A product of Gamma function values at fractions with the same denominator (2009)
Let D(n) be the set of all fractions in the unit interval whose denominator in lowest terms equals $n$. We evaluate the product of the values of the Gamma function at the points of D(n), as a...
Martin, Greg, Brunkhorst, Frank M, Janes, Jonathan M, Reinhart, Konrad, Sundin, David P, Garnett, Kassandra, ...
Abstract Introduction Since the launch of drotrecogin alfa activated (DrotAA), institutions and individual countries have published data on its use in clinical practice, based on audit or registry...
A Diophantine $m$-tuple is a set $A$ of $m$ positive integers such that $ab+1$ is a perfect square for every pair $a,b$ of distinct elements of $A$. We derive an asymptotic formula for the number of...
The bioscience revolution & the biological weapons threat: levers & interventions (2009)
D'Agostino, Mark, Martin, Greg
Abstract In December 2008, the US Commission on the Prevention of Weapons of Mass Destruction Proliferation and Terrorism, released a report, World At Risk . The Report points to the fact that, not...
Global health: where are our priorities? (2009)
Martin, Greg, Bird, Philippa, Crichton, Claire
The subject of ‘global health’ can be considered from multiple points of view. While epidemiologists might describe global health problems in categories of pathology groups, social scientists...
FARMER TED GOES NATURAL (2008)
Greg Martin, Setting The Stage
We’ve all been given a problem in a calculus class remarkably similar to the following one: Farmer Ted is building a chicken coop. He decides he can spare 190 square feet of his land for the coop,...
The number of 2x2 integer matrices having a prescribed integer eigenvalue (2008)
Random matrices arise in many mathematical contexts, and it is natural to ask about the properties that such matrices satisfy. If we choose a matrix with integer entries at random, for example, what...
The supremum of autoconvolutions, with applications to additive number theory (2008)
We adapt a number-theoretic technique of Yu to prove a purely analytic theorem: if f(x) is in L^1 and L^2, is nonnegative, and is supported on an interval of length I, then the supremum of the...
We give explicit constructions of sets S with the property that for each integer k, there are at most g solutions to k = s1 + s2, si ∈ S; such sets are called Sidon sets if g = 2 and generalized...
COMPACTNESS THEOREMS FOR GEOMETRIC PACKINGS (2008)
3 × 4,..., whose total area equals 1, can be packed into the unit square without overlap,
Almost all integer matrices have no integer eigenvalues (2007)
For a fixed $n\ge2$, consider an $n\times n$ matrix $M$ whose entries are random integers bounded by $k$ in absolute value. In this paper, we examine the probability that $M$ is singular (hence has...
Balancing intellectual monopoly privileges and the need for essential medicines (2007)
Martin, Greg, Sorenson, Corinna, Faunce, Thomas
Abstract This issue of Globalization and Health presents a paper by Kerry and Lee that considers the TRIPS agreement and the recent policy debate regarding the protection of public health interest,...
Sets that contain their circle centers (2007)
Say that a subset S of the plane is a "circle-center set" if S is not a subset of a line, and whenever we choose three noncollinear points from S, the center of the unique circle through those three...
Many sets have more sums than differences (2006)
Since addition is commutative but subtraction is not, the sumset S+S of a finite set S is predisposed to be smaller than the difference set S-S. In this paper, however, we show that each of the three...
The global health governance of antimicrobial effectiveness (2006)
Abstract Antimicrobial resistance is a growing threat to public health the world over. Global health governance strategies need to address the erosion of antimicrobial effectiveness on three levels....
Epidemiology studies in critical care (2006)
Abstract Epidemiology studies are an essential part of clinical research, often forming the foundation for studies ranked more highly in the hierarchy of evidence-based medicine. Studies of sepsis to...
Simultaneous inequalities among values of the Euler phi-function (2006)
This paper concerns the values of the Euler phi-function evaluated simultaneously on k arithmetic progressions a_1 n + b_1, a_2 n + b_2, ..., a_k n + b_k. Assuming the necessary condition that no two...
A simple polynomial for a simple transposition (2006)
In this note, we review some facts about polynomials representing functions modulo primes p. In addition we prove that the polynomial f(x) = x^{p-2} + x^{p-3} + ... + x^3 + x^2 + 2x + 1 represents...
Conflicting clinical trial data: a lesson from albumin (2005)
Abstract Albumin is a frequently prescribed drug in hospitalized patients, and its effect on clinical outcomes has been scrutinized in recent years. Data from meta-analyses has suggested harm related...
