Projective quantum spaces

Associated to the standard $SU_{q}(n)$ R-matrices, we introduce quantum spheres $S_{q}^{2n-1}$, projective quantum spaces $CP_{q}^{n-1}$, and quantum Grassmann manifolds $G_{k}(C_{q}^{n})$. These algebras are shown to be homogeneous quantum spaces of standard quantum groups and are also quantum principle bundles in the sense of T Brzezinski and S. Majid (Comm. Math. Phys. 157,591 (1993)).Comment: 8 page

Towards Spinfoam Cosmology

We compute the transition amplitude between coherent quantum-states of geometry peaked on homogeneous isotropic metrics. We use the holomorphic representations of loop quantum gravity and the Kaminski-Kisielowski-Lewandowski generalization of the new vertex, and work at first order in the vertex expansion, second order in the graph (multipole) expansion, and first order in 1/volume. We show that the resulting amplitude is in the kernel of a differential operator whose classical limit is the canonical hamiltonian of a Friedmann-Robertson-Walker cosmology. This result is an indication that the dynamics of loop quantum gravity defined by the new vertex yields the Friedmann equation in the appropriate limit.Comment: 8 page

Quantum Groups and Noncommutative Geometry

Quantum groups emerged in the latter quarter of the 20th century as, on the one hand, a deep and natural generalisation of symmetry groups for certain integrable systems, and on the other as part of a generalisation of geometry itself powerful enough to make sense in the quantum domain. Just as the last century saw the birth of classical geometry, so the present century sees at its end the birth of this quantum or noncommutative geometry, both as an elegant mathematical reality and in the form of the first theoretical predictions for Planck-scale physics via ongoing astronomical measurements. Noncommutativity of spacetime, in particular, amounts to a postulated new force or physical effect called cogravity.Comment: 72 pages, many figures; intended for wider theoretical physics community (special millenium volume of JMP

Notes on two-parameter quantum groups, (II)

This paper is the sequel to [HP1] to study the deformed structures and representations of two-parameter quantum groups $U_{r,s}(\mathfrak{g})$ associated to the finite dimensional simple Lie algebras \mg. An equivalence of the braided tensor categories \O^{r,s} and \O^{q} is explicitly established.Comment: 21 page

Unbraiding the braided tensor product

We show that the braided tensor product algebra $A_1\underline{\otimes}A_2$ of two module algebras $A_1, A_2$ of a quasitriangular Hopf algebra $H$ is equal to the ordinary tensor product algebra of $A_1$ with a subalgebra of $A_1\underline{\otimes}A_2$ isomorphic to $A_2$, provided there exists a realization of $H$ within $A_1$. In other words, under this assumption we construct a transformation of generators which `decouples' $A_1, A_2$ (i.e. makes them commuting). We apply the theorem to the braided tensor product algebras of two or more quantum group covariant quantum spaces, deformed Heisenberg algebras and q-deformed fuzzy spheres.Comment: LaTex file, 29 page

Numerical computation of third order delay differential equations by using direct multistep method

This paper introduces a direct multistep method to solve third order delay differential equations (DDEs) based on the boundary conditions given. The multistep method is presented in direct integration approach to reduce the total function calls involved and the method is derived implicitly so that the accuracy is attained. The method is also in block for every iteration to reduce total steps taken. The DDEs involve the endpoints of boundary conditions, hence, the shooting technique is to choose for the best value of additional initial value. The constant and pantograph delay types are the DDEs problems considered in this study. Lagrange interpolation is used to interpolate the delay involved in pantograph problems. The observation of the multistep method in terms of order, consistency, and convergence is also presented in this paper. The numerical results obtained are compared with the previous multistep method to verify the capability of the proposed method to solve third order DDEs directly

MicroRNA-383 located in frequently deleted chromosomal locus 8p22 regulates CD44 in prostate cancer.

A major genomic alteration in prostate cancer (PCa) is frequent loss of chromosome (chr) 8p with a common region of loss of heterozygosity (LOH) at chr8p22 locus. Genomic studies implicate this locus in the initiation of clinically significant PCa and with progression to metastatic disease. However, the genes within this region have not been fully characterized to date. Here we demonstrate for the first time that a microRNA component of this region-miR-383-is frequently downregulated in prostate cancer, has a critical role in determining tumor-initiating potential and is involved in prostate cancer metastasis via direct regulation of CD44, a ubiquitous marker of PCa tumor-initiating cells (TICs)/stem cells. Expression analyses of miR-383 in PCa clinical tissues established that low miR-383 expression is associated with poor prognosis. Functional data suggest that miR-383 regulates PCa tumor-initiating/stem-like cells via CD44 regulation. Ectopic expression of miR-383 inhibited tumor-initiating capacity of CD44+ PCa cells. Also, 'anti-metastatic' effects of ectopic miR-383 expression were observed in a PCa experimental metastasis model. In view of our results, we propose that frequent loss of miR-383 at chr8p22 region leads to tumor initiation and prostate cancer metastasis. Thus, we have identified a novel finding that associates a long observed genomic alteration to PCa stemness and metastasis. Our data suggest that restoration of miR-383 expression may be an effective therapeutic modality against PCa. Importantly, we identified miR-383 as a novel PCa tissue diagnostic biomarker with a potential that outperforms that of serum PSA

Comparative study of herbal plants on the phenolic and flavonoid content, antioxidant activities and toxicity on cells and zebrafish embryo

Natural antioxidants derived from plants have shown a tremendous inhibitory effect on free radicals in actively metabolizing cells. Overproduction of free radicals increases the risk factor of chronic diseases associated with diabetes, cancer, arthritis and cardiovascular disease. Andrographis paniculata, Cinnamon zeylanicum, Curcuma xanthorrhiza, Eugenia polyantha and Orthosiphon stamineus are ethnomedicinal plants used in the Asian region to treat various illnesses from a common fever to metabolic disease. In this study, we have quantified the total phenolic (TPC) and flavonoid content (TFC) in these plants and its inhibitory effect on 1,1-diphenyl-2-picrylhydrazyl radical (DPPH) and 2,2′-azinobis(3-ethylbenzothiazoline-6-sulfonic acid) (ABTS) free radicals as well as the cytotoxicity effect on cell lines proliferation and zebrafish embryogenesis. Results showed that Cinnamon zeylanicum and E. polyantha have the highest phenolic and flavonoid content. Furthermore, both herbs significantly inhibited the formation of DPPH and ABTS free radicals. Meanwhile, O. stamineus exhibited minimum cytotoxicity and embryotoxicity on tested models. Good correlation between IC50 of 3T3-L1 cells and LC50 embyrotoxicity was also found. This study revealed the potent activity of antioxidant against free radical and the toxicology levels of the tested herbal plants