scholarly journals Spacetimes with continuous linear isotropies II: boosts

2021 ◽  
Vol 53 (6) ◽  
Author(s):  
M. A. H. MacCallum
Keyword(s):  
Local Group ◽  
Riemann Tensor ◽  
Conformally Flat ◽  
Continuous Linear ◽  
Type D ◽  
Flat Spacetimes ◽  
Boost Invariance ◽  
Derivatives Of ◽  
Petrov Type D

AbstractConditions are found which ensure that local boost invariance (LBI), invariance under a linear boost isotropy, implies local boost symmetry (LBS), i.e. the existence of a local group of motions such that for every point P in a neighbourhood there is a boost leaving P fixed. It is shown that for Petrov type D spacetimes this requires LBI of the Riemann tensor and its first derivative. That is also true for most conformally flat spacetimes, but those with Ricci tensors of Segre type [1(11,1)] may require LBI of the first three derivatives of curvature to ensure LBS.

On colliding waves that develop time–like singularities: a new class of solutions of the Einstein–Maxwell equations

1987 ◽  
Vol 410 (1839) ◽  
pp. 311-336 ◽  
Keyword(s):  
Maxwell Equations ◽  
Three Dimensional ◽  
Flat Space ◽  
Conformally Flat ◽  
Schwarzschild Solution ◽  
New Class ◽  
Type D ◽  
New Family ◽  
Static Black Hole ◽  
Petrov Type D

Solutions of the Einstein–Maxwell equations are found that provide generalizations of a solution discovered by Bell and Szekeres, which represents the collision of impulsive gravitational waves coupled with electromagnetic shock-waves in a conformally flat space-time. Starting with the Bell–Szekeres solution in a form more general than their original one (though equivalent to it) and applying to it a so-called Ehlers transformation, we obtain a new family of Petrov type-D space-times in which horizons form and subsequently two-dimensional time-like singularities develop. A second solution provides a generalization of the Bell–Szekeres solution in the same way as the axisymmetric distorted static black-hole solutions provide a generalization of the Schwarzschild solution. This second solution also forms a horizon but the time-like singularity that develops is three-dimensional. The mathematical theory that is developed seems specially adapted to the solution of these and related problems.

On functionally constant invariants of the Riemann tensor

1970 ◽  
Vol 68 (1) ◽  
pp. 179-185 ◽  
Author(s):  
H. A. Buchdahl
Keyword(s):  
Explicit Expression ◽  
Killing Vector ◽  
Riemann Tensor ◽  
Conformally Flat ◽  
Vector Density ◽  
Scalar Density ◽  
Local Character ◽  
Quadratic Invariants ◽  
Derivatives Of ◽  
Special Case

AbstractIn any V4 two quadratic invariants of the Riemann tensor, J4 and K4, say, are known which are functionally constant, i.e. the Hamiltonian derivatives of which vanish identically. Certain natural generalizations, J2n and K2n, of degree n of these are considered, J2n being defined in any Vm but K2n only in a V2n. It is shown by methods having purely local character that J2n is functionally constant in any V2n, and that K2n vanishes identically when n is odd or when n is even and the V2n is either conformally flat or admits a hypersurface-orthogonal Killing vector; whilst in a V4n it is functionally constant. These results follow upon a prior spinorial treatment of the special case n = 3 which leads to an explicit expression for a pseudo-vector density of which the scalar density 6 is the divergence. Finally, it is shown that for appropriate values of n there exist functionally constant invariants other than J2n and K2n

On derivatives of fuzzy multi-dimensional mappings and applications under generalized differentiability

2021 ◽  
pp. 1-19
Author(s):  
M. Miri Karbasaki ◽  
M. R. Balooch Shahriari ◽  
O. Sedaghatfar
Keyword(s):  
Linear Function ◽  
Level Set ◽  
Fuzzy Numbers ◽  
Sufficient Condition ◽  
Continuous Linear ◽  
Generalized Differentiability ◽  
Relationship Of ◽  
The Relationship ◽  
Derivatives Of ◽  
Dimensional Mapping

This article identifies and presents the generalized difference (g-difference) of fuzzy numbers, Fréchet and Gâteaux generalized differentiability (g-differentiability) for fuzzy multi-dimensional mapping which consists of a new concept, fuzzy g-(continuous linear) function; Moreover, the relationship between Fréchet and Gâteaux g-differentiability is studied and shown. The concepts of directional and partial g-differentiability are further framed and the relationship of which will the aforementioned concepts are also explored. Furthermore, characterization is pointed out for Fréchet and Gâteaux g-differentiability; based on level-set and through differentiability of endpoints real-valued functions a characterization is also offered and explored for directional and partial g-differentiability. The sufficient condition for Fréchet and Gâteaux g-differentiability, directional and partial g-differentiability based on level-set and through employing level-wise gH-differentiability (LgH-differentiability) is expressed. Finally, to illustrate the ability and reliability of the aforementioned concepts we have solved some application examples.

scholarly journals Cylindrically Symmetric, Asymptotically Flat, Petrov Type D Spacetime with a Naked Curvature Singularity and Matter Collapse

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Faizuddin Ahmed
Keyword(s):  
Cosmic Time ◽  
Petrov Type ◽  
Energy Conditions ◽  
Anisotropic Fluid ◽  
Curvature Singularity ◽  
Field Equations ◽  
Asymptotically Flat ◽  
Type D ◽  
Cylindrically Symmetric ◽  
Petrov Type D

We present a cylindrically symmetric, Petrov type D, nonexpanding, shear-free, and vorticity-free solution of Einstein’s field equations. The spacetime is asymptotically flat radially and regular everywhere except on the symmetry axis where it possesses a naked curvature singularity. The energy-momentum tensor of the spacetime is that for an anisotropic fluid which satisfies the different energy conditions. This spacetime is used to generate a rotating spacetime which admits closed timelike curves and may represent a Cosmic Time Machine.