Globalization and Health (2005)
Abstract This debut editorial of Globalization and Health introduces the journal, briefly delineating its goals and objectives and outlines its scope of subject matter. 'Open Access' publishing is...
The Symmetric Subset Problem in Continuous Ramsey Theory (2004)
A symmetric subset of the reals is one that remains invariant under some reflection z --> c-z. We consider, for any 0 < x
Granville, Andrew, Martin, Greg
This is a survey article on prime number races. Chebyshev noticed in the first half of the nineteenth century that for any given value of x, there always seem to be more primes of the form 4n+3 less...
Constructions of Generalized Sidon Sets (2004)
We give explicit constructions of sets S with the property that for each integer k, there are at most g solutions to k=s_1+s_2, s_i\in S; such sets are called Sidon sets if g=2 and generalized Sidon...
The iterated Carmichael \lambda-function and the number of cycles of the power generator (2004)
Iteration of the modular l-th power function f(x) = x^l (mod n) provides a common pseudorandom number generator (known as the Blum-Blum-Shub generator when l=2). The period of this pseudorandom...
Dimensions of the Spaces of Cusp Forms and Newforms on Gamma_0(N) and Gamma_1(N) (2003)
A formula for the dimension of the space of cuspidal modular forms on $\Gamma_0(N)$ of weight $k$ ($k\ge2$ even) has been known for several decades. More recent but still well-known is the...
Continuous Ramsey Theory and Sidon Sets (2002)
A symmetric subset of the reals is one that remains invariant under some reflection x --> c-x. Given 0 < x < 1, there exists a real number D(x) with the following property: if 0 < d < D(x), then...
The Unreasonable Effectualness of Continued Function Expansions (2002)
Many generalizations of continued fractions, where the reciprocal function has been replaced by a more general function, have been studied, and it is often asked whether such generalized expansions...
The Limiting Curve of Jarnik's Polygons (2002)
In 1925, Jarnik defined a sequence of convex polygons for use in constructing curves containing many lattice points relative to their curvatures. Properly scaled, these polygons converge to a certain...
Asymmetries in the Shanks-Renyi Prime Number Race (2000)
It has been well-observed that an inequality of the type $\pi(x;q,a) > \pi(x;q,b)$ is more likely to hold if $a$ is a non-square modulo $q$ and $b$ is a square modulo $q$ (the so-called ``Chebyshev...
Biases in the Shanks-Rényi prime number race (2000)
Feuerverger, Andrey, Martin, Greg
Rubinstein and Sarnak investigated systems of inequalities of the form $\pi(x;q,a_1)>\cdots>\pi(x;q,a_r)$, where $\pi(x;q,b)$ denotes the number of primes up to x that are congruent to b mod q. They...
Absolutely Abnormal Numbers (2000)
Despite the fact that almost all real numbers are absolutely normal---that is, the digits in their expansions to any base occur in all possible configurations with the expected frequency---not one...
Restoring Fairness to Dukego (2000)
In this paper we correct an analysis of the two-player perfect-information game Dukego given in Berlekamp, Conway, and Guy's Winning Ways for your Mathematical Plays (Chapter 19). In particular, we...
Compactness Theorems for Geometric Packings (2000)
Moser asked whether the collection of rectangles of dimensions 1 x 1/2, 1/2 x 1/3, 1/3 x 1/4, ..., whose total area equals 1, can be packed into the unit square without overlap, and whether the...
The neuropsychological consequences of repeated strangulation (shime-waza) in judo / (2000)
Thesis (MA--Psychology)--University of Auckland, 2000.
Biases in the Shanks-Renyi Prime Number Race (1999)
Feuerverger, Andrey, Martin, Greg
Rubinstein and Sarnak investigated systems of inequalities of the form pi(x;q,a_1) > ... > pi(x;q,a_r), where pi(x;q,a) denotes the number of primes up to x that are congruent to a mod q. They...
An Asymptotic Formula for the Number of Smooth Values of a Polynomial (1999)
Although we expect to find many smooth numbers (i.e., numbers with no large prime factors) among the values taken by a polynomial with integer coefficients, it is unclear what the asymptotic number...
"College of Sciences Food Engineering project."
Denser Egyptian Fractions (1998)
An Egyptian fraction is a sum of distinct unit fractions (reciprocals of positive integers). We show that every rational number has Egyptian fraction representations where the number of terms is of...
Lower Bounds for the Number of Smooth Values of a Polynomial (1998)
We investigate the problem of showing that the values of a given polynomial are smooth (i.e., have no large prime factors) a positive proportion of the time. Although some results exist that bound...
