Infinitesimal Moments Research Articles

Les forces divines doublées du Mal

The divine forces in Gombrowicz's world do not relate to Virtue, but to cruelty and devilishness. These forces must be grasped within the specific structure of his universe. A key concept is the category of “form”. Further, there is his concept of “the interhuman church”, which implies human interaction with the Other through Form. The Other makes the subject suffer, or even provokes its death. At first sight it might seem that the divine can be conjured up by a youthful body, charming the spectator, spreading the magic of its beauty. However, the body of flesh and blood that triumphs over the power of the Spirit, is devilish by its very nature. Only the existence without Form seems to create a space for liberty. Thanks to the disruption of devilish interaction with the Other, the individual is overwhelmed by a sentiment of victorious joy. But almost immediately he tastes the bitterness of this infinitesimal moment of emptiness. In his nakedness man faces his own obscure, dishonourable devilishness. Since every concept and element considered sacred in the fictional universe of Gombrowicz is in the end bound by Evil, the real space of transcendence (if there is one), must be found outside the human world.

Simulation of First-Passage Times for Alternating Brownian Motions

The first-passage-time problem for a Brownian motion with alternating infinitesimal moments through a constant boundary is considered under the assumption that the time intervals between consecutive changes of these moments are described by an alternating renewal process. Bounds to the first-passage-time density and distribution function are obtained, and a simulation procedure to estimate first-passage-time densities is constructed. Examples of applications to problems in environmental sciences and mathematical finance are also provided.

On the functional estimation of jump–diffusion models

Abstract We provide a general asymptotic theory for the fully functional estimates of the infinitesimal moments of continuous-time models with discontinuous sample paths of the jump–diffusion type. Minimal requirements are placed on the dynamic properties of the underlying jump–diffusion process, i.e., stationarity is not required. Our theoretical framework justifies consistent (in a statistical sense) nonparametric extraction of the parameters and functions that drive the dynamic evolution of the process of interest (i.e., the potentially nonaffine and level-dependent intensity of the jump arrival being an example) from the estimated infinitesimal conditional moments as suggested in Johannes, 2003 (The statistical and economic role of jumps in continuous-time interest rate models, Journal of Finance, forthcoming).

On the inverse of the first hitting time problem for bidimensional processes

Bidimensional processes defined by dx(t) = ρ (x, y)dt and dy(t) = m(x, y)dt + [2v(x, y)]1/2dW(t), where W(t) is a Wiener process, are considered. Let T(x, y) be the first time the process (x(t), y(t)), starting from (x, y), hits the boundary of a given region in . A theorem is proved that gives necessary and sufficient conditions for a given complex function to be considered as the moment generating function of T(x, y) for some bidimensional diffusion process. Examples are given where the theorem is used to construct explicit solutions to first hitting time problems and to compute the infinitesimal moments that correspond to the chosen moment generating function.

On the inverse of the first hitting time problem for bidimensional processes

Bidimensional processes defined by dx(t) = ρ (x, y)dt and dy(t) = m(x, y)dt + [2v(x, y)]1/2dW(t), where W(t) is a Wiener process, are considered. Let T(x, y) be the first time the process (x(t), y(t)), starting from (x, y), hits the boundary of a given region in . A theorem is proved that gives necessary and sufficient conditions for a given complex function to be considered as the moment generating function of T(x, y) for some bidimensional diffusion process. Examples are given where the theorem is used to construct explicit solutions to first hitting time problems and to compute the infinitesimal moments that correspond to the chosen moment generating function.

Diffusion approximation to a queueing system with time-dependent arrival and service rates

A time nonhomogeneous diffusion approximation to a single server-single queue service system is obtained. Under various assumptions on the time-dependent functions appearing in the infinitesimal moments, transient and steady-state behaviour are analyzed. In particular, a diffusion approximation characterized by space-linear and time-varying moments is studied. The density of the busy period and the probability for the busy period to terminate are obtained. Finally, estimates of the goodness of the diffusion approximation are given.

On some time-non-homogeneous diffusion approximations to queueing systems

Time-non-homogeneous diffusion approximations to single server–single queue–FCFS discipline systems are considered. Under various assumptions on the nature of the time-dependent functions appearing in the infinitesimal moments the transient and the regime behaviour of the approximating diffusions are analysed in some detail. Special attention is then given to the study of a diffusion approximation characterized by a linear drift and by a periodically time-varying infinitesimal variance. Unlike the behaviour of transition functions and moments, the p.d.f. of the busy period is seen to be unaffected by the presence of such periodicity.

