Linear operators and their spectra with applications to quantum mechanics.

From lectures given at the New York university Institute for mathematica and mechanics, by R. Cournat and others.

Hodgkin's lymphoma cell lines express a fusion protein encoded by intergenically spliced mRNA for the multilectin receptor DEC-205 (CD205) and a novel C-type lectin receptor DCL-1

Classic Hodgkin's lymphoma (HL) tissue contains a small population of morphologically distinct malignant cells called Hodgkin and Reed-Sternberg (HRS) cells, associated with the development of HL. Using 3'-rapid amplification of cDNA ends ( RACE) we identified an alternative mRNA for the DEC-205 multilectin receptor in the HRS cell line L428. Sequence analysis revealed that the mRNA encodes a fusion protein between DEC-205 and a novel C-type lectin DCL-1. Although the 7.5-kb DEC-205 and 4.2-kb DCL-1 mRNA were expressed independently in myeloid and B lymphoid cell lines, the DEC-205/DCL-1 fusion mRNA (9.5 kb) predominated in the HRS cell lines ( L428, KM-H2, and HDLM-2). The DEC-205 and DCL-1 genes comprising 35 and 6 exons, respectively, are juxtaposed on chromosome band 2q24 and separated by only 5.4 kb. We determined the DCL-1 transcription initiation site within the intervening sequence by 5'-RACE, confirming that DCL-1 is an independent gene. Two DEC-205/DCL-1 fusion mRNA variants may result from cotranscription of DEC-205 and DCL-1, followed by splicing DEC-205 exon 35 or 34-35 along with DCL-1 exon 1. The resulting reading frames encode the DEC-205 ectodomain plus the DCL-1 ectodomain, the transmembrane, and the cytoplasmic domain. Using DCL-1 cytoplasmic domain-specific polyclonal and DEC-205 monoclonal antibodies for immunoprecipitation/Western blot analysis, we showed that the fusion mRNA is translated into a DEC-205/DCL-1 fusion protein, expressed in the HRS cell lines. These results imply an unusual transcriptional control mechanism in HRS cells, which cotranscribe an mRNA containing DEC-205 and DCL-1 prior to generating the intergenically spliced mRNA to produce a DEC-205/DCL-1 fusion protein.

Knowledge beliefs and attitudes of squash venue operators relating to use of protective eyewear

Sports venues are in a position to potentially influence the safety practices of their patrons. This study examined the knowledge, beliefs and attitudes of venue operators that could influence the use of protective eyewear by squash players. A 50% random sample of all private and public squash venues affiliated with the Victorian Squash Federation in metropolitan Melbourne was selected. Face-to-face interviews were conducted with 15 squash venue operators during August 2001. Interviews were transcribed and content and thematic analyses were performed. The content of the interviews covered five topics: (1) overall injury risk perception, (2) eye injury occurrence, (3) knowledge, behaviors, attitudes and beliefs associated with protective eyewear, (4) compulsory protective eyewear and (5) availability of protective eyewear at venues. Venue operators were mainly concerned with the severe nature of eye injuries, rather than the relatively low incidence of these injuries. Some venue operators believed that players should wear any eyewear, rather than none at all, and believed that more players should use protective eyewear. Generally, they did not believe that players with higher levels of experience and expertise needed to wear protective eyewear when playing. Only six venues had at least one type of eyewear available for players to hire or borrow or to purchase. Operators expressed a desire to be informed about correct protective eyewear. Appropriate protective eyewear is not readily available at squash venues. Better-informed venue operators may be more likely to provide suitable protective eyewear.

Operational Rules for a Mixed Operator of the Erdélyi-Kober Type

2000 Mathematics Subject Classification: 26A33 (main), 44A40, 44A35, 33E30, 45J05, 45D05

Herz-Type Hardy Spaces for the Dunkl Operator on the Real Line

2000 Mathematics Subject Classification: Primary 46F12, Secondary 44A15, 44A35

Smoothness Properties of Solutions of Caputo-Type Fractional Differential Equations

Mathematics Subject Classification: 26A33, 34A25, 45D05, 45E10

On a Class of Fractional Type Integral Equations in Variable Exponent Spaces

2000 Mathematics Subject Classification: 45A05, 45B05, 45E05,45P05, 46E30

Fixed Point Theorems of Kannan Type for Cyclical Contractive Conditions

The main aim of this paper is to obtain fixed point theorems for Kannan and Zamfirescu operators in the presence of cyclical contractive condition. A method for approximation of the fixed points is also provided, for which both a priori and a posteriori error estimates are given. Our results generalize, unify and extend several important fixed points theorems in literature. In order to illustrate the efficiency of our generalizations five significant examples are also given.

Lp Microlocal Properties for Multi-Quasi-Elliptic Pseudodifferential Operators

2010 Mathematics Subject Classification: Primary 35S05; Secondary 35A17.

Windowed-Wigner Representations, Interferences and Operators

2010 Mathematics Subject Classification: 42B10, 47A07, 35S05.

Little G. T. for lp-lattice summing operators

2000 Mathematics Subject Classification: 46B28, 47D15.

Non-Gaussian distribution of collective operators in quantum spin chains

We numerically analyse the behavior of the full distribution of collective observables in quantum spin chains. While most of previous studies of quantum critical phenomena are limited to the first moments, here we demonstrate how quantum fluctuations at criticality lead to highly non-Gaussian distributions. Interestingly, we show that the distributions for different system sizes collapse on thesame curve after scaling for a wide range of transitions: first and second order quantum transitions and transitions of the Berezinskii–Kosterlitz–Thouless type. We propose and analyse the feasibility of an experimental reconstruction of the distribution using light–matter interfaces for atoms in optical lattices or in optical resonators.

Homogenization of the p-Laplacian with nonlinear boundary condition on critical size particles: Identifying the strange term for the some non smooth and multivalued operators

We extend previous papers in the literature concerning the homogenization of Robin type boundary conditions for quasilinear equations, in the case of microscopic obstacles of critical size: here we consider nonlinear boundary conditions involving some maximal monotone graphs which may correspond to discontinuous or non-Lipschitz functions arising in some catalysis problems.