On two methods for accelerating convergence of series

Summary The Euler-Knopp transformation and a recently considered transformation, effective for entire function of order 1, are applied to series involving completely monotonic coefficients. Some properties of the resulting series are analyzed; these include uniform convergence with respect to the index, a priori and a posteriori estimates of the remainder. For the latter transformation a compact recursive algorithm is established which enables one to make effective use of the transformation. To illustrate the effectiveness of the transformations three applications, with examples, are included.     

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.

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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).

     

Über einen Homomorphiesatz von G.Köthe

The main object of this paper is to generalize a homomorphism theorem of Köthe [5] for a wide class of not necessarily locally convex topological vector spaces. A sequence =(B_n) of balanced sets B_n in a vector space E(), such that the union of the B_n's equals E and such that B_n+B_nB_n+1 for all nN, is called an absorbent sequence. E() is called -locally topological, if it possesses an absorbent sequence =(B_n) of bounded sets and if a linear mapping A from E() into any other vector space is continuous if all restrictions are continuous at 0. It is shown, that a continuous linear mapping A from a vector space E() with an absorbant sequence of compact sets into a boundedly summing -locally topological space F() is a homomorphism if A(E) is closed in F().     

Penetration and interactions of the antimicrobial peptide, microcin J25, into uncharged phospholipid monolayers

Microcin J25 forms stable monolayers at the air-water interface showing a collapse at a surface pressure of 5 mN/m, 220 mV of surface potential, and 6 fV per squared centimeter of surface potential per unit of molecular surface density. The adsorption of microcin J25 from the subphase at clean interfaces leads to a rise of 10 mN/m in surface pressure and a surface potential of 220 mV. From these data microcin appears to be a poor surfactant per se. Nevertheless, the interaction with the lipid monolayer further increase the stability of the peptide at the interface depending on the mode in which the monolayer is formed. Spreading with egg PC leads to nonideal mixing up to 7 mN/m, with hyperpolarization and expansion of components at the interface, with a small excess free energy of mixing caused by favorable contributions to entropy due to molecular area expansion compensating for the unfavorable enthalpy changes arising from repulsive dipolar interactions. Above 7 mN/m microcin is squeezed out, leaving a film of pure phospholipid. Nevertheless, the presence of lipid at 10 and 20 mN/m stabilize further microcin at the interface and adsorption from the subphase proceeds up to 30 mN/m, equivalent to surface pressure in bilayers.     

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 preperation and coordination properties of 1,4-diaza-3-methylbutadiene-2-ylpalladium(II) complexes with different substituents on the imino nitrogen atoms

The complexes trans-[PdCl{$\text{C(=NR)C}$(ME)=NR'} (PPh₃)₂] (R=C₆H₁₁,p-C₆H₄OMe; R$\text{.}\text{?}$=p-C₆H₄OMe, Me) containing a σ-bonded 1,4-diaza-3-menthyl-butadiene-2-yl group with different substituents on the nitrogen atoms have been prepared by two routes. The first involves initial methylation of the mixed isonitrile complex [PdCl₂(CNR)(CNR')]by HgMe₂, followed by reaction with PPh₃ ($\text{Pd}\text{PPh}{}_3$molar ratio $\text{1}\text{2}$). The second method involves condensation of primary aliphatic amines with the carbonyl group of the 1-azabut-1-en-3-one-2-yl moiety of the complex trans-[PdCl{$\text{C(=NR)C}$(Me) = 0} (PPh₃)₂]. The 1,4-diaza-3-methylbutadiene-2-yl derivatives act through their imino nitrogen atoms as chelating ligands towards anhydrous metal chlorides MCl₂ (M = Co, Ni, Cu, Zn). Magnetic moment measurements and the far-infrared and electronic spectra of these adducts indicate an essentially pseudo-tetrahedral configuration at M in the solid and in solution. With the ZnCl₂ adducts, the ¹H NMR pattern for the phenyl protons of the p-methoxyphenyl N-substituents dependss upon the position of the substituent i the 1,4-diazabutadiene chain.     

