Overcrowded naphthologs of mono-bridged tetraarylethylenes: analogs of bistricyclic aromatic enes

The naphthalogous mono-bridged tetraarylethylenes 9,9′-di-(1-naphthylmethylene)-9H-fluorene (5) and 9,9′-di-(1-naphthylmethylene)-9H-xanthene (6), analogs of bifluorenylidene (1) and bixanthenylidene (2), have been synthesized and their molecular and crystal structures have been determined. Ene 5 has been prepared by two alternative synthetic routes. The molecular structures of 5 and 6 show that each of these enes has very small twist around the central double bond, but the two naphthalene rings in both 5 and 6 are highly twisted. According to the NMR study, 5 and 6 in solution adopt conformations which are similar to those found by X-ray crystal structure analysis. The notable upfield shifts of H¹ and H⁸ (6.11 and 6.83 ppm, respectively) and H² and H⁷ (6.70 and 6.44 ppm, respectively) in 5 and 6 are due to the shielding caused by the nearly orthogonally twisted naphthalene rings. The B3LYP/6-31G(d) calculations of 5, 6, and their 2-naphthyl and phenyl analogs have been performed. In the 1-naphthyl series, the more efficient conjugation between the naphthyl substituents and the central C=C and the overcrowding due to the peri-hydrogen atoms lead to higher twists of the naphthyl groups and to lower twists of the central C=C. In the 2-naphthyl series, the opposite effects are noted. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.

Antiaromaticity in fluorenylidene dications. Experimental and theoretical evidence for the relationship between the HOMO/LUMO gap and antiaromaticity

The relationship between the calculated energy of the HOMO-LUMO gap, where (epsilonLUMO - epsilonHOMO)/2 is defined as DeltaHL, and of the longest wavelength transition in the UV-visible spectrum, DeltaE, was examined for a series of aromatic and antiaromatic cations and dications. TD-DFT calculations accurately modeled the energies of a series of dications including fluorenylidene dications whose UV-visible spectra are reported, as well as the energies of a series of aromatic and antiaromatic monocations whose spectra were previously reported. There is a linear correlation of the energy of the longest wavelength transition, DeltaEcalc, with DeltaHL. There is no linear relationship between DeltaEcalc and the sum of the NICS values, but there is a linear relationship between DeltaEcalc multiplied by the number of atoms in the conjugated system, DeltaEcalcT, and the sum of the NICS values. There is also an approximate linear relationship between the average 1H NMR shift and the sum of the NICS values. These relationships give further support to the suggestion that the magnetic and energetic criteria of aromaticity and antiaromaticity are related. Furthermore, the data suggest that species that have DeltaEcalcT < 20 are antiaromatic whereas those with DeltaEcalcT > 30 are aromatic.     

Spectrophotometric micro-method for the determination of ethanol in commercial beverages

 A sensitive spectrophotometric method for the determination of ethanol with potassium dichromate was developed. Chromium(VI), in 7 mol L^-1 perchloric acid, reacts quantitatively with ethanol to form chromium(III) and acetic acid. The reaction is complete in about 15 min at room temperature and the chromium(VI) consumed may be determined by the decrease of the absorbance at 267 nm. The analytical working parameters (such as acidity and ionic strength of the solution, temperature and time of the reaction, chromium(VI) concentration, matrix interferences) were optimized. The apparent molar absorptivities of chromium(VI), in the monomer and dimer form, and the equilibrium quotient for the dimerization reaction were determined in 3 mol L^-1 perchloric acid solution. The method was applied to the analysis of micro samples of commercial beverages (beers, wines and spirits) without the previous distillation of ethanol. Received: 9 April 1996/Revised: 3 June 1996/Accepted: 11 June 1996     

Analytical approach in torsional multi-mass discrete-continuous systems with variable inertia

In the paper the systems torsionally deformed consisting of an arbitrary number of elastic elements connected by rigid bodies using the perturbation approach are investigated. The first rigid body represents a motor working with a constant speed, and the last one has a mass moment of inertia depending on the angular displacement. The problem is nonlinear and it is linearized after appropriate transformations. Exemplary numerical results for angular displacements for a two-mass and a three-mass systems are presented.     

