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Full-Text Articles in Mathematics
Mathematically Modeling Pcr: An Asymptotic Approximation With Potential For Optimization, Martha J. Garlick
Mathematically Modeling Pcr: An Asymptotic Approximation With Potential For Optimization, Martha J. Garlick
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
A mathematical model for PCR (Polymerase Chain Reaction) is developed using the law of mass action. Differential equations are written from the chemical equations, preserving the detail of the complementary DNA single strand being extended one bas e pair at a time. The equations for the annealing stage are solved analytically. The method of multiple scales is used to approximate solutions for the extension stage. A map is then developed from the solutions to simulate PCR. The advantage of this model is the ability to use the map to optimize the process. Our results suggest that dynamically optimizing the extension …
The Relationship Between Discrete Vector Quantization And The P-Median Problem, Allen G. Holder, G Lim, J Reese
The Relationship Between Discrete Vector Quantization And The P-Median Problem, Allen G. Holder, G Lim, J Reese
Mathematics Faculty Research
We show that a well studied problem in the engineering community is the same as a problem studied by mathematical combinatorialists. Specifically, we show that the question of optimally designing a vector quantizer, which is an important problem in coding theory, is the same as the p-median problem, which is a classic graph theory problem with important applications in operations research. The importance of the relationship lies in the fact that both communities have spent years developing solution methodologies, and this connection permits each community to glean new ideas from the other. We show that two of the most popular …
Some Geometrical Aspects Of The Cone Linear Complementarity Problem., Madhur Malik Dr.
Some Geometrical Aspects Of The Cone Linear Complementarity Problem., Madhur Malik Dr.
Doctoral Theses
Cone Linear Complementarity ProblemLet V be a finite dimensional real inner product space and K be a closed convex cone in V. Given a linear transformation L : V → V and a vector q ∈ V the cone linear complementarity problem or linear complementarity problem over K, denoted as LCP(K, L, q), is to find a vector x ∈ K such thatL(x) + q ∈ K+ and hx, L(x) + qi = 0,where h., .i denotes an inner product on V and K is the dual cone of K defined as:K∗ := {y ∈ V : hx, yi ≥ …