Venues on the verges: London's theater government between 1594 and 1614

In 1594, major decisions were made by the governors of London and the country about plays and playing. We need to learn what lay behind these events, such as what led James Burbage to build his Blackfriars theater in 1596. That initial fiasco might tell us much about what lay behind Shakespeare’s decision to join the new Chamberlain’s Men in 1594 and his subsequent commitment to them as a full-time playwright. When the Globe burned down in 1613, a majority of the shareholders decided to rebuild it at great cost, but Shakespeare withdrew. The rebuilding was old-fashioned thinking, reverting to the company’s desire, asserted in 1594, to play indoors in winter, which helps to clarify their decisions and Shakespeare’s own—to write plays rather than more long poems. The few surviving papers of the Privy Council and the London mayoralty from the time suggest that one of the two new companies of 1594 preferred to play indoors during the winter instead of at their allocated open playhouses in the suburbs. They tried to renew this traditional practice, first in 1594 and again in 1596 when James Burbage built the indoor Blackfriars playhouse for them. The renewal of the Globe in 1614 was part of the same thinking, although Shakespeare evidently opted out of the decision.

Boundary integral equations on unbounded rough surfaces: Fredholmness and the finite section method

We consider a class of boundary integral equations that arise in the study of strongly elliptic BVPs in unbounded domains of the form $D = \{(x, z)\in \mathbb{R}^{n+1} : x\in \mathbb{R}^n, z > f(x)\}$ where $f : \mathbb{R}^n \to\mathbb{R}$ is a sufficiently smooth bounded and continuous function. A number of specific problems of this type, for example acoustic scattering problems, problems involving elastic waves, and problems in potential theory, have been reformulated as second kind integral equations $u+Ku = v$ in the space $BC$ of bounded, continuous functions. Having recourse to the so-called limit operator method, we address two questions for the operator $A = I + K$ under consideration, with an emphasis on the function space setting $BC$. Firstly, under which conditions is $A$ a Fredholm operator, and, secondly, when is the finite section method applicable to $A$?

An evaluation of different growth functions for describing the profile of live weight with time (age) in meat and egg strains of chicken

A total of 86 profiles from meat and egg strains of chickens (male and female) were used in this study. Different flexible growth functions were evaluated with regard to their ability to describe the relationship between live weight and age and were compared with the Gompertz and logistic equations, which have a fixed point of inflection. Six growth functions were used: Gompertz, logistic, Lopez, Richards, France, and von Bertalanffy. A comparative analysis was carried out based on model behavior and statistical performance. The results of this study confirmed the initial concern about the limitation of a fixed point of inflection, such as in the Gompertz equation. Therefore, consideration of flexible growth functions as an alternatives to the simpler equations (with a fixed point of inflection) for describing the relationship between live weight and age are recommended for the following reasons: they are easy to fit, they very often give a closer fit to data points because of their flexibility and therefore a smaller RSS value, than the simpler models, and they encompasses simpler models for the addition of an extra parameter, which is especially important when the behavior of a particular data set is not defined previously.

Molybdenum eta(3)-allyl dicarbonyl complexes as a new class of precursors for highly reactive epoxidation catalysts with tert-butyl hydroperoxide

New Mo(II) diimine derivatives of [Mo(q (3)allyl)X(CO)(2)(CH3CN)(2)] (allyl = C3H5 and C5H5O; X = Cl, Br) were prepared, and [MO(eta(3)-C3H5)Cl(CO)(2)(BIAN)] (BIAN = 1,4-(4-chloro)phenyl-2,3-naphthalene-diazabutadiene) (7) was structurally characterized by single-crystal X-ray diffraction. This complex adopted an equatorial-axial arrangement of the bidentate ligand (axial isomer), in contrast with the precursors, found as the equatorial isomer in the solid and fluxional in solution. The new complexes of the type [Mo(eta(3)-allyl)X(CO)(2)(N-N)l (N-N is a bidentate chelating dinitrogen ligand) were tested for the catalytic epoxidation of cyclooctene using tert-butyl hydroperoxide as oxidant. All catalytic systems were 100% selective toward epoxide formation. While their turnover frequencies paralleled those of related Mo(eta) carbonyl compounds or Mo(VI) compounds bearing similar N-donor ligands, they exhibited similar olefin conversions in consecutive catalytic runs. The acetonitrile precursors were generally more active than the diimine complexes, and the chloro derivatives more active than the bromo ones. Combined vibrational and NMR spectroscopy and computational studies (DFT) were used to investigate the nature of the molybdenum species formed in the catalytic system with [Mo(eta(3)-C3H5)Cl(CO)(2){1,4-(2,6-dimethyl)phenyl-2.3-dimethyldiazabuta diene}] (4) and to propose that the resulting species may be dimeric bearing oxide bridges.

