pα||n α. As usual p will denote primes, pα||n means that p divides n but p does not, and a function f(n) is additive if f(mn) = f(m)+f(n) whenever (m,n) = 1. From the pioneering works of Alladi and Erdős [1]-[2], P. Erdős’s perspicacity and insight have been one of the main driving forces in the research that brought on many results on summatory functions of large additive functions and P (n). ...

Reaction of MoCl3(THF)3 with [Me2Si{NLi(Dipp)}2]2 (Dipp = 2,6-i-PrC6H3) afforded a triply bonded dimolybdenum complex 1,2-Mo2Cl2[Me2Si(NDipp)2]2 1, spanned by two Me2Si[N(Dipp)]2 ligands, thus resulting in a syn conformation. The air- and moisture-sensitive compound 1 was characterized by NMR spectroscopic, elemental, and single-crystal X-ray crystallographic analysis. Reduction of 1 by Na/Hg y...

We investigate the stability properties of two different classes of metabolic cycles using a combination of analytical and computational methods. Using principles from structural kinetic modeling (SKM), we show that the stability of metabolic networks with certain structural regularities can be studied using a combination of analytical and computational techniques. We then apply these technique...

Most analyses of reaction time (RT) data are conducted by using the statistical techniques with which psychologists are most familiar, such as analysis of variance on the sample mean. Unfortunately, these methods are usually inappropriate for RT data, because they have little power to detect genuine differences in RT between conditions. in addition, some statistical approaches can, under certai...

Many exposures of epidemiological interest are time varying, and the values of potential confounders may change over time leading to time varying confounding. The aim of many longitudinal studies is to estimate the causal effect of a time varying exposure on an outcome that requires adjusting for time varying confounding. Time varying confounding affected by previous exposure often occurs in pr...

An accurate representation of three-dimensional (3D) object orientation is essential for interacting with the environment. Where and how the brain visually encodes 3D object orientation remains unknown, but prior studies suggest the caudal intraparietal area (CIP) may be involved. Here, we develop rigorous analytical methods for quantifying 3D orientation tuning curves, and use these tools to t...

Positrons have been used for material analysis not only because of their novel characteristics, such as an ability to detect open-volume type defects in materials, but also because interactions with solids differ from those of electrons in such processes as scattering and diffraction. Monoenergetic positron beams and microbeams were developed in the 1980s, and positron experiments have made pro...

The ability to test hundreds to thousands of cellular phenotypes in a single experiment has opened up new avenues of investigation and exploration and led to important discoveries in very diverse applications of microbiological research and development. The information provided by global phenotyping is complementary to, and often more easily interpretable than information provided by global mol...

The ability to test hundreds to thousands of cellular phenotypes in a single experiment has opened up new avenues of investigation and exploration and led to important discoveries in very diverse applications of microbiological research and development. The information provided by global phenotyping is complementary to, and often more easily interpretable than information provided by global mol...

The need for global feed supply traceability, the high-throughput testing demands of feed industry, and regulatory enforcement drive the need for feed analysis and make extremely complex the issue of the control and evaluation of feed quality, safety, and functional properties, all of which contribute to the very high number of analyses that must be performed. Feed analysis, with respect to ani...