Physical Sciences and Mathematics Commons^™

Transformational Road Trip, John H. Whitmore

Science and Mathematics Faculty Publications

No abstract provided.

The Biblical Concepts Of Potentia Dei Ordinata And Potentia Dei Absoluta In The Development Of Chemistry, Aaron R. Hutchison

Science and Mathematics Faculty Publications

Medieval theologians spoke of the potentia Dei ordinata (the power of God expressed in the orderly working of nature) and the potentia Dei absoluta (the absolute power of God to intervene miraculously) (Kaiser 1997). Scientific creationists accept this understanding – we believe that God has ordained natural laws that result in a comprehensible natural world. But we recognize God is not bound by natural laws but can act miraculously, as when He spoke the world into existence. This understanding was also foundational not just for the development of science itself. It first appeared outside of the Bible in the Hexameron, …

Lithostratigraphic Correlation Of The Coconino Sandstone (Permian) And Its Equivalents, Western United States, John H. Whitmore

Science and Mathematics Faculty Publications

The purpose of this study was to correlate Upper Paleozoic sandstone bodies of Pennsylvanian and Permian ages across the western United States. The cross-bedded Coconino Sandstone (Arizona) is perhaps one of the best-known formations in this collection of sandstones, many of which contain large cross-beds and thus are often interpreted as eolian in origin (McKee and Bigarella 1979). The Coconino Sandstone (Leonardian) is found in northern Arizona in places like Sedona and Grand Canyon.

Stratigraphic columns were obtained from multiple sources including the AAPG’s COSUNA charts and data, the RMAG’s Geological Atlas of the Rocky Mountain Region, and published papers …

Conjugacy Of Embeddings Of Alternating Groups In Exceptional Lie Groups, Darrin D. Frey, Alex Ryba

Science and Mathematics Faculty Publications

We discuss conjugacy classes of embeddings of Alternating groups in Exceptional Lie groups. We settle the count of classes of embeddings in E8 of a subgroup Alt10 and its double cover. This involves computation and the reduction of the problems to relative eigenvector problems. We update previously published tables of embeddings. We comment on the improvements present in our table and on the remaining unsettled conjugacy questions.

On Comparability Of Bigrassmannian Permutations, John Engbers, Adam J. Hammett

Science and Mathematics Faculty Publications

No abstract provided.

I'Ve Got Your Number: A Multiple Choice Guessing Game, Ryan Cushman, Adam J. Hammett

Science and Mathematics Faculty Publications

We consider the following guessing game: fix positive integers k, m, and n. Player A ("Ann") chooses a (uniformly) random integer from the set {1,2,3,...,n}, but does not reveal it to Player B ("Gus"). Gus then presents Ann with a k-option multiple choice question about which number she chose, to which Ann responds truthfully. After m such questions have been asked, Gus must attempt to guess the number chosen by Ann. Gus wins if he guesses Ann's number. The purpose of this note is to find all canonical m-question algorithms which maximize the probability of Gus winning the game. An …

Young Earth Flood Geology In The Grand Canyon, John H. Whitmore

Science and Mathematics Faculty Publications

No abstract provided.

Penalized Spline Estimation In The Partially Linear Model, Ashley D. Holland

Science and Mathematics Faculty Publications

Penalized spline estimators have received considerable attention in recent years because of their good finite-sample performance, especially when many regressors are employed. In this paper, we propose a penalized B-spline estimator in the context of the partially linear model and study its asymptotic properties under a two-sequence asymptotics: both the number of knots and the penalty factor vary with the sample size. We establish asymptotic distributions of the estimators of both the parametric and nonparametric components in the model. In addition, as a previous step, we obtain the rate of convergence of the estimator of the regression function in a …

Effective Integration Of Ultra-Elliptic Solutions Of The Focusing Nonlinear Schrödinger Equation, Otis C. Wright Iii

Science and Mathematics Faculty Publications

An effective integration method based on the classical solution of the Jacobi inversion problem, using Kleinian ultra-elliptic functions and Riemann theta functions, is presented for the quasi-periodic two-phase solutions of the focusing cubic nonlinear Schrödinger equation. Each two-phase solution with real quasi-periods forms a two-real-dimensional torus, modulo a circle of complex-phase factors, expressed as a ratio of theta functions associated with the Riemann surface of the invariant spectral curve. The initial conditions of the Dirichlet eigenvalues satisfy reality conditions which are explicitly parametrized by two physically-meaningful real variables: the squared modulus and a scalar multiple of the wavenumber. Simple new …