Immobilisation of eta(3)-allyidicarbonyl complexes of Mo-II with bidentate nitrogen ligands within aluminium-pillared clays

Molybdenum(II) complexes [MOX(CO)(2)(eta(3)-allyl)(CH3CN)(2)] (X = Cl or Br) were encapsulated in an aluminium-pillared natural clay or a porous clay heterostructure and allowed to react with bidentate diimine ligands. All the materials obtained were characterised by several solid-state techniques. Powder XRD, and Al-27 and Si-29 MAS NMR were used to investigate the integrity of the pillared clay during the modification treatments. C-13 CP MAS NMR, FTIR, elemental analyses and low-temperature nitrogen adsorption showed that the immobilisation of the precursor complexes was successful as well as the in situ ligand-substitution reaction. The new complex [MoBr(CO)(2)(eta(3)-allyl)(2-aminodipyridyl)] was characterised by single-crystal X-ray diffraction and spectroscopic techniques, and NMR studies were used to investigate its fluxional behaviour in solution. The prepared materials are active for the oxidation of cis-cyclooctene using tert-butyl hydroperoxide as oxidant, though the activity of the isolated complexes is higher. ((c) Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2008).

Metal complexes of a tetraazacyclophane: solution and molecular modelling studies

An alternative synthetic approach to yield the compound 2,3,5,6,8,9,11,14-octahydrobenzo[1][ 1,4,7,10]tetraazacyclotetradecine (bz[14]N-4) is presented. The protonation constants of bz[14]N-4 and the stability constants of its complexes with Ni2+, Cu2+, Zn2+, Cd2+, Pb2+ were determined in H2O at 25degreesC with ionic strength 0.10 mol dm(-3) in KNO3 and they were compared with structurally related macrocycles cyclam (1,4,8,11-tetraazacyclotetradecane) and cyclen (1,4,7,10-tetraazacyclododecane). These studies indicate that only 1 : 1 ( M : L) species are formed in solution, and the ligand exhibits a high affinity for larger ions such as Cd2+ and Pb2+. The X-ray study of [bz[14]N4H3](3+) shows that an inclusion compound with a chloride counter-anion is formed through NH...Cl hydrogen bonds. Spectroscopic data in solution ( electronic and NMR spectra) showed that the macrocycle adopts a planar arrangement upon metal complexation. Molecular mechanics calculations reveal that in spite of the presence of the benzene ring in the macrocyclic framework this ligand can encapsulate metal ions with different stereo-electronic sizes in square planar arrangements. Our results indicate that the presence of the benzene ring in the backbone of the bz[14]N-4 confers a coordination behaviour intermediate between that of cyclam and cyclen.

Copper complexes of new benzodioxotetraaza macrocycles with potential applications in nuclear medicine

Two novel benzodioxotetraaza macrocycles [2,9-dioxo-1,4,7,10-tetraazabicyclo[10.4.0]1,11-hexadeca-1(11),13,15-triene (H(2)L1) and 2,10-dioxo-1,4,8,11-tetraazabicyclo[11.4.0]1,12-heptadeca-1(12),14,16-triene (H(2)L2)] were synthesized by a [1 + 1] crablike cyclization. The protonation constants of both ligands were determined by H-1 NMR titration and by potentiometry at 25.0 degrees C in 0.10 M ionic strength in KNO3. The latter method was also used to ascertain the stability constants of their copper(II) complexes. These studies showed that the CuL1 complex has a much lower thermodynamic stability than the CuL2, and the H(2)L2 displays an excellent affinity for copper(II), due to the good fit of copper(II) into its cavity. The copper complexes of the novel ligands were characterized by electronic spectroscopy in solution and by crystal X-ray diffraction. These studies indicated that the copper center in the CuL1 complex adopts a square-pyramidal geometry with the four nitrogen atoms of the macrocycle forming the equatorial plane and a water molecule at axial position, and the copper in the CuL2 complex is square-planar. Several labeling conditions were tested, and only H(2)L2 could be labeled with Cu-67 efficiently (> 98%) in mild conditions (39 degrees C, 15 min) to provide a slightly hydrophilic radioligand (log D = -0.19 +/- 0.03 at pH 7.4). The in vitro stability was studied in the presence of different buffers or with an excess of diethylenetriamine-pentaethanoic acid. Very high stability was shown under these conditions for over 5 days. The incubation of the radiocopper complex in human serum showed 6% protein binding.