The crystallinity of polyaryl ether ether ketone

Measurement of the degree of crystallinity of the polymer matrix in a composite is complicated by the presence of the reinforcing additive. This is particularly the case in APC-2 in which as much as 70% can be carbon fibre. A First Law procedure, developed for determining the degree of crystallinity of PEEK, which involves direct measurement of the enthalpy changes associated with melting, crystallization and heat capacity changes, has found to be an effective method for the determination of the crystallinity of the PEEK matrix. The procedure has been applied to carbon fibre and glass fibre PEEK composites.     

Synthesis and characterization of maleimide polymers with pendant pyrazole groups. IV. Copolymerization of pyrazole-modified maleimides with vinyl ethers

The synthesis of maleimides that have pyrazolic or bipyrazolic pendant groups is described. Their homopolymerization and their copolymerization with 2-chloroethyl vinyl ether (CEVE) is reported. The homopolymerizations of such maleimides were performed under various conditions and led to low molecular-weight polymers. However, alternating copolymers were obtained from CEVE as comonomers whatever the monomers feed compositions. A similar behavior was also observed for maleimides that do not exhibit any spacer, whereas for bulky vinyl ethers, random copolymers were produced. A comparison of the thermal behavior between these copolymers (glass transition temperatures, T_g, and decomposition temperatures) and other copolymers having different spacers between the nitrogenated cycles and the chain are related. Thus, an important decrease of T_g, was observed when C₃H₆CO₂CH₂ groups were used as the spacer instead of methylene groups. Moreover, the thermal weakness of these copolymers may come from the substituents of the vinyl ether and is discussed. © 1994 John Wiley & Sons, Inc.     

Microphase separation of cationic poly(N-isopropylacrylamide) copolymers in water: Effect of the migration of charges

The structures of aqueous copolymer solutions have been examined through small angle neutron scattering. The copolymers contained mostly N-isopropylacrylamide (NIPAM) monomers. Poly (NIPAM) solutions have a lower critical solution temperature (LCST), above which the macromolecules separate from water. A small fraction of ionizable N,N-[(dimethylamino) propyl] methacrylamide (MADAP) monomers was introduced into the macromolecules. This had dramatic consequences on the solution behavior at temperatures above the LCST of PNIPAM, where phase separation would have been expected for the homopolymer. When all MADAP monomers were ionized, it was found that the solutions resisted the phase separation. At short spatial scales, the chains were collapsed but at large scales they formed branched aggregates that did not separate out of water. When only half of the MADAP monomers are ionized, the electrical charges were able to redistribute themselves along the chains. In this case, the rise in temperature caused a microphase separation where the electrical charges were relocated on a fraction of the chains that remained in solution.The other chains (or section of chains) formed large nodules of a polymer rich phase.     

Sequence-specific binding of DNA to liposomes containing di-alkyl peptide nucleic acid (PNA) amphiphiles

We present a method to covalently attach peptide nucleic acid (PNA) to liposomes by conjugation of PNA peptide to charged amino acids and synthetic di-alkyl lipids ("PNA amphiphile," PNAA) followed by co-extrusion with disteroylphosphatidylcholine (DSPC) and cholesterol. Attachment of four Glu residues and two ethylene oxide spacers to the PNAA was required to confer proper hydration for extrusion and presentation for DNA hybridization. The extent of DNA oligomer binding to 10-mer PNAA liposomes was assessed using capillary zone electrophoresis. Nearly all PNAs on the liposome surface are complexed with a stoichiometric amount of complementary DNA 10-mers after 3-h incubation in pH 8.0 Tris buffer. No binding to PNAA liposomes was observed using DNA 10-mers with a single mismatch. Longer DNA showed a greatly attenuated binding efficiency, likely because of electrostatic repulsion between the PNAA liposome double layer and the DNA backbone. Langmuir isotherms of PNAA:DSPC:chol monolayers indicate miscibility of these components at the compositions used for liposome preparation. PNAA liposomes preserve the high sequence-selectivity of PNAs and emerge as a useful sequence tag for highly sensitive bioanalytical devices.