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The nonstandard quantum plane

2008
*
Annals of Pure and Applied Logic
*

These points represent

doi:10.1016/j.apal.2008.06.009
fatcat:eacrlevtubc35od5dzygaqu6b4
*nonstandard*homogeneous components of*the**quantum**plane*. 2*The*lattice of K-invariant pp-definable subspaces A pp-definable subspace ϕ(V ) of a U q -module V is called K-invariant ... Rather than working with*the**quantum**plane*directly, it is easier to prove*the*following theorem for M, and then specialize to*the**quantum**plane*in*the*last section of*the*paper. ...##
###
Page 1392 of Mathematical Reviews Vol. 47, Issue 5
[page]

1974
*
Mathematical Reviews
*

writers have hitherto held, in

*the**plane*of single*quantum*-mechanical events” (p. 96). ... “*The*author has proposed*the*view 1392*QUANTUM*MECHANICS that*the*locus of nonclassical logic in*quantum*mechanic is in*the**plane*in which physical contexts are related to one another, and not, as all ...##
###
Entropic Aspects of Nonlinear Partial Differential Equations: Classical and Quantum Mechanical Perspectives

2017
*
Entropy
*

Acknowledgments: I express my thanks to

doi:10.3390/e19040166
fatcat:o2xnreocfbdxbey7fapwb72nqy
*the*authors of*the*above contributions, and to*the*journal Entropy and MDPI for their support during this work. ... Conflicts of Interest:*The*author declares no conflict of interest. Entropy 2017, 19, 166 ... equations inspired on*quantum*mechanics. ...##
###
Page 2139 of Mathematical Reviews Vol. , Issue 99c
[page]

1991
*
Mathematical Reviews
*

This is proved by a nonlinear transformation of

*the*stan- dard basis for*the*null-*plane**quantum*Poincaré algebra. ... (E-VALD-TP; Valladolid) Bicrossproduct structure of*the*null-*plane**quantum*Poincaré algebra. (English summary) J. Phys. A 31 (1998), no. 1, L1-L7. ...##
###
Page 627 of Mathematical Reviews Vol. , Issue 92b
[page]

1992
*
Mathematical Reviews
*

Then

*the*affine*nonstandard**plane*generated by*the*vectors w; and centered in c(t) is infinitely close (in*the*Grassmannian manifold) to*the*(standard)*plane*generated by*the*c“)(t). ... Now it is easy for*the*author to give a characterisation of*the*osculating*plane*: he takes three consecutive*nonstandard*points *c(so), *c(s,), *c(s2) on c with 5; =s, 5; € (a,b). ...##
###
Quantum deformations of conformal algebras introducing fundamental mass parameters

1996
*
Physics Letters B
*

It appears that for D=4

doi:10.1016/0370-2693(96)01604-8
fatcat:bsanod2hqffa5hsdrbzloayr5q
*the*deformation of*the*Poincare algebra sector coincides with "null*plane*"*quantum*Poincare algebra. ... In such a way we generalize*the*lowest order of known*nonstandard**quantum*deformation of sl(2) to*the*Lie algebras sp(4) = so(5) and sl(4) = so(6). ...*The*mass Casimir is given by*the*formula [24] C 2 = P 2 1 + P 2 2 − MP − sinh( P + M ) (5.10) Because*the*deformation U M (P 4 ) of*the*Poincaré algebra, called in [24]*the*"null*plane*"*quantum*Poincaré ...##
###
Page 1109 of Mathematical Reviews Vol. , Issue 95b
[page]

1995
*
Mathematical Reviews
*

In order to now set up a

*nonstandard*Dirac bra-ket formal- ism*the*author introduces an additional “spectral axiom” besides*the*usual*quantum*logical axioms. ... is bound to contain finite*nonstandard*reals). ...##
###
Page 5451 of Mathematical Reviews Vol. , Issue 94i
[page]

1994
*
Mathematical Reviews
*

*The*Manin

*quantum*

*plane*has two parameters qg and p, and is denoted by Q,,. ... A 26 (1993), no. 5, L217- L220; MR 94d:16035] associated to

*the*

*nonstandard*R-matrix is isomorphic to a

*quantum*deformation of SU(2). ...

