Grid structure impact in sparse point representation of derivatives

In the Sparse Point Representation (SPR) method the principle is to retain the function data indicated by significant interpolatory wavelet coefficients, which are defined as interpolation errors by means of an interpolating subdivision scheme. Typically, a SPR grid is coarse in smooth regions, and refined close to irregularities. Furthermore, the computation of partial derivatives of a function from the information of its SPR content is performed in two steps. The first one is a refinement procedure to extend the SPR by the inclusion of new interpolated point values in a security zone. Then, for points in the refined grid, such derivatives are approximated by uniform finite differences, using a step size proportional to each point local scale. If required neighboring stencils are not present in the grid, the corresponding missing point values are approximated from coarser scales using the interpolating subdivision scheme. Using the cubic interpolation subdivision scheme, we demonstrate that such adaptive finite differences can be formulated in terms of a collocation scheme based on the wavelet expansion associated to the SPR. For this purpose, we prove some results concerning the local behavior of such wavelet reconstruction operators, which stand for SPR grids having appropriate structures. This statement implies that the adaptive finite difference scheme and the one using the step size of the finest level produce the same result at SPR grid points. Consequently, in addition to the refinement strategy, our analysis indicates that some care must be taken concerning the grid structure, in order to keep the truncation error under a certain accuracy limit. Illustrating results are presented for 2D Maxwell's equation numerical solutions.

A dramatic effect of double bond configuration in N-oxy-3-aza Cope rearrangements: a simple synthesis of functionalised allenes

The first examples of low temperature N-oxy-3-aza Cope rearrangements, leading to functionalised allenes are described, where the Z-configuration of the enaminic double bond in the rearranging system proves critical.

Studies in 3-oxy-assisted 3-aza Cope rearrangements

On thermolysis appropriately substituted N-silyloxy-N-allyl enamines undergo smooth 3,3-sigmatropic rearrangments to the corresponding N-silyloxy imino ethers.

Rearranjos 3-aza-cope de N-alil-N-sililoxi enaminas

O rearranjo [3,3]-sigmatrópico térmico (180ºC) de diferentes N-alil-N-sililoxi enaminas foi estudado. Os respectivos produtos de rearranjo (éteres de óxima) foram obtidos com rendimentos elevados (80%). A regiosselectividade, [3,3] vs [1,3], e a diastereosselectividade do processo foram elevadas, superior a 99% e aproximadamente 80%, respectivamente. Foi demonstrada a importância do grupo sililoxilo na promoção do rearranjo face a substratos sem este tipo de substituição. Posteriormente, foi estudada a possibilidade de aceleração aniónica deste tipo de rearranjo por formação de oxianião ligado ao átomo de azoto. A estratégia seguida para a formação do mesmo, consistiu na O-dessililação de diferentes N-alil-N-sililoxi enaminas tendo-se obtido as nitronas correspondentes ou produtos de ciclização. Num exemplo envolvendo um derivado de isoxazole-5-(2H)-ona foi observado um aumento de velocidade do rearranjo por reacção com ião etoxilo. Este aumento de velocidade foi atribuído à abertura de anel do N-O éster cíclico para o N-oxianião, seguida de rearranjo e posterior fecho. Métodos alternativos de aceleração do rearranjo por geração de carga positiva, parcial ou completa, no átomo de azoto levaram apenas à dessililação das N-alil-N-sililoxi enaminas. ABSTRACT - [3,3]-sigmatropic rearrangement of a variety of N-allyl-N-silyloxy enamines was studied. The corresponding rearrangement products (oxime-ethers) were obtained in high yields (80%). High regioselectivity, [3,3] vs [1,3] (> 99%) and in appropriate cases, diastereoselectivity (80%) were observed. The importance of the silyloxy group in promoting the rearrangement, in relation to substrates lacking this functionality, is underlined. The possible anionic acceleration of the rearrangements was next examined by O-desilylation the N-silyloxy group bonded to the nitrogen. Attempted generation of these species however, was found to lead either to the corresponding nitrones or to cyclization products. In one particular example involving an isoxazol-5-(2H)-one derivative rate enhancement of rearrangement was indeed observed with ethoxide ion. It is tentatively attributed to ring opening of the cyclic N-O ester to the N-oxyanion ethyl ester followed by rearrangement and subsequent reclosure. Alternative methods to accelerate the process by generating a partial or complete positive charge on the nitrogen atom led only to desilylation.

