Physical Sciences and Mathematics Commons^™

The Quaternary Bone Caves And Associated Sites At Wallingford, Jamaica, Donald A. Mcfarlane, R. E. Gledhill

WM Keck Science Faculty Papers

A group of caves associated with the sink of the One Eye River in St. Elizabeth Parish, Jamaica, have been the subject of numerous important palaeontological investigations beginning 1919. Unfortunately, considerable confusion has arisen in the literature through inadequate documentation of different sites. The caves of the immediate area are described and located, and their palaeontological significance is summarised in the light of recent taxonomic review and relevant geochronological evidence.

Infinitely Periodic Knots, Erica Flapan

Pomona Faculty Publications and Research

One aspect of the study of 3-manifolds is to determine what infinite group actions a given manifold has. Some important questions that one can ask about these actions on a given manifold are: What periods could they have? and, what sets of points may be fixed by the action?

Some Graph-Colouring Theorems With Applications To Generalized Connection Networks, David G. Kirkpatrick, Maria M. Klawe, Nicholas Pippenger

All HMC Faculty Publications and Research

With the aid of a new graph-colouring theorem, we give a simple explicit construction for generalized n-connectors with 2k - 1 stages and O( n^{1 + 1 / k} (log n )^{( k - 1)/ 2} ) edges. This is asymptotically the best explicit construction known for generalized connectors.

A Model For Orientation Effects In Electron‐Transfer Reactions, Paul Siders, Robert J. Cave, R.A. Marcus

All HMC Faculty Publications and Research

A method for solving the single‐particle Schrödinger equation with an oblate spheroidal potential of finite depth is presented. The wave functions are then used to calculate the matrix element T_BA which appears in theories of nonadiabatic electron transfer. The results illustrate the effects of mutual orientation and separation of the two centers on T_BA. Trends in these results are discussed in terms of geometrical and nodal structure effects. Analytical expressions related to T_BA for states of spherical wells are presented and used to analyze the nodal structure effects for T_BA for the spheroidal wells.

Simulated Performance Of A Reduction-Based Multiprocessing System, Robert M. Keller, Frank C. H. Lin

All HMC Faculty Publications and Research

Multiprocessing systems have the potential for increasing system speed over what is now offered by device technology. They must provide the means of generating work for the processors, getting the work to processors, and coherently collecting the results from the processors. For most applications, they should also ensure the repeatability of behavior, i.e., determinacy, speed-independence, or elimination of "critical races." Determinacy can be destroyed, for example, by permitting-in separate, concurrent processes statements such as "x: = x + 1" and "if x = 0 then… else…", which share a common variable. Here, there may be a critical race, in that …

Group Comparability: A Multiattribute Utility Measurement Approach To The Use Of Random Assignment With Small Numbers Of Aggregated Units, C. Anderson Johnson, John W. Graham, Brian R. Flay, William B. Hansen, Linda M. Collins

CGU Faculty Publications and Research

It is not always possible, especially in large-scale evaluation research, to ensure that random assignment will produce groups that are comparable on any number of potentially important factors. Typically, gaining comparability has been achieved only at the expense of random assignment. A method is presented that allows multivariate comparability while making only minimal restrictions on randomization. The procedure is demonstrated in the context of assigning 63 aggregated units (schools) to 28 experimental and control conditions. Good comparability of groups for all primary main effects and interactions was verified for 15 individual variables.

Rediflow Multiprocessing, Robert M. Keller, Frank C. H. Lin, Jiro Tanaka

All HMC Faculty Publications and Research

We discuss the concepts underlying Rediflow, a multiprocessing system being designed to support concurrent programming through a hybrid model of reduction, dataflow, and von Neumann processes. The techniques of automatic load-balancing in Rediflow are described in some detail.

Alkali Oxides. Analysis Of Bonding And Explanation Of The Reversal Of Ordering Of The 2Σ And 2Π States, Janet N. Allison, Robert J. Cave, William A. Goddard Iii

All HMC Faculty Publications and Research

We analyze the bonding in alkali oxides, MO, for M = Li, Na, K, Rb, and Cs. Using ab initio correlated wave functions we find that the ground state is ²II for M = Li, Na, and K and that the ground state is ²Ʃ^+ for M = Rb and Cs. The origin of this effect is explained.

Uniqueness Of Positive Solutions For A Class Of Elliptic Boundary Value Problems, Alfonso Castro, Ratnasingham Shivaji

All HMC Faculty Publications and Research

Uniqueness of non-negative solutions conjectured in an earlier paper by Shivaji is proved. Our methods are independent of those of that paper, where the problem was considered only in a ball. Further, our results apply to a wider class of nonlinearities.

