The triad of Legionella pneumonia,rhabdomyolysis,and acute kidney injury(AKI)is uncommon but can be devastating.[1]It is vital to recognize Legionella species early as a potential cause of pneumonia.Legionella infecti...The triad of Legionella pneumonia,rhabdomyolysis,and acute kidney injury(AKI)is uncommon but can be devastating.[1]It is vital to recognize Legionella species early as a potential cause of pneumonia.Legionella infection remains underdiagnosed because of the nonspecific nature of clinical features and the shortcomings of routinely available diagnostic tests.[2]Metagenomic next-generation sequencing(mNGS)is a culture-free and hypothesis-free diagnostic method that can rapidly identify almost all known pathogens in a sample.[3]Here,we present a successfully cured case of rhabdomyolysis and AKI caused by Legionella pneumophila with etiologic diagnosis aided by the use of mNGS.展开更多
Tracking the movement of droplets in digital microfluidics is essential to improve its control stability and obtain dynamic information for its applications such as point-of-care testing,environment monitoring and che...Tracking the movement of droplets in digital microfluidics is essential to improve its control stability and obtain dynamic information for its applications such as point-of-care testing,environment monitoring and chemical synthesis.Herein,an intelligent,accurate and fast droplet tracking method based on machine vision is developed for applications of digital microfluidics.To continuously recognize the transparent droplets in real-time and avoid the interferes from background patterns or inhomogeneous illumination,we introduced the correlation filter tracker,enabling online learning of the multi-features of the droplets in Fourier domain.Results show the proposed droplet tracking method could accurately locate the droplets.We also demonstrated the capacity of the proposed method for estimation of the droplet velocity as faster as 20 mm/s,and its application in online monitoring the Griess reaction for both colorimetric assay of nitrite and study of reaction kinetics.展开更多
Let H be a finite-dimensional pointed rank one Hopf algebra of nilpotent type over a finite group G.In this paper,we investigate the McKay matrix WV of H for tensoring with the 2-dimensional indecomposable H-module V:...Let H be a finite-dimensional pointed rank one Hopf algebra of nilpotent type over a finite group G.In this paper,we investigate the McKay matrix WV of H for tensoring with the 2-dimensional indecomposable H-module V:=M(2,0).It turns out that the characteristic polynomial,eigenvalues and eigenvectors of WV are related to the character table of the finite group G and a kind of generalized Fibonacci polynomial.Moreover,we construct some eigenvectors of each eigenvalue for WV by using the factorization of the generalized Fibonacci polynomial.As an example,we explicitly compute the characteristic polynomial and eigenvalues of WV and give all eigenvectors of each eigenvalue for WV when G is a dihedral group of order 4N+2.展开更多
Let H2 be Sweedler's 4-dimensional Hopf algebra and r(H2) be the corresponding Green ring of H2. In this paper, we investigate the automorphism groups of Green ring r(H2) and Green algebra F(H2) = r(H2) zF, ...Let H2 be Sweedler's 4-dimensional Hopf algebra and r(H2) be the corresponding Green ring of H2. In this paper, we investigate the automorphism groups of Green ring r(H2) and Green algebra F(H2) = r(H2) zF, where F is a field, whose characteristics is not equal to 2. We prove that the automorphism group of r(H2) is isomorphic to K4, where K4 is the Klein group, and the automorphism group of F(H2) is the semidirect product of Z2 and G, where G = F / {1/2} with multiplication given by a. b = 1 - a - b + 2ab.展开更多
Let g be the finite dimensional simple Lie algebra of type A_n, and let U = U_q(g,Λ)and U= U_q(g,Q)be the quantum groups defined over the weight lattice and over the root lattice, respectively. In this paper, we find...Let g be the finite dimensional simple Lie algebra of type A_n, and let U = U_q(g,Λ)and U= U_q(g,Q)be the quantum groups defined over the weight lattice and over the root lattice, respectively. In this paper, we find two algebraically independent central elements in U for all n ≥ 2 and give an explicit formula of the Casimir elements for the quantum group U = U_q(g,Λ), which corresponds to the Casimir element of the enveloping algebra U(g). Moreover, for n = 2 we give explicitly generators of the center subalgebras of the quantum groups U = U_q(g,Λ) and U = U_q(g,Q).展开更多
