On the equation of similar profiles

Summary Considerf+ ff+ (1–f²)+ f=0 together with the boundary conditionsf(0)=f(0)=0,f ()=1. If=–1,>0, arbitrary there is at least one solution which satisfies 0<f<1 on (0, ). By the additional conditionf>0 on (0, ) or, alternately 0<1, the uniqueness of the solution is demonstrated.If=1,<0, arbitrary the existence of solutions for which –1<f<0 in some initial interval (0,t) and satisfying generallyf>1 is established. In both problems, bounds forf (0) and qualitative behavior of the solutions are shown.

---

Sommario Si consideri il problema definito dall'equazionef+ f f+ (1–f²)+ f=0 e dalle condizioni al contornof(0)=f (0)=0,f()=1. Assumendo=–1,>0, arbitrario si dimostra che esiste almeno una soluzione che soddisfa 0<f<1 nell'intervallo (0, ). Se in aggiunta si ipotizzaf>0 in (0, ), oppure 0<=1, l'unicità délia soluzione è assicurata.Successivamente si considéra il problema di valori al contorno con=1,<0, arbitrario. In questo caso esiste un'intera classe di soluzioni che soddisfano –1<f<0 in un intorno dell'origine e tali chef>1, in generale.Di detti problemi viene studiato il comportamento délle soluzioni e vengono determinate dalle maggiorazioni e minorazioni del valoref(0).

     

Mechanism of silicon film deposition in the RF plasma reduction of silicon tetrachloride

Plasma-chemical reduction of SiCl₄ in mixtures with H₂ and Ar has been studied by optical emission spectroscopy (OES) and laser interferometry techniques. It has been found that the Ar:H₂ ratio strongly affects the plasma composition as well as the deposition (r _D) and etch (r _E) rates of Si: H, Cl films and that the electron impact dissociation is the most important channel for the production of SiCl_x species, which are the precursors of the film growth. Chemisorption of SiCl_x and the reactive surface reaction SiCl_x+H–SiCl_(x–1)0+HCl are important steps in the deposition process. The suggested deposition model givesr _D [SiCl_x][H], in agreement with the experimental data. Etching of Si: H, Cl films occurs at high Ar: H₂ ratio when Cl atoms in the gas phase become appreciable and increases with increasing Cl concentration. The etch rate is controlled by the Cl atom chemisorption step.     

The convergence of the Rayleigh-Ritz Method in quantum chemistry

Two sufficient criteria for the convergence of the Rayleigh-Ritz Method (RRM) with respect to the eigenvalues (E-convergence) of non-relativistic electronic Hamiltonians of molecules are discussed and compared. Moreover, a necessary and sufficient criterion is given. By example (Sect. 9) it is shown that the L ²-completeness of the basis is not sufficient to guarantee E-convergence. The convergence of the wave functions in different norms (-convergence) is also investigated. In particular, sufficient conditions for the one-particle basis functions (orbitals) are given, such that a CI calculation in this basis is both E- and -convergent.     

Photochemische Reaktionen. 121. Mitteilung. Zur Photochemie von ε,ζ-Methano-α,γ-dienonen und 7,8-Methano-1,3,5-trienen

Photochemistry of ε,ζ-Methano-α,γ-dienones and 7,8-Methano-1,3,5-trienes Irradiation of the δ-cyclopropyl-dienone (E)- 6 (λ ≥ 347 nm) gives (Z)- 6, 10 (1,5-sigmatropic H-shift), (E/Z)- 9 (electrocyclic process involving C(ε), C(ζ)-cleavage) and 11 (ring opening). The corresponding 6-cyclopropyl-triene (E)- 7 gives on singlet excitation (δ > 280 nm) 14 (1,5-sigmatropic H-shift) and, to a smaller extent, the bicyclo [3.2.0] heptenyl-dienes (E/Z)- 13 . However, on triplet excitation (λ ≥ 347 nm, benzophenone) (E)- 7 gives (E/Z)- 13 as the main products. On both ¹π,π*- and ³π,π*-excitation, (Z)- 7 and 15 are formed in small amounts.     

Kalorimetrische untersuchung von binären legierungen des platins und palladiums mit gallium,indium und thallium

Employing tin and lead solution calorimetry, the formation enthalpies of those phases having platinum and palladium as major component have been determined in the PdGa, PdIn, PdTl, PtGa und PtIn systems. These enthalpies are highly exothermic and suggest strong atomic interaction betweens palladium and platinum on the one hand and the third subgroup elements on the other. The experimental values have been compared with those obtained from the Miedema model. The thermodynamic data are discussed and related to the crystal structures found with these alloys.     

