The existence of a positive solution for nonlinear fractional differential equations with integral boundary value conditions

In this paper, first, we consider the existence of a positive solution for the nonlinear fractional differential equation boundary value problem where 0≤λ < 1,^CD^α is the Caputo's differential operator of order α, and f:[0,1] × [0,∞)→[0,∞) is a continuous function. Using some cone theoretic techniques, we deduce a general existence theorem for this problem. Then, we consider two following more general problems for arbitrary α, 1≤n < α≤n + 1: Problem 1: where , 0≤λ < k + 1; Problem 2: where 0≤λ≤α and D^α is the Riemann–Liouville fractional derivative of order α. For these problems, we give existence results, which improve recent results in the literature. Copyright © 2016 John Wiley & Sons, Ltd.     

On q-orthogonal polynomials over a collection of complex origin intervals related to little q-Jacobi polynomials

We construct the sequence of orthogonal polynomials with respect to an inner product which is defined by q-integrals over a collection of intervals in the complex plane. We prove that they are connected with little q-Jacobi polynomials. For such polynomials we discuss a few representations, a recurrence relation, a difference equation, a Rodrigues-type formula and a generating function. 2000 Mathematics Subject Classification Primary—33D45, 42C05     

The deformed exponential functions of two variables in the context of various statistical mechanics

In the recent development in various disciplines of physics, it is noted the need for including the deformed versions of the exponential functions. In last two decades, the Tsallis and Kaniadakis versions have found a lot of applications. In this paper, we consider the deformations which have two purposes. First, we introduce them like beginning of a more general mathematical approach where the Tsallis and Kaniadakis exponential functions are the special cases. Then, we wish to pay attention to the mathematical community that they have a lot of interesting properties from mathematical point of view and possibilities in applications. Really, we will show the differential and difference properties of our deformations which are important for the formation and explanation of continuous and discrete models of numerous phenomena.     

STM images of a large organic molecule adsorbed on a bare metal substrate or on a thin insulating layer: Visualization of HOMO and LUMO

An isomer of the methylterrylene molecule was adsorbed both on Cu(111) and on a NaCl bilayer deposited on Cu(111) and imaged by ultra high vacuum scanning tunneling microscopy at low temperature (5 K). On the bare metal surface, the STM images do not reveal any intramolecular resolution and do not depend on the applied tunnel bias. On the contrary, the images acquired at specific bias voltages for the molecule on the salt layer show a striking similarity with the spatial distribution of the electronic probability density in the highest occupied molecular orbital (HOMO) and in the lowest unoccupied molecular orbital (LUMO) of free methylterrylene. They are well reproduced by elastic scattering quantum chemistry calculations. These data provide a direct view of the hyperconjugative interaction between the methyl group and the frontier orbitals of terrylene.     

Simultaneous Determination of Pb and Cd Traces in Water Samples by Anodic Stripping Voltammetry Using a Modified GC Electrode

The determination of Pb and Cd with a Nafion‐modified glassy carbon electrode and Cu‐DPABA complex (Cu‐DPABA–NA/GCE; DPABA is methyl 3,5‐bis{bis‐[(pyridin‐2‐yl)methyl]amino}methyl‐benzoate) as an alternative electrode for anodic stripping voltammetry was described. Pb and Cd were accumulated in acetate buffer pH 4 at a potential of ?1.4 V (vs. Ag/AgCl electrode) for 120 s followed by a DPASV scan from ?1.2 to ?0.2 V. Under optimum conditions the calibration curves were linear in the range of 4.8×10^?9–5.0×10^?5 and 5.0×10^?9–5×10^?5 mol L^?1 for Pb and Cd, respectively. Detection limits were 1.8×10^?9 and 1.2×10^?9 mol L^?1 for Pb and Cd, respectively. Different parameters and conditions, such as membrane ingredients, accumulation time, potential and pH value were optimized. A study of interfering substances was also performed. A significant increase in current was achieved at the modified electrode in comparison with the bare glassy carbon electrode. The validation of the proposed method was made by Pb and Cd determination in the certified reference material Groundwater CRM 610 (BCR, Community Bureau of Reference, Brussels, Belgium). The electrode was successfully applied for determination of Pb and Cd in river water with a high content of organic contaminants without any pretreatment.     