Solvent effects on solution enthalpies of adamantyl derivatives

Solution enthalpies of 1-bromoadamantane, 1-adamantanol, and 2-adamantanone in a large set of protic and aprotic solvents are reported at 298.15 K. Solvent effects on the solution processes of these solutes are analyzed in terms of a modified TAKA equation, involving delta(cav) h (s) as the cavity term. The nature and magnitude of the major interactions which influence these processes are assessed and discussed in terms of the solutes' characteristics. New insights on the solution processes under scrutiny are presented.

Evaluation of intermolecular interactions in thioxanthone derivatives: substituent effect on crystal diversity

A family of 9H-thioxanthen-9-one derivatives and two precursors, 2-[(4-bromophenyl) sulfanyl]-5-nitrobenzoic acid and 2-[(4-aminophenyl) sulfanyl]-5-nitrobenzoic acid, were synthesized and studied in order to assess the role of the different substituent groups in determining the supramolecular motifs. From our results we can conclude that Etter's rules are obeyed: whenever present the -COOH head to head strong hydrogen bonding dimer, R-2(2)(8) synthon, prevails as the dominant interaction. As for -NH2, the best donor when present also follows the expected hierarchy, an NH center dot center dot center dot O(COOH) was formed in the acid precursor (2) and an NH center dot center dot center dot O(C=O) in the thioxanthone (4). The main role played by weaker hydrogen bonds such as CH center dot center dot center dot O, and other intermolecular interactions, pi-pi and Br center dot center dot center dot O, as well as the geometric restraints of packing patterns shows the energetic interplay governing crystal packing. A common feature is the relation between the p-p stacking and the unit cell dimensions. A new synthon notation, R`, introduced in this paper, refers to the possibility of accounting for intra- and intermolecular interactions into recognizable and recurring aggregate patterns.

Copper(II) aza-bis(oxazoline) complex immobilized onto ITQ-2 and MCM-22 based materials as heterogeneous catalysts for the cyclopropanation of styrene

A copper(II) chiral aza-bis(oxazoline) homogeneous catalyst (CuazaBox) was anchored onto the external surface of MCM-22 and ITQ-2 structures, as well as encapsulated into hierarchical MCM-22. The transition metal complex loading onto the porous solids was determined by ICP-AES and the materials were also characterized by elemental analysis (C, N, H, S), FTIR, XPS, TG and low temperature N-2 adsorption isotherms. The materials were tested as heterogeneous catalysts in the benchmark reaction of cyclopropanation of styrene to check the effect of the immobilization procedure on the catalytic parameters, as well as on their reutilization in several catalytic cycles. Catalyst CuazaBox anchored onto the external surface of MCM-22 and ITQ-2 materials were more active and enantioselective in the cyclopropanation of styrene than the corresponding homogeneous phase reaction run under similar experimental conditions. This is due to the propylation of the acidic aza-Box nitrogen. HMCM-22 was nevertheless the best heterogeneous catalyst. Encapsulation of CuazaBox on post-synthesis modified MCM-22 materials led to low activities and enantioselectivities. But reversal on the stereochemical course of the reaction was observed, probably due to confinement effect. (C) 2013 Elsevier Inc. All rights reserved.

