Revisiting Gouy phase

The aim of this paper is to highlight the added value of the generalized Gouy phase shift introduced by Siegman. Although suited for optical systems study, including those more complex than free space, we note that it did not meet the use that it deserves so far. The analysis of the whole of the ideas and analytical approaches associated to the important concept of the Gouy phase proves its effectiveness.

Usually, the resonance condition is systematically built on the basis of the equivalent empty cavity. Unfortunately, this approach does not cover some of the useful parameters of the real resonator. By means of the generalized Gouy phase and the self-consistent complex parameter q, we derive here a new approach for the calculation of the resonance condition for the real cavity. Moreover, the use of the generalized Gouy phase clearly simplifies the study of resonators, while making it possible to avoid the use of the Huygens’ Fresnel integral.     

Asymptotic Analysis of a Hyperbolic Mixed Problem in One-Dimensional Viscoelasticity

We present an asymptotic analysis of the boundary-generated, small-amplitude, high-frequency waves in a one-dimensional, semi-infinite, viscoelastic solid characterized by a single-integral constitutive functional. The equations governing the wave motion constitute a 2×2 system of hyperbolic Volterra integrodifferential equations. The method of analysis is based on a single-wave expansion of nonlinear geometric optics.     

Selective monodeoxygenation of quinoxaline-amino acid and ester dioxides

Trimethyl phosphite selectively removes the N-1-oxygen in N-(3-methyl-2-quinoxaloyl) L-α-amino ester-1,4-dioxides, whereas it removes the N-4-oxygen in the corresponding series of dioxides lacking the C₃-Me. This selectivity reversal reflects the relative strength of the intrahydrogen-bridging to the N-1-oxygen. The monoxides having the favourable N-oxygen are not reduced to the quinoxalines, implying that the reagent requires doubling of the N-oxide function for deoxygenation. However, alkaline sodium dithionite removes the N-1-oxygen in both series of the amino acid-dioxides, as well as in the parent quinoxaline-2-carboxylic acid-dioxides, a result that contradicts the report stating removal of the N-4-oxygen. The N-oxygenated quinoxalinium ion ($\text{m}\text{e}$ 145 or 159) prevails in the MS of the 4-oxides, but it is not observed (<1%) for the isomeric 1-oxides. ¹H NMR, ¹³C NMR and UV spectral data also offer diagnostic criteria for differentiation between the isomeric 1- and 4-oxides. Aryl-heteryl “interaction” (as revealed by ¹H NMR, though not by ¹³C NMR in the aromatic amino ester dioxides) is not manifested in the corresponding monoxides.     

Theoretical determination of chromophores in the chromogenic effects of aromatic neurotoxicants

We report the first computational study of the chromophores responsible for the chromogenic effects of aromatic neurotoxicants containing a 1,2-diacetyl moiety in their oxidation metabolites. A series of ab initio electronic structure calculations was performed on two representative aromatic compounds, 1,2-diacetylbenzene (1,2-DAB) and 1,2-diacetyl tetramethyl tetralin (1,2-DATT), the putative active metabolites of the neurotoxic aromatic hydrocarbon compounds 1,2-diethylbenzene (1,2-DEB) and acetyl ethyl tetramethyl tetralin (AETT), and on the products of their possible reactions with proteins that result in chromogenic effects. The electronic excitation energies determined by three different computational approaches were found to be consistent with each other. The calculated results are consistent with the conclusion/prediction that the chromogenic effects of 1,2-DAB (or 1,2-DEB) and 1,2-DATT (or AETT) could result from ninhydrin-like reactions, rather than the formation of pyrrole-like compounds. Our pK(a) calculations further indicate that the chromophore, i.e., the product of the ninhydrin-like reaction showing the blue color, is deprotonated in neutral aqueous solution. The corresponding protonated structure has a different color as it absorbs in the blue region of the visible spectrum, and its chromogenic contribution would be significant in solution at low pH.     

Molecular complexes of crown ethers. Part 3. Effect of cations on charge transfer complexes with TCNE

The intermolecular charge transfer complexes (CT) of two crown ethers (CE), viz, B15C5 and DB18C6 (as donors), and tetracyanoethylene (TCNE), as acceptor, were studied in the UV-visible region in dichloroethane (DCE), at 298.2 K. The sequence of addition of the cation was varied in the case of B15C5 such that in one system the sequence was (CE+Cation)+TCNE and in the other (CE+TCNE)+cation. These two systems were found to be non-interchangeable, even under reflux conditions, giving differentK _c values which were explained as being due to the different geometries of the CE. For the first sequence, the values most affected depended on the fit of the metal cation with the ether cavity, thus in B15C5, Na⁺ showed the greatest effect, while for DB18C6 it was K⁺.     

Effect of permodified β‐cyclodextrin on the photophysical properties of poly[2,7‐(9,9‐dioctylfluorene)‐alt‐(5,5′‐bithiophene)] main chain polyrotaxanes

The photophysical properties of two polyrotaxanes ( PFBTh?PSβCD and PFBTh?PMeβCD ) composed of fluorene and bithiophene encapsulated into permodified β‐cyclodextrin cavities have been investigated and compared with those of the reference PFBTh . Rotaxane formation results in improvements of the thermal stability, solubility in common organic solvents, as well as better film forming ability combined with a high transparency. As expected PFBTh and its encapsulated forms absorb at wavelengths beyond 510 nm, and time‐resolved photoluminescence (PL) in solution shows a well‐define vibronic structures with a predominance of the 0‐0 transitions and an energy difference of 0.16 eV. The fluorescence lifetimes follow a monoexponential decay with a value τ = 630 ± 30 ps. Atomic force microscopy, AFM, indicated a tendency of polyrotaxanes to organize into fibers. The advancing contact angles indicated higher surface hydrophobicity and lower surface free‐energy values for polyrotaxanes compared with their unthreaded analogues. The device based on PFBTh?PSβCD: PCBM in a 1/1 w/w ratio under simulated AM 1.5G illumination at 100 mW cm^?2 exhibited improved photovoltaic parameters of cells, resulted in high V_oc (0.68 V), J_sc (1.65 mA cm^?2), FF (31.6%), and PCE (0.35) values, compared with PFBTh or PFBTh?PMeβCD , respectively. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 460–471     

Risk externalities and too big to fail

This paper establishes the case for a fallacy of economies of scale in large aggregate institutions and the effects of scale risks. The problem of rogue trading and excessive risk taking is taken as a case example. Assuming (conservatively) that a firm exposure and losses are limited to its capital while external losses are unbounded, we establish a condition for a firm not to be allowed to be too big to fail. In such a case, the expected external losses second derivative with respect to the firm capital at risk is positive. Examples and analytical results are obtained based on simplifying assumptions and focusing exclusively on the risk externalities that firms too big to fail can have.     

Palladium nanoparticles on modified cellulose as a novel catalyst for low temperature gas reactions

Cellulose - Palladium was incorporated into carboxymethylated cellulose fibers as a support, thereby becoming an efficient and stable catalyst for low temperature gas phase reaction. Thus, NO was...