In the medical field, Single Nucleotide Polymorphism (SNP) genotyping is an important genetics technique. In order to know how SNP affect the function of gene, to amplify SNP regions of the DNA sequences is required. Many researchers prefer to design degenerate primers for polymerase chain reaction (PCR) experiment to amplify these sequences. Finding a primer satisfied all PCR design constraints and low degeneracy is important to save time and money. However, the existing applications can¡¦t design the degenerate primer satisfied the degenerate primer design constraints at the same time. We propose an efficient degenerate primer design algorithm based on multiobjective genetic algorithm. Also, the proposed algorithm uses the voting scheme to decrease the degeneracy of the design primers. Several gene family cDNA sequences and sequence variants are used to verify the proposed algorithm. The dry dock experimental results show that the proposed algorithm can find degenerate primer satisfied as many constraints as possible and low degeneracy.

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Let X = (X1,.....,Xm) be an infinitely degenerate system of vector fields, we study the existence and regularity of multiple solutions of Dirichelt problem for a class of semi-linear infinitely degenerate elliptic operators associated with the sum of square operator Δx = ∑m(j=1) Xj* Xj.

For a sign-changing function a(x) E C^αloc(Rn) with bounded Ω+ = {x E R^n |a(x) > O}, we study non-negative entire solutions u(x) ≥ 0 of the semilinear elliptic equation -Δu = a(x)u^q + b(x)u^p in R^n with n ≥ 3.0 < q < 1, p > q, and λ > 0. We consider two types of coefficient b(x) E C^αloc(R^n), either b(x) ≤ 0 in (R^n) or b(x) ≡ 1. In each case, we give sufficient conditions on a(x) for which all solutions must have compact support. In case Ω+ has several connected components, we also give conditions under which there exist "dead core'' solutions which vanish identically in one or more of these components. In the "logistic" case b(x) ≤ 0, we prove that there can be only one solution with given dead core components. In the case b(x) ≡ 1, the question of existence is more delicate, and we introduce a parametrized family of equations by replacing a(x) by ay = ya^+(x) - a^- (x). We show that there exists a maximal interval y E (0, f] for which there exists a stable (locally minimizing) solution. Under some hypotheses on a^- near infinity, we prove that there are two solutions for each y E (0, f). Some care must be taken to ensure the compactness of Palais-Smale sequences, and we present an example which illustrates how the Palais-Smale condition could fail for certain a(x). The analysis is based on a combination of comparison arguments, a priori estimates, and variational methods. / Thesis / Doctor of Philosophy (PhD)