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101.
    
The aim of this work is to generalize Lomonosov's techniques in order to apply them to a wider class of not necessarily compact operators. We start by establishing a connection between the existence of invariant subspaces and density of what we define as the associated Lomonosov space in a certain function space. On a Hilbert space, approximation with Lomonosov functions results in an extended version of Burnside's Theorem. An application of this theorem to the algebra generated by an essentially self-adjoint operator yields the existence of vector states on the space of all polynomials restricted to the essential spectrum of . Finally, the invariant subspace problem for compact perturbations of self-adjoint operators acting on a real Hilbert space is translated into an extreme problem and the solution is obtained upon differentiating certain real-valued functions at their extreme.

  相似文献   

102.
1,7-Dihalogenated boron dipyrromethene dyes were successfully synthesized and substituted, thus providing an entry to the final, elusive reactivity pattern. The spectroscopic properties of 1,7-disubstituted BODIPY dyes were studied and are discussed as a function of their structure.  相似文献   
103.
Dynamic adsorption of radiocesium on titanium ferrocyanide grains from reactor coolant simulating solution containing salts at moderate concentrations has been investigated. Effective decontamination of the neutral solutions has been achieved, in the amounts of a more than 20 thousand bed volumes. After adsorption the titanium ferrocyanide was transferred to titanates and calcined at 900 °C. The leaching test of the obtained lithium titanates indicates that the loaded adsorbent can serve as an effective primary barrier in nuclear waste repositories.  相似文献   
104.
105.
Every finite disconnected set P is determined (up to automorphism) by the family {P − {a}:a ∈ Max P }.  相似文献   
106.
107.
Let µ be a real number. The Möbius group Gµis the matrix group generated by It is known that Gµ is free if |µ| 2 (see [1])or if µ is transcendental (see [3, 8]). Moreover, thereis a set of irrational algebraic numbers µ which is densein (–2, 2) and for which Gµ is non-free [2, p. 528].We may assume that µ > 0, and in this paper we considerrational µ in (0, 2). The following problem is difficult. Let Gnf denote the set of all rational numbers µ in (0,2) for which Gµ is non-free. In 1969 Lyndon and Ullman[8] proved that Gnf contains the elements of the forms p/(p2+ 1) and 1/(p + 1), where p = 1, 2, ..., and that if µ0 Gnf, then µ0/p Gnf for p = 1, 2, .... In 1993 Beardon[2] studied problem (P) by means of the words of the form ArBs At and Ar Bs At Bu Av, and he obtained a sufficient conditionfor solvability of (P), included implicitly in [2, pp. 530–531],by means of the following Diophantine equations: 1991 Mathematics SubjectClassification 20E05, 20H20, 11D09.  相似文献   
108.
109.
We have studied substituent effects on the properties of the intramolecular hydrogen bond of some ortho-hydroxy Schiff bases using density functional theory (DFT) based first-principle molecular dynamics (FPMD) and path integral molecular dynamics. The studied compounds possess a strong intramolecular hydrogen bond (r((O???N)) ≤ 2.6 A?), which can be tuned by substitution to either (i) enhance the basicity of the acceptor moiety by induction effects or (ii) decrease the hydrogen bond length through steric repulsion. DFT calculations and FPMD were employed to investigate structural and dynamical properties of the selected molecules, while quantum effects on the structural properties were assessed using path integral FPMD. The simulations were performed in vacuo and in the solid state to study the influence of the environment on the hydrogen bond and spectroscopic properties. We give computational support to the suggestion that induction effects are less effective to tune the intramolecular hydrogen bond properties of the discussed ortho-hydroxy Schiff bases than the steric or the environmental effects.  相似文献   
110.
DFT (B3LYP/6-311++G**, B3PW91/6-311++G**) Gibbs free energy and single point CCSD(T)/6-311++G**//DFT total energy calculations were performed to investigate stability and tautomerism of C5-substituted 1,2,4-triazoles. Three different tautomers are possible for the substituted 1,2,4-triazoles: N1–H, N2–H, and N4–H. Unlike for the 1,2,3-triazoles, where the most stable is the N2–H tautomer regardless of substituent applied, for the 1,2,4-triazoles, the electron donating substituents (–OH, –F, –CN, –NH2, and –Cl) and the C5-cation stablize the N2–H tautomer, whereas the electron withdrawing substituents (–CONH2, –COOH, –CHO, –BH2, and –CFO) and the C5-anion stablize the N1–H tautomer. Except for the C5-anion and C5-cation, the N4–H form is the least stable tautomer. The relative stability of the C5-substituted 1,2,4-triazole tautomers is strongly influenced by attractive and/or repulsive intramolecular interactions between substituent and electron donor or electron acceptor centres of the triazole ring.  相似文献   
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