# Existsa

### Numerical integration of DAE's seminar

Scientific Computing Group Consistent Initial Values x (t) =sin(t) x 0 (t) +y (t) =0 x 0 is a consistent initial value, if there **existsa** smooth solution thatfullfillsx (t 0) =x 0 and this solution is definedforallt.

www.win.tue.nl

### On SomeCriteria for the Balanced Projectivity of Modules over ...

Consider the following commutative diagram with exact rows, and torsion-free modules Mand M *: 0 L N α μ M τ 0 0 L * N * β M * 0 If the top row is balanced-exact and there **existsa** homomorphismρ : M * →M suchthatτρ =1 , then the bottom row is likewise balanced-exact.

m-hikari.com

### Sample Problems for Exam II

Recall that a space Xis locally path-connected if for eachx∈Xandeach neighborhood Uofx, there **existsa** neighborhood Vofxsuchthat V⊆Uand Vis path-connected.

www.math.uiowa.edu

### Real valued functions in Pointfree Topology

(2) For everyf 2 USC (X) and everyg 2 LSC (X) withf g, there **existsa** continuoush 2 C (X) such thatf h g. M. Katˇ etov, On real-valued functions in topological spaces, Fund. Math. 38 (1951) 85-91; correction 40 (1953) 203-205.

www.ehu.es

### Undecidability everywhere

There **existsa** nite group! 2. Thef.p. group Zcannotbe embedded in any nite group. Other Markovproperties: trivial, abelian, nilpotent, solvable, free, torsion-free.

www-math.mit.edu

### Separating Hyperplanes

Then there **existsa** hyperplane separating b from K . THEOREM: K R n convex, nonempty. b 62 K . Then K can be separated from b by a hyperplane. COROLLARY: SUPPORTING HYPERPLANE THEOREM: b a boundary point of a convex set K R n .

www-personal.umich.edu

### The Deduction Theorem, Optimal Proof Systems, and Complete ...

There **existsa** polynomial psuch that for all printable sets of tautologies * the proof system P ∪* is closed under substitutions of variables with respect top.

www.informatik.hu-berlin.de

### Chapter1. Limits and Con tinuity

We say that f ( x )has right-hand limit Lat x 0,and write lim x→x + 0 f ( x )= L if for every number *> 0 there **existsa** corresponding number δ> 0such that for all x x 0 <x<x 0 + δ⇒|f ( x ) −L|<*. 6

www.freeinfosociety.com

### Math 231BPartial Differential Equations

B [ u;v ] is bounded and hence by the Riesz Representation Theorem (RRT) there **existsa** unique element Au such that B [ u;v ]= hAu;vi; for all v2H: However the map u!

math.ucsd.edu

### THE CLASSIFICATION PROBLEM FOR TORSION-FREE ABELIAN GROUPS OF ...

Conversely, by Feldman-Moore[10], if E is an arbitrary count-ableBorel equivalence relation on the standard Borelspace X , then there **existsa** countable group G an daB or el action of G on X such that E = E X G.

www.ams.org

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