Triazene derivatives of (1,x-)diazacycloalkanes. Part VI. 3-({5,5-Dimethyl-3-[2-aryl-1-diazenyl]-1-imidazolidinyl}methyl)-4,4-dimethyl-1-[2-aryl-1-diazenyl]imidazolidines — Synthesis, characterization, and X-ray crystal structure

2006 ◽  
Vol 84 (10) ◽  
pp. 1294-1300 ◽  
Author(s):  
Keith Vaughan ◽  
Shasta Lee Moser ◽  
Reid Tingley ◽  
M Brad Peori ◽  
Valerio Bertolasi
Keyword(s):  
Crystal Structure ◽  
Significant Degree ◽  
Ion Trapping ◽  
Published Data ◽  
X Ray ◽  
X Ray Crystallography ◽  
Diazonium Ion ◽  
Derivatives Of ◽  
C Nmr

Reaction of a series of diazonium salts with a mixture of formaldehyde and 1,2-diamino-2-methylpropane affords the 3-({5,5-dimethyl-3-[2-aryl-1-diazenyl]-1-imidazolidinyl}methyl)-4,4-dimethyl-1-[2-aryl-1-diazenyl]imidazolidines (1a–1f) in excellent yield. The products have been characterized by IR and NMR spectroscopic analysis, elemental analysis, and X-ray crystallography. The X-ray crystal structure of the p-methoxycarbonyl derivative (1c) establishes without question the connectivity of these novel molecules, which can be described as linear bicyclic oligomers with two imidazolidinyl groups linked together by a one-carbon spacer. This is indeed a rare molecular building block. The molecular structure is corroborated by 1H and 13C NMR data, which correlates with the previously published data of compounds of types 5 and 6 derived from 1,3-propanediamine. The triazene moieties in the crystal of 1c display significant π conjugation, which gives the N—N bond a significant degree of double-bond character. This in turn causes restricted rotation around the N—N bond, which leads to considerable broadening of signals in both the 1H and 13C NMR spectra. The molecular ion of the p-cyanophenyl derivative (1b) was observed using electrospray mass spectrometry (ES + Na). The mechanism of formation of molecules of type 1 is proposed to involve diazonium ion trapping of the previously unreported bisimidazolidinyl methane (13).Key words: triazene, bistriazene, imidazolidine, synthesis, X-ray crystallography, NMR spectroscopy.

scholarly journals Are D-manno-configured Amadori products ligands of the bacterial lectin FimH?

2015 ◽  
Vol 11 ◽  
pp. 1096-1104 ◽  
Author(s):  
Tobias-Elias Gloe ◽  
Insa Stamer ◽  
Cornelia Hojnik ◽  
Tanja M Wrodnigg ◽  
Thisbe K Lindhorst
Keyword(s):  
Molecular Docking ◽  
Binding Site ◽  
Bacterial Adhesion ◽  
Carbohydrate Binding ◽  
Amadori Products ◽  
E Coli ◽  
Type D ◽  
Amadori Rearrangement ◽  
Carbohydrate Binding Site

The Amadori rearrangement was employed for the synthesis ofC-glycosyl-type D-mannoside analogues, namely 1-propargylamino- and 1-phenylamino-1-deoxy-α-D-manno-heptopyranose. They were investigated as ligands of type 1-fimbriatedE. colibacteria by means of molecular docking and bacterial adhesion studies. It turns out that Amadori rearrangement products have a limited activity as inhibitors of bacterial adhesion because the β-C-glycosidically linked aglycone considerably hampers complexation within the carbohydrate binding site of the type 1-fimbrial lectin FimH.

scholarly journals Structural-Functional Analysis of 2,1,3-Benzoxadiazoles and Their N-oxides As HIV-1 Integrase Inhibitors

Acta Naturae ◽  
2013 ◽  
Vol 5 (1) ◽  
pp. 63-72 ◽  
Author(s):  
S. P. Korolev ◽  
O. V. Kondrashina ◽  
D. S. Druzhilovsky ◽  
A. M. Starosotnikov ◽  
M. D. Dutov ◽  
...  
Keyword(s):  
Integrase Inhibitor ◽  
Integrase Inhibitors ◽  
Mechanism Of Inhibition ◽  
Immunodeficiency Virus ◽  
Pharmacokinetic Properties ◽  
Nitro Derivatives ◽  
Derivatives Of ◽  
Anti Hiv ◽  
Hiv 1

Human immunodeficiency virus type 1 integrase is one of the most attractive targets for the development of anti-HIV-1 inhibitors. The capacity of a series of 2,1,3-benzoxadiazoles (benzofurazans) and their N-oxides (benzofuroxans) selected using the PASS software to inhibit the catalytic activity of HIV-1 integrase was studied in the present work. Only the nitro-derivatives of these compounds were found to display inhibitory activity. The study of the mechanism of inhibition by nitro-benzofurazans/benzofuroxans showed that they impede the substrate DNA binding at the integrase active site. These inhibitors were also active against integrase mutants resistant to raltegravir, which is the first HIV-1 integrase inhibitor approved for clinical use. The comparison of computer-aided estimations of the pharmacodynamic and pharmacokinetic properties of the compounds studied and raltegravir led us to conclude that these compounds show promise and need to be further studied as potential HIV-1 integrase inhibitors.

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