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21.
We establish the existence and stability of multidimensional transonic shocks for the Euler equations for steady potential compressible fluids. The Euler equations, consisting of the conservation law of mass and the Bernoulli law for the velocity, can be written as a second-order, nonlinear equation of mixed elliptic-hyperbolic type for the velocity potential. The transonic shock problem can be formulated into the following free boundary problem: The free boundary is the location of the transonic shock which divides the two regions of smooth flow, and the equation is hyperbolic in the upstream region where the smooth perturbed flow is supersonic. We develop a nonlinear approach to deal with such a free boundary problem in order to solve the transonic shock problem. Our results indicate that there exists a unique solution of the free boundary problem such that the equation is always elliptic in the downstream region and the free boundary is smooth, provided that the hyperbolic phase is close to a uniform flow. We prove that the free boundary is stable under the steady perturbation of the hyperbolic phase. We also establish the existence and stability of multidimensional transonic shocks near spherical or circular transonic shocks.
22.
We investigate the dynamics of the Λ system driven by two resonant laser fields in presence of dissipation for coupling strengths where the rotating‐wave approximation starts to break down. This regime is characterised by Rabi frequencies being approximately equal or smaller than the field frequencies. A systematic procedure to obtain an expansion for the solution of the Bloch evolution equations of the system is presented. The lowest contribution results to be the well‐known rotating‐wave approximation. The method is based on a semi‐classical treatment of the problem, and its predictions are interpreted fully quantum mechanically. The theory is illustrated by a detailed study of the disappearance of coherent population trapping as the intensities of the fields increase. 相似文献
23.
The Iyengar Type Inequalities with Exact Estimations and the Chebyshev Central Algorithms of Integrals 总被引:3,自引:0,他引:3
Xing Hua WANG Shi Jun YANG 《数学学报(英文版)》2005,21(6):1361-1376
In this paper, both low order and high order extensions of the Iyengar type inequality are obtained. Such extensions are the best possible in the same sense as that of the Iyengar inequality. hzrthermore, the Chebyshev central algorithms of integrals for some function classes and some related problems are also considered and investigated. 相似文献
24.
25.
The concept of super hamiltonian semigroup is introduced. As a result, the structure theorems obtained by A. Cherubini and A. Varisco on quasi commutative semi-groups and quasi hamiltonian semigroups respectively are extended to super hamiltonian semigroups. 相似文献
26.
Jacek Doskocz Jadwiga Sołoducho Joanna Cabaj Mieczysław Łapkowski Sylwia Golba Krystyna Palewska 《Electroanalysis》2007,19(13):1394-1401
A convenient and higher yielding synthetic route to N‐alkyl‐bis(thiophene)phenothiazine derivatives is reported and their aggregation, electrochemical properties and polymerization are characterized. The key step in the synthesis of this group of compounds has been the Stille type coupling reaction between the N‐alkyldibromophenothiazine and tin derivatives of thiophene as the best way for preparation of conjugated N‐alkylphenothiazine derivatives. For this group of compounds we also present an electrochemical polymerization effect and widely adopted approach to prepare structurally ordered thin, electroconducting films by Langmuir–Blodgett technique. 相似文献
27.
