Resolvable t-Designs

A general group theoretic approach is used to find resolvable designs. Infinitely many resolvable 3-designs are obtained where each is block transitive under some PSL(2, p ^f ) or PGL(2, p ^f ). Some known Steiner 5-designs are assembled from such resolvable 3-designs such that they are also resolvable. We give some visualizations of Steiner systems which make resolvability obvious.     

Literatur

Ohne Zusammenfassung     

A Steiner 5-Design on 36 Points

Up to now, all known Steiner 5-designs are on q + 1 points where q 3 (mod 4) is a prime power and the design is admitting PSL(2, q) as a group of automorphisms. In this article we present a 5-(36,6,1) design admitting PGL(2, 17) × C ₂ as a group of automorphisms. The design is unique with this automorphism group and even for the commutator group PSL(2, 17) × Id ₂ of this automorphism group there exists no further design with these parameters. We present the incidence matrix of t-orbits and block orbits.     

Quantum mechanics without the position operator

The formula for the differential scattering cross section in quantum mechanics is derived without the usual assumption that the square of the -function is a position probability density for particles. It is argued that position, like time, may be basically a macroscopic parameter rather than a random variable for microparticles.This research was partly supported by a grant from the NSERC.     

A novel approach for the sequential backbone assignment of larger proteins: selective intra-HNCA and DQ-HNCA

Sequential assignment of backbone resonances in larger proteins can be achieved by recording two or more complementary triple-resonance NMR spectra of deuterated proteins. For such proteins, higher fields and experiments based on the TROSY method provide the needed resolution and sensitivity. However, increasingly rapid carbonyl relaxation at the high magnetic field strengths required by TROSY techniques renders assignment strategies that rely on sequential HN(CO)CA-type experiments much less efficient for proteins >40 kDa. Here we present two complementary new experiments, which allow backbone assignments with good sensitivity for larger deuterated proteins. A 3D intra-HNCA experiment provides uniquely the intraresidue connection, while a 3D DQ-HNCA experiment, which detects a (13)C(alpha)(i)()(13)C(alpha)(i-1)() double-quantum (DQ) coherence, contains the sequential information. The experiments work well at high magnetic fields, and their utility is demonstrated on a protein with a correlation time of 28 ns ( approximately 60 kDa). For larger proteins the sensitivity is predicted through simulations which suggest that the approach should work for proteins with correlation times >50 ns.