Connes distance of 2D harmonic oscillators in quantum phase space

We study the Connes distance of quantum states of two-dimensional (2D) harmonic oscillators in phase space. Using the Hilbert-Schmidt operatorial formulation, we construct a boson Fock space and a quantum Hilbert space, and obtain the Dirac operator and a spectral triple corresponding to a four-dimensional (4D) quantum phase space. Based on the ball condition, we obtain some constraint relations about the optimal elements. We construct the corresponding optimal elements and then derive the Connes distance between two arbitrary Fock states of 2D quantum harmonic oscillators. We prove that these two-dimensional distances satisfy the Pythagoras theorem. These results are significant for the study of geometric structures of noncommutative spaces, and it can also help us to study the physical properties of quantum systems in some kinds of noncommutative spaces.     

新型异戊烯并环黄酮化合物的合成

以间苯三酚和3,3-二甲基烯丙酸为起始原料,通过苄基保护、甲基化、脱保护基、Clemmenson还原、乙酰化、Fries重排、Baker-Venkataraman重排和成环等10步反应, 以18.2%的总收率合成了1个新型异戊烯并环黄酮化合物BE-1C,其结构经¹H NMR, ¹³C NMR和HR-MS(ESI-TOF)表征。     

新型二氢色原酮拼接多环吡咯螺环氧化吲哚类化合物的 无催化剂合成及其抗白血病活性

以取代的3-羧酸活化色酮、靛红与消旋脯氨酸为原料，乙腈为溶剂，依次经1,3-偶极子[3+2]环加成和脱羧反应，合成了8个新型的二氢色原酮拼接多环吡咯螺环氧化吲哚类化合物 (3a~3h)，产率68%~87%, dr值15/1~20/1,其结构经¹H NMR, ¹³C NMR和HR-MS（ESI-TOF）表征。采用MTT法研究了3a~3h对人白血病细胞(K562)的体外抑制活性。结果表明：化合物3d,3f, 3g对K562具有一定的抑制活性(IC₅₀=46.3~69.4 μmol·L^-1)。     

A diagrammatic categorification of the fermion algebra

In this paper, we study the diagrammatic categorification of the fermion algebra. We construct a graphical category corresponding to the one-dimensional （1D） fermion algebra, and we investigate the properties of this category. The categorical analogues of the Fock states are some kind of 1-morphisms in our category, and the dimension of the vector space of 2-morphisms is exactly the inner product of the corresponding Fock states. All the results in our categorical framework coincide exnetlv with those in normal quantum mechanics.     

嘧啶拼接3-烯键氧化吲哚衍生物的合成及其抗肿瘤活性

以2-吲哚酮与3,5-二氯嘧啶甲醛为原料,经Knoevenagel加成消除反应和取代反应合成了11个新型的嘧啶拼接3-烯键氧化吲哚衍生物(3a~3k),产率70%~91%,Z/E值15：1~>20 ：1, 其结构经¹H NMR, ¹³C NMR和HR-MS（ESI-TOF）表征。采用MTT法研究了3a~3k对人肺癌细胞(A549)和人白血病细胞(K562)的体外抗肿瘤活性。结果表明：3a, 3c, 3f, 3g和3j对K562具有较好的抑制活性（IC₅₀分别为29.3, 27.6, 28.5, 24.0和27.0 μmol·L^-1）, 3a, 3h和3j对A549具有较好的抑制活性（IC₅₀分别为28.1, 16.4和25.2 μmol·L^-1）。     

A diagrammatic categorification of q-boson and q-fermion algebras

In this paper,we study the diagrammatic categorification of q-boson algebra and also q-fermion algebra.We construct a graphical category corresponding to q-boson algebra.q-Fock states correspond to some kind of 1-morphisms,and the graded dimension of the graded vector space of 2-morphisms is exactly the inner product of the corresponding q-Fock states.We also find that this graphical category can be used to categorify q-fermion algebra.     

Cluster algebra structure on the finite dimensional representations of affine quantum group U_q(_3)

In this paper,we prove one case of conjecture given by Hernandez and Leclerc.We give a cluster algebra structure on the Grothendieck ring of a full subcategory of the finite dimensional representations of affine quantum group Uq(3).As a conclusion,for every exchange relation of cluster algebra,there exists an exact sequence of the full subcategory corresponding to it.     

新型3-五元碳环螺环氧化吲哚类化合物的合成及其抗人白血病细胞活性

以氧化吲哚与邻芳基二甲醛为原料,经Knoevenagel缩合(或Michael,环化反应),制得7个3-五元碳环螺环氧化吲哚(4a~4c,产率67%~86%,d/r值4∶1~10∶1)和4d~4g;4d~4g与哌啶(或四氢吡咯)和多聚甲醛经胺甲基化反应,合成了4个3-五元碳环螺环氧化吲哚(5d~5g),产率55%~67%,d/r值10∶1~20∶1,其结构经~1H NMR,~(13)C NMR和HR-MS(ESI-TOF)表征。采用MTT法研究了4a~4c和5d~5g对人白血病细胞(K562)的体外抗肿瘤活性。结果表明:4b,5d和5f对K562抑制活性较好,IC50分别为29.3μmol·L~(-1),27.4μmol·L~(-1)和34.2μmol·L~(-1),与阳性对照药顺铂(26.8μmol·L~(-1))相当。     

Wigner Functions for the Bateman System on Noncommutative Phase Space

We study an important dissipation system, i.e. the Bateman model on noncommutative phase space. Using the method of deformation quantization, we calculate the Exp functions, and then derive the Wigner functions and the corresponding energy spectra.