In this paper, we prove that for the oper stratification of de Rham moduli space $M_{\mathrm{dR}}(X,r)$, closed stratum is unique minimal with dimension $r^2(g-1)+g+1$, and open dense consisting irreducible flat bundles stable underlying vector maximal stratum.

In the current paper, consider the fuzzy normed linear space $(X,N)$ which is defined by Bag and Samanta. First, we construct a new fuzzy topology on this space and show that these spaces are Hausdorff locally convex fuzzy topological vector space. Some necessary and sufficient conditions are established to illustrate that the presented fuzzy topology is equivalent to two previously studied fuz...

Let $(X,d)$ be an infinite compact metric space, let $(B,parallel . parallel)$ be a unital Banach space, and take $alpha in (0,1).$ In this work, at first we define the big and little $alpha$-Lipschitz vector-valued (B-valued) operator algebras, and consider the little $alpha$-lipschitz $B$-valued operator algebra, $lip_{alpha}(X,B)$. Then we characterize its second dual space.

We propose a transformation from the multi-class SVM classification problem to the single-class SVM problem which is more convenient for optimization. The proposed transformation is based on simplifying the original problem and employing the Kesler construction which can be carried out by the use of properly defined kernel only. The experiments conducted indicate that the proposed method is com...

—The problem of determination of a minimal polynomial basis of a rational vector space is the starting point of many control analysis, synthesis and design techniques. In this paper, we propose a new algorithm for the computation of a minimal polynomial basis of the left kernel of a given polynomial matrix F (s). The proposed method exploits the structure of the left null space of generalized W...

The standard Support Vector Machine formulation does not provide its user with the ability to explicitly control the number of support vectors used to define the generated classifier. We present a modified version of SVM that allows the user to set a budget parameter B and focuses on minimizing the loss attained by the B worst-classified examples while ignoring the remaining examples. This idea...

We propose a transformation from the multi-class SVM classification problem to the single-class SVM problem which is more convenient for optimization. The proposed transformation is based on simplifying the original problem and employing the Kesler construction which can be carried out by the use of properly defined kernel only. The experiments conducted indicate that the proposed method is com...

We show that the character space of the vector-valued Lipschitz algebra $Lip^{alpha}(X, E)$ of order $alpha$ is homeomorphic to the cartesian product $Xtimes M_E$ in the product topology, where $X$ is a compact metric space and $E$ is a unital commutative Banach algebra. We also characterize the form of each character on $Lip^{alpha}(X, E)$. By appealing to the injective tensor product, we the...

We first put forward a new algorithm of reduced support vector regression (RSVR) and adopt a new approach to make a similar mathematical form as that of support vector classification. Then we describe a fast training algorithm for simplified support vector regression, sequential minimal optimization (SMO) which was used to train SVM before. Experiments prove that this newmethod converges consid...