Extremal generalized centralizers in matrix algebras

We describe matrices with extremal generalized centralizers over algebraically closed fields.     

General preservers of quasi-commutativity on self-adjoint operators

Let H be a separable Hilbert space and Bsa(H) the set of all bounded linear self-adjoint operators. We say that A,B∈Bsa(H) quasi-commute if there exists a nonzero ξ∈C such that AB=ξBA. Bijective maps on Bsa(H) which preserve quasi-commutativity in both directions are classified.     

Efficient generation and multiplexing of optical orbital angular momentum modes in a ring fiber by using multiple coherent inputs

We propose an approach to efficiently generate and multiplex optical orbital angular momentum (OAM) modes in a fiber with a ring refractive index profile by using multiple coherent inputs from a Gaussian mode. By controlling the phase relationship of the multiple inputs, one can selectively generate OAM modes of different states l. By controlling both the amplitude and phase of the multiple inputs, multiple OAM modes can be generated simultaneously without additional loss coming from multiplexing. We show, by simulation, the generation of OAM modes (OAM state |l|<3) with mode purity greater than 99%. The power loss of generating and multiplexing seven modes is about 35%. A transmitter for an OAM-based mode-division multiplexing system is proposed based on the discrete Fourier transform between the data carried by the multiple inputs and the data carried by the OAM modes. The experimental implementation of the proposed approach could be achieved by integrating ring fiber, multicore fiber, and photonic integrated circuit technology.     

Octave-spanning supercontinuum generation of vortices in an As2S3 ring photonic crystal fiber

We propose As(2)S(3) ring photonic crystal fiber (PCF) for supercontinuum generation of optical vortex modes. Due to the large material index contrast between As(2)S(3) and air holes in the designed ring PCF, there is a two-orders-of-magnitude improvement of the difference between the effective refractive indices of different vortex modes compared with regular ring fiber. The design freedom of PCFs enables a low dispersion (<60 ps/nm/km variation in total) over a 522 nm optical bandwidth. Moreover, the vortex mode has a large nonlinear coefficient of 11.7/W/m at 1550 nm with a small confinement loss of <0.03 dB/m up to 2000 nm. An octave-spanning supercontinuum spectrum of the vortex mode is generated from 1196 to 2418 nm at -20 dB by launching a 120 fs pulse with a 60 W peak power at 1710 nm into a 1 cm long As(2)S(3) ring PCF.     

Isometries of the space of distribution functions with respect to the Kolmogorov-Smirnov metric

In this paper we describe the general forms of surjective isometries of the space of all probability distribution functions on R with respect to the Kolmogorov-Smirnov metric.     

Single-Chain Fv Antibody Fragments Retain Binding Properties of the Monoclonal Antibody Raised Against Peptide P1 of the Human Prion Protein

Prion diseases are incurable neurodegenerative diseases that affect both humans and animals. The infectious agent is a pathogenic form of the prion protein that accumulates in brain as amyloids. Currently, there is neither cure nor reliable preclinical diagnostics on the market available. The growing number of reports shows that passive immunisation is one of the most promising strategies for prion disease therapy, where antibodies against prions may prevent and even cure the infection. Since antibodies are large molecules and, thus, might not be suitable for the therapy, different antibody fragments are a good alternative. Therefore, we have designed and prepared single-chain antibody fragments (scFvs) derived from the PrP^Sc-specific murine monoclonal antibody V5B2. Using a new expression vector pMD204, we produced scFvs in two opposing chain orientations in the periplasm of Escherichia coli. Both recombinant antibody fragments retained the specificity of the parent antibody and one of these exhibited binding properties comparable to the corresponding murine Fab fragments with the affinity in nM range. Our monovalent antibody fragments are of special interest in view of possible therapeutic reagents for prion diseases as well as for development of a new generation of diagnostics.     

Pólya convertibility problem for symmetric matrices

We investigate symmetric (0, 1) matrices on which the permanent is convertible to the determinant by assigning ± signs to their entries. In particular, we obtain several quantitative bounds for the number of nonzero elements of such matrices, including the analog of Gibson’s theorem for symmetric matrices.     

Star partial order on B(H)

Let H be an infinite-dimensional complex Hilbert space and let B(H) be the algebra of all bounded linear operators on (H). In the paper the equivalent definition of the star partial order on B(H), using selfadjoint idempotent operators, is introduced. Also some properties of the generalized concept of order relations on B(H), defined with the help of idempotent operators, are investigated.