Collineation group as a subgroup of the symmetric group

Let ψ be the projectivization (i.e., the set of one-dimensional vector subspaces) of a vector space of dimension ≥ 3 over a field. Let H be a closed (in the pointwise convergence topology) subgroup of the permutation group $\mathfrak{S}_\psi $ of the set ψ. Suppose that H contains the projective group and an arbitrary self-bijection of ψ transforming a triple of collinear points to a non-collinear triple. It is well known from [Kantor W.M., McDonough T.P., On the maximality of PSL(d+1,q), d ≥ 2, J. London Math. Soc., 1974, 8(3), 426] that if ψ is finite then H contains the alternating subgroup $\mathfrak{A}_\psi $ of $\mathfrak{S}_\psi $ . We show in Theorem 3.1 that H = $\mathfrak{S}_\psi $ , if ψ is infinite.     

Double beta decay: A problem of particle, nuclear and atomic physics

A brief review of recent progress in the field of double beta decay is presented. Different aspects from particle, nuclear and atomic physics of both two-neutrino (2νββ) and neutrinoless (0νββ) modes of the double β decay are discussed. It is argued that the R-parity violating supersymmetry (SUSY) contributes to the 0νββ-decay predominantly via charged pion-exchange between decaying nucleons. Further, a problem of reliable determination of the 0νββ-decay nuclear matrix elements (NMEs) is addressed. It is manifested that the uncertainty associated with the calculation of the 0νββ-decay NMEs can be diminished by suitably chosen nuclear probes. A new possibility for the study of lepton number non-conservation is proposed, namely oscillations plus deexcitations of neutral atoms. A phenomenological analysis of this process leads to a resonant enhancement of the neutrinoless double electron capture, that has a Breit-Wigner form.     

Dialysis-assisted two-dimensional gel electrophoresis

2-DE is an important tool in proteomics research. However, intrinsic gel-to-gel variability of 2-DE often masks the biological differences between the samples and compromises quantitative comparison of protein expression levels. Here, we describe a modification of 2-DE that results in improved matching and quantification of proteins. This was accomplished by performing IEF of two samples in two IPG strips separated by a dialysis membrane. After IEF running, the strips were separated and the SDS-PAGE dimension was accomplished on two individual gels. After gel staining with CBB, ImageMaster 2D Platinum software (Amersham) was used for spot detection and quantification. Analysis of protein extracts from C2C12 myoblasts by this method resulted in 99% spot-matching efficiency and CV in stain intensity (% volume) was less than 0.5 for 98% of spots. We conclude that this technique, called dialysis-assisted gel electrophoresis, gives superior spot matching and quantitative reproducibility compared to IEF conducted on separate strips.     

How many matrices can be spectrally balanced simultaneously?

We prove that any ? positive definite d × d matrices, M₁,...,M_?, of full rank, can be simultaneously spectrally balanced in the following sense: for any k < d such that ? ≤ \(\ell \leqslant \left\lfloor {\frac{{d - 1}}{{k - 1}}} \right\rfloor \), there exists a matrix A satisfying \(\frac{{{\lambda _1}\left( {{A^T}{M_i}A} \right)}}{{Tr\left( {{A^T}{M_i}A} \right)}} < \frac{1}{k}\) 1/k for all i, where λ₁(M) denotes the largest eigenvalue of a matrix M. This answers a question posed by Peres, Popov and Sousi ([PPS13]) and completes the picture described in that paper regarding sufficient conditions for transience of self-interacting random walks. Furthermore, in some cases we give quantitative bounds on the transience of such walks.     

The first example of an intramolecular Diels-Alder furan (IMDAF) reaction of iminium salts and its application in a short and simple synthesis of the isoindolo[1,2-a]isoquinoline core of the jamtine and hirsutine alkaloids

1-(2-Furyl)-3,4-dihydroisoquinolines, easily prepared from readily available phenethylamines, undergo tandem alkylation/[4+2]-cycloaddition with allyl halides. The reaction proceeds via 2-allyl-1-furyl-3,4-dihydroisoquinolinium salt formation and subsequent intramolecular exo-Diels-Alder reaction of furan with the allyl fragment (IMDAF reaction). The adducts formed include the basic structural element of the isoindolo[1,2-a]isoquinoline alkaloids jamtine and hirsutine.     

Induced hyper-valence of carbon in metal:fluorocarbon complexes

Charge-transfer in combination with geometric features induces a pentavalent state of the carbon atom in metastable super-fluorinated alkali-metal compounds, M:C2F7 (M = K to Cs).     

Long-lived coherent oscillations of the femtosecond transients in cyanobacterial photosystem I

The pulsed excitation of electronic levels coupled to specific nuclear modes by a 26 fs laser pulse at 706 nm creates a wavepacket in the nuclear space of photopystem I (PS I) of Synechocystis sp. strain PCC 6803 both in the ground state and in the one-exciton manifold. Fourier transform of transient decay curves shows several low frequency peaks. The most prominent Power Spectral Density (PSD) peaks are at omega = 49 cm(-1) and omega = 88 cm(-1). The peculiarity of the coherent wavepacket in the PS I of S. sp. strain PCC 6803 is the unique, long-lived 49 cm(-1) and 88 cm(-1) oscillations with decay times up to 10 ps. It was suggested that such a long-lived coherence is determined by a contribution of the ground state wavepacket. The dependence of these two PSD peaks on the probe wavelength resembles the profile of the transient absorption spectra of PS I. The pump-probe signal in the Soret region reflects the dynamics of the ground state wavepacket created by pulsed excitation of the Q(y)-band. It was shown that the multimode Brownian oscillator model allows a quantitative fit of the oscillatory patterns of the pump-probe signal to be obtained.     

Characteristic functions of Banach limits

We study the functions {B(rn(t))}, where B is a Banach limit and {rn(t)} are Rademacher functions.