Cm extension

Xem 1-9 trên 9 kết quả Cm extension
• Đề tài " Cm extension by linear operators "

Introduction and statement of results Let E ⊂ Rn , and m ≥ 1. We write C m (E) for the Banach space of all real-valued functions ϕ on E such that ϕ = F on E for some F ∈ C m (Rn ). The natural norm on C m (E) is given by ϕ C m (E) = inf{ F C m (Rn ) : F ∈ C m (Rn ) and F = ϕ on E} . Here, as usual, C m (Rn ) is the space of real-valued functions on Rn with continuous and bounded derivatives through order m; and F C m (Rn ) = |β|≤m x∈Rn max sup |∂ β F (x)| .

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• Đề tài " Whitney’s extension problem for Cm "

Let f be a real-valued function on a compact set in Rn , and let m be a positive integer. We show how to decide whether f extends to a Cm function on Rn . Introduction Continuing from [F2], we answer the following question (“Whitney’s extension problem”; see [hW2]). Question 1. Let ϕ be a real-valued function deﬁned on a compact subset E of Rn . How can we tell whether there exists F ∈ C m (Rn ) with F = ϕ on E? Here, m ≥ 1 is given, and C m (Rn ) denotes the space...

• Đề tài "A sharp form of Whitney’s extension theorem "

In this paper, we solve the following extension problem. Problem 1. Suppose we are given a function f : E → R, where E is a given subset of Rn. How can we decide whether f extends to a Cm−1,1 function F on Rn ? Here, m ≥ 1 is given. As usual, Cm−1,1 denotes the space of functions whose (m − 1)rst derivatives are Lipschitz 1. We make no assumption on the set E or the function f. This problem, with Cm in place of Cm−1,1, goes back to Whitney [15], [16], [17]. To answer it, we prove the following sharp form of the Whitney extension theorem....

• Báo cáo toán học: "An Extension of Uniqueness Theorems for Meromorphic Mappings"

Trong bài báo này, chúng tôi cung cấp cho một số kết quả về số lượng của ánh xạ meromorphic của Cm vào CP n trong điều kiện là những hình ảnh nghịch đảo của hyperplanes trong CP n. Đồng thời, chúng tôi đưa ra một câu trả lời cho một câu hỏi mở được đặt ra bởi H. Fujimoto vào năm 1998.

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Research show that RVT doesn’t has any side effect on fertility. In 200 cases of pregnancy after RVT 66% lead to neonate birth. Premature birth before 37th week happened in 27% of the cases. Abortion rate in first trimester was 16-20% like general population and second trimester abortion was 9.5% (Plante et al., 2005; Jolley et al., 2007). If the tumor volume is less than 500mm, tumor size is less than 2 cm and invasion depth of stroma is less than 2mm we can do ultraconservative operations include simple trachelectomy or extensive conization with knife. In this...

• Chapter 093. Gynecologic Malignancies (Part 5)

Malignant germ cell tumors are usually large (median—16 cm). Bilateral disease is rare except in dysgerminoma (10–15% bilaterality). Abdominal or pelvic pain in young women is the usual presenting symptom. Serum human chorionic gonadotropin (β-hCG) and α fetoprotein levels are useful in the diagnosis and management of these patients. Before the advent of chemotherapy, extensive surgery was routine, but it has now been replaced by careful evaluation of extent of spread, followed by resection of bulky disease and preservation of one ovary, the uterus, and the cervix, if feasible.