FUNCTIONAL STRENGTHS

Description

• cours - matière potentielle : security

- 1 - JAMES MICHAEL WILLIAMSON - 503.784.1031 Jim Williamson leverages his knowledge in business practices with in-depth functional and technical abilities. An expert in Oracle Applications and other relational databases, Jim has been functional lead, technical lead or a combination therein on eight successful ERP/CRM implementations of Oracle Applications. Fifteen years experience with relational databases and ERP software and more than ten years experience with Oracle applications and development toolsets have rendered him a vital asset on Oracle projects of all sizes.

• custom development
• functional strengths crm as functional lead
• crm foundation
• functional lead
• technical lead
• aspects of business process
• order management
• development
• data

Sujets

• Security
• Horizon Software
• Williamson
• Mississippi State University
• Computer Sciences
• Oracle
• United States

Informations

• Publié par: unnu
• Nombre de lectures: 12
• Langue: English

Extrait

Week 11 lectures, Math 804

1.More on Weirstrass Elliptic FunctionP(z): Integral formula Lemma 1.1.Introduce Z ∞ 3−1/2 (1.1)z=h(ζ (4 ) = t−g 2 t−g 3 )dt ζ where the path of integration may be any curve which does not pass 3 through a zero of4t−g 2 t−g 3 , thenh(P(z)) =z. Proof.On differentiating (1.1), we obtain   2 dζ 3 (1.2) = 4ζ−g 2 ζ−g 3 dz so that (1.3)ζ=P(±z+α) =P(z±α) Now, in (1.1), if we letζ→ ∞, we obtainz→means that0. This P(z+±α) blows up atzThis means that= 0. αis either 0 or a point congruent to it. Thusζ=P(z) and the Lemma is proved.

Lemma 1.2.The elliptic functionPsatisfies the following addition theorem:   0 P(z)P(z) 1 0   (1.4) P(y)P(y = 0 ) 1 0 P(z+y)−P(z+y) 1 Proof.Consider the following set of two linear equations for determin- ingAandB: 0 (1.5)P(z) =AP(z) +B

0 (1.6)P(y) =AP(y) +B These determineAandBuniquely in terms ofzandy, unlessP(z) =P(y), i.e. unlessz=±y(mod2ω 1 ,2ω 2 ). ForAandBas determined above, consider 0 (1.7)P(ζ)−AP(ζ)−B It has a triple pole atζ= 0 and consequently three irreducible zeros (i.e. three zeros within a cell). Two of these zeros are clearlyζ=z andζ=yand the third irreducible zero must be congruent to−z−y 1