Physical Sciences and Mathematics Commons^™

Reflected Diffusion Processes With Jumps, José-Luis Menaldi, Maurice Robin

Mathematics Faculty Research Publications

A stochastic differential equation of Wiener-Poisson type is considered in a d-dimensional bounded region. By using a penalization argument on the domain, we are able to prove the existence and uniqueness of solutions in the strong sense. The main assumptions are Lipschitzian coefficients, either convex or smooth domains and a regular outward reflecting direction. As a direct consequence, it is verified that the reflected diffusion process with jumps depends on the initial date in a Lipschitz fashion.

Critical Points In Low-Energy Positron-Atom Scattering, J. M. Wadehra, T. S. Stein, W. E. Kauppila

Physics and Astronomy Faculty Research Publications

Critical points, which represent minima in differential scattering cross sections as a function of scattering angle and incident projectile energy, are theoretically predicted for elastic scattering of low-energy positrons by Ar, Kr, and Xe. It is demonstrated that these points arise due to low-energy positron diffraction effects.

Math 752 Algebraic Topology Ii - Winter '84, David Handel

Mathematics Faculty Research Publications

A collection of notes for the course MAT 752, Algebraic Topology II, prepared by Professor David Handel of the Wayne State University Mathematics Department. This course builds on MAT 751, Algebraic Topology I, and the notes include examples, exercises, and suggestions for further reading.

Optimal Stochastic Scheduling Of Power Generation Systems With Scheduling Delays And Large Cost Differentials, G. L. Blankenship, J.-L. Menaldi

Mathematics Faculty Research Publications

The optimal scheduling or unit commitment of power generation systems to meet a random demand involves the solution of a class of dynamic programming inequalities for the optimal cost and control law. We study the behavior of this optimality system in terms of two parameters: (i) a scheduling delay, e.g., the startup time of a generation unit; and (ii) the relative magnitudes of the costs (operating or starting) of different units. In the first case we show that under reasonable assumptions the optimality system has a solution for all values of the delay, and, as the delay approaches zero, that …

Dissociative Attachment To Rovibrationally Excited H2, J. M. Wadehra

Physics and Astronomy Faculty Research Publications

Using a local-width resonant model, the cross sections for dissociative attachment of low-energy electrons to a rovibrationally excited H_2 molecule in its ground electronic state are obtained. There are 294 such rovibrational levels. Only the contribution of the ^2Σ_u^+ resonant state of H^−_2 to the attachment process is investigated. Assuming a Maxwellian distribution for electron energies, the dissociative attachment cross sections are converted into attachment rates for various rovibrational levels of H_2. A significant enhancement of attachment rates occurs for endoergic reactions only, and the maximum possible rate for attachment to the ground electronic state of H_2 is about 10^(−8) …

Dissociative Attachment In Hcl, Dcl, And F2, J. N. Bardsley, J. M. Wadehra

Physics and Astronomy Faculty Research Publications

Resonant scattering models, using nonlocal decay widths, are developed for dissociative attachment of slow electrons to diatomic molecules. Cross sections are obtained for HCl and DCl in several initial rotational and vibrational states, and the dependence of the average attachment cross section upon the rotational and vibrational temperature is examined. For F_2 the cross section for ground state molecules agrees well with experiment above 0.2 eV but shows no zero energy peak. The attachment cross section is higher for vibrationally excited molecules, but the enhancement is much less than that found in H_2 and HCl.

Elastic Scattering Of Protons From Hydrogen Atoms At Energies 15-200kev, J. M. Wadehra, Robin Shakeshaft

Physics and Astronomy Faculty Research Publications

Differential and integrated cross sections for the elastic process H^+ + H(1s) → H^+ + H(1s) were calculated with the use of results of coupled-state calculations in the energy range 15-200 keV. Results are presented and, at 60 keV, compared favorably with preliminary experimental data. The asymptotic form of the elastic amplitude for b≫a_0 (where b is the impact parameter) is derived for the two cases λ≪1 and λ≫1, where λ is the ratio of the collision duration to the orbital period. The asymptotic form for λ≫1 provides a useful test on the numerical accuracy of the amplitudes.