Dinuclear copper and zinc complexes of a hexaazamacrocycle containing p-xylyl spacers and bridging anions: theoretical and spectroscopic studies

The hexaazamacrocycle 7,22-dimethyl-3,7,11,18,22,26-hexaazatricyclo[26.2.2.2(13,16)] tetratriaconta-1(30), 13,15,28,31,33- hexaene (Me-2[30] pbz(2)N(6)) was synthesized and characterised by single crystal X-ray diffraction. The macrocycle adopts a conformation with the two aromatic rings almost parallel at a distance of ca. 4.24 Angstrom, but displaced relative to each other by ca. 1.51 Angstrom. The protonation constants of this compound and the stability constants of its complexes with Cu2+ and Zn2+, were determined in water - methanol (9 : 1 v/v) at 25 degreesC with ionic strength 0.10 mol dm(-3) in KCl. The potentiometric and spectroscopic studies (NMR of zinc, cadmium and lead complexes, and EPR of the copper complexes) indicate the formation of only dinuclear complexes. The association constants of the dinuclear copper complex with anions ( thiocyanate, terephthalate and glyphosate) and neutral molecules (1,4-benzenedimethanol, p-xylylenediamine and terephthalic acid) were determined at 20 degreesC in methanol. The structural preferences of this ligand and of its dinuclear copper(II) complex with a variety of bridging ligands were evaluated theoretically by molecular mechanics calculations (MM) and molecular dynamics (MD) using quenching techniques.

Binding studies of a protonated dioxatetraazamacrocycle with carboxylate substrates

The tetraprotonated form of the dioxatetraazamacrocycle, 6,19-dioxa-3,9,16,22-tetraaza[22.2.2.2(11,14)]-triaconta-1(26),11,13,24, 27,29-hexaene, (H4L1)(4+), was used as the receptor for binding studies with carboxylate anionic substrates of different shapes, sizes, and charges [succinate (suc(2-)), cyclo- hexanetricarboxylate (cta(3-)), phthalate (ph(2-)), isophthalate (iph(2-)), terephthalate (tph(2-)), and benezenetricarboxylate (btc(3-))]. Association constants were determined by potentiometry in aqueous solution at 298.2 K and 0.10 M KCl and by H-1 NMR titration in D2O. The strongest association was found for the btc3- anion at 5-7 pH region. From both techniques it was possible to establish the binding preference trend of the receptor for the different substrates, and the H-1 NMR spectroscopy gave important suggestions about the type of interactions between partners and the location of the substrates in the supramolecular entities formed. The effective binding constants at pH 6 follow the order: btc(3-)>iph(2-)>cta(3-) =ph(2-)>tph(2-)>suc(2-). All the studies suggest that the anionic substrates bind to the receptor via N-H center dot center dot center dot O = C hydrogen bonds and electrostatic interactions, and the aromatic substrates can also establish pi-pi stacking interactions. The crystal structures of (H4L1)(4+) and its supramolecular assemblies with ph(2-) and tph(2-) were determined by X-ray diffraction. The last two structures showed that the association process in solid state occurs via multiple N-H center dot center dot center dot O = C hydrogen bonds with the anionic substrate located outside the macrocyclic cavity of the receptor. Molecular dynamics simulations carried out for the association of (H4L1)(4+) with tph(2-) and btC(3-) in water solution established at atomic level the existence of all interactions suggested by the experimental studies, which act cooperatively in the binding process. Furthermore, the binding free energies were estimated and the values are in agreement with the experimental ones, indicating that the binding of these two anionic substrates occurs into the receptor cavity. However, the tph(2-) has also propensity to leave the macrocyclic cavity and its molecular recognition can also happen at the top of the receptor. (C) 2008 Elsevier Ltd. All rights reserved.

