Proof of the Fundamental Theorems on Second-Order Cross Partial Derivatives
نویسندگان
چکیده
منابع مشابه
Proof of the Fundamental Theorems on Second-order Cross Partial Derivatives*
almost everywhere on A. At the conclusion of this paper we state a number of interesting problems which are closely connected with the theorems which we prove. We wish to thank Dr. S. Saks for many helpful suggestions. 2. Measurability of second partial derivatives. We require the following lemma. Lemma 1. Let u(x, y) be a function of. Baire, and let Anbe the point set on which the following in...
متن کاملthe impact of training on second language writing assessment: a case of raters’ biasedness
چکیده هدف اول این تحقیق بررسی تأثیر آموزش مصحح بر آموزش گیرندگان براساس پایایی نمره های آنها در پنج بخش شامل محتوا ، سازمان ، لغت ، زبان و مکانیک بود. هدف دوم این بود که بدانیم آیا تفاوتهای بین آموزشی گیرندگان زن و مرد در پایایی نمرات آنها وجود دارد. برای بررسی این موارد ، ما 90 دانشجو در سطح میانه (متوسط) که از طریق تست تعیین سطح شده بودند انتخاب شدند. بعد از آنها خواستیم که درباره دو موضوع ا...
15 صفحه اولGeneralized second-order partial derivatives of 1/r
The generalized second-order partial derivatives of 1/r , where r is the radial distance in three dimensions (3D), are obtained using a result of the potential theory of classical analysis. Some non-spherical-regularization alternatives to the standard spherical-regularization expression for the derivatives are derived. The utility of a spheroidal-regularization expression is illustrated on an ...
متن کاملPartial second-order subdifferentials of -prox-regular functions
Although prox-regular functions in general are nonconvex, they possess properties that one would expect to find in convex or lowerC2 functions. The class of prox-regular functions covers all convex functions, lower C2 functions and strongly amenable functions. At first, these functions have been identified in finite dimension using proximal subdifferential. Then, the definition of prox-regula...
متن کاملApproximating partial derivatives of first and second order by quadratic spline quasi-interpolants on uniform meshes
Given a bivariate function f defined in a rectangular domain Ω, we approximate it by a C1 quadratic spline quasi-interpolant (QI) and we take partial derivatives of this QI as approximations to those of f. We give error estimates and asymptotic expansions for these approximations. We also propose a simple algorithm for the determination of stationary points, illustrated by a numerical example. ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1933
ISSN: 0002-9947
DOI: 10.2307/1989322