The Least Prime Primitive Root and the Shifted Sieve (1998)
We derive, for all prime moduli p except those in a very thin set, an upper bound for the least prime primitive root (mod p) of order of magnitude a constant power of log p. The improvement over...
Uniform Bounds for the Least Almost-Prime Primitive Root (1998)
We investigate, using the weighted linear sieve, the distribution of almost-primes among the residue classes (mod p) that generate the multiplicative group of reduced residue classes. We are...
Farmer Ted Goes Natural (1998)
A traditional "Farmer Ted" calculus problem is to minimize the perimeter of a rectangular chicken coop given the area N, so that as little as possible will be spent on the fencing. But what if N is...
Dense Egyptian Fractions (1998)
Every positive rational number has representations as Egyptian fractions (sums of reciprocals of distinct positive integers) with arbitrarily many terms and with arbitrarily large denominators....
Solubility of Systems of Quadratic Forms (1998)
We derive an upper bound for the least number of variables needed to guarantee that a system of t quadratic forms (t>=2) over a field F has a nontrivial zero. In particular, if F is a local field,...
The Smallest Solution of \phi(30n+1) (1998)
It is known that there are infinitely many solutions to the inequality \phi(30n+1)
Lower Bounds For The Number Of Smooth Values Of A Polynomial (1998)
We investigate the problem of showing that the values of a given polynomial are smooth (i.e., have no large prime factors) a positive proportion of the time. Although some results exist that bound...
Characterization of Plant Epidermal Lens Effects by a Surface Replica Technique (1991)
MARTIN, GREG, MYRES, DAVID A., VOGELMANN, THOMAS C.
Optical replicas of leaf surfaces were made for characterizing the lens properties of individual epidermal cells. Using a dental latex, moulds were made of leaf surfaces and subsequently used to...
Typescript.
Electronics and transducers for an ultrasonic blind mobility aid. (1969)
Thesis (M.E.)--University of Canterbury.
This debut editorial of Globalization and Health introduces the journal, briefly delineating its goals and objectives and outlines its scope of subject matter. 'Open Access' publishing is expected to...
Conflicting clinical trial data: a lesson from albumin
Albumin is a frequently prescribed drug in hospitalized patients, and its effect on clinical outcomes has been scrutinized in recent years. Data from meta-analyses has suggested harm related to...
The global health governance of antimicrobial effectiveness
Antimicrobial resistance is a growing threat to public health the world over. Global health governance strategies need to address the erosion of antimicrobial effectiveness on three levels. Firstly,...
Epidemiology studies in critical care
Epidemiology studies are an essential part of clinical research, often forming the foundation for studies ranked more highly in the hierarchy of evidence-based medicine. Studies of sepsis to date...
This debut editorial of Globalization and Health introduces the journal, briefly delineating its goals and objectives and outlines its scope of subject matter. 'Open Access' publishing is expected to...
Conflicting clinical trial data: a lesson from albumin
Albumin is a frequently prescribed drug in hospitalized patients, and its effect on clinical outcomes has been scrutinized in recent years. Data from meta-analyses has suggested harm related to...
The global health governance of antimicrobial effectiveness
Antimicrobial resistance is a growing threat to public health the world over. Global health governance strategies need to address the erosion of antimicrobial effectiveness on three levels. Firstly,...
Epidemiology studies in critical care
Epidemiology studies are an essential part of clinical research, often forming the foundation for studies ranked more highly in the hierarchy of evidence-based medicine. Studies of sepsis to date...
Balancing intellectual monopoly privileges and the need for essential medicines
Martin, Greg, Sorenson, Corinna, Faunce, Thomas
This issue of Globalization and Health presents a paper by Kerry and Lee that considers the TRIPS agreement and the recent policy debate regarding the protection of public health interest,...
The bioscience revolution & the biological weapons threat: levers & interventions
D'Agostino, Mark, Martin, Greg
In December 2008, the US Commission on the Prevention of Weapons of Mass Destruction Proliferation and Terrorism, released a report, World At Risk. The Report points to the fact that, not only is the...
Martin, Greg, Brunkhorst, Frank M, Janes, Jonathan M, Reinhart, Konrad, Sundin, David P, Garnett, Kassandra, ...
Toll-like Receptor 1 Polymorphisms Affect Innate Immune Responses and Outcomes in Sepsis
Wurfel, Mark M., Gordon, Anthony C., Holden, Tarah D., Radella, Frank, Strout, Jeanna, Kajikawa, Osamu, ...
Rationale: Polymorphisms affecting Toll-like receptor (TLR)–mediated responses could predispose to excessive inflammation during an infection and contribute to an increased risk for poor outcomes...