Chemical ionization desorption mass spectrometry of some quaternary ammonium salts

The ammonia chemical ionization desorption spectra of N,N-dimethyl quaternary ammonium iodides in addition to high protonated molecular ion [M + H]⁺ intensity, show signals for an ion radical composed of N-methyl abstracted salt cation and ammonia [C + NH₃? CH₃]^+˙. These ions corresponding to the cation +2 show increased importance in the chemical ionization mode, using the same reagent gas. The technique of chemical ionization desorption appears suitable for the analysis of salts, and thus for the determination of the molecular weight of both anion and cation.     

Conformationally Controlled Odor Perception in ‘Steroid-type’ Scent Molecules

A series of compounds possessing a ‘Steroid-type’ scent and related to 4-(4′-t-butylcyclohexyl)-4-methyl-2-pentanones ( 1 and 2 ) has been synthesized. The odor of these compounds has been found to be dependent on their conformation; only when the molecule can assume a steroid-like shape there is an interaction with the odor chemoreceptor.     

Glycosylidene Carbenes. Part 15. Synthesis of disaccharides from allopyranose-derived vicinal 1,2-diols. Evidence for the protonation by a H-bonded hydroxy group in the σ-plane of the intermediate carbene,followed by attack on the oxycarbenium ion in the π-plane

The α-D -allo-diol 9 possesses an intramolecular H-bond (HO? C(3) to O? C(1)) in solution and in the solid state (Fig. 2). In solution, it exists as a mixture of the tautomers 9a and 9b (Fig. 3), which possess a bifurcated H-bond, connecting HO? C(2) with both O? C(1) and O? C(3). In addition, 9a possesses the same intramolecular H-bond as in the solid state, while 9b is characterized by an intramolecular H-bond between HO? C(3) and O? C(4). In solution, the β-D -anomer 12 is also a mixture of tautomers, 12a and presumably a dimer. The H-bonding in 9 and 12 is evidenced by their IR and ¹H-NMR spectra and by a comparison with those of 3–8, 10 , and 11 . The expected regioselectivity of glycosidation of 9 and 12 by the diazirine 1 or the trichloroacetimidate 2 is discussed on the basis of the relative degree of acidity/nucleophilicity of individual OH groups, as governed by H-bonding. Additional factors determining the regioselectivity of glycosidation by 1 are the direction of carbene approach/proton transfer by H-bonded OH groups, and the stereoelectronic control of both the proton transfer to the alkoxy-alkyl carbene (in the σ-plane) and the combination of the thereby formed ions (π-plane of the oxycarbenium ion). Glycosidation of 9 by the diazirine 1 or the trichloroacetimidate 2 proceeded in good yields (75–94%) and with high regioselectivity. Glycosidation of 9 and 12 by 1 or 2 gave mixtures of the disaccharides 14–17 and 18–21 , respectively (Scheme 2). As expected, glycosidation of 12 by 1 or by 2 gave a nearly 1:1 mixture of regioisomers and a slight preference for the β-D -anomers (Table 4). Glycosidation of the α-D -anomer 9 gave mostly the 1,3-linked disaccharides 16 and 17 (α-D β-D ) along with the 1,2-linked disaccharides 14 and 15 (α-D < β-D , 1,2-/1,3-linked glycosides ca. 1:4), except in THF and at low temperature, where the β-D -configurated 1,2-linked disaccharide 15 is predominantly formed. Similarly, glycosidation of 9 with 2 yielded mainly the 1,3-linked disaccharides (1,2-/1,3-linked products ca. 1:3 and α-D /β-D ca. 1:4). Yields and selectivity depend upon the solvent and the temperature. The regioselectivity and the unexpected stereoselectivity of the glycosidation of 9 by 1 evidences the combined effect of the above mentioned factors, which also explain the lack of regio-complementarity in the glycosidation of 9 by 1 and by 2 (Scheme 3). THF solvates the intermediate oxycarbenium ion, as evidenced by the strong influence of this solvent on the regio- and stereoselectivity, particularly at low temperatures, where kinetic control leads to a stereoelectronically preferred axial attack of THF on the oxycarbenium ion.     

Xanthones and other constituents of Allanblackia monticola (Guttiferae)

A xanthone derivative, 3,6,7-trihydroxy-1-methoxyxanthone has been isolated from the stem bark of Allanblackia monticola together with other known compounds, 2,6-dihydroxy-1-methoxyxanthone, allanxanthone A, epicathechin and oleanolic acid acetate. The structure of the new compound was elucidated by spectroscopic methods.     

Confirmation of the Structures of Lutein and Zeaxanthin

A series of new esters of lutein ( 1a ) have been prepared with the aim of confirming the structure of lutein via an X‐ray crystal‐structure analysis. Although well crystallized, only one of the derivatives, the (?)‐(1R)‐menthyl carbonate ( 1i ) proved to be useful for a complete structure analysis. The same derivative of zeaxanthin ( 2a ) also allowed its crystal structure to be determined. Both analyses represent the first successful X‐ray crystal structure analyses of the most important xanthophylls. At the same time, they confirm both the constitution and absolute configuration of 1a and 2a that had been deduced earlier by classical methods.