Anuj Mittal Swaminathan Sivaram 《Journal of polymer science. Part A, Polymer chemistry》2005,43(21):4996-5008
A tridentate ligand, BPIEP: 2,6‐bis[1‐(2,6‐diisopropyl phenylimino) ethyl] pyridine, having central pyridine unit and two peripheral imine coordination sites was effectively employed in controlled/“living” radical polymerization of MMA at 90°C in toluene as solvent, CuIBr as catalyst, and ethyl‐2‐bromoisobutyrate (EBiB) as initiator resulting in well‐defined polymers with polydispersities Mw/Mn ≤ 1.23. The rate of polymerization follows first‐order kinetics, kapp = 3.4 × 10?5 s?1, indicating the presence of low radical concentration ([P*] ≤ 10?8) throughout the reaction. The polymerization rate attains a maximum at a ligand‐to‐metal ratio of 2:1 in toluene at 90°C. The solvent concentration (v/v, with respect to monomer) has a significant effect on the polymerization kinetics. The polymerization is faster in polar solvents like, diphenylether, and anisole, as compared to toluene. Increasing the monomer concentration in toluene resulted in a better control of polymerization. The molecular weights (Mn,SEC) increased linearly with conversion and were found to be higher than predicted molecular (Mn,Cal). However, the polydispersity remained narrow, i.e., ≤1.23. The initiator efficiency at lower monomer concentration approaches a value of 0.7 in 110 min as compared to 0.5 in 330 min at higher monomer concentration. The aging of the copper salt complexed with BPIEP had a beneficial effect and resulted in polymers with narrow polydispersitities and higher conversion. PMMA obtained at room temperature in toluene (33%, v/v) gave PDI of 1.22 (Mn = 8500) in 48 h whereas, at 50°C the PDI is 1.18 (Mn = 10,300), which is achieved in 23 h. The plot of lnkapp versus 1/T gave an apparent activation energy of polymerization as (ΔE≠app) 58.29 KJ/mol and enthalpy of equilibrium (ΔH0eq) to 28.8 KJ/mol. Reverse ATRP of MMA was successfully performed using AIBN in bulk as well as solution. The controlled nature of the polymerization reaction was established through kinetic studies and chain extension experiments. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 4996–5008, 2005 相似文献
28.
Vinod Kumar Pragya Das R.P. Singh S. Muralithar R.K. Bhowmik 《The European Physical Journal A - Hadrons and Nuclei》2003,17(2):153-157
The fusion evaporation reaction 122Sn(14N, 4n)132La was used to populate the high-spin states of 132La at the beam energy of 60 MeV. A new band consisting of mostly E2 transitions has been discovered. This band has the interesting links to the ground state 2- and the isomeric state 6-. A new transition of energy 351 keV connecting the low-spin states of the positive-parity band based on the πh
11/2 ⊗ νh
11/2 particle configuration, has been found. This has played a very important role in resolving the existing ambiguities and inconsistencies
in the spin assignment of the band head.
Received: 12 August 2002 / Accepted: 18 March 2003 / Published online: 7 May 2003 相似文献
29.
恩格尔系数衡量城镇居民生活水平适用性 总被引:2,自引:0,他引:2
根据我固1980年和2000年恩格尔系数所反映的各省(市)居民生活水平资料,发现两个不同时期其真实性有很大差异,分析了造成这种差别的原因:(1)职工非现金福利收入的增加;(2)少数职工的非法收入的大量增加;(3)居民饮食结构的改变;(4)物价上涨的影响;(5)恩格尔系数本身存在技术问题;(6)抽样调查本身存在问题,提出用一种“新系数”来衡量城镇居民生活水平,其优点是:(1)不受各地区实际支出,即人为控制调节的影响;(2)不需用其他指标作解释,直观性强;(3)因可以扣除物价因素,它不受物价波动的影响;(4)调查户填报和计算简易方便。可扩大样本调查量,提高反映住户总量可靠性。 相似文献
30.
M. Faucher D. Garcia E. Antic-Fidancev M. Lemaitre-Blaise 《Journal of Physics and Chemistry of Solids》1989,50(12)
Some structural and spectroscopic features of rare earth orthoaluminates are examined.The trigonal→ orthorhombic transition is studied in a series of NdxSm1−xAlO3 compounds. The evolution of the crystal structure is followed by X-ray analysis and optical absorption. The free ion and crystal field parameters of Nd3+ (4f3 configuration) are determined in LuAlO3:Nd3+.The anomaly of the calculated splitting of the
levels is slight, but well characterized in NdAlO3. The spin correlated crystal field and orbitally correlated crystal field models are tested as well as an empirical correction which was proposed earlier. 相似文献