The near-group rings are an important class of fusion rings in the theory of tensor categories. In this paper, the irreducible Z+-modules over the near-group fusion ring K(Z3, 3) are explicitly classified. It turns...The near-group rings are an important class of fusion rings in the theory of tensor categories. In this paper, the irreducible Z+-modules over the near-group fusion ring K(Z3, 3) are explicitly classified. It turns out that there are only four inequivalent irreducible Z+-modules of rank 2 and two inequivalent irreducible Z+-modules of rank 4 over K(Z3, 3).展开更多
Let H be a finite-dimensional pointed Hopf algebra of rank one over an algebraically closed field of characteristic zero.In this paper we show that any finitedimensional indecomposable H-module is generated by one ele...Let H be a finite-dimensional pointed Hopf algebra of rank one over an algebraically closed field of characteristic zero.In this paper we show that any finitedimensional indecomposable H-module is generated by one element.In particular,any indecomposable submodule of H under the adjoint action is generated by a special element of H.Using this result,we show that the Hopf algebra H is a principal ideal ring,i.e.,any two-sided ideal of H is generated by one element.As an application,we give explicitly the generators of ideals,primitive ideals,maximal ideals and completely prime ideals of the Taft algebras.展开更多
Let H3 be the 9-dimensional Taft Hopf algebra,let r(H3)be the corresponding Green ring of H3,and let Aut(R(H3))be the automorphism group of Green algebra R(H3)=R■Zr(H3)over the real number fieldR.We prove that the qu...Let H3 be the 9-dimensional Taft Hopf algebra,let r(H3)be the corresponding Green ring of H3,and let Aut(R(H3))be the automorphism group of Green algebra R(H3)=R■Zr(H3)over the real number fieldR.We prove that the quotient group Aut(R(H3))/T1 is isomorphic to the direct product of the dihedral group of order 12 and the cyclic group of order 2,where T1 is the isomorphism class which contains the identity map and is isomorphic to a group G={(c,d)∈R^(2)∣∣(c,d)≠(−1/3,−1/6)}with multiplication given by(c1,d1)⋅(c2,d2)=(c1+c2+2c1c2−4d1d2+2c1d2+2d1c2,d1+d2−2c1c2−2d1d2+4c1d2+4d1c2).展开更多
文摘The triad of Legionella pneumonia,rhabdomyolysis,and acute kidney injury(AKI)is uncommon but can be devastating.[1]It is vital to recognize Legionella species early as a potential cause of pneumonia.Legionella infection remains underdiagnosed because of the nonspecific nature of clinical features and the shortcomings of routinely available diagnostic tests.[2]Metagenomic next-generation sequencing(mNGS)is a culture-free and hypothesis-free diagnostic method that can rapidly identify almost all known pathogens in a sample.[3]Here,we present a successfully cured case of rhabdomyolysis and AKI caused by Legionella pneumophila with etiologic diagnosis aided by the use of mNGS.
基金the financial support from the National Natural Science Foundation of China(Nos.31701698,81972017)Shanghai Key Laboratory of Forensic Medicine,Academy of Forensic Science(No.KF1910)Shanghai Shenkang Hospital Development Center to promote clinical skills and clinical innovation ability in municipal hospitals of the Three-year Action Plan Project(No.SHDC2020CR3006A).
文摘Tracking the movement of droplets in digital microfluidics is essential to improve its control stability and obtain dynamic information for its applications such as point-of-care testing,environment monitoring and chemical synthesis.Herein,an intelligent,accurate and fast droplet tracking method based on machine vision is developed for applications of digital microfluidics.To continuously recognize the transparent droplets in real-time and avoid the interferes from background patterns or inhomogeneous illumination,we introduced the correlation filter tracker,enabling online learning of the multi-features of the droplets in Fourier domain.Results show the proposed droplet tracking method could accurately locate the droplets.We also demonstrated the capacity of the proposed method for estimation of the droplet velocity as faster as 20 mm/s,and its application in online monitoring the Griess reaction for both colorimetric assay of nitrite and study of reaction kinetics.
