Physical Sciences and Mathematics Commons^™

Regularity Of The Free-Boundary In Singular Stochastic Control, S. A. Williams, P. L. Chow, J. L. Menaldi

Mathematics Faculty Research Publications

No abstract provided.

Speleothems As Proxy For The Carbon Isotope Composition Of Atmospheric Co2, M. Baskaran, R. V. Krishnamurthy

Environmental Science and Geology Faculty Research Publications

We have measured the stable isotope ratios of carbon in a suite of recent cave deposits (<200 >years) from the San Saba County, Texas, USA. The methodology for dating these deposits using excess ²¹⁰Pb was recently established [Baskaran and Iliffe, 1993]. The carbon isotope ratios of these samples, spanning the time period ∼1800–1990 AD, reflect the carbon isotope ratio of atmospheric CO₂ for the same period. The pathways by which the δ¹³C of atmospheric CO₂ is imprinted on these speleothems can be explained using a model developed by Cerling (1984). The results suggest that the …

Atmospheric Depositional Fluxes Of 7Be And 210Pb At Galveston And College Station, Texas, M. Baskaran, Charles H. Coleman, Peter H. Santschi

Environmental Science and Geology Faculty Research Publications

The bulk depositional fluxes of ²¹⁰Pb and ⁷Be were measured at a coastal (Galveston) and an inland (College Station) station for about 3 years, between 1989 and 1991. The annual depositional fluxes of ⁷Be and ²¹⁰Pb at Galveston during this period varied by a factor of about 2.5, between 8.9 and 23.2 disintegrations per minute (dpm) cm⁻² yr⁻¹, with a mean of 14.7 dpm cm⁻² yr⁻¹ for ⁷Be, and 0.67 and 1.71 dpm cm⁻² yr⁻¹, with a mean of 1.03 dpm cm⁻² yr⁻¹ for ^{210 …}

K-Shell Ionization Of Atoms By Electron And Positron Impact, S. P. Khare, Vandana Saksena, J. M. Wadehra

Physics and Astronomy Faculty Research Publications

In the plane-wave Born approximation (PWBA), scaling relations for K-shell generalized oscillator strengths and energy-loss cross sections of atoms are given. The total K-shell ionization cross sections, obtained at high impact energy, are used to obtain the Bethe collisional parameter c_K for atoms ranging from carbon to gold. These values of c_K are, in general, significantly different from those obtained previously with the help of Fano plots at relatively low impact energies. Furthermore, using Hippler’s modification of the PWBA [Phys. Lett. A 144, 81 (1990)], total K-shell ionization cross sections of various atoms by …

Age Determination Of Recent Cave Deposits Using Excess 210Pb - A New Technique, M. Baskaran, Thomas M. Iliffe

Environmental Science and Geology Faculty Research Publications

Cave deposits have been widely used as proxy recorders in deciphering palaeoclimate during the last glacial/interglacial maxima (∼ 120 ka) [Harmon et al., 1975; Atkinson et al., 1978; Goede and Harmon, 1983; Ayliffe and Veeh, 1989]. Palaeoclimatic studies of cave deposits for the past 1–1000 yr time scale require a precise dating technique, that until now has been lacking. Due to the multiple sources of carbon in speleothems, ¹⁴C dates obtained for recently deposited calcite are highly variable and thus, ¹⁴C dating techniques are not suitable to obtain speleothem ages for the past 1–1000 years.

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Ext In The Nineties, Robert R. Bruner

Mathematics Faculty Research Publications

We describe a package of programs to calculate minimal resolutions, chain maps, and null homotopies in the category of modules over a connected algebra overe Z_2 and in the category of unstable modules over the mod 2 Steenrod algebra. They are available for free distribution and intended for use as an Adams spectral sequence 'pocket calculator'. We provide a sample of the results obtained from them.

Generalized Lame-Clapeyron Solution For A One-Phase Source Stefan Problem, José Luis Menaldi, Domingo Alberto Tarzia

Mathematics Faculty Research Publications

In this paper we obtain a generalized Lamé-Clapeyron solution for a one-phase Stefan problem with a particular type of sources. Necessary and sufficient conditions are given in order to characterize the source term which provides a unique solution. Some estimates on the free boundary and the temperature are presented. In particular, asymptotic expansions are given for small Stefan number and source.