Dicopper(II) complexes of a new di-para-xylyldioxatetraazamacrocycle and cascade species with dicarboxylate anions: thermodynamics and structural properties

The new dioxatetraazamacrocycle (L-1) was synthesized by a 2 + 2 condensation and characterized. Stability constants of its copper(II) complexes were determined by spectrophotometry in DMSO at 298.2 K in 0. 10 mol dm(-3) KClO4. Mainly dinuclear complexes are formed and the presence of mononuclear species is dependent on the counterion (Cl- or ClO4-). The association constants of the dinuclear copper(II) complexes with dicarboxylate anions [oxalate (oxa(2-)), malonate (mal(2-)), succinate (suc(2-)), and glutarate (glu(2-))] were also determined by spectrophotometry at 298.2 K in DMSO, and it was found that values decrease with an increase of the alkyl chain between the carboxylate groups. X-Band EPR spectra of the dicopper(II) complexes and of their cascade species in frozen DMSO exhibit dipole-dipole coupling, and their simulation, together with their UV-vis spectra, showed that the copper centres of the complexes in solution had square pyramidal geometries though with different distortions. From the experimental data, it was also possible to predict the Cu...Cu distances, the minimum being found at 6.4 angstrom for the (Cu2LCl4)-Cl-1 complex and then successively this distance slightly increases when the chloride anions are replaced by dicarboxylate anions, from 6.6 angstrom for oxa(2-) to 7.8 for glu(2-). The crystal structures of the dinuclear copper cascade species with oxa(2-) and suc(2-) were determined and showed one anion bridging both copper centres and Cu...Cu distances of 5.485(7) angstrom and 6.442(8) angstrom, respectively.

Cascade dicopper architectures of a dibenzodioxatetraazamacrocycle

The dibenzodioxatetraazamacrocycle [26]pbz(2)N(4)O(2) was characterised by single crystal X-ray diffraction and the protonation constants of this compound and the stability constants of its copper(II) and lead(II) complexes were determined by potentiometry in water at 298.2 K in 0.10 mol dm(-3) in KNO3. Mono- and dinuclear complexes were found for both metal ions, the dinuclear complexes being the main species in the 5-7.5 pH range for copper(II) and 7.5-8.5 for lead(II). As expected the values of the stability constants for the copper(II) complexes are lower than those for related macrocycles containing only nitrogen atoms. The presence of mono- and dinuclear copper complexes was also confirmed by electrospray ionization mass spectrometry. These results suggest that the symmetric macrocyclic cavity of [26]pbZ(2)N(4)O(2) has enough space for the coordination of two metal ions. Additionally, NMR spectroscopy showed that the dinuclear complex of lead(II) has high symmetry. The equilibrium constants of the dinuclear copper(II) complexes and dicarboxylate anions (oxalate, malonate and succinate) were also determined in 0.10 mol dm-3 aqueous KNO3 solution. Only species containing one anion, Cu(2)H(h)LA((2+h)), were found, strongly suggesting that the anion bridges the two copper(II) ions. The binding constants of the cascade species formed by [Cu-2[26]pbZ(2)N(4)O(2)(H2O)(4+) with dicarboxylate anions decrease with the increase in length of the alkyl chain of the anion, a fact which was attributed to a higher conformational energy necessary for the rearrangement of the macrocycle to accommodate the larger anions bridging the two copper(II) centres. The variation of the magnetic susceptibility with temperature Of [Cu-2(H-2[26]pbz(2)N(4)O(2))(oxa)(3)]-4H(2)O and [Cu-2([26]pbz(2)N(4)O(2))(suc)Cl-2] were measured and the two complexes showed different behaviour. (c) 2007 Elsevier Ltd. All rights reserved.

Mono- and binuclear bipyridyl derivatives of the Mo(eta(3)-C3H5)(CO)(2) fragment: structural studies and fluxionality in solution

New mono- and binuclear complexes of the Mo(eta(3)-C3H5)(CO)(2) fragment, containing bipyridyl ligands (2,2'-bpy, 4,4'-Me-2-2,2'-bpy) as chelates, and mono- (4-CNpy, 4-Mepy, NCMe, Br) or bidentate nitrogen ligands (4,4'-bpy, bipyridylethylene, pyrazine) as terminal or bridging ligands, respectively, were prepared. The binuclear complex [{Mo(eta(3)-C3H5)(CO)(2)(2,2'-bpy)}(2)(mu-4,4'-bpy)][PF6](2) (2) was shown by X-ray diffraction to assemble in the crystal forming large channels with a rectangular section. A longer bridge, such as bipyridylethylene, led to a different structure (3). 4-CNpy behaved as monodentate ligand (4), coordinating through the pyridine nitrogen as a terminal ligand. NMR spectroscopy studies showed that the complexes exhibited a fluxional behavior in solution, the endo and exo forms of the more symmetrical equatorial isomers being usually present and interconverting in solution. The solid state structures of the complexes revealed a preference for the more symmetrical equatorial isomer, with the two chelate ligands in trans positions in the binuclear species. The rings tended to become parallel in the organized crystal. (C) 2003 Elsevier B.V. All rights reserved.