关于Hirota-Satsuma系统初值问题的局部和整体适定性

本文利用ＫＤＶ方程所对应的线性方程解所具有的光滑效应及压缩映像原理,得到了Ｈｉｒｏｔａ－Ｓａｔｓｕｍａ系统初值问题的局部和整体适定性结果．     

Controlled Synthesis,Characterization, and Flow Properties of Ethylene–Diene Copolymers

The flow response of branched entangled resins is dominated by the branching topology of the constituent molecules, a property that is not directly accessible using experimental analytical tools for industrially relevant complex resins. In this paper, the controlled terpolymerization of ethylene, 1,9‐decadiene, and either hexene or octene in a continuous stirred tank reactor with a metallocene catalyst, is reported. The synthesized samples are characterized extensively with various analytical tools and their rheological properties are measured with small amplitude oscillatory shear and start‐up uniaxial extension experiments. A model is developed for the polymerization process with the mass balance during synthesis providing strong constraints on the rate constants. In silico ensembles of molecules, generated via Monte Carlo sampling, are used to reproduce the experimental results. The computer model allows us to infer the detailed branching structure of the molecules and to predict the optimum range of reactor conditions for this synthesis.     

Overlapping B3Π0u ← X1Σ g/+ and 1Π1u ← X1Σ g/+ non-radiative characteristic of Br2 vapour in the wavelength region 505–541 nm

The vibronic vapour phase photoacoustic spectrum of Br₂ in the wavelength region 505–541 nm (19796–18480 cm⁻¹) has been recorded using microphone as well as pump-probe method. Discrete vibronic bands superimposed on a monotonically increasing continuum background towards the dissociation limit results from the overlapping B ³Π _0u ^/+ ← X ¹Σ _g ^/+ and ¹Π_1u ← X ¹Σ _g ^/+ electronic transitions. Vibronic bands originating from υ″=0 have been used to estimate the relative rate of non-radiative relaxation as a function of the excited state B ³Π_0u vibrational quantum number υ′. A comparison with the optical absorption spectroscopy of Br₂ leads to the identification of three broad spectral regions between 505 and 541 nm (19796 and 18480 cm⁻¹) on the basis of different non-radiative relaxation processes.     

Peak effect in surface resistance at microwave frequencies in Dy-123 thin films

A pronounced peak in the microwave (at frequency 9.55 GHz) surface resistance, R _s vs. T plot (where T is the temperature) has been observed in epitaxial DyBa₂Cu₃O_7−y superconducting thin films in magnetic fields (parallel to c-axis) in the range 2 to 8 kOe, and temperatures close to the superconducting transition temperature T _c(H). Our data suggest that the nature of peaks observed in the two films is different, thereby indicating different defect structures in the films.     

Ac conduction in Al/Sb2Pb1Se7/Al devices

Metal-glass-metal (MGM) thin film devices are prepared using vacuum deposition of Sb₂Pb₁Se₇ compound. The variation of ac conductance as a function of thickness of films, temperature and frequency is studied. The observed characteristics are explained on the basis of Co-related Barrier Hopping (CBH) of bipolaron. It is shown that the theoretical curve generated using the first order approximation gives excellent fitting with the experimental curve.     

Synthesis anti‐fungal and anti‐bacterial screening of 3‐phenyl‐1,4,5‐trihydro‐pyrazol and 2, 4‐dihydro[ 1,2,4]‐triazol‐3‐one derivatives of 4‐hydroxy‐2‐oxo‐2H‐1‐benzopyran

4‐Hydroxy‐2‐oxo‐2H‐1‐benzopyran‐3‐carboxaldehydes 2a‐d are prepared from 4‐hydroxy‐2‐oxo‐2H‐1‐benzopyrans 1a‐d via the Vielsmeyer Haack reaction. The 4‐hydroxy‐2‐oxo‐3‐(3′oxo‐3′‐phenylprop‐1′‐enyl)‐2H‐1‐benzopyrans 3a‐d are obtained from 2a‐d via the Claisen reaction. Refluxing compounds 3a‐d with hydrazine hydrate gave the 3‐phenyl‐5‐(4‐hydroxy‐2‐oxo‐2H‐1‐benzopyran‐3‐yl)‐1,4,5‐trihydropyra‐zols 4a‐d . Stirring compounds 2a‐d with semicarbazide hydrochloride in acidic medium gave the 4‐hydroxy‐2‐oxo‐2H‐1‐benzopyran‐3‐aldehyde‐semicarbazone 5a‐d , which on cyclisation with ferric chloride hexahydrate gave the 5‐(4‐hydroxy‐2‐oxo‐2H‐1‐benzopyran‐3‐yl)‐2,4‐dihydro[1,2,4]triazol‐3‐ones 6a‐d . All these compounds show significant antibacterial activities.     

Current controlled negative resistance phenomenon in SbPbSe system

Thin film Al/Sb₂Pb₁Se₇/Al metal-glass-metal sandwiched structures prepared using thermal evaporation technique have been studied. The I–V measurements showed that the devices switched from high resistance OFF state to a low resistance ON state when a particular voltage appeared across it. The OFF state I–V characteristics showed non-ohmic behaviour while in the ON state the devices displayed purely linear characteristics. The switching voltage (V _th) was found to depend on film thickness and temperature of the device. A linear relation between V_th and temperature was observed.     

Copper(II) ion-selective microelectrochemical transistor

A device has been developed for the measurement of copper(II) ions (Cu⁺⁺) in aqueous medium. The device reported here is an electrochemical transistor that consists of two platinum electrodes separated by 100-μm spacing and bridged with an anodically grown polycarbazole film. The undoped polycarbazole film is observed to be highly selective for the Cu(II) ions. In a completed device, the conductivity of the polycarbazole film changes on addition of Cu (II)ions. This change in conductivity is attributed to the conformational changes in the polymer phase on occupation of the Cu(II) ions, without affecting electron/proton transfer. The device turns on by adding 2.5×10⁻⁶ M Cu(II) ions and reaches a saturation region above a concentration of 10⁻⁴ M Cu(II) ions. In this concentration range, the plot of I _D vs log[Cu(II)] is linear. The selectivity of the device for other metal ions such as Cu(I), Co(II), Fe(II), Fe(III), Zn(II), and Pb(II) is also studied.