Ground state solution for differential equations with left and right fractional derivatives

In this work, we study the existence of positive solutions for a class of fractional differential equation given by (1) where . Using the mountain pass theorem and comparison argument, we prove that (1) at least has one nontrivial solution. Copyright © 2015 John Wiley & Sons, Ltd.     

A two‐step reaction scheme leading to singlet carbene species that can be detected under matrix conditions for the reaction of Zr(3F) with either CH3F or CH3CN

The results obtained from CASSCF‐MRMP2 calculations are used to rationalize the singlet complexes detected under matrix‐isolation conditions for the reactions of laser‐ablated Zr(³F) atoms with the CH₃F and CH₃CN molecules, without invoking intersystem crossings between electronic states with different multiplicities. The reaction Zr(³F) + CH₃F evolves to the radical products ZrF· + ·CH₃. This radical asymptote is degenerate to that emerging from the singlet channel of the reactants Zr(¹D) + CH₃F because they both exhibit the same electronic configuration in the metal fragment. Hence, the caged radicals obtained under cryogenic‐matrix conditions can recombine through triplet and singlet paths. The recombination of the radical species along the low‐multiplicity channel produces the inserted structures H₃C? Zr? F and H₂C?ZrHF experimentally detected. For the Zr(³F) + CH₃CN reaction, a similar two‐step reaction scheme involving the radical fragments ZrNC· + ·CH₃ explains the presence of the singlet complexes H₃C? Zr? NC and H₂C?Zr(H)NC revealed in the IR‐matrix spectra upon UV irradiation. © 2014 Wiley Periodicals, Inc.     

Characterization and optimization of heroin hapten-BSA conjugates: method development for the synthesis of reproducible hapten-based vaccines

A potential new treatment for drug addiction is immunization with vaccines that induce antibodies that can abrogate the addictive effects of the drug of abuse. One of the challenges in the development of a vaccine against drugs of abuse is the availability of an optimum procedure that gives reproducible and high yielding hapten-protein conjugates. In this study, a heroin/morphine surrogate hapten (MorHap) was coupled to bovine serum albumin (BSA) using maleimide-thiol chemistry. MorHap-BSA conjugates with 3, 5, 10, 15, 22, 28, and 34 haptens were obtained using different linker and hapten ratios. Using this optimized procedure, MorHap-BSA conjugates were synthesized with highly reproducible results and in high yields. The number of haptens attached to BSA was compared by 2,4,6-trinitrobenzenesulfonic acid (TNBS) assay, modified Ellman’s test and matrix assisted laser desorption ionization time-of-flight mass spectrometry (MALDI-TOF MS). Among the three methods, MALDI-TOF MS discriminated subtle differences in hapten density. The effect of hapten density on enzyme-linked immunosorbent assay (ELISA) performance was evaluated with seven MorHap-BSA conjugates of varying hapten densities, which were used as coating antigens. The highest antibody binding was obtained with MorHap-BSA conjugates containing 3–5 haptens. This is the first report that rigorously analyzes, optimizes and characterizes the conjugation of haptens to proteins that can be used for vaccines against drugs of abuse. The effect of hapten density on the ELISA detection of antibodies against haptens demonstrates the importance of careful characterization of the hapten density by the analytical techniques described.     

Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities

Using Lie group theory and canonical transformations, we construct explicit solutions of nonlinear Schr?dinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities can support bound states with an arbitrary number solitons, and discuss other applications of interest to the field of nonlinear matter waves.     

Tunable control of the frequency correlations of entangled photons

We experimentally demonstrate a new technique to control the type of frequency correlations of entangled photon pairs generated by spontaneous parametric downconversion. Frequency-correlated and frequency-anticorrelated photons are produced when a broadband pulse is used as a pump. The method is based on the control of the group velocities of the interacting waves and can be applied in any nonlinear medium and frequency band of interest.     

Peripherally and Axially Carboxylic Acid Substituted Subphthalocyanines for Dye‐Sensitized Solar Cells

A series of subphthalocyanines (SubPcs) bearing a carboxylic acid group either at the peripheral or axial position have been designed and synthesized to investigate the influence of the COOH group positions on the dye‐sensitized solar cell (DSSC) performance. The DSSC devices based on SubPcs with axially substituted carboxylic acid groups showed low photovoltaic performance, whereas peripherally substituted one exhibited higher power conversion efficiency owing to improved injection from LUMO of SubPcs to the TiO₂ conduction band.     

Synthesis and characterization of palladium(II) complexes [PdX2(p-diben)] (X = Cl,Br, I,N3, or NCO; p-diben = N,N′-bis(4-dimethylaminobenzylidene)ethane-1,2-diamine): crystal structure of [Pd(N3)2(p-diben)]

Five new complexes of general formula [PdX₂(p-diben)], where p-diben = N,N′-bis(4-dimethylaminobenzylidene)ethane-1,2-diamine) (1) and X = Cl (2), Br (3), I (4), N₃ (5), or CNO (6), were synthesized and characterized by physicochemical and spectroscopic methods. The crystal structure of compound (5) was determined by single-crystal X-ray diffraction. Complexes 2–6 were characterized as N,N-chelated products. The crystal structure confirmed this formulation for [Pd(N₃)₂(p-diben)], besides showing the isomerism inversion of one of the C=N bonds, caused by Pd(II) coordination.     

On‐Surface Synthesis and Characterization of Triply Fused Porphyrin–Graphene Nanoribbon Hybrids

On‐surface synthesis offers a versatile approach to prepare novel carbon‐based nanostructures that cannot be obtained by conventional solution chemistry. Graphene nanoribbons (GNRs) have potential for a variety of applications. A key issue for their application in molecular electronics is in the fine‐tuning of their electronic properties through structural modifications, such as heteroatom doping or the incorporation of non‐benzenoid rings. In this context, the covalent fusion of GNRs and porphyrins (Pors) is a highly appealing strategy. Herein we present the selective on‐surface synthesis of a Por–GNR hybrid, which consists of two Pors connected by a short GNR segment. The atomically precise structure of the Por–GNR hybrid has been characterized by bond‐resolved scanning tunneling microscopy (STM) and noncontact atomic force microscopy (nc‐AFM). The electronic properties have been investigated by scanning tunneling spectroscopy (STS), in combination with DFT calculations, which reveals a low electronic gap of 0.4 eV.     

MVF Sensor Enables Analysis of Nucleic Acids with Stable Secondary Structures

One major challenge in nucleic acids analysis by hybridization probes is a compromise between the probe's tight binding and sequence‐selective recognition of nucleic acid targets folded into stable secondary structures. We have been developing a four‐way junction (4WJ)‐based sensor that consists of a universal stem‐loop (USL) probe immobilized on an electrode surface and two adaptor strands (M and F). The sensor was shown to be highly selective towards single base mismatches at room temperature, able to detect multiple targets using the same USL probe, and have improved ability to detect folded nucleic acids. However, some nucleic acid targets, including natural RNA, are folded into very stable secondary and tertiary structures, which may represent a challenge even for the 4WJ sensors. This work describes a new sensor, named MVF since it uses three probe stands M, V and F, which further improves the performance of 4WJ sensors with folded targets. The MVF sensor interrogating a 16S rRNA NASBA amplicon with calculated folding energy of ?32.82 kcal/mol has demonstrated 2.5‐fold improvement in a signal‐to‐background ratio in comparison with a 4WJ sensor lacking strand V. The proposed design can be used as a general strategy in the analysis of folded nucleic acids including natural RNA.