On Monotone Formulae With Restricted Depth, Maria M. Klawe, Wolfgang J. Paul, Nicholas J. Pippenger, Mihalis Yannakakis

All HMC Faculty Publications and Research

We prove a hierarchy theorem for the representation of monotone Boolean functions by monotone Boolean functions by monotone formulae with restricted depth. Specifically, we show that there are functions with Π_k-formulae of size n for which every Σ_k-formula has size exp Ω(n^1/(k-1)). A similar lower bound applies to concrete functions such as transitive closure and clique. We also show that any function with a formula of size n (and any depth) has a Σ_k-formula of size exp O(n^1/(k-1)). Thus our hierarchy theorem is the best possible.

Consistency Testing For Data-Flow Circuits, Chu S. Jhon, Robert M. Keller

All HMC Faculty Publications and Research

One means of making VLSI design tractable is to proceed from a high-level specification of a circuit in terms of functionality, to the circuit level. A notable error which may occur in a topdown design starting with a data-flow graph representation of a circuit is a design inconsistency due to deadlock. This paper attempts to further develop the theoretical basis for algorithms which analyze the deadlock property of circuits on the basis of their data-flow graph representations. A systematic scheme to verify the absence of deadlock in data-flow graphs is also presented.

Specification Of Synchronizing Processes, Krithivasan Ramamritham, Robert M. Keller

All HMC Faculty Publications and Research

The formalism of temporal logic has been suggested to be an appropriate tool for expressing the semantics of concurrent programs. This paper is concerned with the application of temporal logic to the specification of factors affecting the synchronization of concurrent processes. Towards this end, we first introduce a model for synchronization and axiomatize its behavior. SYSL, a very high-level language for specifying synchronization properties, is then described. It is designed using the primitives of temporal logic and features constructs to express properties that affect synchronization in a fairly natural and modular fashion. Since the statements in the language have intuitive …

The Changing Concept Of Change: The Derivative From Fermat To Weierstrass, Judith V. Grabiner

Pitzer Faculty Publications and Research

Historically speaking, there were four steps in the development of today's concept of the derivative, which I list here in chronological order. The derivative was first used; it was then discovered; it was then explored and developed; and it was finally defined. That is, examples of what we now recognize as derivatives first were used on an ad hoc basis in solving particular problems; then the general concept lying behind them these uses was identified (as part of the invention of calculus); then many properties of the derivative were explained and developed in applications both to …

Who Gave You The Epsilon? The Origins Of Cauchy's Rigorous Calculus, Judith V. Grabiner

Pitzer Faculty Publications and Research

This paper recounts the history of how calculus came to get a rigorous basis in terms of the algebra of inequalities. The result is a brief history of the 150 years from Newton and Leibniz to Cauchy that produced the foundations of analysis.

On Determinism Versus Non-Determinism And Related Problems, Wolfgang J. Paul, Nicholas Pippenger, Endre Szemeredi, William T. Trotter

All HMC Faculty Publications and Research

We show that, for multi-tape Turing machines, non-deterministic linear time is more deterministic Turing machines (that receive their input on their work tape) require time Q(n2) to powerful than deterministic linear time. We also recognize non-palindromes of length n (it is easy to discuss the prospects for extending this result to see that time O(n log n) is. sufficient for a more general Turing machines. non-deterministic machine). 1. Introduction

Course Syllabus: Perspectives On Computers And Society, Judith V. Grabiner

Pitzer Faculty Publications and Research

Weizenbaum's statement is a compelling exhortation to his fellow professionals; nevertheless, I cannot wholly agree. It should be possible for nonprofessionals to understand, as a result of their own reading and experience, how computers interact with the rest of human life. The problems are not just technical, and their nature is not entirely unprecedented.

Data Flow Program Graphs, Alan L. Davis, Robert M. Keller

All HMC Faculty Publications and Research

Data flow languages form a subclass of the languages which are based primarily upon function application (i.e., applicative languages). By data flow language we mean any applicative language based entirely upon the notion of data flowing from one function entity to another or any language that directly supports such flowing. This flow concept gives data flow languages the advantage of allowing program definitions to be represented exclusively by graphs. Graphical representations and their applications are the subject of this article.

Reduction Methods Via Minimax, Alfonso Castro

All HMC Faculty Publications and Research

Lecture notes in mathematics originally published in Differential Equations book series.

On Multiple Solutions Of Nonlinear Elliptic Equations With Odd Nonlinearities, Alfonso Castro, J. V. A. Gonçalves

All HMC Faculty Publications and Research

In this paper we stablish results on multiplicity of solutions for the boundary value problem where a e IR and f: R - IR is an odd continuous function.

Sums Of Z-Ideals And Semiprime Ideals, Melvin Henriksen, Frank A. Smith

All HMC Faculty Publications and Research

If B is a ring (or module), and K is an ideal (or submodule) of B, let B(K) = {(a,b) є B x B:a-b є K}. The relationship between ideals (or submodules) of B and those of B(K) is examined carefully, and this construction is used to find a lattice-ordered subring of the ring C(R) of all continuous real-valued functions on the real line R with two z-ideals whose sum is not even semiprime.