Intraformational Parabolic Recumbent Folds In The Coconino Sandstone (Permian) And Two Other Formations In Sedona, Arizona (Usa), John Whitmore, Guy Forsythe, Paul A. Garner

Science and Mathematics Faculty Publications

We report sedimentary structures that in all ways resemble parabolic recumbent folds (PRFs) in the cross-bedded portions of the Schnebly Hill Formation, the Coconino Sandstone and the Toroweap Formation (Arizona, USA). Field evidence suggests they are penecontemporaneous and intraformational. Intraformational refers to deformation that occurs between undeformed beds. Recumbent cross-bed sets occur over a wide area (>375 km2 [144 mi2]) at many different locations and horizons in the Sedona area, especially within the Coconino Sandstone. Deformation resulting from slumping dunes (dry or damp) is ruled out because of the nature of the deformation along cross-bed dip, the size and …

The Petrology Of The Coconino Sandstone (Permian), Arizona, Usa, John Whitmore, Raymond Strom, Stephen Cheung, Paul A. Garner

Science and Mathematics Faculty Publications

The purpose of this paper is to give a description of the overall petrology of the Permian Coconino Sandstone that outcrops prominently in Arizona, including the Grand Canyon. The Coconino is often regarded as something like a “type” of the many similar Permian cross-bedded sandstones that occur around the world. It is generally accepted that the Coconino is an eolian sandstone and that its sand grains are well-sorted and well-rounded. However, until now, no detailed petrographic work has ever been published to substantiate these assumptions. We widely sampled the thickness and lateral extent of the formation and then studied hundreds …

Trivial Meet And Join Within The Lattice Of Monotone Triangles, Adam J. Hammett, John Engbers

Science and Mathematics Faculty Publications

The lattice of monotone triangles (�_n, ≼) ordered by entry-wise comparisons is studied. Let τ_min denote the unique minimal element in this lattice, and τ_max the unique maximum. The number of r-tuples of monotone triangles (τ₁...,τ_r) with minimul infimumτ_min (maximul supremum τ_max, resp.) is shown to asymptotically approach r|�_n|^r-1 asn→ ∞. Thus, with high probability this even implies that one of the τ_i is τ_min (τ_max, resp.). Higher-order error terms are also discussed.

Nociceptin Signaling Involves A Calcium-Based Depolarization In Tetrahymena Thermophila, Thomas Lampert, Sarah Nugent, John Weston, Nathanael Braun, Heather G. Kuruvilla

Science and Mathematics Faculty Publications

Tetrahymena thermophila are free-living, ciliated eukaryotes. Their behavioral response to stimuli is well characterized and easily observable, since cells swim toward chemoattractants and avoid chemorepellents. Chemoattractant responses involve increased swim speed or a decreased change in swim direction, while chemorepellent signaling involves ciliary reversal, which causes the organism to jerk back and forth, swim in small circles, or spin in an attempt to get away from the repellent. Many food sources, such as proteins, are chemoattractants for these organisms, while a variety of compounds are repellents. Repellents in nature are thought to come from the secretions of predators or from …

Initial Conditions For A Post-Flood Rapid Ice Age, Steven M. Gollmer

Science and Mathematics Faculty Publications

In the early years of the modern creationist movement questions were raised as to the role of ice ages in explaining geological data. Beginning with Whitcomb and Morris (1961) and formalized by Oard (1979), a proposed scenario of warm oceans and volcanic activity would provide the needed conditions to initiate a post-flood ice age. During the 1990’s Vardiman used the Community Climate Model (CCM) to study the impact of warm oceans on global air circulation and precipitation patterns. Following Vardiman’s lead this study uses the Goddard Institute of Space Studies (GISS) Model E climate model. The first part of the …

What Is The Eternal?, Steven M. Gollmer

Science and Mathematics Faculty Publications

Apologetics arguments related to the creation account in Genesis have ranged from evidential proofs for a young creation to the presuppositional consistency of the biblical worldview. Each of these arguments has its place, but the effectiveness varies depending on the audience’s background. A fundamental assumption for all arguments is that God exists and that he has purposefully communicated with his creation through special revelation. Those not holding this faith commitment resort to other answers that they feel are scientifically based. What they overlook are the faith commitments underlying their scientific answers. This paper poses the question “What is the Eternal?” …