Optimal Control And Differential Games With Measures, E. N. Barron, R. Jensen, J. L. Menaldi

Mathematics Faculty Research Publications

We consider control problems with trajectories which involve ordinary measureable control functions and controls which are measures. The payoff involves a running cost in time and a running cost against the control measures. In the optimal control problem we are trying to minimize this payoff with both controls. In the differential game problem we are trying to minimize the cost with the ordinary controls assuming that the measure controls are chosen to maximize the cost. We will characterize the value functions in both cases using viscosity solution theory by deriving the Bellman and Isaacs equations.

Regularizing Effect For Integro-Differential Parabolic Equations, Maria Giovanna Garroni, José Luis Menaldi

Mathematics Faculty Research Publications

No abstract provided.

Singular Ergodic Control For Multidimensional Gaussian Processes, J. L. Menaldi, M. Robin, M. I. Taksar

Mathematics Faculty Research Publications

A multidimensional Wiener process is controlled by an additive process of bounded variation. A convex nonnegative function measures the cost associated with the position of the state process, and the cost of controlling is proportional to the displacement induced. We minimize a limiting time-average expected (ergodic) criterion. Under reasonable assumptions, we prove that the optimal discounted cost converges to the optimal ergodic cost. Moreover, under some additional conditions there exists a convex Lipschitz continuous function solution to the corresponding Hamilton-Jacobi-Bellman equation which provides an optimal stationary feedback control.

Environmental Radiocesium In Subarctic And Arctic Alaska Following Chernobyl, M. Baskaran, J. J. Kelley, A. S. Naidu, D. F. Holleman

Environmental Science and Geology Faculty Research Publications

Radiocesium (¹³⁴ Cs and ¹³⁷ Cs) concentrations were measured in soil, plant and wildlife samples from subarctic to arctic Alaska. Concentrations of ¹³⁷ Cs ranged from below detectable or low levels in whale and fish samples to as high as 242 Bq/kg in lichen. For all potential human food items, the radiocesium concentrations measured in this study were below accepted permissible levels for human consumption. Chernobyl-derived radiocesium concentrations ranged from below detectable or low levels in all arctic samples (soil, sediment, lichen, whale, fish and caribou) to 32 Bq/kg in subarctic moss. Therefore the distribution and subsequent deposition of Chernobyl-derived …

Relativistic Approach For E± Scattering From Argon, Sultana N. Nahar, J. M. Wadehra

Physics and Astronomy Faculty Research Publications

Differential and integrated elastic, integrated total cross sections as well as various polarization parameters–the spin polarization P and the parameters T and U describing the change in the polarization vector during scattering–for the scattering of electrons and positrons from argon in the energy range of 3–300 eV are calculated using the relativistic Dirac equation. The real part of the projectile-target interaction is represented by a sum of model potentials. The phase shifts for large angular momenta ħl are calculated using the Born approximation. The relativistic calculations for the differential and integrated elastic cross sections obtained using the pure real potential …

Nonlocal Effects In Dissociative Electron Attachment To H2, D E. Atems, J M. Wadehra

Physics and Astronomy Faculty Research Publications

Electron scattering by diatomic molecules involving the formation of a single resonance is treated within the configuration-interaction formalism. A technique is presented for solving the resulting nonlocal integro-differential equation for the nuclear motion in the resonant state. This technique is applied to the scattering of electrons by molecular hydrogen (and its isotopes) via the formation of X^2 Σ^+_u resonance, using a semiempirical model for the resonant state. Numerical cross sections for dissociative attachment, to H_2, of electrons with energies below 5 eV are presented and compared both with available experimental data and with those obtained using the local approximation for …

Rovibrationally Enhanced Dissociative Electron Attachment To Molecular Lithium, J M. Wadehra

Physics and Astronomy Faculty Research Publications

We have investigated the role played by initial rovibrational excitation of Li_2 on the cross sections and rates for dissociative electron attachment to the molecule. For a given internal energy, the vibrational excitation enhances the attachment cross section more than the rotational excitation. The attachment cross sections and the attachment rates reach their maximum values when the process of dissociative attachment to rovibrationally excited molecules is still endoergic and, furthermore, these quantities stay close to their maximum values even when the process changes from being endoergic to exoergic. The upper bounds on the cross sections and the rates for dissociative …

On The Optimal Reward Function Of The Continuous Time Multiarmed Bandit Problem, José Luis Menaldi, Maurice Robin

Mathematics Faculty Research Publications

The optimal reward function associated with the so-called "multiarmed bandit problem" for general Markov-Feller processes is considered. It is shown that this optimal reward function has a simple expression (product form) in terms of individual stopping problems, without any smoothness properties of the optimal reward function neither for the global problem nor for the individual stopping problems. Some results relative to a related problem with switching cost are obtained.

