Differential Representations of SO(4) Dynamical Group

In this paper we present systematic differential representations for the dynamical group SO(4).Theserepresentations include the left and the right differential representations and the left and the right adjoint differentialrepresentations in both the group parameter space and its coset spaces.They are the generalization of the differentialrepresentations of the SO(3) rotation group in the Euler angles.These representations may find their applications in thestudy of the physical systems with SO(4) dynamical symmetry.

Screen for Coronary Artery Disease Specific Genetic Expression by Representational Differential Analysis

Objective To screen coronaryartery disease (CAD) specific expressions and clone their genes. Method Blood samples were collected from CAD and non - CAD patients at the end of coronary angiography. mRNA from samples was isolated and converted into cDNA. After ligated with specific linkers, the cDNA was amplified with complementary primers. PCR products from CAD samples were named as tester; the ones from non - CAD samples were named as driver. With different ratio of tester to driver (1 : 100,1: 1, 000, and 1: 10, 000), they were mixed, denatured, and renatured. Single strand cD-NA was eliminated by Mung bean nuclease. Double strand cDNA presented only in tester was amplified, ligated in vector pUC19 and pUC53, and transformed into E. coll DH5a. Strains with inserted cDNA fragments were picked up based on blue and white selection. Insertions were screened by endonuclease digestion and DNA sequencing. Results were compared with DNA sequences of GeneBank. Results: After the selection with representational differential analysis, CAD specific cDNA fragments with different sizes (about 1kb, 0. 75kb, and 0. 6kb) were cloned. Among them, two fragments from unknown genes were identified. One presented a 43. 3 % similarity with part of the rattus norvegicus lipocortin gene. Another presented a 45. 4 % similarity with part of the human polynucleotide kinase 3' - phosphatase gene. Conclusion There are at least two CAD specific - ex- pressions from unknown genes that were partially similar to lipocortin and polynucleotide kinase 3'- phos-phatase genes, respectively. Expression of these genes might affect the formation and progression of plaque within coronary artery.

The up-regulated differentially expressed genes in HL-60 cell line treated with nocodazole

Objective：Microtubule damaging agents such as nocodazole have been used in the clinical cancer chemotherapy. However, the molecular mechanisms of apoptosis induction activity of these agents are still unclear. We previously demonstrated that nocodazole induced apoptosis in human leukemic HL-60 cells. In order to investigate the genes involved in this process, cDNA RDA was performed to identify upregulated genes in the apoptosis process induced by nocodazole. Methods ：Sixteen up-regulated genes were identified and confirmed to be differentially expressed, including ribosomal proteins, cytochrome b, Wilm＇s tumor related protein QM gene, alpha-tubulin isoform 1, heterogeneous nuclear ribonucleoprotein C enzymes, follicular lymphoma variant translocation 1, Ribophorin I , etc. Results：It was the first time for several genes reported to be related to apoptosis, including one functionally unkown gene, BING4. We also analyzed the expression of these genes in apoptosis induced by etoposide, and results showed 9 genes were also up-regulated, indicating they could be important genes involved in apoptosis. Conclusion：The study provides important clues to understand mechanism of apoptosis induced by nocodazole, and establishes foundation for further study.

Inhomogeneous Cauchy-Riemann equation in Octonion space

The integral representation of differentiable functions in Octonion space is obtained and the explicit solution of the inhomogeneous Cauchy-Riemann equation is given by integral representation. As an application, the Cousin problem analogue of Mittag-Laffier problem is discussed.