Two Generalizations Of The Adams Spectral Sequence, Robert R. Bruner

Mathematics Faculty Research Publications

No abstract provided.

Optimal Control Of Stochastic Integrals And Hamilton-Jacobi-Bellman Equations, Ii, Pierre-Louis Lions, José-Luis Menaldi

Mathematics Faculty Research Publications

We consider the solution of a stochastic integral control problem, and we study its regularity. In particular, we characterize the optimal cost as the maximum solution of ∀v ∈ V, A(v)u ≤ ƒ(v) in D'(Ο), u = 0 on ∂Ο, u ∈ W^1,∞(Ο),

where A(v) is a uniformly elliptic second order operator and V is the set of the values of the control.

Optimal Control Of Stochastic Integrals And Hamilton-Jacobi-Bellman Equations, I, Pierre-Louis Lions, José-Luis Menaldi

Mathematics Faculty Research Publications

We consider the solution of a stochastic integral control problem and we study its regularity. In particular, we characterize the optimal cost as the maximum solution of ∀v ∈ V, A(v)u ≤ ƒ(v) in D'(Ο), u = 0 on ∂Ο, u ∈ W^1,∞(Ο),

where A(v) is a uniformly elliptic second order operator and V is the set of the values of the control.

The Classification Of Extensions Of C*-Algebras, Jonathan Rosenberg, Claude Schochet

Mathematics Faculty Research Publications

Our objective in this note is to outline a number of results concerning the Kasparov groups Ext(A,B) which are analogous to known information about the Brown, Douglass, and Fillmore (BDF) theory regarding groups which classify extensions of the form 0 → B ⊗ K → E → A → 0. These results enable one to compute the groups with relatively mild restrictions on the C*-algebras A and B. This in turn should make it possible to analyze the way in which a wide variety of C*-algebra extensions are put together, at least stably.

On The Optimal Stopping Time Problem For Degenerate Diffusions, J. L. Menaldi

Mathematics Faculty Research Publications

In this paper we give a characterization of the optimal cost of a stopping time problem as the maximum solution of a variational inequality without coercivity. Some properties of continuity for the optimal cost are also given.

On The Optimal Impulse Control Problem For Degenerate Diffusions, J. L. Menaldi

Mathematics Faculty Research Publications

In this paper, we give a characterization of the optimal cost of an impulse control problem as the maximum solution of a quasi-variational inequality without assuming nondegeneracy. An estimate of the velocity of uniform convergence of the sequence of stopping time problems associated with the impulse control problem is given.

Large Momentum Transfer Limit Of Some Matrix Elements, J. M. Wadehra, Larry Spruch

Physics and Astronomy Faculty Research Publications

The matrix element εfi(K), or ε, that appears in the study of elastic and inelastic electron-atom scattering from an initial state i to a final state f in the first Born approximation depends explicitly on the momentum transfer ℏK⃗ . The uncertainty in the value of the calculated cross sections arises not only from the application of the Born approximation but also from the approximate nature of the wave functions used. For the 1 S1−2 P1 transition in helium, we present an analytic expression in terms of the 1 S1 and 2 P1 wave functions for the leading coefficient C1 …

Distorted Wave Born Approximation For Inelastic Collisions: Application To Electron Capture By Positrons From Hydrogen Atoms, Robin Shakeshaft, J. M. Wadehra

Physics and Astronomy Faculty Research Publications

We have re-examined the distorted-wave Born approximation for inelastic collisions. We find that the distortion in the relative motion of the collision partners cannot be neglected even for high-energy ion-atom collisions. Furthermore, if the distortion in the relative motion is not treated exactly, post-prior discrepancies will occur. We have applied the distorted-wave Born approximation, with distortion included through first order, to ground-state-to-ground-state electron capture by positrons from hydrogen atoms. The results are presented in this paper. We have also examined the nonrelativistic asymptotic behavior of the cross section for electron capture from hydrogen by positrons incident with a speed v∼∞. …

Homogeneous Extensions Of C*-Algebras And K-Theory. I, Claude Schochet

Mathematics Faculty Research Publications

No abstract provided.