Experimental And Theoretical Study Of Bound And Quasibound States Of Ce-, C. W. Walter, Lin Pan, N. D. Gibson, Y.-G. Li, D. J. Matyas, R. M. Alton, S. E. Lou, R. L. Field, D. Hanstorp, Donald R. Beck

Science and Mathematics Faculty Publications

The negative ion of cerium is investigated experimentally with tunable infrared laser photodetachment spectroscopy and theoretically with relativistic configuration interaction in the continuum formalism. The relative cross section for neutral atom production is measured with a crossed ion-beam–laser-beam apparatus over the photon energy range of 0.54–0.75 eV. A rich resonance spectrum is revealed near the threshold with, at least, 12 peaks observed due to transitions from bound states of [formula] to either bound or quasibound excited states of the negative ion. Theoretical calculations of the photodetachment cross sections enable identification of the transitions responsible for the measured peaks. Two of …

Percolating Oxide Film Growth During Cu(111) Oxidation, David M. Gallagher

Science and Mathematics Faculty Publications

We report in situ transmission electron microscopy dynamic observations of the early stage oxidation of Cu(111) surfaces at ∼450 °C, which show that the Cu2O filmmorphology evolves with continued oxidation from initially ramified islands to irregularly connected clusters. The geometrical features of these noncompact oxidefilms are analyzed in terms of the scaling theory of percolation. We show by kinetic Monte Carlo simulations that the percolating oxide film growth is related to a mechanism of neighbor-dependent site percolation.

Modeling Biochemical Processes As Designed Systems, Steven M. Gollmer

Science and Mathematics Faculty Publications

Being in the post-genomic era, there is a need for new methodologies from an interdisciplinary perspective, which can complement current genomics research. Bioinformatics and systems biology are rapidly growing research areas that are meeting this need. Operating with the assumption that there is design with a purpose, creationists provide a unique perspective for discovering order in the complexity of genes, regulatory networks, and biochemical reactions.

Since the genome acts as an information storage system, it seems reasonable to apply design concepts, originating from computer and network programming, to make sense of genomic information. One such concept is that of design …

Meet And Join In The Weak Order Lattice, Adam J. Hammett, Boris Pittel

Science and Mathematics Faculty Publications

No abstract provided.

On Powers Of 2 Dividing The Values Of Certain Plane Partition Functions, Darrin D. Frey, James A. Sellers

Science and Mathematics Faculty Publications

We consider two families of plane partitions: totally symmetric self-complementary plane partitions (TSSCPPs) and cyclically symmetric transpose complement plane partitions (CSTCPPs). If T(n) and C(n) are the numbers of such plane partitions in a 2n × 2n × 2nbox, then

ord₂(T(n)) = ord₂(C(n))

for all n >= 1. We also discuss various consequences, along with other results on ord₂(T(n)).

Generalizing Bailey's Generalization Of The Catalan Numbers, Darrin D. Frey, James A. Sellers

Science and Mathematics Faculty Publications

No abstract provided.

Jacobsthal Numbers And Alternating Sign Matrices, Darrin D. Frey, James A. Sellers

Science and Mathematics Faculty Publications

Let A(n) denote the number of n×n alternating sign matrices and J_m the m^thJacobsthal number. It is known that

A(n) = n-1 Õ l = 0 (3l+1)!(n+l)! .

The values of A(n) are in general highly composite. The goal of this paper is to prove that A(n) is odd if and only if n is a Jacobsthal number, thus showing that A(n) is odd infinitely often.

Convexity Properties Of Holomorphic Mappings In CN, Kevin A. Roper, T. J. Suffridge

Science and Mathematics Faculty Publications

Not many convex mappings on the unit ball in Cⁿ for n > 1 are known. We introduce two families of mappings, which we believe are actually identical, that both contain the convex mappings. These families which we have named the "Quasi-Convex Mappings, Types A and B" seem to be natural generalizations of the convex mappings in the plane. It is much easier to check whether a function is in one of these classes than to check for convexity. We show that the upper and lower bounds on the growth rate of such mappings is the same as for the …

Tribological Characteristics Of Perfluoropolyether Liquid Lubricants Under Sliding Conditions In High Vacuum, Masabumi Masuko, William R. Jones Jr, Larry S. Helmick

Science and Mathematics Faculty Publications

Tribological characteristics of three PFPE's (Fomblin Z, Demnum, and Krytox) were studied under high vacuum using a four-ball apparatus with 440C steel specimens. Fomblin Z and Demnum exhibited initial scuffing-like high friction whereas Krytox did not. Steady state friction with Fomblin Z was the lowest among the three oils. Frictional values for Demnum and Krytox were almost the same. The lowest wear rate in air was provided by Krytox regardless of load, and low wear rates in vacuum at high load were achieved with Krytox and Demnum. Results are explained by reactivity and pressure-viscosity characteristics of the oils.

