A Unified Elementary Approach to the Dyson, Morris, Aomoto, and Forrester Constant Term Identities

We introduce an elementary method to give unified proofs of the Dyson, Morris, and Aomoto identities for constant terms of Laurent polynomials. These identities can be expressed as equalities of polynomials and thus can be proved by verifying them for sufficiently many values, usually at negative integers where they vanish. Our method also proves some special cases of the Forrester conjecture.Comment: 20 page

Reproducing Kernel Space Method for the Solution of Linear Fredholm Integro-Differential Equations and Analysis of Stability

We present a numerical method to solve the linear Fredholm integro-differential equation in reproducing kernel space. A simple algorithm is given to obtain the approximate solutions of the equation. Through the comparison of approximate and true solution, we can find that the method can effectively solve the linear Fredholm integro-differential equation. At the same time the numerical solution of the equation is stable

A family of q-Dyson style constant term identities

AbstractBy generalizing Gessel–Xin's Laurent series method for proving the Zeilberger–Bressoud q-Dyson Theorem, we establish a family of q-Dyson style constant term identities. These identities give explicit formulas for certain coefficients of the q-Dyson product, including three conjectures of Sills' as special cases and generalizing Stembridge's first layer formulas for characters of SL(n,C)

Preparation, Characterization, and Bioactivity of Chitosan Microspheres Containing Basic Fibroblast Growth Factor

The aim of this study is to evaluate, prepare, and characterize bioactivity of chitosan microspheres loaded with bFGF for providing sustained release of bFGF. Porous chitosan microspheres were prepared by freeze-drying process based on the interaction between chitosan and tripolyphosphate (TPP). The bFGF-loaded chitosan microspheres were well interconnected and have a narrow size distribution, spherical shape, and positive surface charges. The bFGF-loading capacity and encapsulation efficiency were 7.57 mg/g and 95.1%, respectively. Results of in vitro release showed that the extent of release was 82.1% at Day 25. Schwann cells were used as an in vitro model for cell response to bFGF and bFGF-loaded chitosan microspheres. Results indicated that the number, cell viability, and percentage of cells G2/M+S phase in the bFGF groups are higher than those in the bFGF-loaded chitosan microspheres groups before culturing for 2 days. However, the number, cell viability, and percent of cells G2/M+S phase in the bFGF-loaded chitosan microspheres groups are significantly higher than those in the bFGF groups after culture for 4 and 8 days. These findings indicated that bFGF-loaded chitosan microspheres may help to decrease the release of bFGF and provide a suitable three-dimensional environment for cell growth and proliferation

Joint assembly and genetic mapping of the Atlantic horseshoe crab genome reveals ancient whole genome duplication

Horseshoe crabs are marine arthropods with a fossil record extending back approximately 450 million years. They exhibit remarkable morphological stability over their long evolutionary history, retaining a number of ancestral arthropod traits, and are often cited as examples of "living fossils." As arthropods, they belong to the Ecdysozoa}, an ancient super-phylum whose sequenced genomes (including insects and nematodes) have thus far shown more divergence from the ancestral pattern of eumetazoan genome organization than cnidarians, deuterostomes, and lophotrochozoans. However, much of ecdysozoan diversity remains unrepresented in comparative genomic analyses. Here we use a new strategy of combined de novo assembly and genetic mapping to examine the chromosome-scale genome organization of the Atlantic horseshoe crab Limulus polyphemus. We constructed a genetic linkage map of this 2.7 Gbp genome by sequencing the nuclear DNA of 34 wild-collected, full-sibling embryos and their parents at a mean redundancy of 1.1x per sample. The map includes 84,307 sequence markers and 5,775 candidate conserved protein coding genes. Comparison to other metazoan genomes shows that the L. polyphemus genome preserves ancestral bilaterian linkage groups, and that a common ancestor of modern horseshoe crabs underwent one or more ancient whole genome duplications (WGDs) ~ 300 MYA, followed by extensive chromosome fusion