Physical Sciences and Mathematics Commons^™

Additive Comparisons Of Stop Rule And Supremum Expectations Of Uniformly Bounded Independent Random Variables, Theodore P. Hill, Robert P. Kertz

Research Scholars in Residence

Let X_I, X₂, . . . be independent random variables taking values in [a, b], and let T denote the stop rules for X₁, X₂, Then E(sup_n>1 X_n) - sup{ EX_t t ≡ T} < (1/4)(b - a), and this bound is best possible. Probabilistically, this says that if a prophet (player with complete foresight) makes a side payment of (b - a)/8 to a gambler (player using nonanticipating stop rules), the game becomes at least fair for the gambler.

Comparative Properties Of Old- And Young-Growth Giant Sequoia Of Potential Significance To Wood Utilization, Douglas D. Piirto, W. Wayne Wilcox

Natural Resources Management and Environmental Sciences

A comparative study and a literature review were made on various wood properties (e.g. anatomical characteristics, mechanical properties, specific gravity, content and properties of extractives and decay resistance) of old- and young-growth giant sequoia. Various causes for variability in decay resistance were examined.

Magnetotactic Bacteria At The Geomagnetic Equator, Richard B. Frankel, R. P. Blakemore, F. F. Torres De Araujo, D. M. S. Esquivel, J. Danon

Physics

Magnetotactic bacteria are present in fresh water and marine sediments of Fortaleza, Brazil, situated close to the geomagnetic equator. Both South-seeking and North-seeking bacteria are present in roughly equal numbers in the same samples. This observation is consistent with the hypothesis that the vertical component of the geomagnetic field selects the predominant polarity type among magnetotactic bacteria in natural environments.

Ratio Comparisons Of Supremum And Stop Rule Expectations, Theodore P. Hill, Robert P. Kertz

Research Scholars in Residence

Suppose X₁,X₂,...,X_n are independent non-negative random variables with finite positive expectations. Let T_n denote the stop rules for X₁,...,X_n. The main result of this paper is that E(max{X₁,...,X_n }) sup{EX_t t ε T_n }. The proof given is constructive, and sharpens the corresponding weak inequalities of Krengel and Sucheston and of Garling.

The (Q, R)-Simon Newcomb Problem, Don Rawlings

Mathematics

A new statistic, the r-major index, is defined for sequences. A linear recurrence is then derived that enumerates sequences by r-descent number and r-major index.

The R-Major Index, Don Rawlings

Mathematics

The r-major index is a new permutation statistic that is suggested by the work of Carlitz and Gausner on Foulkes' skew hook rule for computing the r-Eulerian numbers. The new statistic (1) generalizes both the major index and the inversion number of a permutation and (2) leads to a q-analog of the r-Eulerian numbers.

Generalized Worpitzky Identities With Applications To Permutation Enumeration, Don Rawlings

Mathematics

The enumeration of permutations by inversions often leads to a q -analog of the usual generating function. In this paper, two generalizations of the Worpitzky identity for the Eulerian numbers are obtained and used to enumerate permutations by the descent number and the major index of their inverses. The resulting (t, q)-generating series do in fact generalize the q-series obtained when counting by inversions.

Quasi-Extended Asymptotic Functions, Todor D. Todorov

Mathematics

The class F of "quasi-extended asymptotic functions" introduced in the present paper contains all extended asymptotic functions [8, (3.1)] (in particular, all examples constructed in [9, Sec. 1 ]). But F contains also some new asymptotic functions very similar to tht Schwartz distributions. On the other hand, every two quasi-extended asymptotic functions can be multiplied as opposed to the Schwartz distributions; in particular, the square &# 948;² of an asymptotic function &# 948; similar to Dirac's delta-function is constructed as an example. The connection with the asymptotic functions introduced in [2] and [4] is established.

Asymptotic Functions And The Problem Of Multiplication Of Distributions, Todor D. Todorov

Mathematics

The asymptotic functions are a new type of generalized functions. But they are not functionals on some space of test-functions as the Schwartz distributions. They are mappings of the set of the asymptotic numbers (1, 3, 5, 6) into itself. On its part, the set of the asymptotic numbers is a totally-ordered set of generalized numbers including the systems of real and complex numbers, as well as infinitesimals and infinitely large numbers. Every two asymptotic functions can be multiplied. On the other hand, the Schwartz distributions have realizations, in a certain sense, as asymptotic functions. The motivations of this work …

Mossbauer Spectroscopy Of Iron-Containing Dermal Granules From Molpadia Intermedia, S. Ofer, G. C. Papaefthymiou, R. B. Frankel, H. A. Lowenstam

Physics

Dermal granules containing hydrous ferric oxide cores from Molpadia intermedia were studied by Mössbauer spectroscopy from 1.5 t0 300 K and in magnetic fields up to 80 kOersted at 4.2 K. A magnetic phase transition to an antiferromagnetically ordered state is observed at 10 K. The results are compared with the magnetic behavior of micellar cores of ferritin from eukaryotes and iron-storage materials from prokaryotes.

Study Of Iron In Magnetotactic Bacteria, Richard B. Frankel, Richard P. Blakemore

Physics

Bacteria have recently been discovered directing their movements by sensing the earth's magnetic field. They contain arrays of crystals of lodestone or magnetite which they synthesize from iron in the ocean. The discovery of the same type of crystals in the abdomens of honey bees and the brains of homing pigeons suggests that nature is not oblivious to the earth's magnetic field. The biological mechanism for sensing magnetic fields has never been determined. These bacteria are capable of biologically synthesizing highly purified single domain magnets that would be very expensive to produce chemically.

The tiny perfect magnetite crystals made by …