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101.
Consider equations of the form where q is in general a complex vector and the function F depends nontrivially both on q and on qy. We show that a family S of such equations can be investigated by the inverse scattering method. If an equation (*) belongs to S, the function F depends linearly on q and algebraically on qy. We show that the family S contains a subfamily in which each equation can be obtained from the two dimensional Toda lattice equations by a Bäcklund transformation. 相似文献
102.
We give here a rigorous formulation for a pair of consecutive simple positive zeros of the functionH
0 (which is closely related to the Riemann -function) to be a Lehmer pair of zeros ofH
0. With this formulation, we establish that each such pair of zeros gives a lower bound for the de Bruijn-Newman constant (where the Riemann Hypothesis is equivalent to the assertion that 0). We also numerically obtain the following new lower bound for :
相似文献
103.
Richard Ley D. Hagena D. Weil G. Werth W. Arnold H. Schneider 《Hyperfine Interactions》1994,89(1):327-341
Electric dipole transitions in the microwave range have been induced between the fine-structure levels of positronium in the excited staten=2. As an indication of the transitions, we used the increase in Lyman- radiation when the metastable 23S1-level is depopulated. The results for the transitions 23S123P0,1,2 are
0=18499.65±1.20±4.00 MHz,
1=13012.42 ±0.65±1.54 MHz and
2=8624.38±0.54±1.40 MHz. The first error is statistical and the second systematic. The precision of the present measurement has improved by a factor of 3, compared to previous data. Recent bound state QED-calculations have been extended to the orderR
t8
4ln
–1. The not yet completely calculated orderR
t8
4 is estimated to contribute less than 1 MHz. Our experimental results are in good agreement with theory. By applying a weak magnetic field, we were able to observe the transition 23S121P1 which is strictly forbidden byC-invariance in zero field. Our result, corrected for Zeeman- and motional Starkeffect, is
3=11180.0±5.0±4.0 MHz. An upper limit for theC-violating matrix element of
MHz could be deduced. Our experiment used moderated slow positrons from the bremsstrahlung and pair production of a pulsed electron linear accelerator (TEPOS facility at the university of Giessen). 相似文献
104.
Eric Bach Richard Lukes Jeffrey Shallit H. C. Williams. 《Mathematics of Computation》1996,65(216):1737-1747
Let be a positive integer. We say looks like a power of 2 modulo a prime if there exists an integer such that . First, we provide a simple proof of the fact that a positive integer which looks like a power of modulo all but finitely many primes is in fact a power of . Next, we define an -pseudopower of the base to be a positive integer that is not a power of , but looks like a power of modulo all primes . Let denote the least such . We give an unconditional upper bound on , a conditional result (on ERH) that gives a lower bound, and a heuristic argument suggesting that is about for a certain constant . We compare our heuristic model with numerical data obtained by a sieve. Some results for bases other than are also given.
105.
Richard L. Liboff 《International Journal of Theoretical Physics》1996,35(1):189-198
Mapping of the two-dimensional isosceles triangle billiard onto the circular one-dimensional motion of two mass points is described. The singular nature of trajectories directly incident on an acute vertex is discussed in the framework of the present mapping. For an obtuse-angled isosceles triangle, dynamical equations in two-particle space applied to an orbit along a hypotenuse incident on the obtuse vertex suggests irreversible behavior at the critical angle =2/3. Thus it is found that the nonsingular motion of a finite smooth-walled disk on this trajectory exhibits irreversibility. A finite spherical smooth-walled particle moving in a uniform right cylinder whose cross section includes this critical vertex angle likewise exhibits irreversibility. Each such example comprises an irreversible orbit for a single-particle Hamiltonian. 相似文献
106.
107.
We prove the existence of uncountably many nonisomorphic topological projective planes, each universal in the sense that it contains an isomorphic copy of every pseudoline arrangement. 相似文献
108.
This paper estimates a non-parametric production frontier for a population of 117 corn/livestock farms in the Corn Belt region in 1987, employing a hyperbolic graph efficiency approach. There are 7 outputs, 39 variable inputs, 4 fixed inputs, and one bad input (residual nitrogen). Three graph efficiency models are estimated. A profit maximization model is specified to estimate a production frontier constrained only by the fixed factors. Two other models involving tax constraints are also estimated. One involves a tax directly on nitrogen and the other involves a tax directly on residual nitrogen, making the disposal of residual nitrogen costly. The nitrogen tax constraint is more effective in reducing residual nitrogen loadings and causes a larger reduction in income than the residual tax constraint. 相似文献
109.
Richard C. Bradley 《Journal of Theoretical Probability》1996,9(3):659-678
Schmidt(10) showed that if the family of distributions of the partial sums of a strictly stationary random sequence is tight, then that random sequence is a coboundary. Here an analog of that result is proved for some sequences of random matrices, with partial sums replaced by matrix products. 相似文献
110.
Richard Kerner 《Letters in Mathematical Physics》1996,36(4):441-454
We present a possible generalization of the exterior differential calculus, based on the operator d such that d3=0, but d20. The entities dx
i
and d2
x
k
generate an associative algebra; we shall suppose that the products dx
i
dx
k
are independent of dx
k
dx
i
, while theternary products will satisfy the relation: dx
i
dx
k
dx
m
=jdx
k
dx
m
dx
i
=j
2dx
m
dx
m
dx
i
dx
k
, complemented by the relation dx
i
d2
x
k
=jd2
x
k
dx
i
, withj:=e2i/3.We shall attribute grade 1 to the differentials dx
i
and grade 2 to the second differentials d2
x
k
; under the associative multiplication law the grades add up modulo 3.We show how the notion ofcovariant derivation can be generalized with a 1-formA so thatD:=d+A, and we give the expression in local coordinates of thecurvature 3-form defined as :=d2
A+d(A
2)+AdA+A
3.Finally, the introduction of notions of a scalar product and integration of theZ
3-graded exterior forms enables us to define the variational principle and to derive the differential equations satisfied by the 3-form . The Lagrangian obtained in this way contains the invariants of the ordinary gauge field tensorF
ik
and its covariant derivativesD
i
F
km
. 相似文献
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