态|ψ3(3)〉q中广义磁场分量的N次方Y压缩效应

构造了由多模复共轭相干态|{Z_j^*}〉_q、多模复共轭虚相干态|{iZ_j^*}〉_q和多模真空态|{Q_j} 〉_q这三态的线性叠加所组成的第Ⅲ类三态叠加多模叠加态光场|ψ₃⁽³⁾〉_q.利用多模压缩态理论研究了态|ψ₃⁽³⁾〉_q中广义磁场分量的任意偶数次广义非线性等幂次N次方Y压缩特性.结果发现:在压缩次数N取偶数,只要各模的初始相位φ_j(j=1,2,3,…,…,q),态间的初始相位差(θ_i-θ₂)(i=1,3)和各单模相干态光场平均光子数R_j²之和 分别满足各自的取值条件,态|ψ₃⁽³⁾〉_q的广义磁场分量(即第一正交相位分量)就可呈现出周期性变化的、任意偶数次的广义非线性等幂次N次方Y压缩效应.     

On the Froissart phenomenon in multivariate homogeneous Padé approximation

In univariate Padé approximation we learn from the Froissart phenomenon that Padé approximants to perturbed Taylor series exhibit almost cancelling pole–zero combinations that are unwanted. The location of these pole–zero doublets was recently characterized for rational functions by the so‐called Froissart polynomial. In this paper the occurrence of the Froissart phenomenon is explored for the first time in a multivariate setting. Several obvious questions arise. Which definition of Padé approximant is to be used? Which multivariate rational functions should be investigated? When considering univariate projections of these functions, our analysis confirms the univariate results obtained so far in [13], under the condition that the noise is added after projection. At the same time, it is apparent from section 4 that for the unprojected multivariate Froissart polynomial no conjecture can be formulated yet.

     

合成CFC-12替代物HFC-134a的CrF_3/AlF_3催化剂研究(Ⅴ)──CrF_3与AlF_3的相互作用

由于氟氯烃（ＣＦＣｓ）对大气臭氧层的破坏作用，使得开发ＣＦＣｓ无污染替代品的研究成为热门课题［１～４］．氢氟烃（ＨＦＣｓ，如ＨＦＣ－１３４ａ）是ＣＦＣｓ的理想替代物．在氟氯交换合成ＨＦＣ－１３４ａ的反应中，ＡｌＦ３基催化剂的活性、稳定性明显优于ＣｒＦ...     

Studies of silicophosphate derivatives by 31P-->29Si CP MAS NMR

We show that it is possible to efficiently transfer magnetization from ³¹P to ²⁹Si, using variable amplitude CP MAS experiment. This experiment is demonstrated by using Si₅O(PO₄)₆, the synthesis protocol of which is described. From the obtained results, we show that the experiment allows the spectral edition of ²⁹Si spectra from ³¹P→²⁹Si CP, enabling the studies of derivatives involving Si–O–P linkages, such as phosphosilicate glasses, microporous silicoaluminophosphates (SAPO) and bioactive phosphosilicates.     

Domb's numbers and Ramanujan-Sato type series for 1/π

In this article, we construct a general series for . We indicate that Ramanujan's -series are all special cases of this general series and we end the paper with a new class of -series. Our work is motivated by series recently discovered by Takeshi Sato.     

An alternate proof of Cohn's four squares theorem

While various techniques have been used to demonstrate the classical four squares theorem for the rational integers, the method of modular forms of two variables has been the standard way of dealing with sums of squares problems for integers in quadratic fields. The case of representations by sums of four squares in was resolved by Götzky, while those of and were resolved by Cohn. These efforts utilized modular forms. In previous work, the author was able to demonstrate Götzky's theorem by means of the geometry of numbers. Here Cohn's theorem on representation by the sum of four squares for is proven by a combination of geometry of numbers and quaternionic techniques.     

Determining eosin as a groundwater migration tracer by capillary electrophoresis/laser-induced fluorescence using a multiwavelength laser

Measurements for determining of the path of groundwater migration remain an important tool in the overall assessment of environmental processes and transport of pollutants. This paper examines a multiwavelength laser for the determination of eosin, a groundwater tracer, using capillary electrophoresis/laser-induced fluorescence (CE-LIF) at excitation wavelength 514.5 nm. Eosin was one of four dyes used in a study of adjacent resource conservation and recovery act (RCRA) and Superfund sites (created by the comprehensive environmental response, compensation, and liability act) that routinely relied on spectrofluorimetry for determination as we have previously reported. However, the improved specificity of CE-LIF is further illustrated in this work applied to the analysis of adsorbent pads placed in monitoring wells after dye injection and flushing from injection wells. The multiwavelength laser provided the capability to analyze for several dyes with one laser. The advantages/disadvantages of CE-LIF versus spectrofluorimetry are discussed. Spectrofluorimetry is fast and sensitive and will likely continue to be the primary workhorse technique. CE-LIF could provide confirmation when greater specificity is needed in a regulatory context.     

Attempts to Exchange Iron into H-Y and H-ZSM-5 Zeolites by in situ Formed Chloride-Containing Mobile Species

Three variants of solid-state ion exchange were studied. Iron exchange was found to proceed in the first case, in theFeCl₂+NH₄ZSM-5 FeZSM-5 + NH₄Cl process, even at low exchange capacity (Si/Al = 25).The second, Fe₂O₃ (hematite) + HZ direct reaction does not result in any noticeable interaction for eitherZ = Y or ZSM-5. This process can significantly be promoted by introducing CCl₄ vapor via forming chlorine-containingmobile species. However, the structure of the Y zeolite largely collapses during this treatment, whereas the crystalline state of ZSM-5is preserved.