TAILIEUCHUNG - Báo cáo " GENERALIED MASON’S THEOREM "

The purpose of this paper is to give a generalization of Mason’s theorem by the Wronskian technique over fields of characteristic 0. Keywords: The Wronskian technicque, Marson’s theorem. 1. Introduction Let F be a fixed algebraically closed field of characteristic 0. Let f (z) be a polynomial non - constants which coefficients in F and let n(1/f ) be the number of distinct zeros of f . Then we have the following. Marson’s theorem. ([2]). Let a(z), b(z), c(z) be relatively prime polynomials in F and not all constants such that a + b = c. Then max {deg(a), deg(b),. | VNU. JOURNAL OF SCIENCE Mathematics - Physics. N04 - 2005 GENERALIED MASON S THEOREM Nguyen Thanh Quang Phan Duc Tuan Department of Mathematics Vinh University Abstract. The purpose of this paper is to give a generalization of Mason s theorem by the Wronskian technique over fields of characteristic 0. Keywords The Wronskian technicque Marson s theorem. 1. Introduction Let F be a fixed algebraically closed field of characteristic 0. Let f z be a polynomial non - constants which coefficients in F and let n 1 f be the number of distinct zeros of f. Then we have the following. Marson s theorem. 2 . Let a z b z c z be relatively prime polynomials in F and not all constants such that a b c. Then max deg a deg b deg c n abc -1. It is now well known that Mason s Theorem implies the following corollary. Corollary. Fermat s Theorem over polynomials . The equation xn yn zn has no solutions in non - constants and relatively prime polynomials in F if n 3. The main theorem in this paper is as following Theorem . Les fo fl fn be relatively primer polynomials and fo fl fn be linearly independent over F. If f0 fi . fn fn 1 then Á 1 1 max deg f n n I -- I 0 i n 1 jJ n n 1 2 Remark. Theorem is a generalization of Mason s theorem which was obtained for case n 1. Typeset by ẠmS-T ạX 34 Generalied Mason s Theorem 35 2. Proof of the main theorem Let x fx 0 be a rational function where f x g x are non - zero and relatively prime polynomials on F. The degree of x denoted by deg x is defined to be degf x degg x . Here the notation degf x means the degree of polynomial f x . From the properties of polynomial we have. Proposition . If 1 and 2 are the rational functions on F then 1 deg i 2 deg 1 deg 2 2 deg a deg 2 3 deg i 2 max deg 1 deg 2 . Definition . Let x 0 be a rational function on F. For every a E F we write x x a m y m E Z gi x where fi x f2 x are relatively prime polynomials and f1 a 0 g1 a 0. We call m order of at a. Proposition . If 1 2 are rational functions

• Báo cáo khoa học
• MASON’S THEOREM
• Mathematics
• Physics
• Scientific reports
• scientific studies
• natural sciences
• Giới thiệu Thư viện số
• Natural Sciences Digital Library
• Thư viện số
• Digital Library
• Bộ sưu tập Thư viện số
• Summary of Doctoral Thesis
• Educational Sciences
• Methodology in Biology
• Developing textbooks’ models
• Orientation of competency development
• Methods of teaching natural science
• Annals of Agricultural Sciences
• Agricultural Sciences
• Khoa học nông nghiệp
• Natural preservatives
• Cold storage
• the natural sciences
• the social sciences
• conduct and misconduct
• Misconduct and why it occurs
• misconduct affecting
• the truth claims
• Molecular cryocrystal
• Elastic moduli
• Elastic wave
• Elastic constants
• Mathematical sciences
• Physical sciences
• Sciences
• GMAT
• math test
• McGraw Hills GMAT
• Environmental sciences
• Earth sciences
• Natural organic matters removal
• Water purification
• DBPs control
• Technology sciences
• Vecny este epoxy alkyd
• Tính chất điện
• Độ bền dung môi
• Độ bền nhiệt
• Detailed checklist
• Field labels
• Grammitid specimens
• VNU University of Science
• Xác định biên
• Dị thường từ
• Dị thường trọng lực
• Bắc Việt Nam
• Mỡ cá tra
• Etyl cacboxylate
• Etyl biodiesel
• Este axit omega 3 6 9
• Phương pháp đồng dung môi
• Đồng dung môi
• Hợp chất chứa dị vòng
• Chất xúc tác
• Phản ứng Sonogashira
• Hợp chất dị vòng năm cạnh
• Phản ứng Click
• Nano đồng
• Nano silica
• Khả năng kháng nấm
• Pyricularia oryzae
• Rhizoctonia solani
• Phân loại thực vật
• Lạng Sơn
• Aspidistra papillata
• Plant taxonomy
• Arachniodes simplicior
• Flora of Vietnam
• New record
• Phản ứng ngưng tụ croton
• Hoạt tính kháng khuẩn
• Chương trình PASS
• Dẫn xuất thiopodand
• Vật liệu nano
• Tính chất quang
• Tính chất từ
• Vật liệu nano HoFeO3
• Cảm biến miễn dịch điện hóa
• Kháng thể IgY
• Virus Newcastle
• Bình phản ứng mini
• Xúc tác lưỡng kim loại Co2Cu2
• CI NEB cơ chế phản ứng
• Phản ứng hydrogen hóa carbon monoxide
• Bọ rùa hai mảng đỏ
• Lemnia biplagiata
• Tỷ lệ sống sót
• Tỷ lệ vào nhộng
• Năng ăn con mồi
• Chất lượng nước
• Động vật nổi
• Thành phần loài
• Kênh Bún Xáng
• Đa dạng sinh học
• Camphor
• science and technology
• research projects
• scientific research
• Natural resources
• Research
• Natural radioactivity
• Major and accessory minerals
• Gamma ray spectrometry
• Wall rock granitoids
• Natural sciences and Technology
• Immune cells expansion
• Peripheral blood
• Immune cell therapy
• Natural killer cells
• Cytotoxic T lymphocytes
• Peripheral blood mononuclear cells