Direct and Inverse Variational Problems on Time Scales: A Survey

We deal with direct and inverse problems of the calculus of variations on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we give a general form for a variational functional to attain a local minimum at a given point of the vector space. Furthermore, we provide a necessary condition for a dynamic integro-differential equation to be an Euler-Lagrange equation (Helmholtz's problem of the calculus of variations on time scales). New and interesting results for the discrete and quantum settings are obtained as particular cases. Finally, we consider very general problems of the calculus of variations given by the composition of a certain scalar function with delta and nabla integrals of a vector valued field.Comment: This is a preprint of a paper whose final and definite form will be published in the Springer Volume 'Modeling, Dynamics, Optimization and Bioeconomics II', Edited by A. A. Pinto and D. Zilberman (Eds.), Springer Proceedings in Mathematics & Statistics. Submitted 03/Sept/2014; Accepted, after a revision, 19/Jan/201

Influence of Culture Conditions on the Bioreduction of Organic Acids to Alcohols by Thermoanaerobacter pseudoethanolicus

Thermoanaerobacter species have recently been observed to reduce carboxylic acids to their corresponding alcohols. The present investigation shows that Thermoanaerobacter pseudoethanolicus converts C2–C6 short-chain fatty acids (SCFAs) to their corresponding alcohols in the presence of glucose. The conversion yields varied from 21% of 3-methyl-1-butyrate to 57.9% of 1-pentanoate being converted to their corresponding alcohols. Slightly acidic culture conditions (pH 6.5) was optimal for the reduction. By increasing the initial glucose concentration, an increase in the conversion of SCFAs reduced to their corresponding alcohols was observed. Inhibitory experiments on C2–C8 alcohols showed that C4 and higher alcohols are inhibitory to T. pseudoethanolicus suggesting that other culture modes may be necessary to improve the amount of fatty acids reduced to the analogous alcohol. The reduction of SCFAs to their corresponding alcohols was further demonstrated using 13C-labelled fatty acids and the conversion was followed kinetically. Finally, increased activity of alcohol dehydrogenase (ADH) and aldehyde oxidation activity was observed in cultures of T. pseudoethanolicus grown on glucose as compared to glucose supplemented with either 3-methyl-1-butyrate or pentanoate, using both NADH and NADPH as cofactors, although the presence of the latter showed higher ADH and aldehyde oxidoreductase (ALDH) activity

Site-directed spin labeling measurements of nanometer distances in nucleic acids using a sequence-independent nitroxide probe

In site-directed spin labeling (SDSL), local structural and dynamic information is obtained via electron paramagnetic resonance (EPR) spectroscopy of a stable nitroxide radical attached site-specifically to a macromolecule. Analysis of electron spin dipolar interactions between pairs of nitroxides yields the inter-nitroxide distance, which provides quantitative structural information. The development of pulse EPR methods has enabled such distance measurements up to 70 Å in bio-molecules, thus opening up the possibility of SDSL global structural mapping. This study evaluates SDSL distance measurement using a nitroxide (designated as R5) that can be attached, in an efficient and cost-effective manner, to a phosphorothioate backbone position at arbitrary DNA or RNA sequences. R5 pairs were attached to selected positions of a dodecamer DNA duplex with a known NMR structure, and eight distances, ranging from 20 to 40 Å, were measured using double electron-electron resonance (DEER). The measured distances correlated strongly (R(2) = 0.98) with the predicted values calculated based on a search of sterically allowable R5 conformations in the NMR structure, thus demonstrating accurate distance measurements using R5. Furthermore, distance measurement in a 42 kD DNA was demonstrated. The results establish R5 as a sequence-independent probe for global structural mapping of DNA and DNA–protein complexes

RhoGTPase Regulators Orchestrate Distinct Stages of Synaptic Development

Small RhoGTPases regulate changes in post-synaptic spine morphology and density that support learning and memory. They are also major targets of synaptic disorders, including Autism. Here we sought to determine whether upstream RhoGTPase regulators, including GEFs, GAPs, and GDIs, sculpt specific stages of synaptic development. The majority of examined molecules uniquely regulate either early spine precursor formation or later matura- tion. Specifically, an activator of actin polymerization, the Rac1 GEF β-PIX, drives spine pre- cursor formation, whereas both FRABIN, a Cdc42 GEF, and OLIGOPHRENIN-1, a RhoA GAP, regulate spine precursor elongation. However, in later development, a novel Rac1 GAP, ARHGAP23, and RhoGDIs inactivate actomyosin dynamics to stabilize mature synap- ses. Our observations demonstrate that specific combinations of RhoGTPase regulatory pro- teins temporally balance RhoGTPase activity during post-synaptic spine development

A Practical Ab Initio Quantum Chemistry Course Using the. . .

. Teaching quantum chemistry has become an important issue, and the demand for textbooks and practical exercises at different levels of skill and background has risen substantially. At the same time, education is being revolutionized by new technologies available in electronic media. Information networks are changing the way educational programs are developed and disseminated. In this work we present the practical exercises for the ab initio quantum chemistry course at the Department of Chemistry of ETH, Zurich. The course gives an introduction to the methods of ab initio quantum chemistry with the goal of enabling students to perform their own ab initio studies. The lectures are accompanied by practical exercises in which the student solves small problems providing insight into the various theoretical methods, the techniques of their application, and the interpretation of results. The practical exercises, which cover a broad range of topics from different areas of physical chemistry, ..

The diamond integral on time scales

We define a more general type of integral on time scales. The new diamond integral is a refined version of the diamond-alpha integral introduced in 2006 by Sheng et al. A mean value theorem for the diamond integral is proved, as well as versions of Holder’s, Cauchy–Schwarz’s, and Minkowski’s inequalities