A fixed point theorem of Jungck in $$b_v(s)$$-metric spaces

In this paper, we prove the common fixed point theorem of Jungck in \(b_v(s)\)-metric spaces. As a corollary, a common fixed point theorem in the rectangular b-metric space and the well known common fixed point theorem in b-metric spaces are obtained.     

Surface states of titanium dioxide nanoparticles modified with enediol ligands

Control of surface states of titanium dioxide nanoparticles using 2-(3,4-dihydroxyphenyl)ethylamine (dopamine) and 3,4-dihydrophenylacetic acid, which act as ligands to the undercoordinated surface sites (carrier traps), is demonstrated by electrochemical techniques. The deepest traps were found to be most reactive and are selectively removed by the addition of the ligands which enhances the kinetics of electron accumulation in the film. Furthermore, a shift in the Fermi level to more positive potentials was detected for electrodes modified with the negatively charged ligand (3,4-dihydrophenylacetic acid) compared to that of electrodes modified with the positively charged ligand (dopamine). The presence of the negative charge on the ligand also contributed to the underpotential of hydrogen evolution on 3,4-dihydrophenylacetic acid-modified electrodes.     

A coupled best approximations theorem in normed spaces

We prove a coupled best approximations theorem in normed spaces. Also, we derive the results on coupled coincidence points and coupled fixed points, which were introduced by Lakshmikantham and ?iri? [V. Lakshmikantham, LJ. ?iri?, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. TMA, 70 (2009) 4341-4349].     

Bound states in continuum: Quantum dots in a quantum well

We report on the existence of a bound state in the continuum (BIC) of quantum rods (QR). QRs are novel elongated InGaAs quantum dot nanostructures embedded in the shallower InGaAs quantum well. BIC appears as an excited confined dot state and energetically above the bottom of a well subband continuum. We prove that high height-to-diameter QR aspect ratio and the presence of a quantum well are indispensable conditions for accommodating the BIC. QRs are unique semiconductor nanostructures, exhibiting this mathematical curiosity predicted 83 years ago by Wigner and von Neumann.     

Bases of spaces of matrices satisfying rank conditions

Motivated by the problem concerning the existence of non-singular bilinear maps, vector spaces of matrices consisting of matrices with rank bounded below are investigated. It is shown that bases for such spaces of maximum dimension can be chosen in such a way to consist of matrices of the minimal rank. An estimate of the ranks of matrices in particular types of bases for maximal such spaces is also given. This extends previously known results which were valid only in the case of spaces consisting of matrices of rank not equal to one.     

Tailoring the electrochemical charge storage properties of carbonaceous support by redox properties of heteropoly acids: where does the synergy come from?

Journal of Solid State Electrochemistry - The synergistic effects between two Keggin-type heteropoly acids (HPAs) and carbon surface were examined and elucidated. An improved high rate capability...     

Integrated Transmission Electron and Single‐Molecule Fluorescence Microscopy Correlates Reactivity with Ultrastructure in a Single Catalyst Particle

Establishing structure–activity relationships in complex, hierarchically structured nanomaterials, such as fluid catalytic cracking (FCC) catalysts, requires characterization with complementary, correlated analysis techniques. An integrated setup has been developed to perform transmission electron microscopy (TEM) and single‐molecule fluorescence (SMF) microscopy on such nanostructured samples. Correlated structure–reactivity information was obtained for 100 nm thin, microtomed sections of a single FCC catalyst particle using this novel SMF‐TEM high‐resolution combination. High reactivity in a thiophene oligomerization probe reaction correlated well with TEM‐derived zeolite locations, while matrix components, such as clay and amorphous binder material, were found not to display activity. Differences in fluorescence intensity were also observed within and between distinct zeolite aggregate domains, indicating that not all zeolite domains are equally active.