We study the problem of finding the Artin L-functions with the smallest conductor for a given Galois type. We adapt standard analytic techniques to our novel situation of fixed Galois type and obtain much improved lower bounds on the smallest conductor. For small Galois types we use complete tables of number fields to determine the actual smallest conductor.

We consider the problem of encoding range minimum queries (RMQs): given an array A[1..n] of distinct totally ordered values, to pre-process A and create a data structure that can answer the query RMQ(i,j), which returns the index containing the smallest element in A[i..j], without access to the array A at query time. We give a data structure whose space usage is 2n+o(n) bits, which is asymptoti...

We show that the smallest denominator function can be treated with a minimum amount of number theory. Moreover, this function can be used to nicely prove a number of fundamental divisibility and irrationality results. Acta Mathematica Academiae Paedagogicae Ny regyh aziensis 15 (1999), 19{26 www.bgytf.hu/~amapn

The first four smallest values of the spectral radius among all connected graphs with maximum clique size ω ≥ 2 are obtained.

The North Pacific right whale (Eubalaena japonica) was heavily exploited by both nineteenth century whaling and recent (1960s) illegal Soviet catches. Today, the species remains extremely rare especially in the eastern North Pacific. Here, we use photographic and genotype data to calculate the first mark-recapture estimates of abundance for right whales in the Bering Sea and Aleutian Islands. T...

Let p be a prime and p1, . . . , pr be distinct prime divisors of p− 1. We prove that the smallest positive integer n which is a simultaneous p1, . . . , pr-power nonresidue modulo p satisfies n < p 1/4−cr+o(1) (p → ∞) for some positive cr satisfying cr = e −(1+o(1))r (r → ∞). Mathematical Subject Classification: 11A15, 11A07, 11N29

A random forest method has been selected to perform both gene selection and classification of the microarray data. In this embedded method, the selection of smallest possible sets of genes with lowest error rates is the key factor in achieving highest classification accuracy. Hence, improved gene selection method using random forest has been proposed to obtain the smallest subset of genes as we...

This study was concerned with what stimulus information observers use to judge the shape of simple objects. We used a string of four Gabor patches to define a contour. A fifth, center patch served as a test pattern. The observers' task was to judge the location of the test pattern relative to the contour. The contour was either a straight line, or an arc with positive or negative curvature (the...

We investigate the fundamental dimensional limits to thermodynamic machines. In particular, we show that it is possible to construct self-contained refrigerators (i.e., not requiring external sources of work) consisting of only a small number of qubits and/or qutrits. We present three different models, consisting of two qubits, a qubit and a qutrit with nearest-neighbor interactions, and a sing...

We apply G. Prasad’s volume formula for the arithmetic quotients of semi-simple groups and Bruhat-Tits theory to study the covolumes of arithmetic subgroups of SO(1, n). As a result we prove that for any even dimension n there exists a unique compact arithmetic hyperbolic n-orbifold of the smallest volume. We give a formula for the Euler-Poincaré characteristic of the orbifolds and present an e...