Physical Sciences and Mathematics Commons^™

Three-Body Analytical Potential For Interacting Helium Atoms, Carol A. Parish, Clifford E. Dykstra

Chemistry Faculty Publications

Large basis set ab initio calculations have been carried out for a dense grid of points on the He, potential energy surface. Three-body contributions were extracted at every point, and a number of concise functional representations for the three-body potential surface were then examined. Three-body multipolar dispersion terms and other radial and angular terms were used in the representations, and an assessment of relative importance of the different terms is presented. Combined with a two-body He-He potential, the results of this work should offer a high quality interaction potential for simulations of aggregated helium.

A Macro Extension For The Woody Assembly Language, Lewis Barnett Iii

Department of Math & Statistics Technical Report Series

We discuss an extension to the Woody Assembly Language [Cha94] which allows new instructions to be defined. The mechanism is similar to the C language's #define macros, allowing a name to be supplied for a piece of code which will be expanded in line. Provisions are made for writing new non-destructive branching instructions as well as instructions which are simply new names for commonly used bits of code.

Partial Difference Sets In P-Groups, James A. Davis

Department of Math & Statistics Faculty Publications

Most of the examples of PDS have come in p-groups, and most of these examples are in elementary abelian p-groups. In this paper, we will show an exponent bound for PDS with the same parameters as the elementary abelian case.

Bergman Spaces On An Annulus And The Backward Bergman Shift, William T. Ross

Department of Math & Statistics Technical Report Series

In this paper, we will give a complete characterization of the invariant subspaces M (under ƒ → zƒ) of the Bergman space L^p_a(G), 1 < p < 2, G an annulus, which contain the constant function 1. As an application of this result, we will characterize the invariant subspaces of the adjoint of multiplication by z on the Dirichlet spaces D_q, q > 2, as well as the invariant subspaces of the backward Bergman shift ƒ → (ƒ – ƒ(0))/z on L^p_a(𝔻), 1 < p < 2.

Bergman Spaces On Disconnected Domains, Alexandru Aleman, Stefan Richter, William T. Ross

Department of Math & Statistics Technical Report Series

For a bounded region G ⊂ ℂ and a compact set K ⊂G , with area measure zero, we will characterize the invariant subspaces M (under ƒ → z ƒ) of the Bergman space L^p_a(G\K), 1 ≤ p < ∞, which contain L<sup>p_a(G) and with dim(M/(z-⋋)M) = 1 for all ⋋ ∈ G\K. When G\K is connected, we will see that dim(M/(z-⋋)M) = 1 for all ⋋ ∈ G\K and this in this case we will have a complete …

A Construction Of Difference Sets In High Exponent 2-Groups Using Representation Theory, James A. Davis, Ken Smith

Department of Math & Statistics Faculty Publications

Nontrivial difference sets in groups of order a power of 2 are part of the family of difference sets called Menon difference sets (or Hadamard), and they have parameters (2^2d+2, 2^2d+1 ±2^d, 2^2d±2^d). In the abelian case, the group has a difference set if and only if the exponent of the group is less than or equal to 2^d+2. In [14], the authors construct a difference set in a nonabelian group of order 64 and exponent 32. This paper generalizes that result to …

A Topology-Aware Collision Resolution Algorithm, Lewis Barnett Iii

Department of Math & Statistics Technical Report Series

A new collision resolution algorithm called the Space Division Multiple Access protocol (SDMA) is presented. SDMA gains a performance advantage over similar protocols by using information about the positions of stations on the network. The protocol can operate asynchrononsly on a broadcast bus, allowing variable sized packet traffic. Through simulation the protocol is demonstrated to have better performance than Ethernet and the Capetanakis Tree protocol, a similar collision resolution protocol, under some traffic conditions. In particular, under heavy loads, SDMA displays better average throughput and lower variance of delay than Ethernet. The protocol demonstrates a performance bias based on the …

