On the Agmon-Miranda maximum principle for solutions of strongly elliptic equations in domains of ℝn with conical points

In this paper the Agmon-Miranda maximum principle for solutions of strongly elliptic differential equations Lu = 0 in a bounded domain G with a conical point is considered. Necessary and sufficient conditions for the validity of this principle are given both for smooth solutions of the equation Lu = 0 in G and for the generalized solution of the problem Lu = 0 in G, D _k ^v u = gk on G (k = 0,...,m-1). It will be shown that for every elliptic operator L of order 2m > 2 there exists such a cone in ⁿ (n4) that the Agmon-Miranda maximum principle fails in this cone.     

Concrete quantum logics with covering properties

LetL be a concrete (=set-representable) quantum logic. Letn be a natural number (or, more generally, a cardinal). We say thatL admits intrinsic coverings of the ordern, and writeL C _n , if for any pairA, BL we can find a collection {C _i iI}, where cardI<n andC _i L for anyiI, such thatA B= _il C _i . Thus, in a certain sense, ifLC _n , then the rate of noncompatibility of an arbitrary pairA,BL is less than a given numbern. In this paper we first consider general and combinatorial properties of logics ofC _n and exhibit typical examples. In particular, for a givenn we construct examples ofL C _n+1\C _n . Further, we discuss the relation of the classesC _n to other classes of logics important within the quantum theories (e.g., we discover the interesting relation to the class of logics which have an abundance of Jauch-Piron states). We then consider conditions on which a class of concrete logics reduce to Boolean algebras. We conclude with some open questions.     

Influence of solvents on the insertion of methacrolein into zirconacyclopropenes

The reaction of Cp₂Zr(L)(η²-Me₃SiC₂) (L = THF, py) with equimolar amounts of H₂C = CMe-CHO at room temperature depends strongly on the ligands L and the solvents that are used. With L = THF, in the THF solution the insertion product

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1 was isolated, whereas by conducting the reaction in n-hexane solution an alkyne substitution with 1,4-coordination of the methacrolein takes place and the binuclear complex [

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2 was obtained. In conttrast, with L = py (a stronger ligand) only a 1:1 ratio of 1 and 2 was observed in both THF and in n-hexane. At 50°C complex 1 was converted into 2 and the alkyne was eliminated quantitatively.

Complexes 1 and 2 were characterized by IR and NMR spectroscopical measurements and 1 by an additional X-ray structure determination.     

Novel fluorogenic calix[4]arene-bis(crown-6-ether) for selective recognition of thallium(I)

A new fluorogenic, dansyl group-containing derivative of 1,3-alternate calix[4]arene-bis(crown-6-ether) provides optical recognition of Tl+ with selectivity over many other metal cations, including Na+, K+, Ca2+, Ag+, Hg2+ and Pb2+, and embodies the first example of a calixarene-based fluorescent Tl+-chemosensor.     

Mechanism of a strongly anisotropic MoIII-CN-MnII spin-spin coupling in molecular magnets based on the [Mo(CN)(7)](4-) heptacyanometalate: a new strategy for single-molecule magnets with high blocking temperatures

Unusual spin coupling between Mo(III) and Mn(II) cyano-bridged ions in bimetallic molecular magnets based on the [Mo(III)(CN)(7)](4-) heptacyanometalate is analyzed in terms of the superexchange theory. Due to the orbital degeneracy and strong spin-orbit coupling on Mo(III), the ground state of the pentagonal-bipyramidal [Mo(III)(CN)(7)](4-) complex corresponds to an anisotropic Kramers doublet. Using a specially adapted kinetic exchange model we have shown that the Mo(III)-CN-Mn(II) superexchange interaction is extremely anisotropic: it is described by an Ising-like spin Hamiltonian JS(z)(Mo) S(z)(Mn) for the apical pairs and by the J(z)S(z)(Mo) S(z)(Mn) + J(xy)(Sx(Mo) Sx(Mn) + Sy(Mo) Sy(Mn)) spin Hamiltonian for the equatorial pairs (in the latter case J(z) and J(xy) can have opposite signs). This anisotropy resulted from an interplay of several Ising-like (Sz(Mo) Sz(Mn)) and isotropic (S(Mo)S(Mn)) ferro- and antiferromagnetic contributions originating from metal-to-metal electron transfers through the pi and sigma orbitals of the cyano bridges. The Mo(III)-CN-Mn(II) exchange anisotropy is distinct from the anisotropy of the g-tensor of [Mo(III)(CN)(7)](4-); moreover, there is no correlation between the exchange anisotropy and g-tensor anisotropy. We indicate that highly anisotropic spin-spin couplings (such as the Ising-like JS(z)(Mo) S(z)(Mn)) combined with large exchange parameters represent a very important source of the global magnetic anisotropy of polyatomic molecular magnetic clusters. Since the total spin of such clusters is no longer a good quantum number, the spin spectrum pattern can differ considerably from the conventional scheme described by the zero-field splitting of the isotropic spin of the ground state. As a result, the spin reorientation barrier of the magnetic cluster may be considerably larger. This finding opens a new way in the strategy of designing single-molecule magnets (SMM) with unusually high blocking temperatures. The use of orbitally degenerate complexes with a strong spin-orbit coupling (such as [Mo(III)(CN)(7)](4-) or its 5d analogues) as building blocks is therefore very promising for these purposes.     

