Ring completion of rig categories

We offer a solution to the long-standing problem of group completing within the context of rig categories (also known as bimonoidal categories). Given a rig category R we construct a natural additive group completion R' that retains the multiplicative structure, hence has become a ring category. If we start with a commutative rig category R (also known as a symmetric bimonoidal category), the additive group completion R' will be a commutative ring category. In an accompanying paper we show how this can be used to prove the conjecture from [BDR] that the algebraic K-theory of the connective topological K-theory spectrum ku is equivalent to the algebraic K-theory of the rig category V of complex vector spaces.Comment: There was a mathematical error in arXiv:0706.0531v2: the map T in the purported proof of Lemma 3.7(2) is not well defined. Version 4 has been edited for notational consistenc

Thermodynamics of the spin-1/2 Heisenberg antiferromagnet on the star lattice

Using a combination of quantum Monte Carlo simulations in adapted cluster bases, the finite temperature Lanczos method, and an effective Hamiltonian approach, we explore the thermodynamic properties of the spin-1/2 Heisenberg antiferromagnet on the star lattice. We consider various parameter regimes on this strongly frustrated Archimedean lattice, including the case of homogeneous couplings as well as the distinct parameter regimes of dominant vs. weak dimer coupling. For the latter case, we explore the quantum phase diagram in the presence of inhomogeneous trimer couplings, preserving inversion symmetry. We compare the efficiency of different cluster decoupling schemes for the quantum Monte Carlo simulations in terms of the sign problem, contrast the thermodynamic properties to those of other strongly frustrated quantum magnets, such as the kagome lattice model, and comment on previous results from tensor-network calculations regarding a valence bond crystal phase in the regime of weak dimer coupling. Finally, we relate our results to recently reported experimental findings on a Cu-based quantum magnetic spin-1/2 compound with an underlying star lattice structure.Comment: 14 pages, 13 figure

Density Measurements of an Air-Like Binary Mixture over the Temperature Range from 100 K to 298.15 K at Pressures up to 8.0 MPa

AbstractDensities of an air-like binary mixture (0.2094 oxygen + 0.7906 nitrogen, mole fractions) were measured along six isotherms over the temperature range from 100 K to 298.15 K at pressures up to 8.0 MPa, using a low-temperature single-sinker magnetic suspension densimeter. The measurements were carried out at T = (100, 115, and 130) K in the homogeneous gas and liquid region, and at T = (145, 220, and 298.15) K in the supercritical region (critical temperature TC = 132.35 K); in total, we present results for 52 (T, p) state points. The relative expanded combined uncertainty (k = 2) of the experimental densities was estimated to be between 0.03 % and 0.13 %, except for four values near the critical point. The largest error is caused by the magnetic suspension coupling in combination with the mixture component oxygen, which is strongly paramagnetic; the resulting force transmission error is up to 1.1 %. However, this error can be corrected with a proven correction model to an uncertainty contribution in density of less than 0.044 %. Due to a supercritical liquefaction procedure and the integration of a special VLE-cell, it was possible to measure densities in the homogeneous liquid phase without changing the composition of the liquefied mixture. Moreover, saturated liquid and saturated vapor densities were determined at T = (100, 115, and 130) K by extrapolation of the experimental single-phase densities to the saturation pressure. The new experimental results were compared with the mixture model of Lemmon et al. for the system (nitrogen + argon + oxygen) and the GERG-2008 equation of state

Alpha managers - an advantage or disadvantage for the organization

The role of the manager is crucial to the organization. Managers set goals, develop strategies and define tasks of workers, create environment for the development of people and give meaning to their activities. Professional skills are of vital importance to manager’s success. These very skills are the distinguishing characteristics of alpha managers. The aim of the following paper is to present some of the most established ideas in the field of leadership styles, to compare them with the concept of alpha managers and draw some conclusions important to management

The neural network multigrid solver for the Navier-Stokes equations and its application to 3D simulation

We investigate scaling and efficiency of the deep neural network multigrid method (DNN-MG), a novel neural network-based technique for the simulation of the Navier-Stokes equations that combines an adaptive geometric multigrid solver with a recurrent neural network with memory. The neural network replaces in DNN-MG one or multiple finest multigrid layers and provides a correction for the classical solve in the next time step. This leads to little degradation in the solution quality while substantially reducing the overall computational costs. At the same time, the use of the multigrid solver at the coarse scales allows for a compact network that is easy to train, generalizes well, and allows for the incorporation of physical constraints. In this work, we investigate how the network size affects training and solution quality and the overall runtime of the computations