Arithmetically Cohen-Macaulay bundles on complete intersection varieties of sufficiently high multidegree

Recently it has been proved that any arithmetically Cohen-Macaulay (ACM) bundle of rank two on a general, smooth hypersurface of degree at least three and dimension at least four is a sum of line bundles. When the dimension of the hypersurface is three, a similar result is true provided the degree of the hypersurface is at least six. We extend these results to complete intersection subvarieties by proving that any ACM bundle of rank two on a general, smooth complete intersection subvariety of sufficiently high multi-degree and dimension at least four splits. We also obtain partial results in the case of threefolds.

Reduced Grobner bases and Macaulay-Buchberger Basis Theorem over Noetherian rings

In this paper, we extend the characterization of Zx]/(f), where f is an element of Zx] to be a free Z-module to multivariate polynomial rings over any commutative Noetherian ring, A. The characterization allows us to extend the Grobner basis method of computing a k-vector space basis of residue class polynomial rings over a field k (Macaulay-Buchberger Basis Theorem) to rings, i.e. Ax(1), ... , x(n)]/a, where a subset of Ax(1), ... , x(n)] is an ideal. We give some insights into the characterization for two special cases, when A = Z and A = ktheta(1), ... , theta(m)]. As an application of this characterization, we show that the concept of Border bases can be extended to rings when the corresponding residue class ring is a finitely generated, free A-module. (C) 2014 Elsevier B.V. All rights reserved.

CM defect and Hilbert functions of monomial curves

In this article we consider a semigroup ring R = KGamma] of a numerical semigroup Gamma and study the Cohen- Macaulayness of the associated graded ring G(Gamma) := gr(m), (R) := circle plus(n is an element of N) m(n)/m(n+1) and the behaviour of the Hilbert function H-R of R. We define a certain (finite) subset B(Gamma) subset of F and prove that G(Gamma) is Cohen-Macaulay if and only if B(Gamma) = empty set. Therefore the subset B(Gamma) is called the Cohen-Macaulay defect of G(Gamma). Further, we prove that if the degree sequence of elements of the standard basis of is non-decreasing, then B(F) = empty set and hence G(Gamma) is Cohen-Macaulay. We consider a class of numerical semigroups Gamma = Sigma(3)(i=0) Nm(i) generated by 4 elements m(0), m(1), m(2), m(3) such that m(1) + m(2) = mo m3-so called ``balanced semigroups''. We study the structure of the Cohen-Macaulay defect B(Gamma) of Gamma and particularly we give an estimate on the cardinality |B(Gamma, r)| for every r is an element of N. We use these estimates to prove that the Hilbert function of R is non-decreasing. Further, we prove that every balanced ``unitary'' semigroup Gamma is ``2-good'' and is not ``1-good'', in particular, in this case, c(r) is not Cohen-Macaulay. We consider a certain special subclass of balanced semigroups Gamma. For this subclass we try to determine the Cohen-Macaulay defect B(Gamma) using the explicit description of the standard basis of Gamma; in particular, we prove that these balanced semigroups are 2-good and determine when exactly G(Gamma) is Cohen-Macaulay. (C) 2011 Published by Elsevier B.V.

Thomas-Fermi Method For Particles Obeying Generalized Exclusion Statistics

We use the Thomas-Fermi method to examine the thermodynamics of particles obeying Haldane exclusion statistics. Specifically, we study Calogero-Sutherland particles placed in a given external potential in one dimension. For the case of a simple harmonic potential (constant density of states), we obtain the exact one-particle spatial density and a {\it closed} form for the equation of state at finite temperature, which are both new results. We then solve the problem of particles in a $x^{2/3} ~$ potential (linear density of states) and show that Bose-Einstein condensation does not occur for any statistics other than bosons.

Aromatic, microporous polymer networks with high surface area generated in Friedel-Crafts-type polycondensations

A series of novel, microporous polymer networks (MPNs) have been generated in a simple, acid catalysed Friedel-Crafts-type self-condensation of A(2)B(2)- and A(2)B(4)-type fluorenone monomers. Two A2B4-type monomers with 2,7-bis(N, N-diphenylamino) A or 2,7-bis [4-(N, N-diphenylamino) phenyl] D substitution of the fluorenone cores lead to MPNs with high S(BET) surface areas of up to 1400 m(2) g(-1). Two MPNs made of binary monomer mixtures showed the highest Brunauer-Emmett-Teller (BET) surface areas S(BET) of our series (SBET of up to 1800 m(2) g(-1)) after washing the powdery samples with supercritical carbon dioxide. Total pore volumes of up to 1.6 cm(3) g(-1) have been detected. It is observed that the substitution pattern of the monomers is strongly influencing the resulting physicochemical properties of the microporous polymer networks (MPNs).

Climatic variability in Central Indian Himalaya during the last similar to 1800 years: Evidence from a high resolution speleothem record

Stable isotopes from a U/Th dated aragonite stalagmite from the Central Kumaun Himalaya provide evidence of variation in climatic conditions in the last similar to 1800 years. The delta O-18 and delta C-13 values vary from -4.3 parts per thousand to -7.6 parts per thousand and -3.4 parts per thousand to -9.1 parts per thousand respectively, although the stalagmite was not grown in isotopic equilibrium with cave drip water, a clear palaeoclimatic signal in stalagmite delta O-18 values is evident based on the regional climate data. The stalagmite showed a rapid growth rate during 830-910 AD, most likely the lower part of Medieval Warm Period (MWP), and 1600-1640 AD, the middle part of Little Ice Age (LIA). Two distinct phases of reduced precipitation are marked by a 2 parts per thousand shift in 8180 values towards the end of MWP (similar to 1080-1160 AD) and after its termination from similar to 1210 to 1440 AD. The LIA (similar to 1440-1880 AD) is represented by sub-tropical climate similar to modern conditions, whereas the post-LIA was comparatively drier. The Inter Tropical Convergence Zone (ITCZ) was located over the cave location during wetter/warmer conditions. When it shifted southward, precipitation over the study area decreased. A prominent drop in delta O-18 and delta C-13 values during the post-LIA period may also have been additionally influenced by anthropogenic activity in the area. (C) 2013 Elsevier Ltd and INQUA. All rights reserved.