A set S of positive integers has distinct subset sums if there are 2|S| distinct elements of the set {∑ x∈X x : X ⊂ S } . Let f(n) = min{maxS : |S| = n and S has distinct subset sums}. Erdős conjectured f(n) ≥ c2n for some constant c. We give a construction that yields f(n) < 0.22002 · 2n for n sufficiently large. This now stands as the best known upper bound on f(n).

We present a follow-up analysis examining the dynamics and structures of 41 massive, large star-forming galaxies at z~0.67-2.45 using both ionized molecular gas kinematics. fit galaxy with models consisting bulge, thick, turbulent disk, NFW dark matter halo, code that fully forward kinematics, including all observational instrumental effects. explore parameter space Markov Chain Monte Carlo (MC...

In this paper we study the conjugacy problem in polycyclic groups. Our main result is that we create polycyclic groups Gn whose conjugacy problem is at least as hard as the subset sum problem with n indeterminates. As such, the conjugacy problem over the groups Gn is NP-complete where the parameters of the problem are taken in terms of n and the length of the elements given on input.

We define the (w∗-) boundedness property and the (w∗-) surjectivity property for sets in normed spaces. We show that these properties are pairwise equivalent in complete normed spaces by characterizing them in terms of a category-like property called (w∗-) thickness. We give examples of interesting sets having or not having these properties. In particular, we prove that the tensor product of tw...

Root ofPlumbago indica Linn is used in ayurveda and siddha medicine for the treatment of colic inflammations bronchitis, helminthiasis, hemorrhoids, elephantiasis, hepatosplenomegaly, amenorrhea, odontalgia, piles, and diabetes. The present study aims to investigate the anatomical characters of thin and thick root and to confirm the physicochemical characters of the root. Anatomical st...

IAl > ((l/k) + E)n then there is a subset B L A such that 0 < 1 BI 0, let snd(nt) denote the smallest integer that does not divide PI. We prove that for every I-: > 0 there is a constant c = ~(8:) z I, such that for every n > 0 and every rn, n ' +' 6 WI < n'llog'n...

The purpose of this paper is to further the study of countably thick modules via weak injectivity. Among others, for some classes M of modules in σ[M ] we study when direct sums of modules from M satisfies a property P in σ[M ]. In particular, we get characterization of locally countably thick modules, a generalization of locally q.f.d. modules.

We use a K-theory recipe of Thomason to obtain classi cations of triangulated subcategories via re ning some standard thick subcategory theorems. We apply this recipe to the full subcategories of nite objects in the derived categories of rings and the stable homotopy category of spectra. This gives, in the derived categories, a complete classi cation of the triangulated subcategories of perfect...

Davide Marenduzzo, Alessandro Flammini, Antonio Trovato, Jayanth R. Banavar and Amos Maritan 1 Department of Physics, Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, England 2 INFM and Dipartimento di Fisica “G. Galilei”, Universitd̀i Padova, Via Marzolo 8, 35131 Padova, Italy 3 Department of Physics, 104 Davey Laboratory, The Pennsylvania State University, University Pa...