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61.
V. A. KHATSKEVICH V.A. SENDEROV 《数学学报(英文版)》2006,22(6):1687-1694
The operator sets, which are the subject of this paper, have been studied in many papers where, under different restrictions on the generating operators, convexity, compactness in the weak operator topology, and nonemptiness were proved for sets of different classes under study. Then the results obtained were used in these papers to solve several applied problems. Namely, they played the key role in establishing the dichotomy of nonautonomous dynamical systems, with either continuous or discrete time. In the present paper, we generalize and sharpen the already known criteria and obtain several new criteria for convexity, compactness, and nonemptiness of several special operator sets. Then, using the assertions obtained, we construct examples of sets of the form under study which are nonconvex, noncompact in the weak operator topology, as well as empty, and are generated by "smooth" operators of a special class. The existence problem for such sets remained open until the authors of this paper announced some of its results. 相似文献
62.
The thermal conduction and Navier-Stokes equations are usedto obtain the stress field generated by a chopped electron beam incident ona disk sample.The piezoelectric equation is then used to obtain the out-put signal of the transducer coupled to the sample.The results lead to aconsideration of the signal generation mechanism and spatial resolution inscanning electron acoustic microscopy(SEAM).It is shown that atime-variant heat source generated both a thermal wave and an acousticwave simultaneously,and thermal-to-acoustic wave mode conversion oc-cured on the boundary surfaces depends on the amplitudes and the gra-dients at boundary surfaces of both heat source and thermal waves.It isargued that the spatial resolution of a imaging system operated in thenear field,such as SEAM and thermal wave microscope,is dependent onthe distance between the heat source and scatterer and,at best,the lateralresolution in SEAM is of the order of the diameter of the focal spot ofthe electron beam. 相似文献
63.
本文讨论了高效液相色谱死体积的定义和如何以吉布斯热力学理论为基础对其测定。推荐的热力学理论方法能应用于任何一种液相色谱方法,如正相、反相、离子交换、甚至体积排斥色谱。提出了一种能在整个浓度范围内准确计算流动相组分干扰峰死体积的方法。对某些化合物容量因子出现负值也作了解释。 相似文献
64.
P.Sablonniere 《分析论及其应用》1992,(3)
Suppose that we want to approximate fC[0,1]by polynomials in P_n,using only itsvalues on X_n={i/n,0≤i≤n}.This can be done by the Lagrange interpolant L_n f or theclassical Bernstein polynomial B_n f.But,when n tends to infinity,L_n f does not converge to fin general and the convergence of B_n f to fis very slow.We define a family of operators B~(k)_n,n≥k,which are intermediate ones between B(0)_n=B~(1)_n=B_n and B~(n)_n=L_n,and we studysome of their properties.In particular,we prove a Voronovskaja-type theorem which assertsthat B~(k)_n f-f=0(n~(-[(k+2)/2))for f sufficiently regular.Moreover,B(k)_n f uses only values of B_n f and its derivaties and can be computed by DeCasteljau or subdivision algorithms. 相似文献
65.
Studies on the properties of flow-induced oscillation and sound radiation in streamlined protuberant special cavities 总被引:1,自引:0,他引:1
I.IntroductionAsanuidpassingthroughthecavityatcertainflowrate,themediuminthemouthandthccavityisoscillatingandsoundisradiated.Noton1ystochasticturbu1encenoiscispossi-blyproducedbutsinglefrequencysoundofspecia1lydesignatedpitchisalsoproduced.Andthusthespcctrumofthcradiatedsoundisshownascontinuousspectrumandcharacteristiclinespcctrum.Inthiscascwcmaycallitflow-inducedosci1lation.Flow-inducedoscillationandsoundradiationcanbeproducedasafluid(waterorgas)passingthroughthecavitybysinkingcavityunderint… 相似文献
66.
A sufficient condition for the order of approximation of a continuous 2π periodic function with a givenmajorant for the modulus of continuity by the [F, d_n] means of its Fourier serier to be of Jackson order isobtained. This sufficient condition is shown to be not enough for the order of approximation by partial sums oftheir Fourier series to be of Jackson order. The error estimate is shown to be the best possible. 相似文献
67.
68.
The reference [4] proved the consistency of S1 and S2 among Lewis' five strict implication systems in the modal logic by using the method of the Boolean-valued model. But, in this method, the consistency of S3, S4 and S5 in Lewis' five strict implication systems is not decided. This paper makes use of the properties: (1) the equivalence of the modal systems S3 and P3, S4 and P4; (2) the modal systems P3 and P4 all contained the modal axiom T(□p → p); (3) the modal axiom T is correspondence to the reflexive property in VB. Hence, the paper proves: (a) ‖As31‖ = 1; (b) ‖AS41‖ = 1; (c) ‖AS5l‖ = 1 in the model (where B is a complete Boolean algebra, R is reflexive property in VB). Therefore, the paper finally proves that the Boolean-valued model VB of the ZFC axiom system in set theory is also a Boolean-valued model of Lewis' the strict implication system S3, S4 and S5. 相似文献
69.
The present paper establishes sufficient conditions for the uniformly bounded of any solution of (1.1) and which tend to zero as t → ∞. 相似文献
70.
M.I.Gil' 《Annals of Differential Equations》2004,20(2):145-154
The nonlocal initial problem for nonlinear nonautonomous evolution equati-ons in a Banach space is considered. It is assumed that the nonlinearities havethe local Lipschitz properties. The existence and uniqueness of mild solutionsare proved. Applications to integro-differential equations are discussed.The main tool in the paper is the normalizing mapping (the generalizednorm). 相似文献