Remarks On Estimates For The Green Function, Jose Luis Menaldi

Mathematics Faculty Research Publications

No abstract provided.

Mat 751 Algebraic Topology I - Fall '89, David Handel

Mathematics Faculty Research Publications

A collection of notes for the course Mat 751, Algebraic Topology I, prepared by Professor David Handel of the Wayne State University Mathematics Department. The notes include examples, exercises, and additional lecture notes on related concepts.

Exact Time-Dependent Evolution Of Electron Velocity Distribution Functions In A Gas Using The Boltzmann Equation, P J. Drallos, J M. Wadehra

Physics and Astronomy Faculty Research Publications

A numerical technique, starting from the Boltzmann equation, for obtaining the time-dependent behavior of the electron-velocity distribution function in a gas is presented. A unique feature of this technique is that, unlike previously used procedures, it does not make use of any expansion of the distribution function. This allows the full anisotropy of the distribution function to be included in the solution. Furthermore, the problem associated with multiterm-expansion techniques of choosing a sufficient number of terms for convergence is completely avoided. The distribution function obtained by the present method is exact and, in principle, contains all of the expansion terms …

Synthesis Of Site Specific 1, N^2-Ethenodeoxyguanosine In A Small Oligonucleotide, Kathryn A. Carolin

Wayne State University Theses

Malondiadehyde (MDA) is a known carcinogen and mutagen produced by lipid peroxidation and prostaglandin synthesis in vivo. MDA is unique from structurally related compounds, methyl glyoxal and acrolein, because it produces frameshift mutations whereas the latter compounds induce base-pair substitutions. MDA forms several adducts with deoxyguanosine but it is not certain which one causes the frameshift mutations. Ideally, a single adduct on a replicating genome could simulate the in vivo process by which MDA mutagenesis would occur. This technique is known as site-specific mutagenesis. The approach of choice for site-specific mutagenesis experiment is the gapped heteroduplex method which requires the …

Some Estimates For Finite Difference Approximations, José-Luis Menaldi

Mathematics Faculty Research Publications

Some estimates for the approximation of optimal stochastic control problems by discrete time problems are obtained. In particular an estimate for the solutions of the continuous time versus the discrete time Hamilton-Jacobi-Bellman equations is given. The technique used is more analytic than probabilistic.

On Asymptotic Behavior Of Stopping Time Problems, Jose Luis Menaldi, Maurice Robin

Mathematics Faculty Research Publications

No abstract provided.

On The Numerical Approximations Of An Optimal Correction Problem, M. C. Bancora-Imbert, P. L. Chow, J. L. Menaldi

Mathematics Faculty Research Publications

The numerical solution of an optimal correction problem for a damped random linear oscillator is studied. A numerical algorithm for the discretized system of the associated dynamic programming equation is given. To initiate the computation, we adopt a numerical scheme derived from the deterministic version of the problem. Next, a correction-type algorithm based on a discrete maximum principle is introduced to ensure the convergence of the iteration procedure.

A Novel Algorithm For Calculating The Time Evolution Of The Electron Energy Distribution Function In Gaseous Discharges, P J. Drallos, J M. Wadehra

Physics and Astronomy Faculty Research Publications

We are presenting a novel numerical technique for obtaining the time evolution of the electron velocity and electron energy distribution functions in the presence of a uniform electric field. Using this technique, the various swarm parameters can be evolved for sufficiently long times so that equilibrium can be reached without incurring any numerical instabilities. Results are presented for electron swarms in gaseous neon for various values of E/N.

