An average-case analysis of bin packing with uniformly distributed item sizes

We analyze the one-dimensional bin-packing problem under the assumption that bins have unit capacity, and that items to be packed are drawn from a uniform distribution on [0,1]. Building on some recent work by Frederickson, we give an algorithm which uses n/2+0(n^½) bins on the average to pack n items. (Knodel has achieved a similar result.) The analysis involves the use of a certain 1-dimensional random walk. We then show that even an optimum packing under this distribution uses n/2+0(n^1/2) bins on the average, so our algorithm is asymptotically optimal, up to constant factors on the amount of wasted space. Finally, following Frederickson, we show that two well-known greedy bin-packing algorithms use no more bins than our algorithm; thus their behavior is also in asymptotically optimal in this sense

The Gnosticism Opposed and Condemed in the New Testament

It is our purpose in this thesis to trace the movement in the form in which it is opposed and condemned in the New Testament, and, if possible, find external information on these movements. Although many of the passages which condemn false teachers may have been written against gnostics, we shall deal only with those in which gnostic tendencies are revealed

Homiletics: Sermon Study on 1 Peter 3:8-9 For Jubilate

Sermon Study on 1 Peter 3:8-9 For Jubilat

Improved Constraints on Cosmic Microwave Background Secondary Anisotropies from the Complete 2008 South Pole Telescope Data

We report measurements of the cosmic microwave background (CMB) power spectrum from the complete 2008 South Pole Telescope (SPT) data set. We analyze twice as much data as the first SPT power spectrum analysis, using an improved cosmological parameter estimator which fits multi-frequency models to the SPT 150 and 220 GHz bandpowers. We find an excellent fit to the measured bandpowers with a model that includes lensed primary CMB anisotropy, secondary thermal (tSZ) and kinetic (kSZ) Sunyaev-Zel'dovich anisotropies, unclustered synchrotron point sources, and clustered dusty point sources. In addition to measuring the power spectrum of dusty galaxies at high signal-to-noise, the data primarily constrain a linear combination of the kSZ and tSZ anisotropy contributions at 150 GHz and ℓ = 3000: D^(tSZ) ^(3000) + 0.5 D_(kSZ)^(3000) = 4.5 ± 1.0 μK^2. The 95% confidence upper limits on secondary anisotropy power are D ^(tSZ)_(3000) < 5.3 μK^2 and D^(kSZ)_(3000) < 6.5 μK^2. We also consider the potential correlation of dusty and tSZ sources and find it incapable of relaxing the tSZ upper limit. These results increase the significance of the lower than expected tSZ amplitude previously determined from SPT power spectrum measurements. We find that models including non-thermal pressure support in groups and clusters predict tSZ power in better agreement with the SPT data. Combining the tSZ power measurement with primary CMB data halves the statistical uncertainty on σ8. However, the preferred value of σ8 varies significantly between tSZ models. Improved constraints on cosmological parameters from tSZ power spectrum measurements require continued progress in the modeling of the tSZ power

An Investigation of the Origin and Development of the Gesellschaft Zur Unterstutzung Von Prediger- U. Schullehrer- Wittwen U. Waisen Innerhalb Der Ev. Luth. Synode Von Missouri, Ohio U. A. Staaten

It is the purpose of this paper to investigate the origin and development of this organization within Synod as a whole from the proposal for such an organization in 1850 up until 1889, when the various districts officially took over the support of the widows and orphans of Pastors and teachers

A Measurement of the Damping Tail of the Cosmic Microwave Background Power Spectrum with the South Pole Telescope

We present a measurement of the angular power spectrum of the cosmic microwave background (CMB) using data from the South Pole Telescope (SPT). The data consist of 790 deg^2 of sky observed at 150 GHz during 2008 and 2009. Here we present the power spectrum over the multipole range 650 < ℓ < 3000, where it is dominated by primary CMB anisotropy. We combine this power spectrum with the power spectra from the seven-year Wilkinson Microwave Anisotropy Probe (WMAP) data release to constrain cosmological models. We find that the SPT and WMAP data are consistent with each other and, when combined, are well fit by a spatially flat, ΛCDM cosmological model. The SPT+WMAP constraint on the spectral index of scalar fluctuations is n_s = 0.9663 ± 0.0112. We detect, at ~5σ significance, the effect of gravitational lensing on the CMB power spectrum, and find its amplitude to be consistent with the ΛCDM cosmological model. We explore a number of extensions beyond the ΛCDM model. Each extension is tested independently, although there are degeneracies between some of the extension parameters. We constrain the tensor-to-scalar ratio to be r < 0.21 (95% CL) and constrain the running of the scalar spectral index to be dn_s /dln k = –0.024 ± 0.013. We strongly detect the effects of primordial helium and neutrinos on the CMB; a model without helium is rejected at 7.7σ, while a model without neutrinos is rejected at 7.5σ. The primordial helium abundance is measured to be Y_p = 0.296 ± 0.030, and the effective number of relativistic species is measured to be N_eff = 3.85 ± 0.62. The constraints on these models are strengthened when the CMB data are combined with measurements of the Hubble constant and the baryon acoustic oscillation feature. Notable improvements include ns = 0.9668 ± 0.0093, r < 0.17 (95% CL), and N_eff = 3.86 ± 0.42. The SPT+WMAP data show a mild preference for low power in the CMB damping tail, and while this preference may be accommodated by models that have a negative spectral running, a high primordial helium abundance, or a high effective number of relativistic species, such models are disfavored by the abundance of low-redshift galaxy clusters

Book Review. - Literatur

Book Review. - Literatu

Book Review. - Literatur

Book Review. - Literatu

Theology-Philosophy-Poetry: Toward a Synopsis

From his background as professor of systematic theology, as well as that of his deep interest in philosophy and poetry and his writing in these fields over many years, the author sketches his impressions of the nature of the relationship between theology, philosophy, and poetry and indicates the current tendency toward a synopsis. The relationship between literature (especially poetry) and philosophy and theology is receiving increasing attention from scholars in all three areas. It is the author\u27s conviction that the sensitivity of poets often makes them pioneers in recognizing new situations and impending changes and that some of the outstanding theologians and philosophers of our day have been strongly influenced by poetic insights