A Brief Account on Lagrange’s Algebraic Identity

In Indiscrete Thoughts [18], G.-C. Rota remarked, ??The mystery, as well as the glory of mathematics, lies not so much in the fact that abstract theories do turn out to be useful in solving problems, but, wonder of wonders, in the fact that a theory meant for one type of problem is often the only way of solving problems of entirely different kinds, problems for which the theory was not intended. These coincidences occur so frequently, that they must belong to the essence of mathematics.?? Indeed, it happens often that abstract mathematics leads to concrete applications, and real-life problems constitute a source of inspiration for sophisticated theories. The strong synergy between pure mathematics and its applications advocates for teaching methods that intertwine physical intuition with mathematical abstraction, and recognize the universality of mathematical laws throughout the sciences.     

Tapered plasmonic waveguides with efficient and broadband field transmission

In this paper we suggest, numerically simulate and discuss a tapered plasmonic nanostructure which allows efficient transmission of the wave beam energy into a weakly subwavelength (λ/4 … λ/2) spatial region within a broad frequency range. The frequency stable location of this region becomes possible due to unusual plasmonic modes we have theoretically revealed and used. Our structure is promising for prospective transducers between conventional optical waveguides and subwavelength nanoguides or nanocircuits.     

Family constraining of iterative algorithms

In constraining iterative processes, the algorithmic operator of the iterative process is pre-multiplied by a constraining operator at each iterative step. This enables the constrained algorithm, besides solving the original problem, also to find a solution that incorporates some prior knowledge about the solution. This approach has been useful in image restoration and other image processing situations when a single constraining operator was used. In the field of image reconstruction from projections a priori information about the original image, such as smoothness or that it belongs to a certain closed convex set, may be used to improve the reconstruction quality. We study here constraining of iterative processes by a family of operators rather than by a single operator.     

Slow dynamics of a colloidal lamellar phase

We used x-ray photon correlation spectroscopy to study the dynamics in the lamellar phase of a platelet suspension as a function of the particle concentration. We measured the collective diffusion coefficient along the director of the phase, over length scales down to the interparticle distance, and quantified the hydrodynamic interaction between the particles. This interaction sets in with increasing concentration and can be described qualitatively by a simplified model. No change in the microscopic structure or dynamics is observed at the transition between the fluid and the gel-like lamellar phases.     

From a cycloheptatrienylzirconium allyl complex to a cycloheptatrienylzirconium imidazolin-2-iminato "pogo stick" complex with imido-type reactivity

The reaction of the cycloheptatrienylzirconium half-sandwich complex [(η(7)-C(7)H(7))ZrCl(tmeda)] (1) (tmeda = N,N,N',N'-tetramethylethylenediamine) with Li(Im(Dipp)N), generated from bis(2,6-diisopropylphenyl)imidazolin-2-imine (Im(Dipp)NH) with methyllithium, yields the imidazolin-2-iminato complex [(η(7)-C(7)H(7))Zr(Im(Dipp)N)(tmeda)] (2). The corresponding tmeda-free complex [(η(7)-C(7)H(7))Zr(Im(Dipp)N)] (5) can be synthesized via the 1,3-bis(trimethylsilyl)allyl complex [(η(7)-C(7)H(7))Zr{η(3)-C(3)H(3)(TMS)(2)}(THF)] (3; TMS = SiMe(3)), which undergoes an acid-base reaction with Im(Dipp)NH to form 5 and 1,3-bis(trimethylsilyl)propene. 5 exhibits an unusual one-legged piano stool ("pogo stick") geometry with a particularly short Zr-N bond of 1.997(2) ?. Addition of 2,6-dimethylphenyl or tert-butyl isocyanide affords the complexes [(η(7)-C(7)H(7))Zr(Im(Dipp)N)(CNR)] (R = o-Xy, 6; R = t-Bu, 7), while the reaction with 2,6-dimethylphenyl isocyanate results in a [2 + 2] cycloaddition to form the ureato(1-) complex [(η(7)-C(7)H(7))Zr{Im(Dipp)N(C═O)N-o-Xy}] (8). 5 can also act as an initiator for the ring-opening polymerization of ε-caprolactone. These reactivity patterns together with density functional theory calculations reveal a marked similarity of the bonding in imidazolin-2-iminato and conventional imido transition-metal complexes.     

Insights into MWCNTs/polyimide nanocomposites: from synthesis to application as free-standing flexible electrodes in low-cost micro-supercapacitors

In the pursuit to enlarge the library of polyimide materials for energy applications, new polyimide/MWCNTs composite films have been developed by MWCNTs-assisted polycondensation reaction of a hydroxyl and triphenylmethane-containing diamine with benzophenone tetracarboxylic dianhydride targeting to highlight their electrical storage capability as flexible electrodes in micro-supercapacitors (mSCs). The Fourier-transform infrared spectroscopy, proton nuclear magnetic resonance, UV–vis, fluorescence, and Raman spectroscopies were used to demonstrate the evolution of interfacial interactions between MWCNTs and the precursors (diamine monomer and intermediate polyamidic acid) and polyimide matrix that proved to be the origin of MWCNTs homogeneous dispersion. Thus, composite films incorporating 1, 3, 5, and 10 w.t.% MWCNTs were obtained and thoroughly investigated with regard to their morphology, mechanical behavior, thermal stability, and electrical conductivity. The electrochemical performance of these composites was first analyzed in a classical three-electrode cell by cyclic voltammetry and galvanostatic charge-discharge in both aqueous and organic electrolyte systems. By far, the best electrical storage capacity was obtained with the composite polyimide film containing 10% MWCNTs that was further used as both active material and current collector in a flexible symmetric mSC realized by a straightforward and low-cost procedure. In the attempt to better exploit the advantages of this composite film, it was layered with a graphite-containing paint and tested as an electrode in a flexible mSC, which provided satisfactory results. To our knowledge, this is the first report on the electrical charge storage capability of a polyimide/MWCNTs free-standing film as a flexible electrode in mSCs, which do not require time- and resource-consuming processing steps.     

