Optimal mining of a stratiform phosphate field

An optimal control model is developed to determine optimal surface mining operations of a phosphate field. This field1806 1040 contains both a bottom layer and a top layer of phosphates. The deeper the digging, the more phosphates will be exploited but the higher will be the cost per ton. If the bottom layer is not exploited, it will be lost to future production. The methods of Optimal Control Theory are applied and produce expressions which can be evaluated for the optimal scheduling around the phosphate field.     

On repeated games with general information function

For a class of repeated two-person zero-sum games with incomplete information it was proved byAumann andMaschler that limν _n exists,ν _n being the value of the game withn repetitions. If the players know at each stage the moves done by both players at all previous stages,Aumann andMaschler could prove that the error termδ _n=¦ν _n — limν _n ¦ satisfiesδ _n≤c/√n for somec>0. It was then shown byZamir that this bound is the lowest possible. In this paper it is shown that if previous moves are not always announced,δ _n may be of higher order of magnitude e.g.δ _n≥c/n ^1/3 for somec>0. New upper bounds forδ _n are given for two classes of games.     

Matrix methods in decompositions of modules

Matrix methods of elementary linear algebra are extended to general direct-sum decompositions of modules. These methods are then shown to yield simple proofs of some well-known theorems, notably the Beck-Warfield “mutual exchange property” and the Krull-Schmidt theorem.     

Nonoscillation theorems in convex sets

This paper presents a new and simple technique for a certain class of variational problems which includes many of the important problems of mathematical physics, e.g., the Brachistochrone, geodesies, and minimal surface of revolution problems. The technique uses Caratheodory's equivalent problems approach but combines two equivalent problems at the same time to get the sufficiency and uniqueness results. It does not use any of the classical sufficiency conditions such as the Weierstrass condition. The equations that we are led to by this new approach turn out to be the Hamilton-Jacobi and Euler-Lagrange equations for the problem, but here we have not had to use any of the classical Hamilton-Jacobi theory nor derivations to get its results (e.g., orthogonality of the extremals to the wave fronts) for this class of problems. The cases for one and n dependent variables are presented and illustrated. Implications and generalizations of the method are discussed.     

Workload distributions in ASIP queueing networks

Queueing Systems - The workload of a generalized n-site asymmetric simple inclusion process (ASIP) is investigated. Three models are analyzed. The first model is a serial network for which the...     

Coherently controlled molecular junctions

Within a generic model, we discuss the possibility of coherent control of charge fluxes in unbiased molecular junctions. The control is induced by resonances between the Rabi frequency due to a pumping laser field and internal characteristic frequencies of pre-designed molecular donor-bridge-acceptor complexes. Two models are considered: a coherently controlled molecular charge pump and a molecular switch. The study generalizes previous consideration of light induced current [M. Galperin and A. Nitzan, Phys. Rev. Lett. 95, 206802 (2005)] and of a molecular electron pump [R. Volkovich and U. Peskin, Phys. Rev. B 83, 033403 (2011)] and accounts for the coherently driven charge transport in an unbiased molecular junction with symmetric coupling to leads. Numerical examples demonstrate the feasibility of the control mechanism for realistic junctions parameters.     

Crystal Structure-Guided Design of Bisubstrate Inhibitors and Photoluminescent Probes for Protein Kinases of the PIM Family

We performed an X-ray crystallographic study of complexes of protein kinase PIM-1 with three inhibitors comprising an adenosine mimetic moiety, a linker, and a peptide-mimetic (d-Arg)₆ fragment. Guided by the structural models, simplified chemical structures with a reduced number of polar groups and chiral centers were designed. The developed inhibitors retained low-nanomolar potency and possessed remarkable selectivity toward the PIM kinases. The new inhibitors were derivatized with biotin or fluorescent dye Cy5 and then applied for the detection of PIM kinases in biochemical solutions and in complex biological samples. The sandwich assay utilizing a PIM-2-selective detection antibody featured a low limit of quantification (44 pg of active recombinant PIM-2). Fluorescent probes were efficiently taken up by U2OS cells and showed a high extent of co-localization with PIM-1 fused with a fluorescent protein. Overall, the developed inhibitors and derivatives represent versatile chemical tools for studying PIM function in cellular systems in normal and disease physiology.