Preparation of sugar derived β,β′-dihydroxy α,α-disubstituted α-amino acids

A novel strategy for the preparation of β,β′-dihydroxy α,α-disubstituted α-amino acids bearing a sugar moiety has been developed. The procedure is based on two Henry reactions: the first Henry reaction involves a sugar aldehyde and nitroethanol to furnish a sugar derived α-hydroxymethyl α-nitroalkanol while the second Henry reaction is between this nitro sugar and formaldehyde. This sequence provided the expected epimers of sugar derived α,α-dihydroxymethyl α -nitroalkanols, from which the corresponding β,β′-dibenzyloxy α-N-benzyloxycarbonylamino esters were easily obtained. All rights reserved.     

Leaf cuticle topography retrieved by using fringe projection

The combination (often referred to as phase-stepping profilometry, PSP) of the fringe projection technique and the phase-stepping method allowed us to retrieve topographic maps of cuticles isolated from the abaxial surface of leaves; these were in turn sampled from an apple tree (Malus domestica) of the variety Golden Delicious. The topographic maps enabled us to assess the natural features on the illuminated surface and also to detect the whole-field spatial variations in the thickness of the cuticle. Most of our attention was paid to retrieve the highly-resolved elevation information from the cuticle surface, which included the trace (in the order of tens of micrometers) left by ribs and veins. We expect that the PSP application for retrieving the cuticle topography will facilitate further studies on the dispersion and coverage of state-of-the-art agrochemical compounds meant to improve the defending properties of the cuticle. Methodological details are provided below.     

Particular aspects of the forced response of finite-dimensional modular structures

Summary The paper analyzes, from an engineering point of view, a problem strictly connected to the Large Space Structures dynamics, precisely the dynamics of modular structures of arbitrary length, arbitrarily constrained at either end and arbitrarily subject to external loads at the boundaries of each repetitive element. In particular the attention is focused on the relation between the propagation characteristics of an indefinite structure and the forced response of a finite-dimensional one; this relation is established in closed form for a periodic beam in transverse vibration. A detailed numerical investigation on the same structure confirms the analytical results and shows the peculiar dynamic properties of finite-dimensional modular structures.

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Sommario Viene presentata una analisi ingegneristica di un problema estremamente attuale delle grandi strutture spaziali, ovvero lo studio della dinamica di strutture modulari di lunghezza arbitraria, soggette ad arbitrary vincoli alle estremità e ad arbitrari carichi esterni applicati in corrispondenza delle giunzioni tra due moduli adiacenti. In particolare l'interesse del lavoro è rivolto alla determinazione di una relazione tra le caratteristiche di propagazione di una struttura indefinita e la risposta forzata della omologa struttura di lunghezza finita; tale relazione viene ricavata in forma chiusa per una trave periodica. Una serie di simulazioni numeriche sulla medesima struttura conferma i risultati analitici, mostrando le peculiarità del comportamento dinamico di strutture periodiche di lunghezza finita.

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Paper presented as Particular Aspects of the Dynamics of Finite-Dimensional Modular Structures at the ESA Workshop on Modal Representation of Flexible Structures by Continuum Methods, ESTEC, Noordwijk, The Netherlands, June 1989.     

Selection by rank in K‐dimensional binary search trees

In this work we show how to augment general purpose multidimensional data structures, such as K‐d trees, to efficiently support search by rank (that is, to locate the i‐th smallest element along the j‐th coordinate, for given i and j) and to find the rank of a given item along a given coordinate. To do so, we introduce two simple, practical and very flexible algorithms – Select‐by‐Rank and Find‐Rank – with very little overhead. Both algorithms can be easily implemented and adapted to several spatial indexes, although their analysis is far from trivial. We are able to show that for random K‐d trees of size n the expected number of nodes visited by Find‐Rank is for or , and for (with ), where depends on the dimension K and the variant of K‐d tree under consideration. We also show that Select‐by‐Rank visits nodes on average, where is the given rank and the exponent α is as above. We give the explicit form of the functions and , both are bounded in [0, 1] and they depend on K, on the variant of K‐d tree under consideration, and, eventually, on the specific coordinate j for which we execute our algorithms. As a byproduct of the analysis of our algorithms, but no less important, we give the average‐case analysis of a partial match search in random K‐d trees when the query is not random. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 45, 14–37, 2014     

B?H,C?H,and B?C Bond Activation: The Role of Two Adjacent Agostic Interactions

Tuning the nature of the linker in a L∼BHR phosphinoborane compound led to the isolation of a ruthenium complex stabilized by two adjacent, δ‐C H and ε‐B_sp2 H, agostic interactions. Such a unique coordination mode stabilizes a 14‐electron “RuH₂P₂” fragment through connected σ‐bonds of different polarity, and affords selective B H, C H, and B C bond activation as illustrated by reactivity studies with H₂ and boranes.