Topological function-theoretic proofs in spectral theory

In this paper, the spectral theorem and related characterizations of the spectrum and the spectral projections for bounded self adjoint and normal operators on a Hilbert space, are proved in purely topological —function theoretic terms. The basis for such a development, is the Gelfand—Naimark theorem for commutativeC ^*-algebras and the fact that the structure space of the (abelian) von Neumann algebra generated by the operator is a Stonean space.     

A route for bulk separation of semiconducting from metallic single-wall carbon nanotubes

Substantial separation of single-wall carbon nanotubes (SWNTs) according to type (metallic versus semiconducting) has been achieved for HiPco and laser-ablated SWNTs. We presently argue that stable dispersions of SWNTs with octadecylamine (ODA) in tetrahydrofuran (THF) originate from the physisorption and organization of ODA along the SWNT sidewalls in addition to the originally proposed zwitterion model. Furthermore, the reported affinity of amine groups for semiconducting SWNTs, as opposed to their metallic counterparts, contributes additional stability to the physisorbed ODA. This provides a venue for the selective precipitation of metallic SWNTs upon increasing dispersion concentration, as indicated by Raman investigations.     

Separation of organoselenium compounds and their electrochemical detection

A simplified procedure based on ion-exchange separation of selenourea (Se-U) and selenocystamine (Se-CM), which have very close half-wave potential when they are simultaneously analyzed by voltammetric techniques, has been developed and optimized. Thus, selenocystamine remains in the cation exchanger Purolite C 100 H, whereas selenourea is found in the effluent and is determined by square wave cathodic stripping voltammetry using Na₂CO₃ as electrolyte. Selenocystamine is then eluted from the cation exchanger using 4 M HCl and analyzed by square wave cathodic stripping voltammetry in the HCl solution. For each voltammetric determination the corresponding parameters were investigated and optimized; the obtained detection limits were 0.3 ng Se mL^–1 for Se-CM and 2 ng Se mL^–1 for Se-U. A flow sheet for the separation of inorganic (Se(IV) and Se(VI)) and organoselenium compounds (Se-U, Se-CM, (CH₃)₂Se₂, and (CH₃)₂Se) developed for their electrochemical detection is presented and it was successfully applied to a certified reference material, an environmental soil sample, and a urine sample.     

Quantum algorithm for alchemical optimization in material design

The development of tailored materials for specific applications is an active field of research in chemistry, material science and drug discovery. The number of possible molecules obtainable from a set of atomic species grow exponentially with the size of the system, limiting the efficiency of classical sampling algorithms. On the other hand, quantum computers can provide an efficient solution to the sampling of the chemical compound space for the optimization of a given molecular property. In this work, we propose a quantum algorithm for addressing the material design problem with a favourable scaling. The core of this approach is the representation of the space of candidate structures as a linear superposition of all possible atomic compositions. The corresponding ‘alchemical’ Hamiltonian drives the optimization in both the atomic and electronic spaces leading to the selection of the best fitting molecule, which optimizes a given property of the system, e.g., the interaction with an external potential as in drug design. The quantum advantage resides in the efficient calculation of the electronic structure properties together with the sampling of the exponentially large chemical compound space. We demonstrate both in simulations and with IBM Quantum hardware the efficiency of our scheme and highlight the results in a few test cases. This preliminary study can serve as a basis for the development of further material design quantum algorithms for near-term quantum computers.

‘Alchemical’ quantum algorithm for the simultaneous optimisation of chemical composition and electronic structure for material design. By exploiting quantum mechanical principles this approach will boost drug discovery in the near future.     

Dielectrophoretic assembly of grain-boundary-free 2D colloidal single crystals

Dielectrophoresis (DEP) force-assisted assembly of a colloidal single photonic-crystal monolayer in a microfluidic chamber was demonstrated. Negative DEP force with a high-frequency AC electric field induced the compression of colloidal microspheres to form a colloidal crystal domain at the center of a hexapolar-shaped electrode. While typical assembly by monotonic DEP force forms multicrystalline domains containing crystal defects, repetitions of the DEP/relaxation cycle significantly facilitated crystal growth of 10μm monodispersed polystyrene microspheres, allowing a grain-boundary-free single-crystal monolayer domain of ca. 200μm in size. Microsphere size as well as size distribution affected the formation of the single-crystal domain. A simple method was used to immobilize the single-crystal domain on the glass substrate without losing its crystallinity.     

