On the Algebraic Bethe Ansatz for XXX spin chain: creation operators " beyond the equator ". Abstract Considering the XXX spin-1/2 chain in the framework of the Algebraic Bethe Ansatz (ABA) we make the following short comment: the product of the creation operators corresponding to the recently found solution of the Bethe equations " on the wrong side of the equator " [1] is just zero (not only ...

The sign of a Latin square is −1 if it has an odd number of rows and columns that are odd permutations; otherwise, it is +1. Let Ln and L o n be, respectively, the number of Latin squares of order n with sign +1 and −1. The Alon-Tarsi conjecture asserts that Ln = Ln when n is even. Drisko showed that Lp+1 ≡ Lp+1 (mod p) for prime p ≥ 3 and asked if similar congruences hold for orders of the for...

This note provides an elementary proof of the folklore fact that draws from a Dirichlet distribution (with parameters less than 1) are typically sparse (most coordinates are small). 1 Bounds Let Dir(α) denote a Dirichlet distribution with all parameters equal to α. Theorem 1.1. Suppose n ≥ 2 and (X1, . . . , Xn) ∼ Dir(1/n). Then, for any c0 ≥ 1 satisfying 6c0 ln(n) + 1 < 3n, Pr [∣∣∣∣{i : Xi ≥ 1...

It is shown that the four element Boolean algebra can be embedded in the recursively enumerable truth-table degrees with least and greatest elements preserved. Corresponding results for other lattices and other reducibilites are also discussed. For sets A, B ç co, we say that A is a truth-table (tt) reducible to B if there exists an effective procedure for reducing any question of the form "m e...

The logarithmically enhanced α3 ln(1/α) corrections to the paraand orthopositronium decay widths are calculated in the framework of dimensionally regularized nonrelativistic quantum electrodynamics. In the case of parapositronium, the correction is negative, approximately doubles the effect of the leading logarithmic α3 ln(1/α) one, and is comparable to the nonlogarithmic O(α2) one. As for orth...

The logarithmically enhanced α ln(1/α) contribution to the hyperfine splitting of the positronium ground-state energy levels is calculated in the framework of dimensionally regularized nonrelativistic quantum electrodynamics. The correction is negative and amounts to about 1/3 of the leading logarithmic α ln(1/α) one. The discrepancy between the experimental measurements and the theoretical pre...

In this paper we suggest a new efficient technique for solving integer knapsack problems. Our algorithms can be seen as application of Fast Fourier Transform to generating functions of integer polytopes. Using this approach, it is possible to count the number of boolean solutions of a single n-dimensional Diophantine equation 〈a, x〉 = b in O(‖a‖1 ln ‖a1‖ ln n) operations. Another application ex...

Immunogenicity and safety of ACWY-TT compared with licensed ACWY polysaccharide vaccine (MenPS) in healthy adults, and lot-to-lot consistency of three ACWY-TT lots were evaluated in a phase 3, open, controlled study. Adults aged 18-55 y were randomized to receive ACWY-TT (one of three lots) or MenPS. Serum bactericidal antibodies (rSBA) were measured pre- and 1 mo post-vaccination. Adverse even...

OBJECTIVE Two polymorphisms in the promoter region of the gene encoding cytosolic aldehyde dehydrogenase (ALDH1A1), ALDH1A1*2 and ALDH1A1*3, have recently been identified. The present study sought to determine whether an association exists between ALDH1A1 genotypes, alcohol dependence, drinking history, and liver function tests in the two major ethnic groups of Trinidad and Tobago (TT). METHO...

Carbohydrate supplementation (CHOS) typically improves prolonged time-trial (TT) performance at sea level (SL). This study determined whether CHOS also improves TT performance at high altitude (ALT; 4,300 M) despite increased hypoxemia and while in negative energy balance (approximately 1,250 kcal/day). Two groups of fasting, fitness-matched men performed a 720-kJ cycle TT at SL and while livin...