Rates Of Dissociative Attachment Of Electrons To Excited H2 And D2, J. M. Wadehra

Physics and Astronomy Faculty Research Publications

Calculations are reported of the contributions of the lowest 2Σ+ u and 2Σ+ g resonant states to the rates of dissociative attachment of electrons to H2 and D2. For all electron temperatures, the rate is significantly enhanced by vibrational and rotational excitation of the initial molecule. Typically, for an electron temperature of 1.5 eV, the attachment rates for various (v, J) levels are, in cm3 sec−1, 5.4×10−15 for (0,0), 7.2×10−11 for (0,20), and 7.8×10−9 for (8,0), for H2; and 4.5×10−17 for (0,0), 1.4×10−14 for (0,20), and 6.0×10−9 for (11,0), for D2.

Low-Energy Collisions Of D+ With D And He++ With He, J. M. Wadehra

Physics and Astronomy Faculty Research Publications

Quantum-mechanical calculations for differential cross sections and various transport cross sections describing the thermal-energy collisions of D+ with D and He2+ with He are presented. Lowest-order Viehland-Mason theory is used to calculate mobility of D+ in D. The zero-field mobility at 77, 303, and 10000 K is, in units of cm2V−1s−1, 10.5, 7.0, and 2.1, respectively.

Dissociative Attachment And Vibrational Excitation In Low-Energy Collisions Of Electrons With H2 And D2, J. N. Bardsley, J. M. Wadehra

Physics and Astronomy Faculty Research Publications

A semiempirical analysis is made of the contributions of the two lowest resonant states to dissociative attachment and vibrational excitation in low-energy collisions of electrons with H2 and D2. The resonance models are based both on ab initio calculations and on fits to experimental data. The dissociative-attachment cross section near threshold is enhanced significantly by vibrational or rotational excitation of the initial molecule. Near 10 eV, contributions from both resonances are required to explain the observed cross sections for vibrational excitation.

Resonant Contributions To Single Charge Transfer Between He++ And He, J. N. Bardsley, James S. Cohen, J. M. Wadehra

Physics and Astronomy Faculty Research Publications

Energy levels and lifetimes are calculated for the resonant states that are important in radiative single charge transfer in He2+-He collisions at thermal energies. The resonant contribution to the charge-transfer rate decreases with increasing temperature and is approximately 12% of the total rate at 300 K.

Vibrational And Rotational State Dependence Of Dissociative Attachment In E-H2 Collisions, J. M. Wadehra, J. N. Bardsley

Physics and Astronomy Faculty Research Publications

Resonant scattering theory is applied to the calculation of e-H2 dissociative attachment cross sections near threshold for several vibrational and rotational states of the H2 molecule. Typical values just above threshold are, in cm2, 2.8×10−21 for the ground state (v=0, J=0), 8.3×10−20 for (1, 0), 1.0×10−18 for (2, 0), and 3.5×10−20 for (0, 10). The effect of rotational excitation is found to be significant, although it is not as large as suggested by Chen and Peacher.

Mobility Of Α Particles In Helium, J. M. Wadehra, James S. Cohen, J. N. Bardsley

Physics and Astronomy Faculty Research Publications

The mobility of α particles in helium gas is calculated using the zeroth-order Viehland-Mason theory with interaction potentials recently computed by Cohen and Bardsley. The results show a dependence on field strength similar to the measurements of Johnsen and Biondi but are lower in magnitude by about 5%.

