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Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
Services
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I. Basic math.
II. Pricing and Hedging.
III. Explicit techniques.
IV. Data Analysis.
V. Implementation tools.
VI. Basic Math II.
VII. Implementation tools II.
1. Calculational Linear Algebra.
2. Wavelet Analysis.
3. Finite element method.
4. Construction of approximation spaces.
5. Time discretization.
6. Variational inequalities.
A. Stationary variational inequalities.
a. Weak and strong formulations for stationary variational inequality problem.
b. Existence and uniqueness for coercive stationary problem.
c. Penalized stationary problem.
d. Proof of existence for stationary problem.
e. Estimate of penalization error for stationary problem.
f. Monotonicity of solution of stationary problem.
g. Existence and uniqueness for non-coercive stationary problem.
B. Evolutionary variational inequalities.
VIII. Bibliography
Notation. Index. Contents.

Proof of existence for stationary problem.


e prove existence part of the proposition ( Existence and uniqueness for stationary problem ).

According to the proposition ( A priory estimates for Galerkin solution 1 )-1 and ( Weak compactness of bounded set ) there is a sequence MATH such that MATH Then by the proposition ( Rellich-Kondrachov compactness theorem ), MATH According to the proposition ( A priory estimates for Galerkin solution 1 )-2 MATH so that MATH We cannot immediately pass to the limit in MATH because of the MATH term in MATH . Hence we write MATH and, assuming that $v\in K$ , MATH , MATH Since MATH , MATH we now get rid of the problem term: MATH and pass to the limit MATH





Notation. Index. Contents.


















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