Constructing Uniquely Realizable Graphs

In the Graph Realization Problem (GRP), one is given a graph  $G$ , a set of non-negative edge-weights, and an integer  $d$ . The goal is to find, if possible, a realization of  $G$ in the Euclidian space $\mathbb R ^d$ , such that the distance between any two vertices is the assigned edge weight. The problem has many applications in mathematics and computer science, but is NP-hard when the dimension  $d$ is fixed. Characterizing tractable instances of GRP is a classical problem, first studied by Menger in 1931. We construct two new infinite families of GRP instances which can be solved in polynomial time. Both constructions are based on the blow-up of fixed small graphs with large expanders. Our main tool is the Connelly’s condition in Rigidity Theory, combined with an explicit construction and algebraic calculations of the rigidity (stress) matrix. As an application of our results, we describe a general framework to construct uniquely k-colorable graphs. These graphs have the extra property of being uniquely vector k-colorable. We give a deterministic explicit construction of such a family using Cayley expander graphs.     

Special Features of Sorption and Luminescence of Tb3+ Cations and Azomethine Bases in Perfluorosulfonic Membrane

Russian Journal of General Chemistry - The limiting value of ion-exchange sorption capacity of the perfluorosulfonic membrane with respect to Tb3+ is reproducible when the cation is in excess in...     

Development of electron-proton density functionals for multicomponent density functional theory

We present a strategy for the development of electron-proton density functionals in multicomponent density functional theory, treating electrons and selected nuclei quantum mechanically without the Born-Oppenheimer approximation. An electron-proton functional is derived using an explicitly correlated electron-proton pair density. This functional provides accurate hydrogen nuclear densities, thereby enabling reliable calculations of molecular properties. This approach is potentially applicable to relatively large molecular systems with key hydrogen nuclei treated quantum mechanically.     

New strategy for reversal tolerant anode for automotive polymer electrolyte fuel cell

New approach for the reversal tolerant anode for polymer electrolyte membrane fuel cell is suggested by using the multifunctional IrRu alloy catalyst having concurrent superior activities towards hydrogen oxidation reaction and oxygen evolution reaction to mitigate the degradation of anode under the fuel starvation condition.     

Photochromic Properties of Porous Glass Modified with Molybdenum Oxide Groups

Porous glass plates were modified via their interaction with molybdenum(V) chloride, followed by a treatment with humid air at 473°C. The extent of the reaction is characterized on the basis of IR spectra of OH groups on the starting glass surface and grafted layer. The photochromism of the resulting plates is exhibited under their UV irradiation as a progressive blue coloration. The suggested photoreduction mechanism consists in splitting-off oxygen atoms from bridge bonds?Mo?O?Mo?, with transition of molybdenum atoms to the pentavalent state. The subsequent discoloration of the plates is provided by their heating in air at 473°C. The full reversibility of the photoreduction and oxidation processes is observed in their multiple repetitions.     

A Zero‐Dimensional Organic Seesaw‐Shaped Tin Bromide with Highly Efficient Strongly Stokes‐Shifted Deep‐Red Emission

The synthesis and characterization is reported of (C₉NH₂₀)₂SnBr₄, a novel organic metal halide hybrid with a zero‐dimensional (0D) structure, in which individual seesaw‐shaped tin (II) bromide anions (SnBr₄^2?) are co‐crystallized with 1‐butyl‐1‐methylpyrrolidinium cations (C₉NH₂₀⁺). Upon photoexcitation, the bulk crystals exhibit a highly efficient broadband deep‐red emission peaked at 695 nm, with a large Stokes shift of 332 nm and a high quantum efficiency of around 46 %. The unique photophysical properties of this hybrid material are attributed to two major factors: 1) the 0D structure allowing the bulk crystals to exhibit the intrinsic properties of individual SnBr₄^2? species, and 2) the seesaw structure enabling a pronounced excited state structural deformation as confirmed by density functional theory (DFT) calculations.     

λ-Automorphisms of a Riemannian Foliation II

In Pak (Ann. Global Anal. Geom.13 (1995), 281–288), the notion of -automorphisms of a harmonic Riemannian foliation was extended to a general Riemannian foliation. By applying the characterization obtained in Pak of a -automorphism to be transversal Killing, we here consider the problem that a transversal conformal or projective field is transversal Killing. A special condition, namely _{B B} = 0, is discussed.     

Internal energy distribution of peptides in electrospray ionization : ESI and collision-induced dissociation spectra calculation

The internal energy of ions and the timescale play fundamental roles in mass spectrometry. The main objective of this study is to estimate and compare the internal energy distributions of different ions (different nature, degree of freedom 'DOF' and fragmentations) produced in an electrospray source (ESI) of a triple-quadrupole instrument (Quattro I Micromass). These measurements were performed using both the Survival Yield method (as proposed by De Pauw) and the MassKinetics software (kinetic model introduced by Vékey). The internal energy calibration is the preliminary step for ESI and collision-induced dissociation (CID) spectra calculation. meta-Methyl-benzylpyridinium ion and four protonated peptides (YGGFL, LDIFSDF, LDIFSDFR and RLDIFSDF) were produced using an electrospray source. These ions were used as thermometer probe compounds. Cone voltages (V(c)) were linearly correlated with the mean internal energy values () carried by desolvated ions. These mean internal energy values seem to be slightly dependent on the size of the studied ion. ESI mass spectra and CID spectra were then simulated using the MassKinetics software to propose an empirical equation for the mean internal energy () versus cone voltage (V(c)) for different source temperatures (T): < E(int) > = [405 x 10(-6) - 480 x 10(-9) (DOF)] V(c)T + E(therm)(T). In this equation, the E(therm)(T) parameter is the mean internal energy due to the source temperature at 0 V(c).     

A double-stranded molecular probe for homogeneous nucleic acid analysis

This paper reports the design and optimization of a double-stranded molecular probe for homogeneous detection of specific nucleotide sequences. The probes are labeled with either a fluorophore or a quencher such that the probe hybridization brings the two labels into close proximity, and this diminishes the fluorescence signal in the absence of a target. In the presence of a target, the fluorophore probe is thermodynamically driven to unzip from its hybridized form and bind with the target. An equilibrium analysis, which successfully describes all the major features of the assay without any fitting parameter, is performed to generalize the design of the probe. Several key parameters affecting the performance of the assay are examined. We show that the dynamic range and the signal-to-noise ratio of the assay can be optimized by the probe concentration, the quencher-to-fluorophore ratio, and the probe strand sequence. By proper design of the sequence, the probe discriminates single nucleotide mismatches in a single step without any separation step or measurement of melting profile.