Amine-assisted facetted etching of CdSe nanocrystals

The treatment of CdSe nanocrystals (NCs) in a 3-amino-1-propanol (APOL)/water (v/v = 10:1) mixture at 80 degrees C in the presence of O(2) causes them to undergo a slow chemical etching process, as evidenced by spectroscopic and structural investigations. Instead of the continuous blue shift expected from a gradual decrease in NC dimensions, a bottleneck behavior was observed with distinct plateaus in the peak position of photoluminescence (PL) and corresponding maxima in PL quantum yield (i.e., 34 +/-7%). It is presently argued that such etching behavior is a result of two competitive processes taking place on the surface of these CdSe NCs: (i) oxidation of the exposed Se-sites to acidic SeO(x)() entities, which are readily solubilized in the basic APOL/H(2)O mixture, and (ii) coordination of the underlying Cd-sites with both amines and hydroxyl moieties to temporally impede NC dissolution. This is consistent with the HRTEM results, which suggest that the etched NCs adopt pyramidal morphologies with Cd-terminated facets (i.e., (0001) bases and either {011} or {21} sides) and account for the apparent resistance to etching at the plateau regions.     

Antioxidant behaviour of 2′‐hydroxy‐chalcones: a study of their electrochemical properties

The electrochemical behaviour of 13 chalcone analogues was systematically studied by means of cyclic voltammetry and chronoamperometry at a glassy carbon (GC), gold and platinum working electrodes using two different supporting electrolyte/solvent combinations. It was found that chalcone analogues can be easily oxidized at both GC and gold working electrodes, but not at a platinum electrode. Principal component analysis was further employed to reveal similarities/dissimilarities between oxidation potentials, chronoamperometric signals and ability of the compounds to scavenge the reactive oxygen species H₂O₂. The study reveals the inverse proportional relationship between the scavenging ability of H₂O₂, expressed as IC₅₀, and chronoamperometric signal at 800 mV using gold as working electrode. Copyright © 2012 John Wiley & Sons, Ltd.     

Poly(allylamine)-encapsulated water-soluble CdSe nanocrystals

Water-soluble CdSe nanocrystal/poly(allylamine) clusters with sizes ranging between 50 and 200 nm were prepared using 3-amino-1-propanol as a compatibilizing agent. Photoluminescence (PL) quantum yields (QY) up to 20% were achieved in water without the need to clad these CdSe nanocrystals (NCs) with higher band gap inorganic layers. The polymer-to-nanocrystal ratio plays an important role in the internal structure and stability of these polymer/NC clusters, as determined by static and dynamic light scattering in conjunction with PL studies. These results were modeled by using an effective-mass approximation and perturbation theory on the change in dielectric constant of the immediate NC environment. The time evolution of the average cluster radius of gyration and hydrodynamic radius revealed that a higher polymer-to-NC ratio leads to increased PL stability and QY. This is a result of a denser cluster configuration, which affords improved NC passivation. Increasing the ionic strength results in greater nanocluster compaction and higher PL QYs. Decreasing the pH value below 12 resulted in dramatic reduction in PL brightness, despite cluster densification, due to partial ionization and dissolution of the amine-based NC surface-capping agents.     

An extension of labeling techniques for finding shortest path trees

Label setting techniques are all based on Dijkstra’s condition of always scanning the node with the minimum label, which guarantees that each node will be scanned exactly once; while this condition is sufficient it is not necessary. In this paper, we discuss less restrictive conditions that allow the scanning of a node that does not have the minimum label, yet still maintaining sufficiency in scanning each node exactly once; various potential shortest path schemes are discussed, based on these conditions. Two approaches, a label setting and a flexible hybrid one are designed and implemented. The performance of the algorithms is assessed both theoretically and computationally. For comparative analysis purposes, three additional shortest path algorithms – the commonly cited in the literature – are coded and tested. The results indicate that the approaches that rely on the less restrictive optimality conditions perform substantially better for a wide range of network topologies.     

Equations of motion of rotating composite beam with a nonconstant rotation speed and an arbitrary preset angle

In the presented paper the equations of motion of a rotating composite Timoshenko beam are derived by utilising the Hamilton principle. The non-classical effects like material anisotropy, transverse shear and both primary and secondary cross-section warpings are taken into account in the analysis. As an extension of the other papers known to the authors a nonconstant rotating speed and an arbitrary beam’s preset (pitch) angle are considered. It is shown that the resulting general equations of motion are coupled together and form a nonlinear system of PDEs. Two cases of an open and closed box-beam cross-section made of symmetric laminate are analysed in details. It is shown that considering different pitch angles there is a strong effect in coupling of flapwise bending with chordwise bending motions due to a centrifugal force. Moreover, a consequence of terms related to nonconstant rotating speed is presented. Therefore it is shown that both the variable rotating speed and nonzero pitch angle have significant impact on systems dynamics and need to be considered in modelling of rotating beams.