Preparation,structures, and redox and emission characteristics of the isothiocyanate complexes of hexarhenium(III) clusters [Re6(mu3-E)8(NCS)6]4- (E = S,Se)

Hexarhenium(III) complexes with terminal isothiocyanate ligands, [(n-C(4)H(9))(4)N](4)[Re(6)(mu(3)-S)(8)(NCS)(6)] (1) and (L)(4)[Re(6)(mu(3)-Se)(8)(NCS)(6)] (L(+) = PPN(+) (2a), (n-C(4)H(9))(4)N(+) (2b)), have been prepared by three different methods. Complex 1 was prepared by the reaction of [(n-C(4)H(9))(4)N](4)[Re(6)(mu(3)-S)(8)Cl(6)] with molten KSCN at 200 degrees C, while 2b was obtained by refluxing the chlorobenzene-DMF (2:1 v/v) solution of [Re(6)(mu(3)-Se)(8)(CH(3)CN)(6)](SbF(6))(2) and [(n-C(4)H(9))(4)N]SCN. The [Re(6)(mu(3)-Se)(8)(NCS)(6)](4)(-) anion was also obtained from a mixture of Cs(2)[Re(6)(mu(3)-Se)(8)Br(4)] and KSCN in C(2)H(5)OH by a mechanochemical activation at room temperature for 20 h and isolated as 2a. The X-ray structures of 1 and 2a.4DMF have been determined (1, C(70)H(144)N(10)S(14)Re(6), monoclinic, space group P2(1)/n (No. 14), a = 14.464(7) A, b = 22.059(6) A, c = 16.642(8) A, beta = 113.62(3) degrees, V = 4864(3) A(3), Z = 2; 2a.4DMF, C(162)H(144)N(14)O(4)P(8)S(6)Se(8)Re(6), triclinic, space group P1 (No. 2), a = 15.263(2) A, b = 16.429(2) A, c = 17.111(3) A, alpha = 84.07(1) degrees, beta = 84.95(1) degrees, gamma = 74.21(1) degrees, V = 4098.3(8) A(3), Z = 1). All the NCS(-) ligands in both complexes are coordinated to the metal center via nitrogen site with the Re-N distances in the range of 2.07-2.13 A. The redox potentials of the reversible Re(III)(6)/Re(III)(5)Re(IV) process in acetonitrile are +0.84 and +0.70 V vs. Ag/AgCl for [Re(6)(mu(3)-S)(8)(NCS)(6)](4)(-) and [Re(6)(mu(3)-Se)(8)(NCS)(6)](4)(-), respectively, which are the most positive among the known hexarhenium complexes with six terminal anionic ligands. The complexes show strong red luminescence with the emission maxima (lambda(max)/nm), lifetimes (tau(em)/micros), and quantum yields (phi(em)) being 745 and 715, 10.4 and 11.8, and 0.091 and 0.15 for 1 and 2b, respectively, in acetonitrile. The data reasonably well fit in the energy-gap plots of other hexarhenium(III) complexes. The temperature dependence of the emission spectra and tau(em) of 1 and [(n-C(4)H(9))(4)N](4)[Re(6)(mu(3)-S)(8)Cl(6)] are also reported.     

Reactions of Allyl Alcohols of the Pinane Series and of Their Epoxides in the Presence of Montmorillonite Clay

The reactivity of allyl alcohols of the pinane series and of their epoxides in the presence of montmorillonite clay in intra‐ and intermolecular reactions was studied. Mutual transformations of (+)‐trans‐pinocarveol ((+)‐ 2 ) and (?)‐myrtenol ((?)‐ 3a ) were major reactions of these compounds on askanite–bentonite clay (Schemes 1 and 2). However, the two reactions gave different isomerization products, indicating that the reactivity of the starting alcohol (+)‐ 2 or (?)‐ 3a was different from that of the same compound (+)‐ 2 or (?)‐ 3 formed in the course of the reactions. (?)‐cis‐ and (+)‐trans‐Verbenol ((?)‐ 16 and (+)‐ 12 , resp.), as well as (?)‐cis‐verbenol epoxide ((?)‐ 20 ) reacted with both aliphatic and aromatic aldehydes on askanite–bentonite clay giving various heterocyclic compounds (Schemes 4, 5 and 7); the reaction path depended on the structure of both the terpenoid and the aldehyde.     