Cobalt and Zinc Compounds Bearing 1,10-Phenanthroline-5,6-dione or 1,3,5-Triaza-7-phosphaadamantane Derivatives - Synthesis, Characterization, Cytotoxicity, and Cell Selectivity Studies

The compounds [mPTA][CoCl4] (1, mPTA = N-methyl-1,3,5-triaza-7-phosphaadamantane cation), [CoCl(H2O)(DION)(2)][BF4] (2, DION = 1,10-phenanthroline-5,6-dione), [Zn(DION)(2)]Cl-2 (3) and [ZnCl(O-PTA=O)(DION)][BF4] (4) were synthesized by reaction of CoCl2 with [mPTA]I or DION and ZnCl2 with DION or 1,3,5-triaza-7-phosphaadamantane-7-oxide (PTA=O) and DION, respectively. All complexes are water soluble and have been characterized by IR, far-IR, H-1, C-13 and P-31{H-1} NMR spectroscopy, ESI-MS, elemental analyses and single-crystal X-ray diffraction structural analysis (for 1). They were screened against the human tumour cell lines HCT116, HepG2 and MCF7. Complexes 2 and 3 exhibit the highest in vitro cytotoxicity and show lower cytotoxic activities in normal human fibroblast cell line than in HCT116 tumour cell line, which demonstrates their slight specificity for this type of tumour cell.

How to mimic the shapes of plant tendrils on the nano and microscale: spirals and helices of electrospun liquid crystalline cellulose derivatives

We show that suspended nano and microfibres electrospun from liquid crystalline cellulosic solutions will curl into spirals if they are supported at just one end, or, if they are supported at both ends, will twist into a helix of one handedness over half of its length and of the opposite handedness over the other half, the two halves being connected by a short straight section. This latter phenomenon, known as perversion, is a consequence of the intrinsic curvature of the fibres and of a topological conservation law. Furthermore, agreement between theory and experiment can only be achieved if account is taken of the intrinsic torsion of the fibres. Precisely the same behaviour is known to be exhibited by the tendrils of climbing plants such as Passiflora edulis, albeit on a lengthscale of millimetres, i.e., three to four orders of magnitude larger than in our fibres. This suggests that the same basic, coarse-grained physical model is applicable across a range of lengthscales.

Benzo[c]thiophene chromophores linked to cationic Fe and Ru derivatives for NLO materials: synthesis characterization and quadratic hyperpolarizabilities

5-Monocyclopentadienyliron(II)/ruthenium(II) complexes of the general formula [M(5-C5H5)(PP)(L1)][PF6] {M = Fe, PP = dppe; M = Ru, PP = dppe or 2PPh3; L1 = 5-[3-(thiophen-2-yl)benzo[c]thiophenyl]thiophene-2-carbonitrile} have been synthesized and studied to evaluate their molecular quadratic hyperpolarizabilities. The compounds were fully characterized by NMR, FTIR and UV/Vis spectroscopy and their electrochemical behaviour studied by cyclic voltammetry. Quadratic hyperpolarizabilities () were determined by hyper-Rayleigh scattering measurements at a fundamental wavelength of 1500 nm. Density functional theory calculations were employed to rationalize the second-order non-linear optical properties of these complexes.

Design, synthesis and biologival evaluation of novel isoniazid derivatives with potente antitubercular activity

The disturbing emergence of multidrug-resistant strains of Mycobacterium tuberculosis (Mtb) has been driving the scientific community to urgently search for new and efficient antitubercular drugs. Despite the various drugs currently under evaluation, isoniazid is still the key and most effective component in all multi-therapeutic regimens recommended by the WHO. This paper describes the QSAR-oriented design, synthesis and in vitro antitubercular activity of several potent isoniazid derivatives (isonicotinoyl hydrazones and isonicotinoyl hydrazides) against H37Rv and two resistant Mtb strains. QSAR studies entailed RFs and ASNNs classification models, as well as MLR models. Strict validation procedures were used to guarantee the models' robustness and predictive ability. Lipophilicity was shown not to be relevant to explain the activity of these derivatives, whereas shorter N-N distances and lengthy substituents lead to more active compounds. Compounds I, 2, 4, 5 and 6, showed measured activities against H37Rv higher than INH (i.e., MIC <= 0.28 mu M), while compound 9 exhibited a six fold decrease in MIC against the katG (S315T) mutated strain, by comparison with INH (Le., 6.9 vs. 43.8 mu M). All compounds were ineffective against H37Rv(INH) (Delta katG), a strain with a full deletion of the katG gene, thus corroborating the importance of KatG in the activation of INH-based compounds. The most potent compounds were also shown not to be cytotoxic up to a concentration 500 times higher than MIC. (C) 2014 Elsevier Masson SAS. All rights reserved.

