Calculations at the prime 2

1978 ◽  
pp. 250-292
Author(s):  
Zbigniew Fiedorowicz ◽  
Stewart Priddy
Keyword(s):  
Prime 2

scholarly journals 434 The study design of two trials of dupilumab in patients with prurigo nodularis inadequately controlled with topical therapies: LIBERTY PN PRIME and PRIME 2

2021 ◽  
Vol 141 (5) ◽  
pp. S75
Author(s):  
G. Yosipovitch ◽  
N. Mollanazar ◽  
S. Ständer ◽  
S.G. Kwatra ◽  
J. Luo ◽  
...  
Keyword(s):  
Study Design ◽  
Prurigo Nodularis ◽  
Prime 2

scholarly journals Quantum Field Theory over $\mathbb{F}_q$

10.37236/589 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Oliver Schnetz
Keyword(s):  
Field Theory ◽  
Perturbation Series ◽  
The Other ◽  
Field Theories ◽  
Roots Of Unity ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Feynman Rules ◽  
Graph Hypersurfaces ◽  
Prime 2

We consider the number $\bar N(q)$ of points in the projective complement of graph hypersurfaces over $\mathbb{F}_q$ and show that the smallest graphs with non-polynomial $\bar N(q)$ have 14 edges. We give six examples which fall into two classes. One class has an exceptional prime 2 whereas in the other class $\bar N(q)$ depends on the number of cube roots of unity in $\mathbb{F}_q$. At graphs with 16 edges we find examples where $\bar N(q)$ is given by a polynomial in $q$ plus $q^2$ times the number of points in the projective complement of a singular K3 in $\mathbb{P}^3$. In the second part of the paper we show that applying momentum space Feynman-rules over $\mathbb{F}_q$ lets the perturbation series terminate for renormalizable and non-renormalizable bosonic quantum field theories.

scholarly journals Structures of mono-unsaturated triacylglycerols. IV. The highest melting β′-2 polymorphs of trans-mono-unsaturated triacylglycerols and related saturated TAGs and their polymorphic stability

2008 ◽  
Vol 64 (2) ◽  
pp. 249-259 ◽  
Author(s):  
Jan B. van Mechelen ◽  
Rene Peschar ◽  
Henk Schenk
Keyword(s):  
Powder Diffraction Data ◽  
Asymmetric Unit ◽  
Double Chain ◽  
Molecular Conformations ◽  
X Ray ◽  
Acyl Chains ◽  
Independent Molecules ◽  
The Difference ◽  
Polymorphic Stability ◽  
Prime 2

The β_1^{\prime}-2 crystal structures of a series of mixed-chain saturated and trans-mono-unsaturated triacylglycerols containing palmitoyl, stearoyl and elaidoyl acyl chains have been solved from high-resolution powder diffraction data, from synchrotron as well as laboratory X-ray sources. The structures crystallized in the space group I2 with two independent molecules forming a dimer in the asymmetric unit, and packed in double-chain length layers. Unlike the corresponding β-2 structures the solved β_1^{\prime}-2 structures have different molecular conformations for the symmetric and the asymmetric mixed triacylglycerols, both with the sn-2 chain in a leg position of the chair-shaped conformation. A transformation to the β-2 structure with the sn-2 chain in the back position is complicated and unlikely to take place in the solid state. A novel β′-2 polymorph of PSS has been crystallized and its structure has been solved. The melting point (239 K) of this so-called β_0^{\prime}-2 polymorph is 2 K above that of the β_1^{\prime}-2 polymorph and almost equal to that of the β-2 polymorph of PSS. The difference in packing of the β_0^{\prime}-2 versus β_1^{\prime}-2 structure explains the slow β_1^{\prime}-2 to β_0^{\prime}-2 phase transition. The transition is strikingly similar to the β2-3 to β1-3 transition in cis-mono-unsaturated triacylglycerols.

Stable summands of U(n)

1997 ◽  
Vol 127 (5) ◽  
pp. 963-973 ◽  
Author(s):  
M. C. Crabb ◽  
J. R. Hubbuck ◽  
J. A. W. McCall
Keyword(s):  
Homotopy Type ◽  
Unitary Group ◽  
Stable Homotopy ◽  
Finite Complex ◽  
Special Unitary Group ◽  
Prime 2

SynopsisThe special unitary group SU(n) has the stable homotopy type of a wedge of n − 1 finite complexes. The ‘first’ of these complexes is ΣℂPn–1, which is well known to be indecomposable at the prime 2 whether n is finite or infinite. We show that the ‘second’ finite complex is again indecomposable at the prime 2 when n is finite, but splits into a wedge of two pieces when n is infinite.

The non-existence of odd primary Arf invariant elements in stable homotopy

1978 ◽  
Vol 83 (3) ◽  
pp. 429-443 ◽  
Author(s):  
Douglas C. Ravenel
Keyword(s):  
Spectral Sequence ◽  
Stable Homotopy ◽  
Homotopy Groups ◽  
Homotopy Groups Of Spheres ◽  
Stable Homotopy Groups ◽  
Arf Invariant ◽  
Prime 2

In this paper we will show that certain elements of order p (p an odd prime) on the 2-line of the Adams-Novikov spectral sequence support non-trivial differentials and therefore do not detect elements in the stable homotopy groups of spheres. These elements are analogous to the so-called Arf invariant elements of order 2, hence the title. However, it is evident that the methods presented here do not extend to the prime 2.

scholarly journals Synthesis of 4′, 5′-Dimethoxy-3, 4, 5, 6, 7, 8-hexahydro-(1, 2: 1′, 2′-benzoquinolicine)

1951 ◽  
Vol 71 (12) ◽  
pp. 1341-1343 ◽  
Author(s):  
Shigehiko Sugasawa ◽  
San-ya Akahoshi ◽  
Michihiro Yamada
Keyword(s):  
Prime 2
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