Orthogonal and unitary tensor decomposition from an algebraic perspective

While every matrix admits a singular value decomposition, in which the terms are pairwise orthogonal in a strong sense, higher-order tensors typically do not admit such an orthogonal decomposition. Those that do have attracted attention from theoretical computer science and scientific computing. We complement this existing body of literature with an algebro-geometric analysis of the set of orthogonally decomposable tensors.More specifically, we prove that they form a real-algebraic variety defined by polynomials of degree at most four. The exact degrees, and the corresponding polynomials, are different in each of three times two scenarios: ordinary, symmetric, or alternating tensors; and real-orthogonal versus complex-unitary. A key feature of our approach is a surprising connection between orthogonally decomposable tensors and semisimple algebras—associative in the ordinary and symmetric settings and of compact Lie type in the alternating setting.     

Some metrological aspects of the comparison between two ordinal measuring systems

The usage of ordinal scales (sometimes called ‘semi-quantitative’ scales) for performing measurements in the area of applied chemical metrology and quality assurance is widespread. This paper presents a method for handling actions such as calibration, measuring systems’ capabilities comparison and reproducibility evaluation as a comparison between two measuring systems (MSs) referring to a known/unknown reference standard. The strength of the agreement between these MSs is evaluated through two known versions of Cohen’s kappa statistics (the traditional one and the modified one). The effectiveness of these statistics from the metrological point of view is examined, and the preferability of the modified kappa statistics is demonstrated via an example.     

Evidence for a near-resonant charge transfer mechanism for double-stranded peptide nucleic acid

We present evidence for a near-resonant mechanism of charge transfer in short peptide nucleic acid (PNA) duplexes obtained through electrochemical, STM break junction (STM-BJ), and computational studies. A seven base pair (7-bp) PNA duplex with the sequence (TA)(3)-(XY)-(TA)(3) was studied, in which XY is a complementary nucleobase pair. The experiments showed that the heterogeneous charge transfer rate constant (k(0)) and the single-molecule conductance (σ) correlate with the oxidation potential of the purine base in the XY base pair. The electrochemical measurements showed that the enhancement of k(0) is independent, within experimental error, of which of the two PNA strands contains the purine base of the XY base pair. 7-bp PNA duplexes with one or two GC base pairs had similar measured k(0) and conductance values. While a simple superexchange model, previously used to rationalize charge transfer in single stranded PNA (Paul et al. J. Am. Chem. Soc. 2009, 131, 6498-6507), describes some of the experimental observations, the model does not explain the absence of an enhancement in the experimental k(0) and σ upon increasing the G content in the duplexes from one to two. Moreover, the superexchange model is not consistent with other studies (Paul et al. J. Phys. Chem. B 2010, 114, 14140), that showed a hopping charge transport mechanism is likely important for PNA duplexes longer than seven base pairs. A quantitative computational analysis shows that a near-resonant charge transfer regime, wherein a mix of superexchange and hopping mechanisms are expected to coexist, can rationalize all of the experimental results.     

Carbon-carbon bond formation from azaallyl and imine couplings about metal-metal bonds

Typical C-C bond-forming processes feature oxidative addition, insertion, and reductive elimination reactions. An alternative strategy toward C-C bond formation involves the generation of transient radicals that can couple at or around one or more metal centers. Generation of transient azaallyl ligands that reductively couple at CH positions possessing radical character is described. Two C-C bonds form, and the redox non-innocence of the resulting pyridine-imines may be critical to formation of a third C-C bond via dinuclear di-imine oxidative coupling. Unique metal-metal bonds are a consequence of the chelation.     

Cyclisation of α,ω-dienes promoted by bis(indenyl)zirconium sandwich and ansa-titanocene dinitrogen complexes

Metallation of a variety of α,ω-dienes has been explored with an η(9),η(5)-bis(indenyl)zirconium sandwich compound and an ansa-titanocene dinitrogen complex. The η(9),η(5)-bis(indenyl)zirconium sandwich compound, (η(9)-C(9)H(5)-1,3-Pr(2))(η(5)-C(9)H(5)-1,3-(i)Pr(2))Zr, served as an isolable source of Negishi's reagent and readily formed a kinetic mixture of cis and trans diastereomers of the corresponding zirconacyclopentanes upon diene metallation. For pure hydrocarbon substrates such as 1,6-heptadiene and 1,7-octadiene, an equimolar amount of cis and trans diastereomers were the kinetic products; isomerization to the thermodynamically favoured trans isomers was observed over time at ambient temperature or upon heating to 105 °C, respectively. By contrast, substitution of the methylene or ethylene spacer in the α, ω-diene with a fluorenyl group (e.g. 9,9-diallylfluorene) resulted in exclusive kinetic formation of the trans diastereomer. Amino-substituted dienes were also readily cyclised and one example was characterised by single-crystal X-ray diffraction. Similar studies were also conducted with the ansa-titanocene dinitrogen complex, [Me(2)Si(η(5)-C(5)Me(4))(η(5)-C(5)H(3)-3-(t)Bu)Ti](2)(μ(2),η(1),η(1)-N(2)), and both kinetic and thermodynamic selectivities evaluated. The use of a C(1) symmetric ansa-metallocene increases the number of isomeric possibilities. For diallyl tert-butyl amine, diene metallation was more selective than for the bis(indenyl)zirconium sandwich compound and isomerization was also more rapid. Preliminary functionalisation reactivity for both the zircona- and titanocycles was also explored.     

