# Existsa

### Group Activity 12A: Rings

An element a 2Risaunit provided there existsa 1 2Rsuchthataa 1 is a unity. (1) LetR=f0; 2; 4; 6; 8 gwithadditionand multiplication modulo 10 bearing.

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### ALLEE EFFECTS INA DISCRETE-TIME HOST-PARASITOID MODEL WITH ...

It is proved that there existsa population threshold below which the population becomes extinct. When the population is initiated above the threshold, the two age classes will either be synchronizing or 2000 Mathematics Subject Classification.

aimsciences.org

### 3Lecture3

Definition 14 For any real sequence , wesaythat∈ ¯ Risa subsequential limit of  if there existsa subsequence   → For example, the sequence  =(−1)  has two subsequential limits, −1 and 1.

www.econ.brown.edu

### Integer values of polynomials

Besides the obvious solutiong=f we may want to impose some conditions on the polynomialg; for example, iff (S) Z we wonder if there existsa polynomial with integer coecients which parametrizes the setf (S).

www.dm.unipi.it

### MathS-101. Worksheet 13. Limits and Continuity in Rn

Restating this result in terms of the Euclidean metricd, afunctionf: X! Y is continuous if and only if for eachx 2 Xandeach > 0, there existsa > 0 such that d (x,y) <=) d (f (x) ,f (y)) <.

math.harvard.edu

### Homework 2 -Solutions

Sincew∈L 2 and|w|≥p, by the pumping lemma, there existsa decomposition w=xyzsuchthat|y|>0, |xy|≤pandxy i z∈L 2 foreachi≥0. Fori=0 this implies that xz=0 r 1 0 pisinLwherer<q.

www.cs.iit.edu

### Math 221: Final Exam

Show that if Ris Cohen-Macaulay, then there existsa (nonzero) nitely generated R-module Mwhose length and projective dimension are both nite. (4) Let Rbealocal Noetherianring which contains the eld Qofrational numbers, let Gbea nite group actingonR, and let R G Rbethe xedpointsforthe action of G. Show that ...

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### CHARACTERIZING ASYMPTOTIC ST ABILITY WITHDULAC FUNCTIONS

R n beananalytic vector eld and suppose that the system_ x=F (x) has LAS atp: Is it true that there existsa C 1 Dulacfunction B for system (1) dene din W s (p) ?

www.math.grin.edu

### *-normal spaces and decompositions of normality

199 (iii) Functionally *-normalif for every pair of disjoint closed sets A and Boneofwhich is*-closed there existsa continuous function f: X! [0,1]such thatf (A) =0 and f (B) =1; (iv) Weakly functionally*-normal (wf*-normal) if for every pair of disjoint*-closed sets A and Bthereexistsa continuous ...

agt.webs.upv.es

### IMO Shortlist 2008

Suppose that there existsa circleωtangenttotheray BA beyond A and to the ray BC beyond C , which is also tangent to the lines AD and CD . Prove that the common external tangents of ω 1 andω 2 intersectonω. 1.1.2 Shortlisted Problems 1.

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