An extreme values of the function <Emphasis Type="Italic">S</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) in short intervals

We obtain new estimates for the maximum and minimum of the argument of the Riemann zetafunction on very short segments of the critical line. These results are based on the Riemann hypothesis.     

Optical technique for classification, recognition and identification of obscured objects

The capability to classify, recognize and to identify objects from spatially low resolution images has high significance in security related applications especially in a case that recognition of camouflaged object is required.In this paper we present a novel approach in which the scenery containing obscured objects which we wish to classify, recognize or identify is illuminated by spatially coherent beam (e.g. laser) and therefore secondary speckles pattern is reflected from the objects. By special image processing algorithm developed for this research and which is basically based upon temporal tracking of the random speckle pattern one may extract the temporal signature of the object. And right after, to use it for its classification (e.g. its separation from the other objects in the scenery), its recognition and identification even in a case that the imager provides poor spatial resolution that by itself does not allow doing the specified detection related operations.     

Converting homotopies to isotopies and dividing homotopies in half in an effective way

We prove two theorems about homotopies of curves on two-dimensional Riemannian manifolds. We show that, for any \({\epsilon > 0}\) , if two simple closed curves are homotopic through curves of bounded length L, then they are also isotopic through curves of length bounded by \({L + \epsilon}\) . If the manifold is orientable, then for any \({\epsilon > 0}\) we show that, if we can contract a curve \({\gamma}\) traversed twice through curves of length bounded by L, then we can also contract \({\gamma}\) through curves bounded in length by \({L + \epsilon}\) . Our method involves cutting curves at their self-intersection points and reconnecting them in a prescribed way. We consider the space of all curves obtained in this way from the original homotopy, and use a novel approach to show that this space contains a path which yields the desired homotopy.     

Phase size effect in thin Ge-Se polycrystalline films

The Raman spectra of thin (d = 60–170 nm) Ge-Se polycrystalline films obtained by vacuum thermal evaporation of Ge₁₀Se₉₀ glass are investigated in the spectral range 110–310 cm^?1. The coexistence of the glasslike and crystalline phases α-Se, β-Se, and β-GeSe₂ is established using the X-ray diffraction method. Analysis of diffraction patterns and the Raman spectra of polycrystalline samples of various thicknesses demonstrates a phase size effect in the transition of Se from the α-monoclinic to the β monoclinic modification (d ～ 120 nm). It is found that the crystalline phase of Se is of the nanodisperse type with an average grain size of ～30–50 nm. Crystallites of β-GeSe₂ have an average size of ～100–130 nm.     

DNA-templated polymerization of side-chain-functionalized peptide nucleic acid aldehydes

The DNA-templated polymerization of synthetic building blocks provides a potential route to the laboratory evolution of sequence-defined polymers with structures and properties not necessarily limited to those of natural biopolymers. We previously reported the efficient and sequence-specific DNA-templated polymerization of peptide nucleic acid (PNA) aldehydes. Here, we report the enzyme-free, DNA-templated polymerization of side-chain-functionalized PNA tetramer and pentamer aldehydes. We observed that polymerization of tetramer and pentamer PNA building blocks with a single lysine-based side chain at various positions in the building block could proceed efficiently and sequence specifically. In addition, DNA-templated polymerization also proceeded efficiently and in a sequence-specific manner with pentamer PNA aldehydes containing two or three lysine side chains in a single building block to generate more densely functionalized polymers. To further our understanding of side-chain compatibility and expand the capabilities of this system, we also examined the polymerization efficiencies of 20 pentamer building blocks each containing one of five different side-chain groups and four different side-chain regio- and stereochemistries. Polymerization reactions were efficient for all five different side-chain groups and for three of the four combinations of side-chain regio- and stereochemistries. Differences in the efficiency and initial rate of polymerization correlate with the apparent melting temperature of each building block, which is dependent on side-chain regio- and stereochemistry but relatively insensitive to side-chain structure among the substrates tested. Our findings represent a significant step toward the evolution of sequence-defined synthetic polymers and also demonstrate that enzyme-free nucleic acid-templated polymerization can occur efficiently using substrates with a wide range of side-chain structures, functionalization positions within each building block, and functionalization densities.     

New Type of Nanocomposite CsH2PO4-UiO-66 Electrolyte with High Proton Conductivity

New (1−x)CsH₂PO₄–xUiO-66 electrolytes with high proton conductivity and thermal stability at 230–250 °C were developed. The phase composition and proton conductivity of nanocomposites (x = 0–0.15) were investigated in detail. As shown, the UiO-66 matrix is thermally and chemically suitable for creating composites based on CsH₂PO₄. The CsH₂PO₄ crystal structure remains, but the degree of salt crystallinity changes in nanocomposites. As a result of interface interaction, dispersion, and partial salt amorphization, the proton conductivity of the composite increases by two orders of magnitude in the low-temperature range (up to 200 °C), depending on the UiO-66 fraction, and goes through a maximum. At higher temperatures, up to 250 °C, the conductivity of nanocomposites is close to the superprotonic values of the original salt at low UiO-66 values; then, it decreases linearly within one order of magnitude and drops sharply at x > 0.07. The stability of CsH₂PO₄-UiO-66 composites with high proton conductivity was shown. This creates prospects for their use as proton membranes in electrochemical devices.     

3′-Keto-1-nitro-2-phenylspiro[cyclopropane-3,2′-quinuclidine]: Synthesis and reactions with nucleophiles

3′-Keto-1-nitro-2-phenylspiro[cyclopropane-3,2′-quinuclidine] was synthesized by a two-step procedure from 2-benzylidenequinuclidin-3-one. Ring-opening reactions of the cyclopropane ring using a variety of N-, O-, and C-nucleophiles (amines, methoxide, nitromethanate, cyanide anions, and lithium diphenylcopper) were studied, and a general mechanism for the transformations is proposed.