文摘Let H be a finite-dimensional pointed rank one Hopf algebra of nilpotent type over a finite group G.In this paper,we investigate the McKay matrix WV of H for tensoring with the 2-dimensional indecomposable H-module V:=M(2,0).It turns out that the characteristic polynomial,eigenvalues and eigenvectors of WV are related to the character table of the finite group G and a kind of generalized Fibonacci polynomial.Moreover,we construct some eigenvectors of each eigenvalue for WV by using the factorization of the generalized Fibonacci polynomial.As an example,we explicitly compute the characteristic polynomial and eigenvalues of WV and give all eigenvectors of each eigenvalue for WV when G is a dihedral group of order 4N+2.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 11471282).
文摘Let H2 be Sweedler's 4-dimensional Hopf algebra and r(H2) be the corresponding Green ring of H2. In this paper, we investigate the automorphism groups of Green ring r(H2) and Green algebra F(H2) = r(H2) zF, where F is a field, whose characteristics is not equal to 2. We prove that the automorphism group of r(H2) is isomorphic to K4, where K4 is the Klein group, and the automorphism group of F(H2) is the semidirect product of Z2 and G, where G = F / {1/2} with multiplication given by a. b = 1 - a - b + 2ab.
基金supported by National Natural Science Foundation of China(Grant No.11471282)
文摘Let g be the finite dimensional simple Lie algebra of type A_n, and let U = U_q(g,Λ)and U= U_q(g,Q)be the quantum groups defined over the weight lattice and over the root lattice, respectively. In this paper, we find two algebraically independent central elements in U for all n ≥ 2 and give an explicit formula of the Casimir elements for the quantum group U = U_q(g,Λ), which corresponds to the Casimir element of the enveloping algebra U(g). Moreover, for n = 2 we give explicitly generators of the center subalgebras of the quantum groups U = U_q(g,Λ) and U = U_q(g,Q).
基金This work was supported in part by the National Natural Science Foundation of China (Grant No. 11471282).
文摘The near-group rings are an important class of fusion rings in the theory of tensor categories. In this paper, the irreducible Z+-modules over the near-group fusion ring K(Z3, 3) are explicitly classified. It turns out that there are only four inequivalent irreducible Z+-modules of rank 2 and two inequivalent irreducible Z+-modules of rank 4 over K(Z3, 3).
基金supported by the National Natural Science Foundation of China(Grant No.11871063)supported by the Qing Lan project.
文摘Let H be a finite-dimensional pointed Hopf algebra of rank one over an algebraically closed field of characteristic zero.In this paper we show that any finitedimensional indecomposable H-module is generated by one element.In particular,any indecomposable submodule of H under the adjoint action is generated by a special element of H.Using this result,we show that the Hopf algebra H is a principal ideal ring,i.e.,any two-sided ideal of H is generated by one element.As an application,we give explicitly the generators of ideals,primitive ideals,maximal ideals and completely prime ideals of the Taft algebras.
基金Supported by the National Natural Science Foundation of China(Nos.11661014,11701499,11871063,and 11711530703)the Research Innovation Program Project of Academic Degree Graduate Students in Jiangsu(XKYCX17_029)the Excellent Doctoral Dissertation Foundation Project of Yangzhou University in 2018.
文摘Let H3 be the 9-dimensional Taft Hopf algebra,let r(H3)be the corresponding Green ring of H3,and let Aut(R(H3))be the automorphism group of Green algebra R(H3)=R■Zr(H3)over the real number fieldR.We prove that the quotient group Aut(R(H3))/T1 is isomorphic to the direct product of the dihedral group of order 12 and the cyclic group of order 2,where T1 is the isomorphism class which contains the identity map and is isomorphic to a group G={(c,d)∈R^(2)∣∣(c,d)≠(−1/3,−1/6)}with multiplication given by(c1,d1)⋅(c2,d2)=(c1+c2+2c1c2−4d1d2+2c1d2+2d1c2,d1+d2−2c1c2−2d1d2+4c1d2+4d1c2).
基金This work was supported by the National Natural Science Foundation of China (Grant No. 11471282), the China Postdoctoral Science Foundation (Grant No. 2017M610316), and the Natural Science Foundation of Jiangsu Province (Grant No. BK20170589).