منابع مشابه
Five Squares in Arithmetic Progression over Quadratic Fields
We give several criteria to show over which quadratic number fields Q( √ D) there should exists a non-constant arithmetic progressions of five squares. This is done by translating the problem to determining when some genus five curves CD defined over Q have rational points, and then using a Mordell-Weil sieve argument among others. Using a elliptic Chabauty-like method, we prove that the only n...
متن کاملbiaccessibility in quadratic julia sets
در این رساله برای چندجمله ای های درجه ی دوم با مجموعه ی ژولیای همبند موضعی; ثابت خواهیم کرد: اندازه برولین مجموعه نقاط از دو سو دست یافتنی در چندجمله ای های درجه دو برابر با صفر است مگر چندجمله ای چبی شف که برابر با یک است. و برای چندجمله ای های درجه دوم با نقاط ثابت خنثی غیر گویا ثابت خواهیم کرد: 1)هر نقطه ی از دو سو دست یافتنی در حالت زیگل نهایتا به نقطه ی بحرانی و در حالت کرمر به نقطه ث...
Least Squares Problems with Absolute Quadratic Constraints
This paper analyzes linear least squares problems with absolute quadratic constraints. We develop a generalized theory following Bookstein’s conic-fitting and Fitzgibbon’s direct ellipse-specific fitting. Under simple preconditions, it can be shown that a minimum always exists and can be determined by a generalized eigenvalue problem. This problem is numerically reduced to an eigenvalue problem...
متن کاملQuadratic Convexity and Sums of Squares
Quadratic Convexity and Sums of Squares Martin Ames Harrison The length of a sum of squares σ in a ring R is the smallest natural k such that σ can be realized as a sum of k squares in R. For a set S ⊆ R, the pythagoras number of S, denoted by P(S), is the maximum value of length over all σ ∈ S. This dissertation is motivated by the following simple question: if R = R[x1, . . . , xn] and S = R[...
متن کاملOn 4 Squares in Arithmetic Progression
x1 − 2x2 + x3 = 0 x2 − 2x3 + x4 = 0 are given by (x1, x2, x3, x4) = (±1,±1,±1,±1). Now, the above variety is an intersection between 2 quadrics in P. In general – i.e., except for the possibility of the variety being reducible or singular – an intersection between 2 quadrics in P is (isomorphic to) an elliptic curve and there is an algorithm that brings the curve to Weierstraß form by means of ...
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: Mathematics of Computation
سال: 1993
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1993-1181330-x