Comparison theorems for weak splittings of bounded operators

Summary Comparison theorems for weak splittings of bounded operators are presented. These theorems extend the classical comparison theorem for regular splittings of matrices by Varga, the less known result by Wonicki, and the recent results for regular and weak regular splittings of matrices by Neumann and Plemmons, Elsner, and Lanzkron, Rose and Szyld. The hypotheses of the theorems presented here are weaker and the theorems hold for general Banach spaces and rather general cones. Hypotheses are given which provide strict inequalities for the comparisons. It is also shown that the comparison theorem by Alefeld and Volkmann applies exclusively to monotone sequences of iterates and is not equivalent to the comparison of the spectral radius of the iteration operators.This work was supported by the National Science Foundation grants DMS-8807338 and INT-8918502     

On two mean value properties and functional equations associated with them

Summary Motivated by different mean value properties, the functional equationsf(x) – f(y)/x–y=[(x, y)], (i)xf(y) – yf(x)/x–y=[(x, y)] (ii) (x y) are completely solved when, are arithmetic, geometric or harmonic means andx, y elements of proper real intervals. In view of a duality between (i) and (ii), three of the results are consequences of other three.The equation (ii) is also solved when is a (strictly monotonic) quasiarithmetic mean while the real interval contains 0 and when is the arithmetic mean while the domain is a field of characteristic different from 2 and 3. (A result similar to the latter has been proved previously for (i).)     

The dynamics of multidimensional cosmological models in the presence of quantum effects. I. The case FRW ×T D at high temperatures

The dynamical system approach is applied to the study of dynamics of multidimensional cosmological models with topology FRW ×T ^D (D-dimensional torus) in the presence of high-temperature quantum effects. The stability methods developed in the paper of Szydowski (Gen. Rel. Grav.,20, 221, 1988) are used in the analysis of typical states of the metric in the neighborhood of singularities and for large time values. The problems of dynamical dimensional reduction, structure of singularities, isotropization, etc., are discussed in this context.     

On the solution of singular linear systems of algebraic equations by semiiterative methods

Summary For a square matrixT ^n,n , where (I–T) is possibly singular, we investigate the solution of the linear fixed point problemx=T x+c by applying semiiterative methods (SIM's) to the basic iterationx ₀ ⁿ ,x _k T c _k–1+c(k1). Such problems arise if one splits the coefficient matrix of a linear systemA x=b of algebraic equations according toA=M–N (M nonsingular) which leads tox=M ^–1 N x+M ^–1 bT x+c. Even ifx=T x+c is consistent there are cases where the basic iteration fails to converge, namely ifT possesses eigenvalues 1 with ||1, or if =1 is an eigenvalue ofT with nonlinear elementary divisors. In these cases — and also ifx=T x+c is incompatible — we derive necessary and sufficient conditions implying that a SIM tends to a vector which can be described in terms of the Drazin inverse of (I–T). We further give conditions under which is a solution or a least squares solution of (I–T)x=c.Research supported in part by the Alexander von Humboldt-Stiftung     

Structure and Magnetic Properties of Ce3Ge0.66In4.34 and Ce11Ge4.74In5.26

New indides Ce₃Ge_0.66In_4.34 and Ce₁₁Ge_4.74In_5.26 were synthesized from the elements by arc‐melting and subsequent annealing at 870 K. Single crystals were grown through special annealing procedures in sealed tantalum tubes in a high‐frequency furnace. Both compounds were investigated on the basis of X‐ray powder and single crystal data: I4/mcm, La₃GeIn₄ type, a = 848.8(1), c = 1192.0(2) pm, Z = 4, wR2 = 0.0453, 499 F² values, 17 variables for Ce₃Ge_0.66In_4.34 and I4/mmm, Sm₁₁Ge₄In₆ type (ordered version of the Ho₁₁Ge₁₀ type), a = 1199.3(2), c = 1662.0(3) pm, wR2 = 0.0507, 1217 F² values, 41 variables for Ce₁₁Ge_4.74In_5.26. The Ce₃Ge_0.66In_4.34 structure shows a mixed Ge/In occupancy on the 4c Wyckoff position. This site is octahedrally coordinated by cerium atoms. These octahedra share all edges, leading to a three‐dimensional network. The latter is penetrated by a two‐dimensional indium substructure which consists of flattened tetrahedra at In–In distances of 291 and 300 pm. The Ce₁₁Ge_4.74In_5.26 structure contains three crystallographically independent germanium sites. The latter are coordinated by eight or nine cerium neighbors. These CN8 and CN9 polyhedra are condensed to a complex network which is penetrated by a three‐dimensional indium network with In–In distances of 301–314 pm. The 16m site shows a mixed In/Ge occupancy. Chemical bonding in both compounds is dominated by the p elements. Both ternaries studied exhibit localized magnetism due to the presence of Ce³⁺ ions. The compound Ce₃GeIn₄ remains paramagnetic down to 1.72 K, whereas Ce₁₁Ge₄In₆ orders ferromagnetically at T_C = 7.5 K.     

