Characteristic measurement of spark transients due to finger touch

To understand a mechanism of spark transients, using a 12-GHz digital oscilloscope, we measured discharge currents due to a finger touch through a hand-held metal bar or a fingertip with an aluminum foil attachment from a charged human body with a charge voltage of 600 V. As a result, we found that the hand-held metal bar and aluminum foil attachment produce a one-shot discharge current with steeply rising time shorter than a 100 ps, while the fingertip without any aluminum foil attachments produces multiple-shot discharge currents with gently rising time larger than a 100 ps and significantly low amplitudes.     

A study of the physico-chemical properties of 1,3,5-trihydroxy-1,3,5-triazin-2,4,6[1H,3H,5H]-trione

Acetyl (Ia) and pivaloyl (Ib) triesters of the 1N,3N,5N-trihydroxy-1,3,5-triazin-2,4,6[1H,3H,5H]-trione (I) were synthesised. The spectrophotometric and potentiometric investigation of I revealed a weak acidic properties of triprotonic acid (pK_a1=5.23, pK_a2=6.32, and pK_a3=7.93). The MS and TGA analyses of I indicated on hydroxyisocyanate as possible degradation product. The chelating ability of I with Fe(III)-ion was preliminary explored. IR measurements of aqueous solutions of I in the presence of Fe(III) ion showed the possible chelating ability of all hydroxamic moieties. The chemical structures and properties of investigated compounds were derived from the results of IR, ¹H and ¹³C NMR, UV and MS spectrometric data, as well as thermogravimetric and potentiometric analysis.     

Nonoscillatory half-linear differential equations and generalized Karamata functions

We introduce a natural generalization of the concept of regularly varying functions in the sense of Karamata, and show that the class of generalized Karamata functions is a well-suited framework for the study of the asymptotic behavior of nonoscillatory solutions of the half-linear differential equation of the type

equation(A)

(p(t)|y^′|^α-1y^′)^′+q(t)|y|^α-1y=0.$(p(t)|y^{\prime }{|}^{\alpha -1}{y}^{\prime }{)}^{\prime }+q(t)|y{|}^{\alpha -1}y=0\text{.}$

Nonoscillation theory for second order half-linear differential equations in the framework of regular variation

Criteria are established for nonoscillation of all solutions of the second order half-linear differential equation A $(\mid y^\prime \mid^{\alpha-1}y^\prime)^\prime + q(t)\mid y \mid^{\alpha -1}y = 0,\ \ \ t \geq 0,$ where α > 0 is a constant and q: [0, ∞) → ? is continuous. The criteria are designed to exhibit the role played by the integral of q(t) in guaranteeing the existence of nonoscillatory solutions of (A) in specific classes of regularly varying functions in the sense of Karamata.     

Decaying entire positive solutions of quasilinear elliptic equations

The quasilinear elliptic equation (^*)u+f(x,u,u)=0 is considered in the whole Euclidean space ^N ,N3. Under suitable structure hypotheses it is shown that (^*) has an entire positive solution which decays to zero at infinity. In particular, conditions are established for the existence of an entire positive solution of (^*) which behaves like a constant multiple of |x| ^2–N as |x|.Supported in part by Grant-in-Aid for Scientific Research (No. 5860004), Ministry of Education (Japan).Research supported by NSERC (Canada) under Grant A-3105.     

Anion Effect on Structure of Silver(I) Complexes with New Unsymmetrical Tripodal Ligand

Reactions of new unsymmetrical pyridyl‐ and imidazoyl‐containing tripodal ligand, 3‐(1H‐imidazol‐1‐yl)‐N,N‐bis(2‐pyridylmethyl)propan‐1‐amine ( L ), with varied silver(I) salts result in formation of three supramolecular architectures [Ag₂L₂](BF₄)₂·H₂O ( 1 ), [Ag₂L₂](ClO₄)₂·H₂O ( 2 ) and [Ag₃L₂](CF₃SO₃)₃ ( 3 ). All the structures were established by single‐crystal X‐ray diffraction analysis. In the solid state, three complexes consist of one‐dimensional infinite chains, in which the conformation and the bridging mode of L for complexes 1 and 2 are the same but 3 different. There are Ag···Ag and π‐π interactions in 3 . The results imply that the shape and size of the anion have great impact on the structure of the complexes. The complexes were also characterized by electrospray mass spectrometry.     

On second order functional differential equations and inequalities with deviating arguments

A necessary and sufficient condition is established in order that (i) the retarded differential equation $$y''(t) = p_0 y(t) + f(y(t - \tau _1 ),...,y(t - \tau _N ))$$ has no bounded nonoscillatory solution and (ii) the advanced differential equation $$y''(t) = p_0 y(t) + f(y(t + \tau _1 ),...,y(t + \tau _N ))$$ has no unbounded nonoscillatory solution, wherep ₀≥0 and τ _j > 0,1 ?i ?N, are constants. Differential inequalities related to (^*) and (^**) are also studied. Finally, an oscillation criterion is given for a class of differential equations containing both retarded and advanced arguments.     

Mathematical and simulation models of traffic flow

The viscous Burgers' equation, appearing in the traffic flow theory, is solved in the frames of the g -calculus. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Reconstructed 3D flame structures in noise-controlled swirl-stabilized combustor

Flame structures of turbulent premixed flames in a noise-controlled, swirl-stabilized combustor are investigated to clarify the mechanism of combustion noise reduction by the secondary fuel injection. Planar laser-induced fluorescence (PLIF) is conducted for several cases with different secondary fuel injection, and 3D flame structure is reconstructed from PLIF results on multiple planes. The secondary fuel injection suppresses the fluctuation of high-temperature gas in the recirculation zone and reduces Reynolds stress and entropy terms in the acoustic sound source. In the flame zone, effects of the injection frequency are discussed by introducing mean progress variable. The flame brush is very wide for the no control case, whereas it becomes thin and is confined to a narrow space for the secondary fuel injection cases. The investigated combustor gives minimum sound level at a relevant fuel injection frequency, which is very low compared with the natural acoustic mode of the combustor. The flame brush becomes very thin, and self-induced oscillations of the flame brush disappear at this relevant frequency. The oscillation of the flame brush represents large-scale fluctuation of the mean heat release rate. The relations between characteristics of flame brush and combustion noise are discussed by introducing instantaneous and dynamical effects of flame front on the entropy term of the sound source. The secondary fuel injection works for the control of the entropy term in the sound source because the thin flame brush represents suppression of the instantaneous and dynamical effects.