Burn-in and the performance quality measures in heterogeneous populations

Burn-in is a widely used engineering method of elimination of defective items before they are shipped to customers or put into field operation. Under the assumption that a population is described by the decreasing or bathtub-shaped failure rate functions, various optimal burn-in problems have been intensively studied in the literature. In this paper, we consider a new model and assume that a population is composed of stochastically ordered subpopulations described by their own performance quality measures. It turns out that this setting can justify burn-in even in situations when it is not justified in the framework of conventional approaches. For instance, it is shown that it can be reasonable to perform burn-in even when the failure rate function that describes the heterogeneous population of items increases and this is one of the main and important findings of our study.     

Topological Links between Duplex DNA and a Circular DNA Single Strand

DNA nanostructures of building blocks topologically linked at a precise position can be assembled from DNA duplexes and circularized oligonucleotides with the aid of peptide nucleic acids (PNAs). Shown schematically is a linked catenane yielding an earring topological DNA label.     

Topological solitons in branched aliphatic molecules

Polymorphic transitions are typical for molecular crystals of long chain aliphatic compounds. In the present work we studied the possibility of polymorphic transitions via the mechanism of topological solitons. The solitons correspond to stretching/compression of aliphatic chain by a half of the period, accompanied by 180° turn in branched molecules. Triacyglycerides (TAG) were chosen as an object of study; temperature dependencies of the specific heat capacity at constant pressure, complex dielectric permittivity, spectral (IR) and structural (powder XRD) properties of TAGs were characterized performed at ?170 ÷ 70°C. Following model was proposed to explain the experimental results. Thermal transformations of TAGs started from initiation of topological solitons on the methyl groups. The solitons passed along the alkyl chains and reoriented the ester groups, resulted in thermal dipole-relaxation polarization defrost observed as a relaxation process in the range (?80÷0)°C. Reaching the stoichiometric obstruction (branching), the solitons reflect from it. When the temperature increases up to 60°C, melting of TAG polycrystals takes place.     

Effective preconditioning of Uzawa type schemes for a generalized Stokes problem

Summary. The Schur complement of a model problem is considered as a preconditioner for the Uzawa type schemes for the generalized Stokes problem (the Stokes problem with the additional term in the motion equation). The implementation of the preconditioned method requires for each iteration only one extra solution of the Poisson equation with Neumann boundary conditions. For a wide class of 2D and 3D domains a theorem on its convergence is proved. In particular, it is established that the method converges with a rate that is bounded by some constant independent of . Some finite difference and finite element methods are discussed. Numerical results for finite difference MAC scheme are provided. Received May 2, 1997 / Revised version received May 10, 1999 / Published online May 8, 2000     

Multi PCET in symmetrically substituted benzimidazoles

Proton-coupled electron transfer (PCET) reactions depend on the hydrogen-bond connectivity between sites of proton donors and acceptors. The 2-(2′-hydroxyphenyl) benzimidazole (BIP) based systems, which mimic the natural Tyr_Z-His190 pair of Photosystem II, have been useful for understanding the associated PCET process triggered by one-electron oxidation of the phenol. Substitution of the benzimidazole by an appropriate terminal proton acceptor (TPA) group allows for two-proton translocations. However, the prototropic properties of substituted benzimidazole rings and rotation around the bond linking the phenol and the benzimidazole can lead to isomers that interrupt the intramolecular hydrogen-bonded network and thereby prevent a second proton translocation. Herein, a strategic symmetrization of a benzimidazole based system with two identical TPAs yields an uninterrupted network of intramolecular hydrogen bonds regardless of the isomeric form. NMR data confirms the presence of a single isomeric form in the disubstituted system but not in the monosubstituted system in certain solvents. Infrared spectroelectrochemistry demonstrates a two-proton transfer process associated with the oxidation of the phenol occurring at a lower redox potential in the disubstituted system relative to its monosubstituted analogue. Computational studies support these findings and show that the disubstituted system stabilizes the oxidized two-proton transfer product through the formation of a bifurcated hydrogen bond. Considering the prototropic properties of the benzimidazole heterocycle in the context of multiple PCET will improve the next generation of novel, bioinspired constructs built by concatenated units of benzimidazoles, thus allowing proton translocations at nanoscale length.

Proton-coupled electron transfer (PCET) reactions depend on the hydrogen-bond connectivity between sites of proton donors and acceptors.     

A Generic Result in Linear Semi-Infinite Optimization

In this paper we consider the space of all the linear semi-infinite programming problems with the same index set, endowed with a suitable topology. We provide a constructive proof of the following generic result: if we confine ourselves to the class of problems having a bounded set of coefficient vectors (those vectors appearing in the left-hand side of the constraints), the set of those problems which have a strongly unique optimal solution contains an open and dense subset of the set of solvable problems in the same class.     

Steroid 19,B‐dinor‐8,10‐iso‐analogues

The Birch reduction of 3‐methoxy‐B‐nor‐8‐isoestra‐1,3,5(10)‐trienes followed by acid hydro­lysis produces steroid androgen 19,B‐dinor‐8,10‐iso‐analogues. By means of X‐ray analysis and correlation NMR spectroscopy of 16,16‐di­methyl‐D‐homo‐19,B‐dinor‐8‐isotestosterone, C₂₀H₃₀O₂, it is demonstrated that the main conformations in the crystal and in solution for two 19,B‐dinor‐8,10‐iso‐analogues are, in general, the same.     

Trans-etherification of catechol-type benzylic ether with diols as a route to new sterically hindered bis-catechols

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