We examine the notion of α-strong singularity for subfactors of a II1 factor, which is a metric quantity that relates the distance of a unitary to a subalgebra with the distance between that subalgebra and its unitary conjugate. Using work of Popa, Sinclair, and Smith, we show that there exists an absolute constant 0 < c < 1 such that all subfactors are c-strongly singular. Under additional hyp...

Using the Gaussian 2003 software and MP2 /6 – 311+ G method for the C2H4 : O2, CO:Cl2 andCO2:CO2 pairs and MP2/6-311++G** method for the CO2:H2O pair and B3lyp/6-31G methodfor the O2:O2 pair the optimized interaction energies between two considered pair molecules ofstudied gases(C2H4:O2, CO:Cl2, CO2:H2O, O2:O2 and CO2:CO2 pairs) as a function of thedistances between the centers of two considere...

8 G. Salton, " A simple blueprint for automatic Boolean query processing " , Information Another potential solution to this problem comes from recognising that a retrieved set of documents can usually be grouped into collections covering only a few subjects. It might be possible to cluster the retrieved documents, showing the user a sample from each cluster. If the user is interested in one of ...

We provide a new proof of Brylawski’s formula for the Tutte polynomial of the tensor product of two matroids. Our proof involves extending Tutte’s formula, expressing the Tutte polynomial using a calculus of activities, to all polynomials involved in Brylawski’s formula. The approach presented here may be used to show a signed generalization of Brylawski’s formula, which may be used to compute ...

An analytical equation of state was applied to calculate the thermodynamic properties for argon.The equation of state is that of Song and Mason. It is based on a statistical-mechanical perturbationtheory of the hard convex bodies and can be written as fifth-order polynomial in the density. Thereexist three temperature-dependent parameters: the second virial coefficient, an effective molecularvo...