Nuclear Techniques in the Elucidation of Chemical Structure

The paper offers three applications of nuclear methods in the research of chemical structure. First, progress in positron annihilation spectroscopy is illustrated by a positron beamline study, which obtained results that are not available through conventional experiments. The positron beam was used for the study of Langmuir-Blodgett (LB) films containing 4-58 layers of arachidic acid and its salts. These measurements have shown that this emerging technique is capable of characterizing even such elusive systems. Second, the potential of Mössbauer spectroscopy to answer current challenges of solid state chemistry are shown in a study on perovskites of recent interest. ¹⁵¹Eu Mössbauer spectroscopy was used to study the effect of Pr substitution in EuBa₂Cu₃O_7-. It was shown that the introduction of Pr into the rare earth site as well as into the Ba site results in the appearance of extra electrons both in the copper oxide planes and at the 4f shell of Eu cations. The observed effects were explained by the hole filling effect of Pr. Finally, a survey is presented on the recently developed techniques for nuclear resonant scattering of synchrotron radiation, an exciting and very rapidly developing extension to conventional Mössbauer spectroscopy. An interesting new result is that nuclear inelastic scattering experiments performed on solutions of ⁵⁷Fe complexes show contribution from vibrations rather than from diffusion to the inelastic spectra.     

Acyclic congener of cucurbituril: synthesis and recognition properties

The cucurbit[n]uril (CB[n]) family of macrocycles occupies a prominent role in molecular recognition and self-assembly studies despite the current inability to access specific cucurbit[n]uril homologues, derivatives, and analogues by straightforward tailor-made synthetic procedures. In this paper, we explore an approach that circumvents the challenges posed by the tailor-made synthesis of macrocyclic CB[n] by preparing 1, which functions as an acyclic CB[6] congener. The o-xylylene connections to the glycoluril rings preorganize 1 into the (a,a,a,a)-1 conformation required for binding and reduce its tendency to undergo self-association. We surveyed the binding properties of 1 toward 16 amines (K(a) 相似文献   

Compressibility and Volume Effects of Mixing of 1-Propanol with Heavy Water

Speed of sound and density of 1-propanol + heavy water were measured in the whole concentration range at temperatures from 293 to 313 K. Isentropic compressibility was calculated from the Laplace formula. The partial molar volume of 1-propanol reaches a minimum at the mole fraction of 1-propanol x ₁ 0.03. At the same concentration, the compressibility isotherms intersect one another. These features of the investigated system are similar to those of 1-propanol + H₂O, that points to essential similarity of the two mixtures. A clathrate-like structure was suggested to explain the experimental results for dilute solutions of the alcohol. Somewhat more pronounced hydrophobic hydration in D₂O than in H₂O is manifested by an effect similar to that resulting from the elongation of the alcohol molecule.     

Cinnamaldehyde hydrogenation using ruthenium-tin catalyst type

Bimetallic ruthenium-tin catalysts were prepared using the sol-gel method and the method of carrier impregnation. Two different procedures were used for their reduction — reduction in hydrogen atmosphere under an increased temperature, and reduction using an aqueous solution of sodium borohydride. Hydrogenation of 3-phenylpropenal (cinnamaldehyde) in tetrahydrofuran at 433 K and the total pressure 7 MPa was used as the model reaction for comparing the catalytic properties of the prepared catalysts. It was demonstrated that a tin addition notably affected catalytic properties of ruthenium in the sense of a selectivity increment related to the production of an unsaturated alcohol.     

Electron-stimulated desorption from ionic crystal surfaces

Inelastic interactions of electrons with surfaces of ionic crystals result in emission of various particles such as ions, atoms and molecules. We will review such electron-stimulated desorption processes for the particular class of ionic crystals, namely for alkali halides. In this case, a dominant fraction of the emission is in the form of halogen and alkali atoms characterized by a thermal (Maxwellian) spectrum of translational energies. For several alkali halides (potassium and rubidium chlorides, bromides, and iodides), however, a significant part of the halogen atoms is ejected with nonthermal energies, i.e. energies of the order of 0.1 eV. The results of recent systematic studies of angular-resolved kinetic energy distributions of the emitted particles will be reported and current views on the electronic mechanisms of desorption will be described. In particular, it will be shown that the ESD mechanism can be understood in terms of the model involving a surface localisation of the so called “hot-holes” created by electron bombardment of alkali halides. A role of hot holes in ESD processes will further be discussed in relation to very recent experimental results obtained for the KBr crystals doped with In impurities which act as efficient hole traps.