The maximum number of q-cliques in a graph with no p-clique

Let $\text{?(n, p, q)}$ be the maximum possible number of q-cliques among all graphs on n nodes with no p-clique. Turán, in 1941, determined $\text{?(n, p, 2)}$ for all n and p. For each n and p, he found the unique graph which attains this maximum. In this paper we determine $\text{?(n, p, q)}$ for all values of n, p and q. We show that, except for the trivial case 1 ? n < q, Turán's graph is the unique graph which attains the maximum $\text{?(n, p, q)}$ for all q such that 1 < q < p.     

Group representations in certain lattices of propositions

Preparatory to a possible in-depth study of dynamical symmetries in quantal systems, this paper establishes the fundamental aspects of group representations in complete orthocomplemented weakly modular lattices (CROC's). Several related results, pertaining to the structure, direct sum decomposition, and invariance of CROC's, are also found.     

Harmonische Analysis bei Aussagenkalkülen

Ohne ZusammenfassungHerrn Prof. Wolfgang Gröbner zum 70. Geburtstag gewidmet.Diese Arbeit wurde im Rahmen eines Alexander v. Humboldtstipendiums verfaßt. Herrn Prof. Kurt Schütte sei für seine beratende Tätigkeit und sein Interesse an dieser Arbeit herzlichster Dank ausgesprochen.     

Products of Michael spaces and completely metrizable spaces

For disjoint subsets of the Michael space has the topology obtained by isolating the points in and letting the points in retain the neighborhoods inherited from . We study normality of the product of Michael spaces with complete metric spaces. There is a ZFC example of a Lindelöf Michael space , of minimal weight , with Lindelöf but with not normal. ( denotes the countable product of a discrete space of cardinality .) If denotes , the normality of implies the normality of for any complete metric space (of arbitrary weight). However, the statement `` normal implies normal' is axiom sensitive.

     

Wagner-Meerwein skeletal rearrangement of 3-spiroannulated 6,8a-epoxy- and 6,8a;7,8-diepoxyisoquinolines (3-aza-11-oxatricyclo[6.2.1.0(1,6)]undec-9-enes). Isolation and identification of 5-aza-2-oxatricyclo[6.2.1.0(3,9)]undec-3-enes

The reactions of 3-acetyl-3-aza-11-oxatricyclo[6.2.1.0(1,6)]undec-9-ene and its 9,10-epoxy derivative with bromine and Ac(2)O/BF(3).OEt(2) under different conditions were studied. Unusual products of Wagner-Meerwein rearrangement bearing the olefin fragment (5-aza-2-oxatricyclo[6.2.1.0(3,9)]undecen-3-enes) were isolated and characterized by X-ray analysis.     

Some results about geometric Whittaker model

Let G be an algebraic reductive group over a field of positive characteristic. Choose a parabolic subgroup P in G and denote by U its unipotent radical. Let X be a G-variety. The purpose of this paper is to give two examples of a situation in which the functor of averaging of ?-adic sheaves on X with respect to a generic character commutes with Verdier duality. Namely, in the first example we take X to be an arbitrary G-variety and we prove the above property for all -equivariant sheaves on X where is the unipotent radical of an opposite parabolic subgroup; in the second example we take X=G and we prove the corresponding result for sheaves which are equivariant under the adjoint action (the latter result was conjectured by B. C. Ngo who proved it for G=GL(n)). As an application of the proof of the first statement we reprove a theorem of N. Katz and G. Laumon about local acyclicity of the kernel of the Fourier-Deligne transform.     

Reconstruction of protein structures from a vectorial representation

We show that the contact map of the native structure of globular proteins can be reconstructed starting from the sole knowledge of the contact map's principal eigenvector, and present an exact algorithm for this purpose. Our algorithm yields a unique contact map for all 221 globular structures of PDBselect25 of length N相似文献   

Polarization squeezing of continuous variable stokes parameters

We report the first direct experimental characterization of continuous variable quantum Stokes parameters. We generate a continuous wave light beam with more than 3 dB of simultaneous squeezing in three of the four Stokes parameters. The polarization squeezed beam is produced by mixing two quadrature squeezed beams on a polarizing beam splitter. Depending on the squeezed quadrature of these two beams the quantum uncertainty volume on the Poincaré sphere becomes a "cigarlike" or "pancakelike" ellipsoid.     

Two-dimensional type I quadratic spatial solitons in KNbO(3) near noncritical phase matching

Experiments on the properties of quadratic, two-dimensional spatial soliton properties in KNbO(3) near and at noncritical phase matching (NCPM) are reported. The NCPM geometry leads to unique features such as a large angular bandwidth for soliton generation, weak dependence of soliton composition on intensity and incidence angle, and unique multisoliton-generation properties.     

Synthesis of dicobalt hexacarbonyl 5-p-tolylethynyl-2'-deoxyuridine

Reactions of 5-p-tolylethynyl-2'-deoxyuridine and 3',5'-di-O-acetyl-5-p-tolylethynyl-2'-deoxyuridine with Co2(CO)8 in THF gave 5-p-tolC2[CO2(CO)6]-2'-deoxyuridine and 3',5'-di-O-acetyl-5-p-tolC2[CO2(CO)6]-2'-deoxyuridine (92 and 66%).