Subgroup S-commutativity degrees of finite groups

The so--called subgroup commutativity degree $sd(G)$ of a finite group $G$ is the number of permuting subgroups $(H,K) \in \mathrm{L}(G) \times \mathrm{L}(G)$, where $\mathrm{L}(G)$ is the subgroup lattice of $G$, divided by $|\mathrm{L}(G)|^2$. It allows us to measure how $G$ is far from the celebrated classification of quasihamiltonian groups of K. Iwasawa. Here we generalize $sd(G)$, looking at suitable sublattices of $\mathrm{L}(G)$, and show some new lower bounds.Comment: 8 pages; to appear in Bull. Belgian Math. Soc. with revision

A note on the invariance in the nonabelian tensor product

In the nonabelian tensor product $G\otimes H$ of two groups $G$ and $H$ many properties pass from $G$ and $H$ to $G\otimes H$. There is a wide literature for different properties involved in this passage. We look at weak conditions for which such a passage may happen.Comment: 4 pages ; to appear in Bull. Korean Math. Soc. jointly with D.E.Otera and C.Tanasi, who added further results of topological natur

Near-infrared spectroscopy study of tourniquet-induced forearm ischaemia in patients with coronary artery disease

Near-Infrared Spectroscopy (NIRS) can be employed to monitor local changes in haemodynamics and oxygenation of human tissues. A preliminary study has been performed in order to evaluate the NIRS transmittance response to induced forearm ischaemia in patients with coronary artery disease (CAD). The population consists in 40 patients with cardiovascular risk factors and angiographically documented CAD, compared to a group of 13 normal subjects. By inflating and subsequently deflating a cuff placed around the patient arm, an ischaemia has been induced and released, and the patients have been observed until recovery of the basal conditions. A custom NIRS spectrometer (IRIS) has been used to collect the backscattered light intensities from the patient forearm throughout the ischaemic and the recovery phase. The time dependence of the near-infrared transmittance on the control group is consistent with the available literature. On the contrary, the magnitude and dynamics of the NIRS signal on the CAD patients show deviations from the documented normal behavior, which can be tentatively attributed to abnormal vessel stiffness. These preliminary results, while validating the performance of the IRIS spectrometer, are strongly conducive towards the applicability of the NIRS technique to ischaemia analysis and to endothelial dysfunction characterization in CAD patients with cardiovascular risk factors

A Survey on Just-Non- Groups

Let𝔛be a class of groups. A group which does not belong to𝔛but all of whose proper quotient groups belong to𝔛is called just-non-𝔛group. The present note is a survey of recent results on the topic with a special attention to topological groups

Recursion relations for Hylleraas three-electron integral

Recursion relations for Hylleraas three-electron integral are obtained in a closed form by using integration by parts identities. Numerically fast and well stable algorithm for the calculation of the integral with high powers of inter-electronic coordinates is presented.Comment: 12 pages, requires RevTeX4, submitted to Phys. Rev.

Corrections to scaling in multicomponent polymer solutions

We calculate the correction-to-scaling exponent $\omega_T$ that characterizes the approach to the scaling limit in multicomponent polymer solutions. A direct Monte Carlo determination of $\omega_T$ in a system of interacting self-avoiding walks gives $\omega_T = 0.415(20)$. A field-theory analysis based on five- and six-loop perturbative series leads to $\omega_T = 0.41(4)$. We also verify the renormalization-group predictions for the scaling behavior close to the ideal-mixing point.Comment: 21 page