179 research outputs found
Admissible fundamental operators
Let and be two bounded operators on two Hilbert spaces. Let their
numerical radii be no greater than one. This note investigate when there is a
-contraction such that is the fundamental operator of
and is the fundamental operator of . Theorem 1 puts a
necessary condition on and for them to be the fundamental operators of
and 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 -contractions are then applied to tetrablock
contractions to figure out when two pairs and acting
on two Hilbert spaces can be fundamental operators of a tetrablock contraction
and its adjoint 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-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 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 3.0Β±0.3, 3.9Β±0.4 and 1.9Β± 0.2 kpc respectively while the ages are log (age)=8.5Β±0.1, 8.8 Β±0.1 and 9.2Β±0.1 respectively. The red giant clump is clearly visible in the CMDs of cluster King 1
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