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1.
Clemens G. Raab Georg Regensburger Jamal Hossein Poor 《Journal of Pure and Applied Algebra》2021,225(5):106564
A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be modelled by noncommutative polynomials and such a formal computation proves that the polynomial corresponding to the new identity lies in the ideal generated by the polynomials corresponding to the known identities. In order to prove an operator identity, however, just proving membership of the polynomial in the ideal is not enough, since the ring of noncommutative polynomials ignores domains and codomains. We show that it suffices to additionally verify compatibility of this polynomial and of the generators of the ideal with the labelled quiver that encodes which polynomials can be realized as linear operators. Then, for every consistent representation of such a quiver in a linear category, there exists a computation in the category that proves the corresponding instance of the identity. Moreover, by assigning the same label to several edges of the quiver, the algebraic framework developed allows to model different versions of an operator by the same indeterminate in the noncommutative polynomials. 相似文献
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《Indagationes Mathematicae》2022,33(4):801-815
We consider the irreducibility of polynomial where is a negative integer. We observe that the constant term of vanishes if and only if . Therefore we assume that where is a non-negative integer. Let and more general polynomial, let where with are integers such that . Schur was the first to prove the irreducibility of for . It has been proved that is irreducible for . In this paper, by a different method, we prove: Apart from finitely many explicitly given possibilities, either is irreducible or is linear factor times irreducible polynomial. This is a consequence of the estimate whenever has a factor of degree and . This sharpens earlier estimates of Shorey and Tijdeman and Nair and Shorey. 相似文献
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G. Dattoli 《Journal of Mathematical Analysis and Applications》2002,269(2):716-725
Bilateral generating functions are those involving products of different types of polynomials. We show that operational methods offer a powerful tool to derive these families of generating functions. We study cases relevant to products of Hermite polynomials with Laguerre, Legendre and other polynomials. We also propose further extensions of the method which we develop here. 相似文献
8.
[Na(18-C-6)]2[Cu(i-mnt)2]的合成与结构分析 总被引:2,自引:2,他引:0
研究了18-冠-6与Na2[Cu(i-mnt)2][i-mnt=异丁二腈烯二硫醇阴离子,S2CC(CN)2-2]的反应,得到的配合物[Na(18-C-6)]2[Cu(i-mnt)2](1)通过元素分析、红外光谱、X射线单晶衍射进行了结构分析.配合物为单斜晶系,空间群P2(1)/c.晶体学结构数据a=1.2819(11),b=1.1793(10),c=1.4928(13)nm,β=99.121(16)°,V=2.228(3)nm3,Z=2,Dcaled.=1.369g/cm3,F(000)=958,R1=0.0521,wR2=0.1003.1中的[Cu(i-mnt)2]基团通过配体i-mnt的氮原子与两个[Na(18-C-6)]基团中的钠原子成键,形成稳定的中性配合物. 相似文献
9.
On Best Approximations from RS-sets in Complex Banach Spaces 总被引:2,自引:0,他引:2
ChongLI 《数学学报(英文版)》2005,21(1):31-38
The concept of an RS-set in a complex Banach space is introduced and the problem of best approximation from an RS-set in a complex space is investigated. Results consisting of characterizations, uniqueness and strong uniqueness are established, 相似文献
10.
室温下,通过双核配合物[Cu(dppm)(NO3)]2(dppm=双二苯基膦甲烷)与四苯基硼钠在甲醇和二氯甲烷混合溶剂中反应制备了三核铜(I)配合物[Cu3(dppm)3(NO3)(OH)](NO3),经过红外光谱、热重分析、核磁和ES-MS等现代分析手段表征了配合物的物理化学性质,并进一步研究了配合物在室温下的荧光光谱特征。 相似文献