The K-Th derivatives of the immanant and the X-symmetric power of an operator

In recent papers, formulas are obtained for directional derivatives, of all orders, of the determinant, the permanent, the m-th compound map and the m-th induced power map. This paper generalizes these results for immanants and for other symmetric powers of a matrix.

Acylated cyanoimido-complexes trans-[Mo(NCN){NCN(O)R}(DPPE)(2)]Cl and their reactons with electrophiles: Chemical, electrochemical and theoretical study

Treatment of a dichloromethane solution of trans-[Mo(NCN){NCNC(O)R}(dppe)(2)]Cl [R = Me (1a), Et (1b)] (dppe = Ph2PCH2CH2PPh2) with HBF4, [Et3O][BF4] or EtC(O)Cl gives trans-[Mo(NCN)Cl-(dppe)(2)]X [X = BF4 (2a) or Cl (2b)] and the corresponding acylcyanamides NCN(R')C(O)Et (R' = H, Et or C(O)Et). X-ray diffraction analysis of 2a (X = BF4) reveals a multiple-bond coordination of the cyanoimide ligand. Compounds 1 convert to the bis(cyanoimide) trans-[Mo(NCN)(2)(dppe)(2)] complex upon reaction with an excess of NaOMe (with formation of the respective ester). In an aprotic medium and at a Pt electrode, compounds 1 (R = Me, Et or Ph) undergo a cathodically induced isomerization. Full quantitative kinetic analysis of the voltammetric behaviour is presented and allows the determination of the first-order rate constants and the equilibrium constant of the trans to cis isomerization reaction. The mechanisms of electrophilic addition (protonation) to complexes 1 and the precursor trans[Mo(NCN)(2)(dppe)(2)], as well as the electronic structures, nature of the coordination bonds and electrochemical behaviour of these species are investigated in detail by theoretical methods which indicate that the most probable sites of the proton attack are the oxygen atom of the acyl group and the terminal nitrogen atom, respectively.

The key role of coligands in novel ruthenium(II)-cyclopentadienyl bipyridine derivatives: Ranging from non-cytotoxic to highly cytotoxic compounds

A new family of eight ruthenium(II)-cyclopentadienyl bipyridine derivatives, bearing nitrogen, sulfur, phosphorous and carbonyl sigma bonded coligands, has been synthesized. Compounds bearing nitrogen bonded coligands were found to be unstable in aqueous solution, while the others presented appropriate stabilities for the biologic assays and pursued for determination of IC50 values in ovarian (A2780) and breast (MCF7 and MDAMB231) human cancer cell lines. These studies were also carried out for the [5: HSA] and [6: HSA] adducts (HSA = human serum albumin) and a better performance was found for the first case. Spectroscopic, electrochemical studies by cyclic voltammetry and density functional theory calculations allowed us to get some understanding on the electronic flow directions within the molecules and to find a possible clue concerning the structural features of coligands that can activate bipyridyl ligands toward an increased cytotoxic effect. X-ray structure analysis of compound [Ru(eta(5)-C5H5)(bipy)(PPh3)][PF6] (7; bipy = bipyridine) showed crystallization on C2/c space group with two enantiomers of the [Ru(eta(5)-C5H5)(bipy)(PPh3)](+) cation complex in the racemic crystal packing. (C) 2015 Elsevier Inc All rights reserved.

On derivatives and norms of generalized matrix functions and respective symmetric powers

In recent papers, the authors obtained formulas for directional derivatives of all orders, of the immanant and of the m-th xi-symmetric tensor power of an operator and a matrix, when xi is a character of the full symmetric group. The operator norm of these derivatives was also calculated. In this paper, similar results are established for generalized matrix functions and for every symmetric tensor power.