On some time-non-homogeneous diffusion approximations to queueing systems

Time-non-homogeneous diffusion approximations to single server–single queue–FCFS discipline systems are considered. Under various assumptions on the nature of the time-dependent functions appearing in the infinitesimal moments the transient and the regime behaviour of the approximating diffusions are analysed in some detail. Special attention is then given to the study of a diffusion approximation characterized by a linear drift and by a periodically time-varying infinitesimal variance. Unlike the behaviour of transition functions and moments, the p.d.f. of the busy period is seen to be unaffected by the presence of such periodicity.

Diffusion approximations to channel noise

A birth and death process is considered in which Xn(t) is the number of open channels in a patch of membrane containing n channels. The voltage response of such a patch to conductance fluctuations is obtained including moments and spectral density. Furthermore, a diffusion approximation, an Ornstein-Uhlenbeck process, is obtained based on a weak convergence result to represent the patch conductance. Results are also obtained for a second diffusion approximation, that having the same first two infinitesimal moments as the birth and death process.

The rotating current dipole

The rotating horizontal electric dipole ring source of this frequency‐domain EM method possesses the property that its E and H fields will couple strongly with steeply dipping conductive targets regardless of their strike direction. The extent to which this coupling is optimized depends upon the polarization of the source field and upon varying source‐target proximity. The state of polarization in E and H is determined by applying infinitesimal dipole moment theory to a rotating HED source on the surface of a conducting half‐space. It is shown that the source is equivalent to a 2-HED ring source of orthogonal dipoles with a phase difference of π/2 between them. Anomaly optimization is examined by analog modeling observations of the vertical magnetic field response of a vertically dipping graphitic target immersed in an NaCl electrolyte and oriented 0, 45, 90, and 135 degrees with respect to the source‐target center line. It is found that the extent of optimization for this model configuration is 60–85 percent for near‐surface targets. Since the method maximizes both conductive and inductive secondary response, modeling surveys are repeated with graphitic targets insulated from and in electrical contact with the modeled host electrolyte. By discriminating in this way between inductive and conductive response, it is found that, at the inductive limit of the response, current gathering provides the major portion of the anomaly and the individual conductive and inductive optimizations combine in such a manner as to improve the net optimizing ability.

Scattering of an electron by a dyon with magnetic chargegand electric charge±Ze

The scattering amplitudes of an electron by an infinitely heavy dyon are calculated. The so-called Lipkin-Weisberger-Peshkin difficulty occurring in the radial wave function corresponding to the lowest-angular-momentum state is discussed by adding a finite rather than an infinitesimal magnetic moment to the electron. The differential cross section, which depends weakly on this extra magnetic moment, is tabulated. MS code no. DD1360 1977 PACS numbers 14.80Hb, 13.10+q

Accuracy of neuronal interspike times calculated from a diffusion approximation

The theory of neuronal firing in Stein's model is outlined as well as the corresponding theory for a diffusion approximation which has the same first two infinitesimal moments. The diffusion approximation is derived from the discontinuous model in the limit of large input frequencies and small postsynaptic potential amplitudes. A comparison of the calculated mean interspike intervals is made for various values of the threshold for firing and various input frequencies. The diffusion approximation can underestimate the interspike interval by up to 100% or severely overestimate it, depending on the input frequencies and the threshold. A general relation between the predictions of the two models is deduced.

Dependence of flux flow voltages on field profile in type II superconductors

The integrated voltages observed across an open single layer superconducting coil when its magnetization is thermally destroyed by rapid heating at the inner (or outer) surface depend on (i) the initial temperature, (ii) the applied magnetic field and (iii) the diamagnetic, paramagnetic or hybrid nature of the initial magnetization. The signals normalized to the initial magnetic moments, are also seen to increase as the initial moment decreases with all the curves approaching a common extremum value in the limit of infinitesimal moment. By exploiting critical state concepts together with the viewpoint that the observed voltages are produced only by the change of magnetic flux embraced by the measuring circuit excluding the volume of the superconductor all observations are explained.

Magnetic Properties of Compounds with Singlet Ground State: Exchange Correlation Effects

Magnetic systems where the crystal-field ground state of the isolated ion is a singlet show no magnetic ordering for exchange small compared to crystal-field effects. We consider the effect of exchange as it increases from zero toward the critical value necessary for magnetic ordering with infinitesimal moment at $T=0$. In particular, we have calculated the susceptibility, nonlinear magnetization, and critical ratio of exchange to crystal-field splitting required for magnetic ordering for such systems, including exchange correlation effects by use of the constant coupling approximation. Substantial deviations from the molecularfield behavior are found at low temperatures as the exchange approaches the value required for magnetic ordering. Also we critically examine the pertinence of using boson spin-wave-like excitations to discuss thermodynamic properties in the paramagnetic case. While this formulation has certain inadequacies for treating such properties, this point of view could be quite valuable with regard to low-temperature inelastic neutron scattering experiments. Finally, the results are discussed with respect to the present experimental situation and with respect to the most promising line of investigation for future experiments.