Limiting subdifferentials of indefinite integrals

We compute the limiting subdifferential of the indefinite integral of the form where f is an essentially bounded measurable function, or a function continuous on an interval containing (except for, possibly, ), or a step-function which has a countable number of steps around . The related problem of computing the Aumann integral of the limiting subdifferential mapping ∂f(⋅), where f is a Lipschitz real function defined on an open set U⊂Rn, is also investigated.     

Rhenium and technetium complexes with N,N-dialkyl-N'-benzoylthioureas

N,N-Dialkyl-N'-benzoylthioureas, HR(1)R(2)btu, react under single deprotonation and form air-stable chelate complexes with common rhenium or technetium complexes such as (NBu(4))[MOCl(4)] (M = Re, Tc) or [ReOCl(3)(PPh(3))(2)]. Compositions and molecular structures of the products are strongly dependent on the precursors used and the reaction conditions applied. Reactions with [ReOCl(3)(PPh(3))(2)] in CH(2)Cl(2) give complexes of the general formula [ReOCl(2)(R(1)R(2)btu)(PPh(3))] (3), with the benzoyl oxygen atom of the chelating benzoylthiourea being trans to the oxo ligand, and/or Re(III) complexes of the composition [ReCl(2)(R(1)R(2)btu)(PPh(3))(2)] (4) with the PPh(3) ligands in trans positions to each other. In polar solvents such as MeOH, EtOH or acetone, corresponding reactions without addition of a supporting base only result in intractable brown solutions, from which no crystalline complexes could be isolated. The addition of NEt(3), however, allows the isolation of the bis-chelates [ReOCl(R(1)R(2)btu)(2)] (1) in good yields. In this type of complex, one of the chelating R(1)R(2)btu- ligands coordinates equatorially, while the second occupies the position trans to the oxo ligand with its oxygen atom. The latter compounds can also be prepared from (NBu(4))[ReOCl(4)] in MeOH when no base is added, while the addition of NEt(3) results in the formation of [ReO(OMe)(R(1)R(2)btu)(2)] (5) complexes with the methoxo ligand trans to O(2-). Compounds of the type 5 can alternatively be prepared by heating 1 in MeOH with addition of NEt(3). A reversible conversion of 5 into oxo-bridged dimers of the composition [{ReO(R(1)R(1)btu)(2)}(2)O] (6) is observed in water-containing solvents. Starting from (NBu(4))[TcOCl(4)], a series of technetium complexes of the type [TcOCl(R(1)R(2)btu)(2)] (2) could be prepared. The structures of such compounds are similar to those of the rhenium analogues 1. Reduction of 2 with PPh(3) in CH(2)Cl(2) gives Tc(III) complexes of the composition [TcCl(R(1)R(2)btu)(2)(PPh(3))] (7) having the chloro and PPh(3) ligands in cis positions. When this reaction is performed in the presence of excess chelating ligand, the Tc(III) tris-chelates [Tc(R(1)R(2)btu)(3)] (8) are formed.     

Three-hole microstructured optical fiber for efficient fiber Bragg grating refractometer

We present a photosensitive three-hole microstructured optical fiber specifically designed to improve the refractive index sensitivity of a standard fiber Bragg grating (FBG) sensor photowritten in the suspended Ge-doped silica core. We describe the specific photowriting procedure used to realize gratings in such a fiber. We then determine their spectral sensitivity to the refractive index changes of material filling the holes surrounding the core. The sensitivity is compared with that of standard FBGs photowritten in a six-hole fiber with a larger core diameter. We demonstrate an improvement in the sensitivity by two orders of magnitude and reach a resolution of 3 x 10(-5) and 6 x 10(-6) around mean refractive index values of 1.33 and 1.40, respectively.     

Synthesis and H NMR spectroscopic properties of substituted (η-tetraarylcyclobutadiene)(η-cyclopentadienyl)cobalt metallocenes

The reaction of diarylacetylenes with CoCl(PPh₃)₃ and sodium cyclopentadienylide or sodium carbomethoxycyclopentadienylide gave (η⁴-tetra-arylcyclobutadiene)(η⁵-cyclopentadienyl)cobalt and (η⁴-tetra-arylcyclobutadiene)(η⁵-carbomethoxycyclopentadienyl)cobalt, respectively, where aryl = para-XC₆H₄ (X = CF₃, F, MeO). The reaction was unsuccessful for the synthesis of (η⁴-tetra(para-methoxyphenyl)cyclobutadiene)(η⁵-cyclopentadienyl)cobalt, which was synthesised instead from dicarbonyl(η⁵-cyclopentadienyl)cobalt. In all of the examples starting with CoCl(PPh₃)₃ an intermediate (η⁵-cyclopentadienyl)- or (η⁵-carbomethoxycyclopentadienyl)(triphenylphosphine)-2,3,4,5-tetraarylcobaltacyclopentadiene complex was isolated, and two examples were characterised by X-ray crystallography. Heating the (η⁵-cyclopentadienyl)- or (η⁵-carbomethoxycyclopentadienyl)(triphenylphosphine)-2,3,4,5-tetraarylcobaltacyclopentadiene complexes resulted in clean conversion to the corresponding metallocenes. The influence of the para-aryl substituents on the ¹H NMR of the cyclopentadienyl moiety is tabulated, together with the influence of a range of R substituents in (η⁴-tetraphenylcyclobutadiene)(η⁵-RC₅H₄)cobalt (R = CO₂Me, CH₂OH, Me, CHO, CCH, CO₂H, CN, CONHR¹, 2-oxazolinyl, NH₂, NHAc, HgCl, Br, I, SiMe₃, SnMe₃, Ph).     