Circadian variations in biologically closed electrochemical circuits in Aloe vera and Mimosa pudica

The circadian clock regulates a wide range of electrophysiological and developmental processes in plants. This paper presents, for the first time, the direct influence of a circadian clock on biologically closed electrochemical circuits in vivo. Here we show circadian variation of the plant responses to electrical stimulation. The biologically closed electrochemical circuits in the leaves of Aloe vera and Mimosa pudica, which regulate their physiology, were analyzed using the charge stimulation method. The electrostimulation was provided with different timing and different voltages. Resistance between Ag/AgCl electrodes in the leaf of Aloe vera was higher during the day than at night. Discharge of the capacitor in Aloe vera at night was faster than during the day. Discharge of the capacitor in a pulvinus of Mimosa pudica was faster during the day. The biologically closed electrical circuits with voltage gated ion channels in Mimosa pudica are also activated the next day, even in the darkness. These results show that the circadian clock can be maintained endogenously and has electrochemical oscillators, which can activate ion channels in biologically closed electrochemical circuits. We present the equivalent electrical circuits in both plants and their circadian variation to explain the experimental data.     

Core, shell, and surface-optimized dendrimers for blue light-emitting diodes

We present a novel core-shell-surface multifunctional structure for dendrimers using a blue fluorescent pyrene core with triphenylene dendrons and triphenylamine surface groups. We find efficient excitation energy transfer from the triphenylene shell to the pyrene core, substantially enhancing the quantum yield in solution and the solid state (4-fold) compared to dendrimers without a core emitter, while TPA groups facilitate the hole capturing and injection ability in the device applications. With a luminance of up to 1400 cd/m(2), a saturated blue emission CIE(xy) = (0.15, 0.17) and high operational stability, these dendrimers belong to the best reported fluorescence-based blue-emitting organic molecules.     

Iron-catalyzed intermolecular [2π+2π] cycloaddition

The bis(imino)pyridine iron dinitrogen compounds, ((iPr)PDI)Fe(N(2))(2) and [((Me)PDI)Fe(N(2))](2)(μ(2)-N(2)) ((R)PDI = 2,6-(2,6-R(2)-C(6)H(3)N═CMe)(2)C(5)H(3)N; R = (i)Pr, Me), promote the catalytic intermolecular [2π + 2π] cycloaddition of ethylene and butadiene to form vinylcyclobutane. Stoichiometric experiments resulted in isolation of a catalytically competent iron metallocycle intermediate, which was shown to undergo diene-induced C-C reductive elimination. Deuterium labeling experiments establish competitive cyclometalation of the bis(imino)pyridine aryl substituents during catalytic turnover.     

Phenol adsorption on closed carbon nanotubes

We present the results of systematic studies of phenol adsorption on closed commercially available, unmodified carbon nanotubes. Phenol adsorption is determined by the value of tube-specific surface area, the presence of small amount of surface groups influence adsorption only in very small amount. Phenol can be applied as a probe molecule for comparative analysis of tube surface areas. Tube curvature influences adsorption from solution, i.e., we observe increasing adsorption energy (and slower desorption process) with the decrease in tube curvature. This is in full accordance with molecular simulation results.     

Synthesis and characterization of (smif)2M(n) (n = 0, M = V, Cr, Mn, Fe, Co, Ni, Ru; n = +1, M = Cr, Mn, Co, Rh, Ir; smif =1,3-di-(2-pyridyl)-2-azaallyl)

A series of Werner complexes featuring the tridentate ligand smif, that is, 1,3-di-(2-pyridyl)-2-azaallyl, have been prepared. Syntheses of (smif)(2)M (1-M; M = Cr, Fe) were accomplished via treatment of M(NSiMe(3))(2)(THF)(n) (M = Cr, n = 2; Fe, n = 1) with 2 equiv of (smif)H (1,3-di-(2-pyridyl)-2-azapropene); ortho-methylated ((o)Mesmif)(2)Fe (2-Fe) and ((o)Me(2)smif)(2)Fe (3-Fe) were similarly prepared. Metatheses of MX(2) variants with 2 equiv of Li(smif) or Na(smif) generated 1-M (M = Cr, Mn, Fe, Co, Ni, Zn, Ru). Metathesis of VCl(3)(THF)(3) with 2 Li(smif) with a reducing equiv of Na/Hg present afforded 1-V, while 2 Na(smif) and IrCl(3)(THF)(3) in the presence of NaBPh(4) gave [(smif)(2)Ir]BPh(4) (1(+)-Ir). Electrochemical experiments led to the oxidation of 1-M (M = Cr, Mn, Co) by AgOTf to produce [(smif)(2)M]OTf (1(+)-M), and treatment of Rh(2)(O(2)CCF(3))(4) with 4 equiv Na(smif) and 2 AgOTf gave 1(+)-Rh. Characterizations by NMR, EPR, and UV-vis spectroscopies, SQUID magnetometry, X-ray crystallography, and DFT calculations are presented. Intraligand (IL) transitions derived from promotion of electrons from the unique CNC(nb) (nonbonding) orbitals of the smif backbone to ligand π*-type orbitals are intense (ε ≈ 10,000-60,000 M(-1)cm(-1)), dominate the UV-visible spectra, and give crystals a metallic-looking appearance. High energy K-edge spectroscopy was used to show that the smif in 1-Cr is redox noninnocent, and its electron configuration is best described as (smif(-))(smif(2-))Cr(III); an unusual S = 1 EPR spectrum (X-band) was obtained for 1-Cr.