How Old Is The Earth?, Larry S. Helmick, Donald Baumann

Science and Mathematics Faculty Publications

No abstract provided.

Determination Of The Oxidative Stability Of Perfluoropolyalkyl Ethers And Correlation With Chemical Structure, Larry S. Helmick, William R. Jones Jr

Science and Mathematics Faculty Publications

The oxidative stabilities of several perfluoropolyalkyl ethers (PFPAE) with related chemical structures were determined by thermal gravimetric analysis and correlated with their chemical structures. These results show that oxidative stability increases as the number of difluoroformal groups decreases and as trifluoromethyl substituents are added. They are also consistent with a recently proposed intramolecular disproportionation reaction mechanism involving coordination of successive ether oxygens to a Lewis acid. Since polytetrafluoroethylene contains no oxygen, it provides an indication of the upper limit to oxidative stability of PFPAE fluids. These results also show that oxidative decomposition of PFPAE fluids requires the presence of an …

Determination Of The Thermal Stability Of Perfluoropolyalkyl Ethers By Tensimetry, Larry S. Helmick, William R. Jones Jr

Science and Mathematics Faculty Publications

The thermal decomposition temperatures of several perfluoropolyalkyl ether fluids were determined with a computerized tensimeter. In general, the decomposition temperatures of the commercial fluids were all similar and significantly higher than those for noncommercial fluids. Correlation of the decomposition temperatures with the molecular structures of the primary components of the commercial fluids revealed that the stability of the fluids was not affected by carbon chain length, branching, or adjacent difluoroformal groups. Instead, stability was limited by the presence of small quantities of thermally unstable material and/or chlorine-containing material arising from the use of chlorine containing solvents during synthesis. Finally, correlation …

Determination Of The Thermal Stability Of Perfluoroalkylethers, Larry S. Helmick, William R. Jones Jr

Science and Mathematics Faculty Publications

The thermal decomposition temperatures of several commercial and custom synthesized perfluoroalkylether fluids were determined with a computerized tensimeter. In general, the decomposition temperatures of the commercial fluids were all similar and significantly higher than those for custom synthesized fluids. Correlation of the decomposition temperatures with the molecular structures of the primary components of the commercial fluids revealed that the stability of the fluids is not affected by intrinsic factors such as carbon chain length, branching, or cumulated difluoroformal groups. Instead, correlation with extrinsic factors revealed that the stability may be limited by the presence of small quantities of thermally unstable …

Determination Of The Thermal Stability Of Perfluoroalkylethers By Tensimetry: Instrumentation And Procedure, Larry S. Helmick, William R. Jones

Science and Mathematics Faculty Publications

A computerized tensimeter and experimental procedure for determination of the thermal decomposition temperature (Td) of perfluoroalkylethers have been developed and tested. Both the I+ m apparatus and the procedure are described in detail. Results of QU) testing with bis(2-ethylhexyl) phthlalate and trimethylolpropane wI triheptanoate demonstrate that the reciprocal of the decomposition temperature is a linear function of the logarithm of the gas volume/heated liquid volume ratio. The Td obtained for each compound at a gas volume/heated liquid volume ratio of one was similar to the value previously reported using an isoteniscope technique. Results of testing with a polymer of hexafluoropropylene …

Estimates Of Maximum Past Overburden For The Pierre Shale, Hayes Area, South Dakota, Thomas L. Rice

Science and Mathematics Faculty Publications

The Pierre Shale of the Northern Great Plains area of the United State is an Upper Cretaceous shale which was deposited in a marine environment. Geotechnically, the shale has been classified as an overconsolidated clay-shale. In South Dakota the Pierre Shale crops out extensively in the central and western portions of the state.

In this study an investigation was conducted for the purpose of clarifying and examining the existence of a discrepancy between geotechnically and geologically derived estimates of maximum past overburden for the Pierre Shale at Hayes, South Dakota.

The geological determination involved examining the topographic high points of …