An Algorithmic Palette Tool, Gary R. Greenfield

Department of Math & Statistics Technical Report Series

Our algorithmic tool follows the model of RGB percentage curves, but now the control of these curves is though algorithms that indirectly, and more abstractly, create, evolve, and modify such curves. To fully explain our methods we must first introduce the topic "mutating expressions." This is done in Section Two. In Section Three we document the user-interface problems we dealt with, and finally in Section Four discuss conclusions and suggest ideas for future exploration. Before commencing with the technical details however, we wish to emphasize the nature of the "colorization" problem that led to the conception and development of our …

Analytic Besov Spaces And Invariant Subspaces Of Bergman Spaces, William T. Ross

Department of Math & Statistics Faculty Publications

In this paper, we examine the invariant subspaces (under the operator f -->z f) M of the Bergman space ^p_a (G\T) (where 1 < p < 2, G is a bounded region in C containing D, T is the unit circle, and D is the unit disk) which contain the characteristic functions x_D and x_G, i.e. the constant functions on the components of G\T. We will show that such M are in one-to-one correspondence with the invariant subspaces of the analytic Besov space AB_q (q is the conjugate index to p) and …

Invariant Subspaces Of Bergman Spaces On Slit Domains, William T. Ross

Department of Math & Statistics Faculty Publications

In this paper, we characterize the z-invariant subspaces that lie between the Bergman spaces A^p(G) and A^p(G\K), where 1 < p < ∞, G is a bounded region in C, and K is a closed subset of a simple, compact, C¹ arc.

Determination Of A Potential From Cauchy Data: Uniqueness And Distinguishability, Lester Caudill

Department of Math & Statistics Faculty Publications

The problem of recovering a potential q(y) in the differential equation:

−∆u + q(y)u = 0 (x,y) &∈ (0, 1) × (0,1)
u(0, y) = u(1, y) = u(x, 0) = 0
u(x, 1) = f(x), u_y(x, 1) = g(x)

is investigated. The method of separation of variables reduces the recovery of q(y) to a non-standard inverse Sturm-Liouville problem. Employing asymptotic techniques and integral operators of Gel'fand-Levitan type, it is shown that, under appropriate conditions on the Cauchy pair (f, g ), q(y) is uniquely determined, in a local sense, up to its mean. We characterize …

Hyperinvariant Subspaces Of The Harmonic Dirichlet Space, William T. Ross, Stefan Richter, Carl Sundberg

Department of Math & Statistics Faculty Publications

No abstract provided.

A Direct Method For The Inversion Of Physical Systems, Lester Caudill, Herschel Rabitz, Attila Askar

Department of Math & Statistics Faculty Publications

A general algorithm for the direct inversion of data to yield unknown functions entering physical systems is presented. Of particular interest are linear and non-linear dynamical systems. The potential broad applicability of this method is examined in the context of a number of coefficient-recovery problems for partial differential equations. Stability issues are addressed and a stabilization approach, based on inverse asymptotic tracking, is proposed. Numerical examples for a simple illustration are presented, demonstrating the effectiveness of the algorithm.

An Invariant Subspace Problem For P = 1 Bergman Spaces On Slit Domains, William T. Ross

Department of Math & Statistics Faculty Publications

In this paper, we characterize the z-invariant subspaces that lie between the Bergman spaces A¹(G) and A¹(G/K), where G is a bounded region in the complex plane and K is a compact subset of a simple arc of class C¹.

Merlin's Magic Square Enhanced, Gary R. Greenfield

Department of Math & Statistics Technical Report Series

This paper first considers questions about games related to Merlin's Magic Square from the point of view of group actions. At this juncture, little beyond the formal model is new, but the exposition sets the stage for considering certain "enhanced" versions of these games. The analysis of enhanced games, with the aid of semigroup actions, is carried out in complete detail for an ostensibly simpler (k = 3) game before turning to a Merlin ( k = 4) game. Concluding sections discuss various ways to generalize our games.

To review the solution to Merlin's Magic Square, we begin by introducing …