Mean-value theorem and distribution densities

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The Mean Value Theorem and Its Consequences

The point (M,f(M)) is called an absolute maximum of f if f(x) ≤ f(M) for every x in the domain of f . The point (m, f(m)) is called an absolute minimum of f if f(x) ≥ f(m) for every x in the domain of f . More than one absolute maximum or minimum may exist. For example, if f(x) = |x| for x ∈ [−1, 1] then f(x) ≤ 1 and there are absolute maxima at (1, 1) and at (−1, 1), but only one absolute mini...

متن کامل

Vinogradov’s Mean Value Theorem via Efficient Congruencing

We obtain estimates for Vinogradov’s integral which for the first time approach those conjectured to be the best possible. Several applications of these new bounds are provided. In particular, the conjectured asymptotic formula in Waring’s problem holds for sums of s kth powers of natural numbers whenever s > 2k + 2k − 3.

متن کامل

The First Mean Value Theorem for Integrals

For simplicity, we use the following convention: X is a non empty set, S is a σ-field of subsets of X, M is a σ-measure on S, f , g are partial functions from X to R, and E is an element of S. One can prove the following three propositions: (1) If for every element x of X such that x ∈ dom f holds f(x) ≤ g(x), then g − f is non-negative. (2) For every set Y and for every partial function f from...

متن کامل

On Generalized Flett's Mean Value Theorem

We present a new proof of generalized Flett’s mean value theorem due to Pawlikowska (from 1999) using only the original Flett’s mean value theorem. Also, a Trahan-type condition is established in general case.

متن کامل

Multigrade Efficient Congruencing and Vinogradov’s Mean Value Theorem

We develop a substantial enhancement of the efficient congruencing method to estimate Vinogradov’s integral of degree k for moments of order 2s, thereby obtaining for the first time near-optimal estimates for s > 5 8k . There are numerous applications. In particular, when k is large, the anticipated asymptotic formula in Waring’s problem is established for sums of s kth powers of natural number...

متن کامل

ذخیره 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: Kodai Mathematical Journal

سال: 1950

ISSN: 0386-5991

DOI: 10.2996/kmj/1138833916