共查询到20条相似文献,搜索用时 9 毫秒
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讨论一个微分中值命题条件的弱化,将条件“f′(x)g′(x)〉0”弱化为“f(a)≠f(b)”,利用介值定理和柯西中值定理给出证明,以扩大命题的适用范围,并举出实例予以说明. 相似文献
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正则函数是Clifford分析中的一类重要函数,加权正则函数是正则函数的进一步发展,也是一类重要的函数,因此具有一定的研究意义.在正则函数的研究基础上,并利用加权正则函数自身的性质,讨论了加权正则函数的平均值定理,最大模原理,Weierstrass定理以及一些其它推论. 相似文献
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This work is devoted to a systematic study of the inversion of nondecreasing one variable extended real-valued functions. Its results are preparatory for a new duality theory for quasiconvex problem [6]. However the question arises in a variety of situations and as such deserves a separate treatment. Applications to topology, probability theory, monotone rearrangements, convex analysis are either pointed out or sketched.
Zusammenfassung In dieser Arbeit wird systematisch die Umkehrung monoton nichtfallender Funktionenf: {–, +} studiert. Die Ergebnisse bilden die Grundlage für eine neue Dualitätstheorie quasikonvexer Probleme [6]. Da jedoch die Fragestellung bei einer ganzen Anzahl weiterer Situationen auftritt, verdient sie eine gesonderte Behandlung. Anwendungen in der Topologie, Wahrscheinlichkeitstheorie, monotonen Umordnungen und in der konvexen Analysis werden aufgezeigt und skizziert.相似文献
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微分中值定理的另类证明与推广 总被引:1,自引:0,他引:1
通常教科书中,微分中值定理的证明建立在罗尔(Rolle)定理之上.本文以实数连续性中的重要定理———区间套定理为依据,给出了拉格朗日微分中值定理的另类证明.此外,还给出了中值定理的若干推广形式. 相似文献
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A. J. B. Ward 《International Journal of Mathematical Education in Science & Technology》2013,44(1):158-160
A simple method for teaching the algebraic solution of cubic equations is presented. The approach is via ‘completion of the cube’. It is found that this method is readily accepted by students already familiar with completion of the square as a method for quadratic equations. Many people are surprised at how simple the algebraic solution of cubic equations turns out to be. It is not normally necessary to resort to numerical techniques for these equations. 相似文献
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Ebrahim Samei 《Proceedings of the American Mathematical Society》2007,135(7):2045-2049
Let be an open connected subset of the plane, and let be a Banach algebra of analytic functions on . We show that the space of bounded derivations from into is not reflexive. We also obtain similar results when for .
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L. Kuntz 《Journal of Optimization Theory and Applications》1995,86(1):263-270
A new implicit function theorem for a class of nonsmooth functions is proved. It is used to improve the directional implicit function theorem of Demidova and Demyanov (Ref. 1). 相似文献
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M.A. Qazi 《Journal of Mathematical Analysis and Applications》2006,324(1):30-38
The mean value theorem for real-valued differentiable functions defined on an interval is one of the most fundamental results in Analysis. When it comes to complex-valued functions the theorem fails even if the function is differentiable throughout the complex plane. we illustrate this by means of examples and also present three results of a positive nature. 相似文献
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Summary Napoleon's original theorem refers to arbitrary triangles in the
Euclidean plane. If equilateral triangles are externally erected on the sides
of a given triangle, then their three corresponding circumcenters form an
equilateral triangle. We present some analogous theorems and related statements
for the isotropic (Galilean) plane. 相似文献
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B Tomas Johansson 《International Journal of Mathematical Education in Science & Technology》2016,47(1):144-148
Exercises involving the calculation of the derivative of piecewise defined functions are common in calculus, with the aim of consolidating beginners’ knowledge of applying the definition of the derivative. In such exercises, the piecewise function is commonly made up of two smooth pieces joined together at one point. A strategy which avoids using the definition of the derivative is to find the derivative function of each smooth piece and check whether these functions agree at the chosen point. Showing that this strategy works together with investigating discontinuities of the derivative is usually beyond a calculus course. However, we shall show that elementary arguments can be used to clarify the calculation and behaviour of the derivative for piecewise functions. 相似文献
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Hiroaki Aikawa 《Proceedings of the American Mathematical Society》1997,125(1):229-234
Let be a bounded domain in , , and let . We consider positive functions on such that for all bounded harmonic functions on . We determine Lipschitz domains having such with .
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黄龙光 《纯粹数学与应用数学》2001,17(4):314-317
研究拓扑向量空间半准内凸函数的特性,给出半内凸弧方向可微函数的最小值可由一类似变分不等式问题的解表示及一类广义变分不等式解的唯一性。 相似文献
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ThomasRIEDEL MaciejSABLIK 《数学学报(英文版)》2004,20(6):1073-1078
In this paper we present a mean value theorem derived from Flett‘s mean value theorem. It turns out that cubic polynomials have the midpoint of the interval as their mean value point. To answer what class of functions have this property, we consider a functional equation associated with this mean value theorem. This equation is then solved in a general setting on abelian groups. 相似文献
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Graciela Silvia Birman 《Journal of Geometry》2001,72(1-2):11-17
In the Lorentzian plane, the support function of a closed convex curve is not a periodic one. We redefine this concept and the envelope of a families of lines. Using these, we prove integral formulas in the Crofton's style for convex sets in the Lorentzian plane. Received 10 February 2000. 相似文献
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《Mathematical Methods in the Applied Sciences》2018,41(13):5096-5111
A pedal curve (a contrapedal curve) of a regular plane curve is the locus of the feet of the perpendiculars from a point to the tangents (normals) to the curve. These curves can be parametrized by using the Frenet frame of the curve. Yet provided that the curve has some singular points, the Frenet frame at these singular points is not well‐defined. Thus, we cannot use the Frenet frame to examine pedal or contrapedal curves. In this paper, pedal and contrapedal curves of plane curves, which have singular points, are investigated. By using the Legendrian Frenet frame along a front, the pedal and contrapedal curves of a front are introduced and properties of these curves are given. Then, the condition for a pedal (and a contrapedal) curve of a front to be a frontal is obtained. Furthermore, by considering the definitions of the evolute, the involute, and the offset of a front, some relationships are given. Finally, some illustrated examples are presented. 相似文献
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