Embedding of bases: from the M(2,2k+1) to the M(3,4k+2-delta) models

A new quasi-particle basis of states is presented for all the irreducible modules of the M(3,p) models. It is formulated in terms of a combination of Virasoro modes and the modes of the field phi_{2,1}. This leads to a fermionic expression for particular combinations of irreducible M(3,p) characters, which turns out to be identical with the previously known formula. Quite remarkably, this new quasi-particle basis embodies a sort of embedding, at the level of bases, of the minimal models M(2,2k+1) into the M(3,4k+2-delta) ones, with 0 \leq delta \leq 3.Comment: corrected a typo in the title, 7 page

Some extensions of Alon's Nullstellensatz

Alon's combinatorial Nullstellensatz, and in particular the resulting nonvanishing criterion is one of the most powerful algebraic tools in combinatorics, with many important applications. In this paper we extend the nonvanishing theorem in two directions. We prove a version allowing multiple points. Also, we establish a variant which is valid over arbitrary commutative rings, not merely over subrings of fields. As an application, we prove extensions of the theorem of Alon and F\"uredi on hyperplane coverings of discrete cubes.Comment: Inital submission: Thu, 24 Mar 201

Alon's Nullstellensatz for multisets

Alon's combinatorial Nullstellensatz (Theorem 1.1 from \cite{Alon1}) is one of the most powerful algebraic tools in combinatorics, with a diverse array of applications. Let \F be a field, $S_1,S_2,..., S_n$ be finite nonempty subsets of \F. Alon's theorem is a specialized, precise version of the Hilbertsche Nullstellensatz for the ideal of all polynomial functions vanishing on the set S=S_1\times S_2\times ... \times S_n\subseteq \F^n. From this Alon deduces a simple and amazingly widely applicable nonvanishing criterion (Theorem 1.2 in \cite{Alon1}). It provides a sufficient condition for a polynomial $f(x_1,...,x_n)$ which guarantees that $f$ is not identically zero on the set $S$. In this paper we extend these two results from sets of points to multisets. We give two different proofs of the generalized nonvanishing theorem. We extend some of the known applications of the original nonvanishing theorem to a setting allowing multiplicities, including the theorem of Alon and F\"uredi on the hyperplane coverings of discrete cubes.Comment: Submitted to the journal Combinatorica of the J\'anos Bolyai Mathematical Society on August 5, 201

Bone mineral density and chronic lung disease mortality: the Rotterdam study

Context: Low bone mineral density (BMD) has been associated with increased all-cause mortality. Cause-specific mortality studies have been controversial. Objective: The aim of the study was to investigate associations between BMD and all-cause mortality and in-depth cause-specific mortality. Design and Setting: We studied two cohorts from the prospective Rotterdam Study (RS), initiated in 1990 (RS-I) and 2000 (RS-II) with average follow-up of 17.1 (RS-I) and 10.2 (RS-II) years until January 2011. Baseline femoral neck BMD was analyzed in SD values. Deaths were classified according to International Classification of Diseases into seven groups: cardiovascular diseases, cancer, infections, external, dementia, chronic lung diseases, and other causes. Gender-stratified Cox and competing-risks models were adjusted for age, body mass index, and smoking. Participants: The study included 5779 subjects from RS-I and 2055 from RS-II. Main Outcome Measurements: We measured all-cause and cause-specific mortality. Results: A significant inverse association between BMD and all-cause mortality was found in males [expressed as hazard ratio (95% confidence interval)]: RS-I, 1.07 (1.01-1.13), P = .020; RS-II, 1.31 (1.12-1.55), P = .001); but it was not found in females: RS-I, 1.05 (0.99-1.11), P = .098; RS-II, 0.91 (0.74-1.12), P = .362. An inverse association with chronic lung disease mortality was found in males [RS-I, 1.75 (1.34-2.29), P < .001; RS-II, 2.15 (1.05-4.42), P = .037] and in RS-I in females [1.72 (1.16-2.57); P = .008], persisting after multiple adjustments and excluding prevalent chronic obstructive pulmonary disease. A positive association between BMD and cancer mortality was detected in females in RS-I [0.89 (0.80-0.99); P = .043]. No association was found with cardiovascular mortality. Conclusions: BMD is inversely associated with mortality. The strong association of BMD with chronic lung disease mortality is a novel finding that needs further analysis to clarify underlying mechanisms

