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41.
42.
43.
Yong-Long Wang 《International Journal of Theoretical Physics》2009,48(5):1422-1430
In the framework of Faddeev-Senjanovic (FS) path-integral quantization, CP
1 nonlinear σ model coupled to Non-Abelian Chern-Simons (CS) fields is quantized. Generalized canonical Ward identities (WI) are deduced
from the invariance of the canonical effective action under gauge transformations, which are obtained from the generators
of gauge transformations, including all first-class constraints, in Dirac’s sense. The generalized canonical WI has brief
form and is equivalent to canonical WI under gauge transformations in Dirac’s sense.
This project is supported by Foundation of National Natural Science (10671086), Foundation of Shandong Natural Science (Y2007A01)
and National Laboratory for Superlattices and Microstructures (CHJG200605). 相似文献
44.
Krishnaswami Alladi Alexander Berkovich 《Transactions of the American Mathematical Society》2002,354(7):2557-2577
This paper has a two-fold purpose. First, by considering a reformulation of a deep theorem of Göllnitz, we obtain a new weighted partition identity involving the Rogers-Ramanujan partitions, namely, partitions into parts differing by at least two. Consequences of this include Jacobi's celebrated triple product identity for theta functions, Sylvester's famous refinement of Euler's theorem, as well as certain weighted partition identities. Next, by studying partitions with prescribed bounds on successive ranks and replacing these with weighted Rogers-Ramanujan partitions, we obtain two new sets of theorems - a set of three theorems involving partitions into parts (mod 6), and a set of three theorems involving partitions into parts (mod 7), .
45.
Zhi-Guo Liu 《The Ramanujan Journal》2002,6(4):429-447
In this paper the author proves a q-expansion formula which utilizes the Leibniz formula for the q-differential operator. This expansion leads to new proofs of the Rogers–Fine identity, the nonterminating 65 summation formula, and Watson's q-analog of Whipple's theorem. Andrews' identities for sums of three squares and sums of three triangular numbers are also derived. Other identities of Andrews and new identities for Hecke type series are also discussed. 相似文献
46.
47.
导数光谱法测定污水中十二烷基苯磺酸钠 总被引:2,自引:0,他引:2
本文介绍了用导数分光光度法直接定量分析污水中十二烷基苯磺酸钠的方法。本法消除了混浊背景干扰,操作简便快速。应用于实际污水样品的分析,获得了良好的结果,十二烷基苯磺酸钠的校准曲线线性范围为0-82mg/L。 相似文献
48.
We consider two tests of the null hypothesis that the k-th derivative of a regression function is uniformly bounded by a specified constant. These tests can be used to study the shape of the regression function. For instance, we can test for convexity of the regression function by setting k=2 and the constant equal to zero. Our tests are based on k-th order divided difference of the observations. The asymptotic distribution and efficacies of these tests are computed and simulation results presented.Research supported by Natural Sciences and Engineering Research Council of Canada Grant OGP0007969.Research supported by National Science Foundation Grant DMS-9306738. 相似文献
49.
A (u1,
u2, . . . )-parking function of length
n is a sequence (x1,
x2, . . . ,
xn)
whose order
statistics (the sequence (x(1),
x(2), . . . ,
x(n)) obtained by rearranging the original sequence in
non-decreasing order) satisfy
x(i)
u(i).
The Gonarov polynomials g
n
(x; a0, a
1, . . . , a
n-1) are
polynomials biorthogonal to the linear functionals (a
i)
Di,
where (a) is evaluation at
a and D
is differentiation. In this paper, we give explicit formulas for the first and second moments of
sums of u-parking functions using Gonarov polynomials by
solving a linear recursion based on a decomposition of the set of sequences of positive integers.
We also give a combinatorial proof of one of the formulas for the expected sum. We specialize
these formulas to the classical case when u
i=a+
(i-1)b and obtain, by
transformations with Abel identities, different but equivalent
formulas for expected sums. These formulas are used to verify the classical case of the
conjecture that the expected sums are increasing functions of the gaps
ui+1
- ui.
Finally, we give analogues of our results for real-valued parking functions.AMS Subject Classification: 05A15, 05A19, 05A20, 05E35. 相似文献
50.
离子交换富集-导数火焰原子吸收法测定自来水中Cu,Fe和Zn 总被引:7,自引:0,他引:7
本文研究了用 2 0 1× 7阳离子交换树脂对自来水中的微量元素进行交换富集 ,采用微量脉冲进样 导数火焰原子吸收法测定富集后溶液中的Cu ,Fe和Zn ,该方法灵敏度分别为 0 2 9,0 5 9和 0 0 6 μg·L- 1 ,精密度分别为 4 2 8% ,1 95 %和 2 2 8% ,检测限分别为 1 2 8,5 85和 0 6 8μg·L- 1 ,回收率分别为 91 13% ,10 1 34%和99 84 % ,本方法大大减少了需样量 ,简便快速 ,灵敏度高。 相似文献