Optimal controls with equality state constraints

In this paper, we derive necessary conditions for a measurable controlu with values in a compact convex subsetU ofR ^P to minimize the integral $$\int_a^b {b^0 (s,x(s),u(s))} ds$$ subject to equality and inequality state constraints. The general conditions take the form of a maximum principle which involves an integration with respect to a finitely additive set function, but conditions are given under which this reduces to the classical maximum principle. These results are similar to results derived in Ref. 1 for relaxed controls.     

Multiplexed analyte and oligonucleotide detection on microarrays using several redox enzymes in conjunction with electrochemical detection

We show that multiple enzyme tags may be used in an immunoassay format or for the detection of sequence-specific DNA on microarrays. The assays may be multiplexed and monitored under separate solution and voltage differences. Thus, the detection method relies on an electrochemical detection format, whereby multiple enzymes can be sensed. In our case we utilize horseradish peroxidase, laccase, and glucose dehydrogenase as enzymes attached to specific antibodies or to streptavidin.     

The Hadwiger Number of Jordan Regions Is Unbounded

We show that for every n > 0 there is a planar topological disk A₀ and n translates A₁, A₂, ..., A_n of A₀ such that the interiors of A₀, ..., A_n are pairwise disjoint, but with each A_i touching A₀ for 1 ≤ i ≤ n.     

Interocular induction of illusory size perception

Background  

The perceived size of objects not only depends on their physical size but also on the surroundings in which they appear. For example, an object surrounded by small items looks larger than a physically identical object surrounded by big items (Ebbinghaus illusion), and a physically identical but distant object looks larger than an object that appears closer in space (Ponzo illusion). Activity in human primary visual cortex (V1) reflects the perceived rather than the physical size of objects, indicating an involvement of V1 in illusory size perception. Here we investigate the role of eye-specific signals in two common size illusions in order to provide further information about the mechanisms underlying illusory size perception.     

Reynolds-averaged Navier–Stokes initialization and benchmarking in shock-driven turbulent mixing

We investigate a strategy for benchmarking Reynolds-averaged Navier–Stokes (RANS) models by comparing moments extracted from averaged large eddy simulation (LES) data and those predicted directly by RANS. We consider the Besnard–Harlow–Rauenzahn (BHR) RANS approach designed for variable-density compressible flows, which has been previously applied to a wide variety of turbulence problems of interest. We focus on the model's ability to predict moments relevant to shock-driven material mixing. A prototypical inverse chevron shock tube configuration is considered, for which laboratory and previous LES studies are available for comparison and validation. We show that when appropriately initialized, BHR is capable of accurately capturing various characteristic integral measures of the flow; strategies for initialization are demonstrated while addressing sensitivity of BHR predictions to closure and initialization specifics, initial material interface conditions, and grid resolution. The reference simulations are performed using implicit LES based on the Los Alamos National Laboratory RAGE hydrodynamics code.     

HPLC-DAD-qTOF Compositional Analysis of the Phenolic Compounds Present in Crude Tomato Protein Extracts Derived from Food Processing

The conversion of raw fruits and vegetables, including tomatoes into processed food products creates side streams of residues that can place a burden on the environment. However, these processed residues are still rich in bioactive compounds and in an effort to valorize these materials in tomato by-product streams, the main aim of this study is to extract proteins and identify the main phenolic compounds present in tomato pomace (TP), peel and skins (TPS) by HPLC-DAD-ESI-QTOF. Forty different phenolic compounds were identified in the different tomato extracts, encompassing different groups of phenolic compounds, including derivatives of simple phenolic acid derivatives, hydroxycinnamoylquinic acid, flavones, flavonones, flavonol, and dihydrochalcone. In the crude protein extract (TPE) derived from tomatoes, most of these compounds were still present, confirming that valuable phenolic compounds were not degraded during food processing of these co-product streams. Moreover, phenolic compounds present in the tomato protein crude extract could provide a valuable contribution to the required daily intake of phenolics that are usually supplied by consuming fresh vegetables and fruits.     

Bell inequalities for graph states

We investigate the nonlocal properties of graph states. To this aim, we derive a family of Bell inequalities which require three measurement settings for each party and are maximally violated by graph states. In turn, for each graph state there is an inequality maximally violated only by that state. We show that for certain types of graph states the violation of these inequalities increases exponentially with the number of qubits. We also discuss connections to other entanglement properties such as the positivity of the partial transpose or the geometric measure of entanglement.     

Detecting genuine multipartite entanglement with two local measurements

We present entanglement witness operators for detecting genuine multipartite entanglement. These witnesses are robust against noise and require only two local measurement settings when used in an experiment, independent of the number of qubits. This allows detection of entanglement for an increasing number of parties without a corresponding increase in effort. The witnesses presented detect states close to Greenberger-Horne-Zeilinger, cluster, and graph states. Connections to Bell inequalities are also discussed.