Abstract:
Numerical simulation of the content of unburned carbon in fly ash on the 300MW tangentially pulverized coal fired boiler is performed by the numerical simulation software COALFIRE, which is based on international advanced TASCFLOW software platform. Firstly, take the result of calculation of number value as the sample, and then set up the support vector machine model of unburned carbon content on the boiler. The relative error between the predicted output and measured value is 0.00186%, which proves the modeling is good for the unburned carbon in fly ash predict.

Abstract:
A. Casson defined an intersection number invariant which can be roughly thought of as the number of conjugacy classes of irreducible representations of $\pi_1(Y)$ into $SU(2)$ counted with signs, where $Y$ is an oriented integral homology 3-sphere. X.S. Lin defined an similar invariant (signature of a knot) to a braid representative of a knot in $S^3$. In this paper, we give a natural generalization of the Casson-Lin's invariant to be (instead of using the instanton Floer homology) the symplectic Floer homology for the representation space (one singular point) of $\pi_1(S^3 \setminus K)$ into $SU(2)$ with trace-free along all meridians. The symplectic Floer homology of braids is a new invariant of knots and its Euler number of such a symplectic Floer homology is the negative of the Casson-Lin's invariant.

Abstract:
We define an integer graded symplectic Floer cohomology and a spectral sequence which are new invariants for monotone Lagrangian sub-manifolds and exact isotopies. Such an integer graded Floer cohomology is an integral lifting of the usual Floer-Oh cohomology with $Z_{\Si (L)}$ grading. As one of applications of the spectral sequence, we offer an affirmative answer to an Audin's question for oriented, embedded, monotone Lagrangian tori, i.e. $\Si (L) = 2$.

Abstract:
To an integral homology 3-sphere $Y$, we assign a well-defined $\Z$-graded (monopole) homology $MH_*(Y, I_{\e}(\T; \e_0))$ whose construction in principle follows from the instanton Floer theory with the dependence of the spectral flow $I_{\e}(\T; \e_0)$, where $\T$ is the unique U(1)-reducible monopole of the Seiberg-Witten equation on $Y$ and $\e_0$ is a reference perturbation datum. The definition uses the moduli space of monopoles on $Y \x \R$ introduced by Seiberg-Witten in studying smooth 4-manifolds. We show that the monopole homology $MH_*(Y, I_{\e}(\T; \e_0))$ is invariant among Riemannian metrics with same $I_{\e}(\T; \e_0)$. This provides a chamber-like structure for the monopole homology of integral homology 3-spheres. The assigned function $MH_{SWF}: \{I_{\e}(\T; \e_0)\} \to \{MH_*(Y, I_{\e}(\T; \e_0))\}$ is a topological invariant (as Seiberg-Witten-Floer Theory).

Abstract:
In this paper, we compute the symplectic Floer homology of the figure eight knot. This provides first nontrivial knot with trivial symplectic Floer homology.

Abstract:
We develop a method of calculation for the symplectic Floer homology of composite knots. The symplectic Floer homology of knots defined in \cite{li} naturally admits an integer graded lifting, and it formulates a filtration and induced spectral sequence. Such a spectral sequence converges to the symplectic homology of knots in \cite{li}. We show that there is another spectral sequence which converges to the $\Z$-graded symplectic Floer homology for composite knots represented by braids.

Abstract:
We prove the Chern-Weil formula for SU(n+1)-singular connections over the complement of an embedded oriented surface in smooth four manifolds. The expression of the representation of a number as a sum of nonvanishing squares is given in terms of the representations of a number as a sum of squares. Using the number theory result, we study the irreducible SU(n+1)-representations of the fundamental group of the complement of an embedded oriented surface in smooth four manifolds.

Abstract:
We define an integer graded symplectic Floer cohomology and a Fintushel-Stern type spectral sequence which are new invariants for monotone Lagrangian sub-manifolds and exact isotopes. The Z-graded symplectic Floer cohomology is an integral lifting of the usual Z_Sigma(L)-graded Floer-Oh cohomology. We prove the Kunneth formula for the spectral sequence and an ring structure on it. The ring structure on the Z_Sigma(L)-graded Floer cohomology is induced from the ring structure of the cohomology of the Lagrangian sub-manifold via the spectral sequence. Using the Z-graded symplectic Floer cohomology, we show some intertwining relations among the Hofer energy e_H(L) of the embedded Lagrangian, the minimal symplectic action sigma(L), the minimal Maslov index Sigma(L)$ and the smallest integer k(L, phi$ of the converging spectral sequence of the Lagrangian L.

Abstract:
We show that there is a well-defined cap-product structure on the Fintushel-Stern spectral sequence. Hence we obtain the induced cap-product structure on the ${\BZ}_8$-graded instanton Floer homology. The cap-product structure provides an essentially new property of the instanton Floer homology, from a topological point of view, which multiplies a finite dimensional cohomology class by an infinite dimensional homology class (Floer cycles) to get another infinite dimensional homology class.

Abstract:
With the growth of the internet and open software, there are additional software developers available from the open community that can participate in the development of software application systems. Aiming to leverage these resources, a new development model, CFI (call for implementation), is proposed. The basic idea of CFI is to publish some part of a software project to the open community, whole or part, in certain phases of the software development lifecycle to call for implementation. This paper discusses the basic concept and method for a software development process in CFI mode. Two different modes of CFI with different granularities are analyzed. And one of the CFI modes, fine-granularity-CFI mode, is thoroughly discussed including the main methods and basic steps. To verify the ideas a pilot project, an online store system, is built up with the CFI development process. The online store system takes the traditional Model-View-Control architecture and some common technologies such as Struts, Hibernate, Spring are used. The result shows that this new kind of software development mode is feasible though there are many problems that are still requiring further study.