique Magnetic Field on the Magnetic Susceptibility of the Super-Paramagnetics Nanoparticles in Very Low Damping

The Magnetic Susceptibility of an individual Super-Paramagnetic nanoparticle in a presence of DC Oblique magnetic fields of arbitrary amplitude is investigated using Brown’s continuous diffusion model. The susceptibility is calculated and compared when for extensive ranges of the anisotropy, the dc magnetic fields in the very low damping with Matrix continued Fraction. It is shown that the shape of the Spectrum of Super-Paramagnetic nanoparticles is substantially altered by applying a dc oblique field. There is also an inherent geometric dependence of the complex susceptibility on the damping parameter arising from coupling of longitudinal and transverse relaxation modes

Thermal resonating Hartree–Bogoliubov theory based on the projection method

We propose a rigorous thermal resonating mean-field theory (Res-MFT). A state is approximated by superposition of multiple MF wavefunctions (WFs) composed of non-orthogonal Hartree–Bogoliubov (HB) WFs. We adopt a Res-HB subspace spanned by Res-HB ground and excited states. A partition function (PF) in a SO (2N) coherent state representation (CS Reps) |g 〉(N: Number of single-particle states) is expressed as Tr (e-βH) = 2N-1∫〈g|e-βH|g〉dg (β = 1/kBT). Introducing a projection operator P to the Res-HB subspace, the PF in the Res-HB subspace is given as Tr (Pe-βH), which is calculated within the Res-HB subspace by using the Laplace transform of e-βH and the projection method. The variation of the Res-HB free energy is made, which leads to a thermal HB density matrix [Formula: see text] expressed in terms of a thermal Res-FB operator [Formula: see text] as [Formula: see text]. A calculation of the PF by an infinite matrix continued fraction (IMCF) is cumbersome and a procedure of tractable optimization is too complicated. Instead, we seek for another possible and more practical way of computing the PF and the Res-HB free energy within the Res-MFT.

AN EFFICIENT METHOD FOR PERFORMANCE ANALYSIS OF BLENDED CALL CENTERS WITH REDIAL

This paper considers a multiserver retrial queue with two-way communication for blended call centers. Primary incoming calls arrive at the servers according to a Poisson process and request an exponentially distributed service time. Incoming calls that find all the servers fully occupied join the orbit and retry to occupy a server again after some random time. A retrial incoming call behaves the same as a primary incoming call. A server not only serves as an incoming call but also makes an outgoing call after some random idle time. We assume that the distribution of the duration of outgoing calls is different from that of incoming calls. Artalejo and Phung-Duc (2012) have extensively studied the single server case and have obtained some preliminary results for the multiserver model. In this paper, we present an extensive analysis for the multiserver model in which, we propose a new formulation by a level-dependent quasi birth-and-death (QBD) process, whose block matrices have some special block structure. Based on a matrix continued fraction approach and a censoring technique, we develop an efficient algorithm utilizing the special structure for computing the stationary distribution. Furthermore, we derive explicit formulae for the mean number of incoming calls and that of outgoing calls in the servers. Through various numerical results, we study the characteristics of the queueing system and find some insights into the optimal outgoing call rate.

Fluctuating noise drives Brownian transport

The transport properties of Brownian ratchet were studied in the presence of stochastic intensity noise in both overdamped and underdamped regimes. In the overdamped case, an analytical solution using the matrix-continued fraction method revealed the existence of a maximum current when the noise intensity fluctuates on intermediate timescale regions. Similar effects were observed for the underdamped case by Monte Carlo simulations. The optimal time-correlation for Brownian transport coincided with the experimentally observed time-correlation of the extrinsic noise in Escherichia coli gene expression and implied the importance of environmental noise for molecular mechanisms.