4U 0115+63 from RXTE and INTEGRAL Data: Pulse Profile and Cyclotron Line Energy

We analyze the observations of the transient X-ray pulsar 4U 0115+63 with the RXTE and INTEGRAL observatories in a wide X-ray (3-100 keV) energy band during its intense outbursts in 1999 and 2004. The energy of the fundamental harmonic of the cyclotron resonance absorption line near the maximum of the X-ray flux from the source (luminosity range 5x10^{37} - 2x10^{38} erg/s) is ~11 keV. When the pulsar luminosity falls below ~5x10^{37} erg/s, the energy of the fundamental harmonic is displaced sharply toward the high energies, up to ~16 keV. Under the assumption of a dipole magnetic field configuration, this change in cyclotron harmonic energy corresponds to a decrease in the height of the emitting region by ~2 km, while other spectral parameters, in particular, the cutoff energy, remain essentially constant. At a luminosity ~7x10^{37} erg/s, four almost equidistant cyclotron line harmonics are clearly seen in the spectrum. This suggests that either the region where the emission originates is compact or the emergent spectrum from different (in height) segments of the accretion column is uniform. We have found significant pulse profile variations with energy, luminosity, and time. In particular, we show that the profile variations from pulse to pulse are not reduced to a simple modulation of the accretion rate specified by external conditions.Comment: 30 pages, 13 figures, Astronomy Letters, 33, 368 (2007

Fundamental polytopes of metric trees via parallel connections of matroids

We tackle the problem of a combinatorial classification of finite metric spaces via their fundamental polytopes, as suggested by Vershik in 2010. In this paper we consider a hyperplane arrangement associated to every split pseudometric and, for tree-like metrics, we study the combinatorics of its underlying matroid. We give explicit formulas for the face numbers of fundamental polytopes and Lipschitz polytopes of all tree-like metrics, and we characterize the metric trees for which the fundamental polytope is simplicial.Comment: 20 pages, 2 Figures, 1 Table. Exposition improved, references and new results (last section) adde

Dynamic Model for LES Without Test Filtering: Quantifying the Accuracy of Taylor Series Approximations

The dynamic model for large-eddy simulation (LES) of turbulent flows requires test filtering the resolved velocity fields in order to determine model coefficients. However, test filtering is costly to perform in large-eddy simulation of complex geometry flows, especially on unstructured grids. The objective of this work is to develop and test an approximate but less costly dynamic procedure which does not require test filtering. The proposed method is based on Taylor series expansions of the resolved velocity fields. Accuracy is governed by the derivative schemes used in the calculation and the number of terms considered in the approximation to the test filtering operator. The expansion is developed up to fourth order, and results are tested a priori based on direct numerical simulation data of forced isotropic turbulence in the context of the dynamic Smagorinsky model. The tests compare the dynamic Smagorinsky coefficient obtained from filtering with those obtained from application of the Taylor series expansion. They show that the expansion up to second order provides a reasonable approximation to the true dynamic coefficient (with errors on the order of about 5 % for c_s^2), but that including higher-order terms does not necessarily lead to improvements in the results due to inherent limitations in accurately evaluating high-order derivatives. A posteriori tests using the Taylor series approximation in LES of forced isotropic turbulence and channel flow confirm that the Taylor series approximation yields accurate results for the dynamic coefficient. Moreover, the simulations are stable and yield accurate resolved velocity statistics.Comment: submitted to Theoretical and Computational Fluid Dynamics, 20 pages, 11 figure