Strained Ammonium Precursors for Radiofluorinations

The increasing application of positron emission tomography (PET) in nuclear medicine has stimulated the extensive development of a multitude of novel and versatile techniques to introduce fluorine-18, especially for the radiolabelling of biologically or pharmacologically active molecules. Taking into consideration that the introduction of fluorine-18 (t_1/2=109.8 min) mostly proceeds under harsh conditions, radiolabelling of such molecules represents a challenge and is of enormous interest. Ideally, it should proceed in a regioselective manner under mild physiological conditions, in an acceptable time span, with high yields and high specific activities. Special attention has been drawn to 2-fluoroethyl and 3-fluoropropyl groups, which are often the active sites of radiofluorinated compounds. Precursors containing an ammonium leaving group – such as a strained azetidinium or aziridinium moiety – can help to overcome these obstacles leading to a convenient and mild introduction of [¹⁸F]fluoride with high radiochemical yields.     

Chloroplast Biogenesis 77: Two Novel Monovinyl and Divinyl Light-Dark Greening Groups of Plants and Their Relationship to the Chlorophyll a Biosynthetic Heterogeneity of Green Plants

Abstract— On the basis of the steady-state accumulation of divinyl (DV) or monovinyl (MV) protochlorophyllide (Pchlide) a in darkness (D) or in the light (L), green plants have been classified into three different greening groups namely dark divinyl-light divinyl (DDV-LDV), dark monovinyl-light divinyl (DMV-LDV) and dark monovinyl-light monovinyl (DMV-LMV) (Ionannides et al., Biochem. Syst. Ecol. 22, 211-220,1994). Interruption of the L phase of the photoperiod by a brief period of darkness (LD condition) revealed a predominance of different chlorophyll (Chl) a biosynthetic routes, depending upon the greening group affiliation of the plant species. For example, in DMV-LDV and DMV-LMV plants, the predominant Chl a biosynthetic routes under the LD condition appear to be the MV Chi a biosynthetic route and/or a mixed DV-MV Chi a biosynthetic route that bifurcates at the level of DV Pchlide a. On the basis of DV and MV Pchlide a accumulation rates after re-darkening, this greening group is designated as a light-dark MV (LDMV) subgroup. In DDV-LDV plants, the predominant LD Chi a biosynthetic routes appear to be the DV Chi a biosynthetic route and/or a mixed DV-MV Chi a biosynthetic route that bifurcates at the level of DV Chlide a. This greening group is designated as a light-dark DV (LDDV) subgroup. It is proposed that upon inhibiting the conversion of Pchlide a to Chi a by interruption of the L phase of the photoperiod by a brief period of D, the rates of DV and MV Pchlide a regeneration may reflect the carryover rates of DV and MV Pchlide a biosynthesis in L instead of reflecting a differential use of DV and MV carboxylic biosynthetic rates in D. It is also shown that in LDMV plants, MV Chlide a and MV Chi a are formed without the participation of [4-vinyl] Chlide a reductase. On the basis of recently published evidence, it is also argued that Pchlide oxidoreductase-A (POR-A) may be active in LDDV plants, while POR-B may predominate in LDMV plant species. The evolutionary significance of the LDDV and LDMV greening subgroups is discussed.     

ICP-MS Assessment of Essential and Toxic Trace Elements in Foodstuffs with Different Geographic Origins Available in Romanian Supermarkets

The present study was conducted to quantify the daily intake and target hazard quotient of four essential elements, namely, chromium, cobalt, nickel, and copper, and four toxic trace elements, mercury, cadmium, lead, and arsenic. Thirty food items were assigned to five food categories (seeds, leaves, powders, beans, and fruits) and analyzed using inductively coupled plasma-mass spectrometry. Factor analysis after principal component extraction revealed common metal patterns in all foodstuffs, and using hierarchical cluster analysis, an association map was created to illustrate their similarity. The results indicate that the internationally recommended dietary allowance was exceeded for Cu and Cr in 27 and 29 foodstuffs, respectively. According to the tolerable upper level for Ni and Cu, everyday consumption of these elements through repeated consumption of seeds (fennel, opium poppy, and cannabis) and fruits (almond) can have adverse health effects. Moreover, a robust correlation between Cu and As (p < 0.001) was established when all samples were analyzed. Principal component analysis (PCA) demonstrated an association between Pb, As, Co, and Ni in one group and Cr, Cu, Hg, and Cd in a second group, comprising 56.85% of the total variance. For all elements investigated, the cancer risk index was within safe limits, highlighting that lifetime consumption does not increase the risk of carcinogens.