Results On Periodic Solutions Of Parabolic Equations Suggested By Elliptic Theory, Alfonso Castro, A. C. Lazer

All HMC Faculty Publications and Research

No abstract provided.

Probabilistic Simulations, Nicholas J. Pippenger

All HMC Faculty Publications and Research

The results of this paper concern the question of how fast machines with one type of storage media can simulate machines with a different type of storage media. Most work on this question has focused on the question of how fast one deterministic machine can simulate another. In this paper we shall look at the question of how fast a probabilistic machine can simulate another. This approach should be of interest in its own right, in view of the great attention that probabilistic algorithms have recently attracted.

Rearrangeable Networks With Limited Depth, Nicholas Pippenger, Andrew C.-C. Yao

All HMC Faculty Publications and Research

Rearrangeable networks are switching systems capable of establishing simultaneous independent communication paths in accordance with any one-to-one correspondence between their n inputs and n outputs. Classical results show that Ω( n log n ) switches are necessary and that O( n log n ) switches are sufficient for such networks. We are interested in the minimum possible number of switches in rearrangeable networks in which the depth (the length of the longest path from an input to an output) is at most k, where k is fixed as n increases. We show that Ω( n^{1 + 1/k} ) switches …

Some Properties Of Positive Derivations On F-Rings, Melvin Henriksen, Frank A. Smith

All HMC Faculty Publications and Research

Throughout A denotes an f-ring; that is, a lattice-ordered ring that is a subdirect union of totally ordered rings. We let D(A) denote the set of derivations D: A --> A such that a ≥ 0 implies Da ≥ 0, and we call such derivations positive. In [CDK], P. Coleville, G. Davis, and K. Keimel initiated a study of positive derivations on f-rings. Their main results are (i) D ε D(A) and A archimedean imply D = 0, and (ii) if A has an identity element 1 and a is the supremum of a set …

Specifying And Proving Properties Of Sentinels, Krithivasan Ramamritham, Robert M. Keller

All HMC Faculty Publications and Research

This paper presents a technique for specifying and verifying properties of "sentinels," a high-level language construct for synchronizing access to shared resources. Statements in the specification language possess formal temporal semantics. As a prelude to proving the correctness of sentinels, the semantics of constructs used in sentinels is given. The proof technique involves showing that the temporal behavior of a sentinel conforms to that defined by the specification. The methodology is illustrated by applying it to a typical synchronization problem.

The Design Of Oxygen Rebreather Equipment For Use In Foul-Air Speleology, Donald A. Mcfarlane

WM Keck Science Faculty Papers

The design of a lightweight oxygen rebreather set suitable for short duration explorations in foul-air caves is described, together with a discussion of its performance, limitations, and possible improvement.

Algebraic Complexity Theory, Nicholas Pippenger

All HMC Faculty Publications and Research

Algebraic complexity theory, the study of the minimum number of operations sufficient to perform algebraic computations, is surveyed with emphasis on the general theory of bilinear forms and two of its applications: polynomial multiplication and matrix multiplication. Though by no means exhausting algebraic complexity theory, these topics illustrate well its development and its methods, and provide examples of its most striking successes.

Bounds On The Performance Of Protocols For A Multiple-Access Broadcast Channel, Nicholas Pippenger

All HMC Faculty Publications and Research

A general model is presented for synchronous protocols that resolve conflicts among message transmissions to a multiple-access broadcast channel. An information-theoretic method is used now to show that if only finitely many types of conflicts can be distinguished by the protocol, utilization of the channel at rates approaching capacity is impossible. A random-coding argument is used to show that if the number of conflicting transmissions can be determined (which requires distinguishing infinitely many types of conflicts) then utilization of the channel at rates arbitrarily close to capacity can be achieved.

On Periodic Solutions Of Weakly Coupled Systems Of Differential Equations, Alfonso Castro, A. C. Lazer

All HMC Faculty Publications and Research

No abstract provided.

Existence And Uniqueness For A Variational Hyperbolic System Without Resonance, Peter W. Bates, Alfonso Castro

All HMC Faculty Publications and Research

In this paper, we study the existence of weak solutions of the problem

□u + ∇G(u) = f(t,x) ; (t,x) є Ω ≡ (0,π)x(0,π)

u(t,x) = 0 ; (t,x) є ∂Ω

where □ is the wave operator ∂²/∂t² - ∂²/∂x², G: Rⁿ→R is a function of class C² such that ∇G(0) = 0 and f:Ώ→R^n is a continuous function having first derivative with respect to t in (L₂,(Ω))ⁿ and satisfying

f(0,x) = f(π,x) = 0

for all x є [0,π].