Formation Of Ground And Excited States Of Antihydrogen, Sultana N. Nahar, J M. Wadehra

Physics and Astronomy Faculty Research Publications

Differential and integrated cross sections for the formation of antihydrogen by the impact of intermediate-energy (20–500 keV) antiprotons on positronium are calculated using the first Born approximation. The calculations are carried out for the formation of antihydrogen in ground and various excited electronic states (n=1–3) when positronium, the target atom, is in the ground state, and for the formation of antihydrogen in the ground state when the positronium is in various excited electronic states (n=1–2). The 1/n^3 behavior for the capture cross sections is used to calculate the total (that is, all states added together) integrated cross sections. The cross …

Simple Model For The Resonant Vibrational Excitation Of Molecules And Its Application To Li2 And N2, J M. Wadehra, P J. Drallos

Physics and Astronomy Faculty Research Publications

A simple model for the resonant vibrational excitation of a molecule by electron impact is proposed in which the potential curves of the electronic states of the molecule and its resonant anion are replaced by those of linear harmonic oscillators of arbitrary frequencies and equilibrium internuclear separations. A closed-form expression for the excitation amplitude is derived. Useful recursion relations among amplitudes are obtained which allow convenient evaluation of cross sections for any inelastic or superelastic vibrational transition. The model is used to generate the cross sections for vibrational excitation of Li_2 and N_2 by the impact of low-energy electrons.

Contributions Of Higher Partial Waves To The Elastic Scattering Amplitude For Various Long Range Interactions, J M. Wadehra, Sultana N. Nahar

Physics and Astronomy Faculty Research Publications

The contributions of higher partial waves to the elastic scattering amplitude are dominated by long-range interactions which fall off as r^(−n) as r→∞. Closed-form expressions for the contributions of higher partial waves (2l>n-3) to the scattering amplitude for various long-range interactions (n ranging from 3 to 8) are presented.

Positronium Formation From Li And Na Atoms By Use Of Pseudopotential, Sultana N. Nahar, J M. Wadehra

Physics and Astronomy Faculty Research Publications

The differential and total cross sections for the formation of positronium in its ground state from Li and Na atoms by the impact of intermediate-energy positrons are calculated in the first Born and distorted-wave Born approximations. Hellmann-type pseudopotentials are used to represent the alkali-metal ion cores. The difference in the use of pseudopotentials and the static potential for the core representation for evaluating various rearrangement cross sections is discussed.

Exact Evaluation And Recursion Relations Of Two-Center Harmonic Oscillator Matrix Elements, P. J. Drallos, J. M. Wadehra

Physics and Astronomy Faculty Research Publications

Using vibrational wave functions of two relatively displaced harmonic oscillators of arbitrary frequencies, Franck–Condon overlap integrals and matrix elements of x^l, exp(−2cx), and exp(−cx^2) (x is the internuclear separation) are obtained. Useful three‐term, four‐term, and five‐term recursion relations among these matrix elements are derived. It is shown that all of the relevant matrix elements can be obtained from a mere knowledge of the lowest two Franck–Condon overlap integrals. Results are illustrated by computation of Franck–Condon factors for the A ^1∑^+_u –X ^1∑^+_g and the B ^1Π_u –X ^1∑^+_g systems of ^7Li_2.

Elastic Scattering Of Positrons And Electrons By Argon, Sultana N. Nahar, J. M. Wadehra

Physics and Astronomy Faculty Research Publications

Differential and integrated cross sections for the elastic scattering of low- and intermediate-energy (3–300 eV) positrons and electrons by argon atoms are calculated. Higher transport cross sections, representing moments of 1-(costheta)^n, for these systems are also obtained for n=1–4. Model potentials are used to represent the interactions between positrons or electrons and argon atoms. For each impact energy, the phase shifts of the lower partial waves are obtained exactly by numerical integration of the radial equation. The Born approximation is used to obtain the contribution of the higher partial waves to the scattering amplitude. The phase shifts of the seven …

Additive Control Of Stochastic Linear Systems With Finite Horizon, Pao-Liu Chow, José-Luis Menaldi, Maurice Robin

Mathematics Faculty Research Publications

We consider a dynamic system whose state is governed by a linear stochastic differential equation with time-dependent coefficients. The control acts additively on the state of the system. Our objective is to minimize an integral cost which depends upon the evolution of the state and the total variation of the control process. It is proved that the optimal cost is the unique solution of an appropriate free boundary problem in a space-time domain. By using some decomposition arguments, the problems of a two-sided control, i.e. optimal corrections, and the case with constraints on the resources, i.e. finite fuel, can be …