Application Of An Extremum Principle To The Variational Determination Of The Generalized Oscillator Strengths Of Helium, J. M. Wadehra, Larry Spruch, Robin Shakeshaft

Physics and Astronomy Faculty Research Publications

Variational principles have been used extensively for estimating some given functional F(φ, φ^†) where the functions φ and φ^† are well defined by a set of differential equations and boundary conditions but cannot be determined exactly. The variational principle for the estimation of a matrix element of an arbitrary Hermitian operator W involves not only the trial wave functions φ_t but also trial auxiliary Lagrange functions L_t; the L_t depend on the φ_t and on W. To determine the parameters in the L_t efficiently, a functional M …

Calculations Of Ion‐Ion Recombination Rates At High Pressures, J. M. Wadehra, J. N. Bardsley

Physics and Astronomy Faculty Research Publications

The classical theory of ion‐ion recombination in gases of high density is extended to allow for arbitrary ratios of the masses of the three species involved. Calculations are performed for the recombination of Ar+, Ar+ 2, Kr+, and Kr+ 2 ions with F− and of Hg+ and Ar+ with Cl− in an argon gas. The effective two‐body rates peak between 2×10−6 and 3×10−6 cm3 sec−1 at pressures above 1 atm.

Determination Of Size Distributions In Heterodisperse Systems Of Homogeneous, Non-Absorbing Spheres From Angular Light Scattering Extrema, Werner Bergman

Wayne State University Dissertations

No abstract provided.

K-Theory And Steenrod Homology: Applications To The Brown-Douglas-Fillmore Theory Of Operator Algebras, Jerome Kaminker, Claude Schochet

Mathematics Faculty Research Publications

The remarkable work of L. G. Brown, R. Douglas and P. Fillmore on operators with compact self-commutators once again ties together algebraic topology and operator theory. This paper gives a comprehensive treatment of certain aspects of that connection and some adjacent topics. In anticipation that both operator theorists and topologists may be interested in this work, additional background material is included to facilitate access.

K₁ Of The Compact Operators Is Zero, L. G. Brown, Claude Schochet

Mathematics Faculty Research Publications

We prove that K₁ of the compact operators is zero. This theorem has the following operator-theoretic formulation: any invertible operator of the form (identity) + (compact) is the product of (at most eight) multiplicative commutators (A_jB_jA_j⁻¹B_j⁻¹)^±1, where each B_j is of the form (identity) + (compact). The proof uses results of L. G. Brown, R. G. Douglas, and P. A. Fillmore on essentially normal operators and a theorem of A. Brown and C. Pearcy on multiplicative …

Theory Of Impurity-Induced Infrared Absorption In Cubic Crystals, S. S. Jaswal, J. M. Wadehra

Physics and Astronomy Faculty Research Publications

A method to calculate the infrared absorption due to a very low concentration of defects in a diatomic cubic crystal is developed directly from the basic absorption equation in quantum mechanics when the impurity produces changes in mass and short-range force constants. It is shown that the absorption is due to the modes of T_1u symmetry about the defect and is proportional to the square of the projection of the amplitudes of the ions in the defect space onto the transverse-optic modes at the zone center as determined by the perturbation. A procedure to calculate the amplitudes of …

Steenrod Homology And Operator Algebras, Jerome Kaminker, Claude Schochet

Mathematics Faculty Research Publications

The recent work of Larry Brown, R. G. Douglas, and Peter Fillmore on operator algebras has created a new bridge between functional analysis and algebraic topology. This note constitutes an effort to make that bridge more concrete.

On The Bordism Ring Of Complex Projective Space, Claude Schochet

Mathematics Faculty Research Publications

The bordism ring MU∗(CP^∞) is central to the theory of formal groups as applied by D. Quillen, J. F. Adams, and others recently to complex cobordism. In the present paper, rings E∗(CP^∞) are considered, where E is an oriented ring spectrum, R=π∗(E), and pR=0 for a prime p. It is known that E∗(CP^∞) is freely generated as an R-module by elements {β_τ|r≧0}. The ring structure, however, is not known. It is shown that the elements {β …