##
###
Page 4731 of Mathematical Reviews Vol. , Issue 92i
[page]

1992
*
Mathematical Reviews
*

*The*methods used are

*nonstandard*methods which allow

*the*author to characterize differentiability of a function f by

*the*fact that

*the*graph of f has a non-S-vertical, S-tangent

*plane*over all standard ... and to characterize a function f of class C' by

*the*fact that

*the*graph of f has a non-S-vertical, S-tangent

*plane*over all finite points in R?*.

*The*results are related to those of J. ...

##
###
The coloured quantum plane

2003
*
Journal of Geometry and Physics
*

We study

doi:10.1016/s0393-0440(02)00051-7
fatcat:vsataxe5ubfc5eattcahj3hdsm
*the**quantum**plane*associated to*the*coloured*quantum*group GL_q^λ,μ(2) and solve*the*problem of constructing*the*corresponding differential geometric structure. ...*The*coloured h-*plane*corresponding to*the*coloured Jordanian*quantum*group GL_h^λ,μ(2) is also obtained by contraction of*the*coloured q-*plane*. ... Coloured h-*plane*We now look at*the**nonstandard*(or Jordanian) counterpart of*the*q-*plane*, known as*the*h-*plane*[4, 5] . ...##
###
Page 3296 of Mathematical Reviews Vol. , Issue 98E
[page]

1998
*
Mathematical Reviews
*

*The*presented approach is illustrated by an example of a system with its phase space equal to a half-

*plane*. ...

*The*idea of

*the*paper is based on

*the*similar but much simpler

*nonstandard*construction of Wiener measure from a

*nonstandard*flat integral given by Cutland [J. London Math. ...

##
###
Acoustoconductance of quantum contacts

1999
*
Physica. B, Condensed matter
*

We describe theoretically

doi:10.1016/s0921-4526(98)01250-2
fatcat:c2a6msnejbfk5lgsgrfwcypn5m
*the*acoustoconductance (AC) of*quantum*contacts. ... Electrons which are forward scattered by phonons can contribute to AC and, furthermore, AC can have positive sign (i.e. a conductance-increase under*the*influence of phonons). ... ACKNOWLEDGMENTS*The*authors would like to thank*the*organizers of Phonons 98 for providing*the*opportunity to present this work. Funding by*the*EPSRC under Grant Nos. ...##
###
Page 495 of Mathematical Reviews Vol. , Issue 92a
[page]

1992
*
Mathematical Reviews
*

Furthermore, we illustrate

*the*method by discussing some specific potential problems on*the*Poincaré up- per half-*plane*.*The*first one is Vi(x,y) = y?[V(x) +(m/2)w?y?] ...*The*pur- pose of*the*authors is to investigate to what extent Haag duality holds in conformal*quantum*field theory. ...##
###
Superluminal Phenomena and the Quantum Preferred Frame
[article]

2000
*
arXiv
*
pre-print

experiments, we discuss in this paper a speculative but physically admissible form and solutions of effective Maxwell-like equations describing propagation of electromagnetic field in a medium which "feels" a

arXiv:quant-ph/0010026v2
fatcat:6da375octvfcpmls63udrn63re
*quantum*... This paper was financially supported by*the*University of Lodz. ... It is convenient to consider our*plane*wave solution in*the*preferred frame. ...##
###
Page 4711 of Mathematical Reviews Vol. , Issue 2003f
[page]

2003
*
Mathematical Reviews
*

Summary: “We give solutions of

*the**quantum*conformal defor- mations of*the*Maxwell and potential equations in terms of defor- mations of*the**plane*wave. ... Motivated by some problems in theoretical physics,*the*authors 2003f:8 1 128 set out to construct*nonstandard*bases for finite-dimensional irre- ducible representations of*the**quantum*algebra su,(2) by ...
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