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51.
We obtain the complete set of states of theq-oscillator in both configuration space and momentum space as well as the transformation between these spaces. The states as well as the matrix elements lie in the SU
q
(2) algebra. To obtain transition probabilities, one must take the Woronowicz square. 相似文献
52.
Maria Rosaria Enea 《Geometriae Dedicata》1994,51(3):257-286
In this paper we develop a structure theory of algebraic right distributive quasigroups which correspond to closed and connected conjugacy classes
generating algebraic Fischer groups (in the sense of [6]) such that the mappingx x
–1
ax, fora
, is an automorphism of
(as variety). We also give examples of algebraic Fischer groups where this does not happen. It becomes clear that the class of algebraic right distributive quasigroups has nice properties concerning subquasigroups, normal subquasigroups and direct product.We give a complete classification of one- and two-dimensional as well as of minimal algebraic right distributive quasigroups. 相似文献
53.
Uwe Grimm 《Letters in Mathematical Physics》1994,32(3):183-187
Explicit expressions for three series ofR matrices which are related to a dilute generalisation of the Birman-Wenzl-Murakami algebra are presented. Of those, one series is equivalent to the quantumR matrices of theD
n+1
(2)
generalised Toda systems, whereas the remaining two series appear to be new. 相似文献
54.
T. Sandrock T. Danger E. Heumann G. Huber B. H. T. Chai 《Applied physics. B, Lasers and optics》1994,58(2):149-151
We report, to our knowledge for the first time, Continuous Wave (CW) laser emission at room temperature of Pr:LiYF4 (Pr.YLF) at six wavelengths: 522, 545, 607, 639.5, 720 and 907.4 nm. The pump source was an argon-ion laser tuned to a wavelength of = 457.9 nm. The maximum output powers at 522 nm (3Pi 3H5) and 639.5 nm (3P0 3F2) were 144 and 266 mW, respectively. We also observed CW laser action of Pr:GdLiF4 (Pr: GLF) at = 639 nm and of Pr:KYF4 (Pr: KYF) at = 642.5 nm. 相似文献
55.
Inclusion-exclusion: Exact and approximate 总被引:1,自引:0,他引:1
It is often required to find the probability of the union of givenn eventsA
1
,...,A
n
. The answer is provided, of course, by the inclusion-exclusion formula: Pr(A
i
)=
i
–
i<j
Pr(A
i
A
j
)±.... Unfortunately, this formula has exponentially many terms, and only rarely does one manage to carry out the exact calculation. From a computational point of view, finding the probability of the union is an intractable, #P-hard problem, even in very restricted cases. This state of affairs makes it reasonable to seek approximate solutions that are computationally feasible. Attempts to find such approximate solutions have a long history starting already with Boole [1]. A recent step in this direction was taken by Linial and Nisan [4] who sought approximations to the probability of the union, given the probabilities of allj-wise intersections of the events forj=1,...k. The developed a method to approximate Pr(A
i
), from the above data with an additive error of exp
. In the present article we develop an expression that can be computed in polynomial time, that, given the sums |S|=j
Pr(
iS
A
i
) forj=1,...k, approximates Pr(A
i
) with an additive error of exp
. This error is optimal, up to the logarithmic factor implicit in the
notation.The problem of enumerating satisfying assignments of a boolean formula in DNF formF=v
l
m
C
i
is an instance of the general problem that had been extensively studied [7]. HereA
i
is the set of assignments that satisfyC
i
, and Pr(
iS
A
i
)=a
S
/2n where
iS
C
i
is satisfied bya
S
assignments. Judging from the general results, it is hard to expect a decent approximation ofF's number of satisfying assignments, without knowledge of the numbersa
S
for, say, all cardinalities
. Quite surprisingly, already the numbersa
S
over |S|log(n+1)uniquely determine the number of satisfying assignments for F.We point out a connection between our work and the edge-reconstruction conjecture. Finally we discuss other special instances of the problem, e.g., computing permanents of 0,1 matrices, evaluating chromatic polynomials of graphs and for families of events whose VC dimension is bounded.Work supported in part by a grant of the Binational Israel-US Science Foundation.Work supported in part by a grant of the Binational Israel-US Science Foundation and by the Israel Science Foundation. 相似文献
56.
We realize the
current algebra at an arbitrary level in terms of one deformed free bosonic field and a pair of deformed parafermionic fields. It is shown that the operator product expansions of these parafermionic fields involve an infinite number of simple poles and simple zeros, which then condensate to form a branch cut in the classical limitq1. Our realization coincides with those of Frenkel-Jing and Bernard when the levelk takes the values 1 and 2, respectively. 相似文献
57.
We use a quite concrete and simple realization of sl
q
(2, ) involving finite difference operators. We interpret them as derivations (in the noncommutative sense) on a suitable graded algebra, which gives rise to the noncommutative scheme 1 II 1* as the counterpart of the standard 1 = Sl(2, )/B. 相似文献
58.
By combining the generalized exterior algebra of forms over a noncommutative algebra with the gauging of discrete directions and the associated Higgs fields, we consider the construction of the bosonic sector of left-right symmetric models of the form SU(2)
L
SU(2)
R
U(1). We see that within this formalism maximal use can be made of the gauge connection associated with the noncommutative graded algebra. 相似文献
59.
The property of self-adjointness of the operatorQ =a
+ +a
- in three types ofq-oscillator algebras is considered. Spectral measures and generalized eigenfunctions ofQ are found in the cases when this operator is bounded. Generalized eigenvectors are expressed in terms ofq-Hermite polynomials. If the operatorQ is unbounded, then its closure
is not self-adjoint. However, in this case,
admits self-adjoint extensions. Deficiency subspaces are one-dimensional. These subspaces are explicitly found. 相似文献
60.
G. Zerza G. Sliwinski N. Schwentner 《Applied Physics A: Materials Science & Processing》1993,56(2):156-158
From line narrowing in amplified spontaneous emission at the D-X transition (269nm) of XeF in solid Ne a gain coefficient of 3.4 cm–1 has been derived and ground-state losses of 2.8 cm–1 have been determined by variation of the absorption length. A dielectric laser cavity has been optimized with the reflectivities R1=100% and R2=70% for 1 cm long crystals; laser action has been achieved. 相似文献