Will learning to solve one-step equations pose a challenge to 8th grade students?

Assimilating multiple interactive elements simultaneously in working memory to allow understanding to occur, while solving an equation, would impose a high cognitive load. Element interactivity arises from the interaction between elements within and across operational and relational lines. Moreover, operating with special features (e.g. negative pronumeral) poses additional challenge to master equation solving skills. In an experiment, 41 8th grade students (girls = 16, boys = 25) sat for a pre-test, attended a session about equation solving, completed an acquisition phase which constituted the main intervention and were tested again in a post-test. The results showed that at post-test, students performed better on one-step equations tapping low rather than high element interactivity knowledge. In addition, students performed better on those one-step equations that contained no special features. Thus, both the degree of element interactivity and the operation with special features affect the challenge posed to 8th grade students on learning how to solve one-step equations.     

Highly fluorescence quenching graphene oxide-based oligodeoxynucleotide hairpin systems for probing CNG DNA repeat sequences

In this study we synthesized a novel graphene-oxide (GO) based CNG repeat hairpin probing system capable of detecting target CAG and CTG DNA repeat sequences. The fluorescence of the 30-mer CNG repeat hairpin structure was quenched dramatically by GO in the absence of the target sequence, with a high quenching constant [K = 0.030 (mg/mL)^?1]. We optimized the quenching behavior of this probing system by using graphene oxide (GO) to induce a high degree of discrimination factor (44.6 times) between the fluorescence of the target sequence and that of other non-target sequences. All detection process is explained by displacement mechanism using adsorption, desorption, and hybridization of probe with target DNA sequence on the GO. Graphene-oxide (GO) based CNG repeat hairpin probing system exhibited high sensitivity and selectivity to the target CNG repeat sequence and its detection process is so simple and quick.     

Synthesis of plate-like Li<Subscript>3</Subscript>PS<Subscript>4</Subscript> solid electrolyte via liquid-phase shaking for all-solid-state lithium batteries

The precursor of plate-like Li₃PS₄ solid electrolyte (75Li₂S?25P₂S₅, SE (LS)), about 3 μm in length, 500 nm in width, and 100–200 nm in thickness, was successfully prepared from Li₂S and P₂S₅ using ethyl propionate (EP) as a synthetic medium via liquid-phase shaking. Upon evacuating at 170 °C, the precursor decomposed to SE (LS), which exhibited ionic conductivity of about 2.0 × 10^?4 Scm^?1 at room temperature. SEM observation revealed that the SE (LS) thus obtained had plate-like morphology with dimension of 3 μm in length, 500 nm in width, and 100–200 nm in thickness. Owing to the nanosized SE (LS), an all-solid-state half-cell using composite anode consisting of 90 wt% LiNi_1/3Mn_1/3Co_1/3O₂ (NMC) and 10 wt% SE (LS) delivered a high capacity up to 130 mAhg^?1(NMC) at the first discharge.     

Characterization of deformation behavior of heterogeneous polymer systems using spectroscopic and microscopic methods

Rheo-optical Fourier-transform infrared (FTIR) spectroscopy in combination with Atomic Force Microscopy (AFM) was used to clarify the correlation between the morphology and the mechanical properties of two groups of heterogeneous polymers: different styrene-block-butadiene-block-styrene triblock copolymers and a dynamic vulcanizate based on polypropylene/ethylene-octene-copolymer. In all the polymers investigated the soft phase always oriented more than the hard phase. The degree of orientation in different phases depended on the nature of the phases as well as on the stress distribution in correlation to the morphology and their alignment. The observations at the molecular level corresponded well with the results from morphological studies at the microscopic level, which, in fact, enables an extensive and complex understanding of the structure-properties correlation of these types of polymers.     

Electrophilic Terminal‐Phosphinidene Complexes: Versatile Phosphorus Analogues of Singlet Carbenes

Electrophilic and nucleophilic terminal‐phosphinidene complexes are compared in terms of electronic structures and reactivities. Various precursors of the unstable electrophilic species [R−P−M] (M=Cr, Mo, W(CO)₅ and Fe(CO)₄) are discussed. The addition reactions of the electrophilic phosphinidene complexes with Lewis bases, insertion reactions into O−H, N−H, and activated C−H bonds, and cycloaddition reactions with double and triple bonds are described, as well as some rearrangements and autocondensations. Various applications to the synthesis of new organophosphorus molecules are discussed and techniques available for demetallation are given.