Transition metal complexes with Girard reagent-based ligands

The ligand, salicylaldehyde Girard-T hydrazonium chloride, [H₂SalGT]Cl (1), and two complexes [Cu(HSalGT)X₂]·H₂O (X = Br(2); Cl(3)) were synthesized and their crystal structures were determined by single-crystal X-ray analysis. In the two isostructural complexes, the Cu(II) is located in a square-pyramidal environment, with the chelating ligand and one halogen atom in the basal plane and the second halogen in the apical position. The most apparent structural difference between the 1 and its complexes 2 and 3 is the orientation of the N(CH₃)₃ group: in 1, it is practically coplanar to the rest of the molecule, while in 2 and 3 it is oriented to the side of the axially bonded halogen, which can be explained by the C–H…X intramolecular interactions. The compounds were characterized by elemental analysis, molar conductivity, magnetic susceptibility and electronic absorption spectra.     

Weak intermolecular interactions in 11‐chloro‐2,3,4,5‐tetrahydro‐1H‐cyclohepta[b]quinoline

The title compound, C₁₄H₁₄ClN, is a chloro analogue of tacrine, an acetylcholinesterase inhibitor. The compound comprises a seven‐membered alicyclic ring whose CH donor groups are engaged in extensive intermolecular interactions. The important feature of this crystal structure is that, regardless of the presence of two typical hydrogen‐bonding acceptors, viz. chlorine and nitrogen, the corresponding C—H...Cl and C—H...N interactions take no significant role in crystal stabilization. The molecules form dimers through π–π interactions with an interplanar distance between interacting pyridine rings of 3.576 (1) Å. Within the dimers, the molecules are additionally interconnected by four C—H...π interactions. The dimers arrange into regular columns via further intermolecular C—H...π interactions.     

(E)‐4‐[(2‐Carbamoylhydrazinylidene)methyl]‐3‐hydroxy‐5‐hydroxymethyl‐2‐methylpyridin‐1‐ium nitrate

The title compound, C₉H₁₃N₄O₃⁺·NO₃⁻, is the first structurally characterized Schiff base derived from semicarbazide and pyridoxal. Unusually for an unsubstituted semicarbazone, the compound adopts a syn conformation, in which the carbonyl O atom is in a cis disposition relative to the azomethine N atom. This arrangement is supported by a pair of hydrogen bonds between the organic cation and the nitrate anion. The cation is essentially planar, with only a hydroxymethyl O atom deviating significantly from the mean plane of the remaining atoms (r.m.s. deviation of the remaining non‐H atoms = 0.01 Å). The molecules are linked into flat layers by N—H...O and C—H...O hydrogen bonds. O—H...O hydrogen bonds involving the hydroxymethyl group as a donor interconnect the layers into a three‐dimensional structure.     

Novel Radioiodinated and Radiofluorinated Analogues of FT-2102 for SPECT or PET Imaging of mIDH1 Mutant Tumours

Isocitrate dehydrogenases (IDHs) are metabolic enzymes commonly mutated in human cancers (glioma, acute myeloid leukaemia, chondrosarcoma, and intrahepatic cholangiocarcinoma). These mutated variants of IDH (mIDH) acquire a neomorphic activity, namely, conversion of α-ketoglutarate to the oncometabolite D-2-hydroxyglutarate involved in tumourigenesis. Thus, mIDHs have emerged as highly promising therapeutic targets, and several mIDH specific inhibitors have been developed. However, the evaluation of mIDH status, currently performed by biopsy, is essential for patient stratification and thus treatment and follow-up. We report herein the development of new radioiodinated and radiofluorinated analogues of olutasidenib (FT-2102) as tools for noninvasive single photon emission computed tomography (SPECT) or positron emission tomography (PET) imaging of mIDH1 up- and dysregulation in tumours. Nonradiolabelled derivatives 2 and 3 halogenated at position 6 of the quinolinone scaffold were synthesised and tested in vitro for their inhibitory potencies and selectivities in comparison with the lead compound FT-2102. Using a common organotin precursor, (S)-[¹²⁵I]2 and (S)-[¹⁸F]3 were efficiently synthesised by radio-iododemetallation and copper-mediated radiofluorination, respectively. Both radiotracers were stable at room temperature in saline or DPBS solution and at 37 °C in mouse serum, allowing future planning of their in vitro and in vivo evaluations in glioma and chondrosarcoma models.     

Chiral close-packing of achiral star-shaped molecules on solid surfaces

From the interplay of scanning tunneling microscopy and theoretical calculations, we study the chiral self-assembly of achiral HtB-HBC molecules upon adsorption on the Cu(110) surface. We find that chirality is expressed at two different levels: a +/-5 degrees rotation of the molecular axis with respect to the close-packed direction of the Cu(110) substrate and a chiral close-packed arrangement expected for star-shaped molecules in 2D. Out of the four possible chiral expressions, only two are found to exist due the effect of van der Waals (vdW) interactions forcing the molecules to simultaneously adjust to the atomic template of the substrate geometry and self-assemble in a close-packed geometry.