INTRODUCTION Patients who cannot support their nutritional needs via the enteral route due to intestinal failure often require parenteral nutrition (PN). Prolonged PN may be necessary in patients suffering from a variety of gastrointestinal motility, malabsorptive, or metabolic disorders (1). As the number of patients relying on prolonged PN support increases, associations between PN and an arr...

Finding mathematical proofs for easily observed properties of the distribution of prime numbers is a difficult and often humbling task, at least for the authors of this paper. The twin prime conjecture is a famous example of this, but we are concerned here with the much more modest problem of proving that there are arbitrarily large primes that are “unusually close ” together. Statistically thi...

The currently best method is the one by Nagai, using df-pn+ to solve brinkmate problems. We have proposed a new threat based and proof number based algorithm called df-pn driven λ-search. We have conducted some preliminary experiments, showing that df-pn driven λ-search seems to be better than Nagai’s method in solving Shogi brinkmate problems. Although more invesigation is requiered, df-pn λ-s...

Depth-first proof-number (df-pn) search is a powerful member of the family of algorithms based on proof and disproof numbers. While df-pn has succeeded in practice, its theoretical properties remain poorly understood. This paper resolves the question of completeness of df-pn: its ability to solve any finite boolean-valued game tree search problem in principle, given unlimited amounts of time an...

Here we describe several fundamental principles of olfactory processing in the Drosophila melanogaster antennal lobe (the analog of the vertebrate olfactory bulb), through the systematic analysis of input and output spike trains of seven identified glomeruli. Repeated presentations of the same odor elicit more reproducible responses in second-order projection neurons (PNs) than in their presyna...

In this paper, let Pn,n+k;≤n+k (resp. Pn;≤s) denote the set of parking functions α = (a1, · · · , an) of length n with n+k (respe. n)parking spaces satisfying 1 ≤ ai ≤ n+k (resp. 1 ≤ ai ≤ s) for all i. Let pn,n+k;≤n+k = |Pn,n+k;≤n+k| and pn;≤s = |Pn;≤s|. Let P l n;≤s denote the set of parking functions α = (a1, · · · , an) ∈ Pn;≤s such that a1 = l and pn;≤s = |P l n;≤s|. We derive some formulas...

We present a population synthesis calculation to derive the total number of planetary nebulae (PN) in the Galaxy that descend from single stars and stars in binary systems. Using the most recent literature results on galactic and stellar formation as well as stellar evolution, we predict the total number of galactic PNe with radii <0.9 pc to be (4.6 ± 1.3) × 10. We do not claim this to be the c...

Let pn denote the nth prime. Goldston, Pintz, and Yıldırım recently proved that lim inf n→∞ (pn+1 − pn) log pn = 0. We give an alternative proof of this result. We also prove some corresponding results for numbers with two prime factors. Let qn denote the nth number that is a product of exactly two distinct primes. We prove that lim inf n→∞ (qn+1 − qn) ≤ 26. If an appropriate generalization of ...

In [6] , Nada S. and Hamouda E. defined the folding number, F (G), to be the order of the set of all folding maps of G into itself. Also they introduced a formula to compute the folding number of Pn, a path with n edges. In this paper, the concept of based folding of a based graph is introduced and the number of based folding F (Pn, v) is given. Mathematics Subject Classification: 05C30

We give an upper bound in O(d) for the number of critical points of a normal random polynomial. The number of minima (resp. maxima) is in O(d)Pn, where Pn is the (unknown) measure of the set of symmetric positive matrices in the Gaussian Orthogonal Ensemble GOE(n). Finally, we give a closed form expression for the number of maxima (resp. minima) of a random univariate polynomial, in terms of hy...