Tautomerism,electronic structures,and electronic spectra of indolo[2,3-b]quinoxaline and its derivatives

The tautomerism, electronic spectra, and electronic structures of the ground and excited states of indolo [2,3-b]quinoxaline and its 2,3- and 1,4-dibutoxy derivatives were investigated by the Pariser-Parr-Pople (PPP) method. It is shown that these compounds exist primarily in the 6H form; the long-wave s^* transition is due to transfer of charge from the indole fragment to the quinoxaline fragment, and in the first excited state many of the bonds in the quinoxaline fragment are loosened significantly. The effect of butoxy substituents on the first s^* transition of indolo [2,3-b] quinoxaline was analyzed by means of perturbation theory within the framework of the Hückel MO method.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 9, pp. 1259–1263, September, 1982.     

Effects of Photobiomodulation on Daphnia magna Straus and their Sensitivity to Toxicant

This paper deals with the effect of photobiomodulation (PBM) on Daphnia magna S. and their sensitivity to cadmium sulfate, a known high toxic pollutant. In a first series of experiments, the effect of different He-Ne laser fluences irradiation (range 0.9-4300 mJ cm⁻²) on the fertility of both parent and filial generations (F1–F3) of the crustacean was studied. It was found that PBM in some cases significantly influenced the fertility of both irradiated crustaceans and their nonirradiated offspring. By selecting two fluences (9 ± 2 mJ cm⁻² reducing fertility and 4.3 ± 0.9 J cm⁻² increasing it), the effect of these on toxicity of cadmium sulfate was evaluated. These experiments have shown that prior irradiation with low-intensity light of a helium–neon laser with 632.8 nm wavelength can change the sensitivity of aquatic organisms to toxin cadmium sulfate. The degree and direction of changes depend on the toxicant concentration and the irradiation dose.     

First investigation of non-classical dihydrogen bonding between an early transition-metal hydride and alcohols: IR, NMR, and DFT approach

The interaction of [NbCp(2)H(3)] with fluorinated alcohols to give dihydrogen-bonded complexes was studied by a combination of IR, NMR and DFT methods. IR spectra were examined in the range from 200-295 K, affording a clear picture of dihydrogen-bond formation when [NbCp(2)H(3)]/HOR(f) mixtures (HOR(f) = hexafluoroisopropanol (HFIP) or perfluoro-tert-butanol (PFTB)) were quickly cooled to 200 K. Through examination of the OH region, the dihydrogen-bond energetics were determined to be 4.5+/-0.3 kcal mol(-1) for TFE (TFE = trifluoroethanol) and 5.7+/-0.3 kcal mol(-1) for HFIP. (1)H NMR studies of solutions of [NbCp(2)H(2)(B)H(A)] and HFIP in [D(8)]toluene revealed high-field shifts of the hydrides H(A) and H(B), characteristic of dihydrogen-bond formation, upon addition of alcohol. The magnitude of signal shifts and T(1) relaxation time measurements show preferential coordination of the alcohol to the central hydride H(A), but are also consistent with a bifurcated character of the dihydrogen bonding. Estimations of hydride-proton distances based on T(1) data are in good accord with the results of DFT calculations. DFT calculations for the interaction of [NbCp(2)H(3)] with a series of non-fluorinated (MeOH, CH(3)COOH) and fluorinated (CF(3)OH, TFE, HFIP, PFTB and CF(3)COOH) proton donors of different strengths showed dihydrogen-bond formation, with binding energies ranging from -5.7 to -12.3 kcal mol(-1), depending on the proton donor strength. Coordination of proton donors occurs both to the central and to the lateral hydrides of [NbCp(2)H(3)], the former interaction being of bifurcated type and energetically slightly more favourable. In the case of the strong acid H(3)O(+), the proton transfer occurs without any barrier, and no dihydrogen-bonded intermediates are found. Proton transfer to [NbCp(2)H(3)] gives bis(dihydrogen) [NbCp(2)(eta(2)-H(2))(2)](+) and dihydride(dihydrogen) complexes [NbCp(2)(H)(2)(eta(2)-H(2))](+) (with lateral hydrides and central dihydrogen), the former product being slightly more stable. When two molecules of TFA were included in the calculations, in addition to the dihydrogen-bonded adduct, an ionic pair formed by the cationic bis(dihydrogen) complex [NbCp(2)(eta(2)-H(2))(2)](+) and the homoconjugated anion pair (CF(3)COO...H...OOCCF(3))(-) was found as a minimum. It is very likely that these ionic pairs may be intermediates in the H/D exchange between the hydride ligands and the OD group observed with the more acidic alcohols in the NMR studies.