Zero modes, gauge fixing, monodromies, ζ\zeta-functions and all that

We discuss various issues associated with the calculation of the reduced functional determinant of a special second order differential operator \boldmath{F}$=-d^2/d\tau^2+\ddot g/g$, $\ddot g\equiv d^2g/d\tau^2$, with a generic function $g(\tau)$, subject to periodic and Dirichlet boundary conditions. These issues include the gauge-fixed path integral representation of this determinant, the monodromy method of its calculation and the combination of the heat kernel and zeta-function technique for the derivation of its period dependence. Motivations for this particular problem, coming from applications in quantum cosmology, are also briefly discussed. They include the problem of microcanonical initial conditions in cosmology driven by a conformal field theory, cosmological constant and cosmic microwave background problems.Comment: 17 pages, to appear in J. Phys. A: Math. Theor. arXiv admin note: substantial text overlap with arXiv:1111.447

Geometric phase shift for detection of gravitational radiation

An effect of geometrical phase shift is predicted for a light beam propagating in the field of a gravitational wave. Gravitational radiation detection experiments are proposed using this new effect, the corresponding estimates being given.Comment: LaTeX2e, 12 p

Non-associative geometry and discrete structure of spacetime

A new mathematical theory, non-associative geometry, providing a unified algebraic description of continuous and discrete spacetime, is introduced.Comment: LATeX2e file, 11 pages, talk given at "Loop's 99 meeting" (Prague, July 27 - August 1, 1999). To appear in Comment. Math. Univ. Carolin

3,5-Bis(4-chloro­benzyl­idene)-1-methyl­piperidin-4-one

In the title mol­ecule, C20H17Cl2NO, the central heterocyclic ring adopts a flattened boat conformation. The dihedral angles between the planar part of this central heterocyclic ring [maximum deviation = 0.004 (1) Å] and the two almost planar side-chain fragments [maximum deviations = 0.015 (1) and 0.019 (1) Å], that include the aromatic ring and bridging atoms, are 18.1 (1) and 18.0 (1)°. In the crystal, pairs of weak inter­molecular C—H⋯O hydrogen bonds link mol­ecules into inversion dimers that form stacks along the a axis. The structure is further stabilized by weak inter­molecular C—H⋯π inter­actions involving the benzene rings

Life after Brexit: United Kingdom Independence Party in post-referendum

The article considers the situation that has developed in British politics after the United Kingdom European Union membership referendum in 2016. The major causes of the crisis of the United Kingdom Independence Party are presented. The estimated characteristic and ways of possible further party development are given

1-Benzyl-3,5-bis­(4-chloro­benzyl­idene)piperidin-4-one

The title compound, C26H21Cl2NO, crystallizes with two symmetry-independent mol­ecules (A and B) in the asymmetric unit. In both mol­ecules, the central heterocyclic ring adopts a sofa conformation. The dihedral angles between the planar part of this central heterocyclic ring [maximum deviations of 0.011 (1) and 0.036 (1) Å in mol­ecules A and B, respectively] and the two almost planar [maximum deviations of 0.020 (1) and 0.008 (1) Å in A and 0.007 (1) and 0.011 (1) in B] side-chain fragments that include the aromatic ring and bridging atoms are 20.1 (1) and 31.2 (1)° in mol­ecule A, and 26.4 (1) and 19.6 (1)° in mol­ecule B. The dihedral angles between the planar part of the heterocyclic ring and the benzyl substituent are 79.7 (1) and 53.2 (1)° in mol­ecules A and B, respectively. In the crystal, weak inter­molecular C—H⋯O hydrogen bonds link the two independent mol­ecules into dimers

Quasigroups, Asymptotic Symmetries and Conservation Laws in General Relativity

A new quasigroup approach to conservation laws in general relativity is applied to study asymptotically flat at future null infinity spacetime. The infinite-parametric Newman-Unti group of asymptotic symmetries is reduced to the Poincar\'e quasigroup and the Noether charge associated with any element of the Poincar\'e quasialgebra is defined. The integral conserved quantities of energy-momentum and angular momentum are linear on generators of Poincar\'e quasigroup, free of the supertranslation ambiguity, posess the flux and identically equal to zero in Minkowski spacetime.Comment: RevTeX4, 5 page