Admissible fundamental operators

Let $F$ and $G$ be two bounded operators on two Hilbert spaces. Let their numerical radii be no greater than one. This note investigate when there is a $\Gamma$-contraction $(S,P)$ such that $F$ is the fundamental operator of $(S,P)$ and $G$ is the fundamental operator of $(S^*,P^*)$. Theorem 1 puts a necessary condition on $F$ and $G$ for them to be the fundamental operators of $(S,P)$ and $(S^*,P^*)$ respectively. Theorem 2 shows that this necessary condition is sufficient too provided we restrict our attention to a certain special case. The general case is investigated in Theorem 3. Some of the results obtained for $\Gamma$-contractions are then applied to tetrablock contractions to figure out when two pairs $(F_1, F_2)$ and $(G_1, G_2)$ acting on two Hilbert spaces can be fundamental operators of a tetrablock contraction $(A, B, P)$ and its adjoint $(A^*, B^*, P^*)$ respectively. This is the content of Theorem 4

Text Clustering and Classification Techniques using Data Mining

Text classification is the task of automatically sorting a set of documents into categories from a predefined set. Text Classification is a data mining technique used to predict group membership for data instances within a given dataset. It is used for classifying data into different classes by considering some constrains. Instead of traditional feature selection techniques used for text document classification. A Naive Bayesian model is easy to build, with no complicated iterative parameter estimation which makes it particularly useful for very large datasets. Automated Text categorization and class prediction is important for text categorization to reduce the feature size and to speed up the learning process of classifiers

Revisiting the Gleason-Kahane-$\dot{\text{Z}

This paper presents a fairly general version of the well-known Gleason-Kahane-$\dot{\text{Z}}$elazko (GKZ) theorem in the spirit of a GKZ type theorem obtained recently by Mashreghi and Ransford for Banach spaces. In effect, we characterize a class of linear functionals as point evaluations on the vector space of all polynomials \cl P. We do not make any topological assumptions on \cl P. We then apply this characterization to present a version of the GKZ theorem for a class of metric spaces of complex-valued functions on an open disc centered at the origin. We obtain this result under the assumption of continuity of the linear functional, which we show, with the help of an example, to be a necessary condition for the desired conclusion. Lastly, we use the GKZ theorem for polynomials to obtain a version of the GKZ theorem for weighted Hardy spaces on which the operator of multiplication with the coordinate function $z$ is strictly cyclic

Text Clustering and Classification Techniques- A Review

Text classification is the task of automatically sorting a set of documents into categories from a predefined set. Text Classification is a data mining technique used to predict group membership for data instances within a given dataset. It is used for classifying data into different classes by considering some constrains. Instead of traditional feature selection techniques used for text document classification. A Naive Bayesian model is easy to build, with no complicated iterative parameter estimation which makes it particularly useful for very large datasets. Automated Text categorization and class prediction is important for text categorization to reduce the feature size and to speed up the learning process of classifiers

CCD photometry of the galactic star clusters Be 15, Be 71 and King 1

We present UBV RI CCD photometry of three open star clusters Be 15, Be 71 and King 1 for the fist time. Base on these data, optical colour magnitude diagrams (CMDs) for the stars in the clusters down to V = 22 mag are studied. There are 1408, 1887 and 2485 stars located in the regions of Be 15, Be 71 and King 1 respectively. We also provide estimates of their fundamental parameters such as radius, reddening, distance and age. The radius values for the clusters Be 15, Be 71 and King 1 are 4.5, 3.0 and 4.0 arcmin respectively. The corresponding distances are 3.0±0.3, 3.9±0.4 and 1.9± 0.2 kpc respectively while the ages are log (age)=8.5±0.1, 8.8 ±0.1 and 9.2±0.1 respectively. The red giant clump is clearly visible in the CMDs of cluster King 1