University courses should have both breadth and depth.However,most courses in universities only focus on the breadth construction,while neglecting the depth construction,resulting in students being unable to apply the...University courses should have both breadth and depth.However,most courses in universities only focus on the breadth construction,while neglecting the depth construction,resulting in students being unable to apply the knowledge they have learned to conduct research or solve real-world application problems.The students’high-level abilities are insufficient and not well-trained.Therefore,in this paper,we propose a T-structured course design method to ensure both breadth and depth of a course.The proposed T-structured course design method includes four aspects:T-structured course contents,T-structured teaching activities,T-structured examination formats,and T-structured homework difficulty.By applying our proposed T-structured course design strategy to the course Optimization Algorithms and Intelligent Computing,good results are achieved,demonstrating the applicability of our proposed strategy.展开更多
In this paper, we study the homotopy category of unbounded complexes of strongly copure projective modules with bounded relative homologies K;（SCP）.We show that the existence of a right recollement of K;（SCP） with...In this paper, we study the homotopy category of unbounded complexes of strongly copure projective modules with bounded relative homologies K;（SCP）.We show that the existence of a right recollement of K;（SCP） with respect to K;（SCP）, K;（SCP） and K;（SCP） has the homotopy category of strongly copure projective acyclic complexes as a triangulated subcategory in some case.展开更多
The aim of this paper is two-fold.Given a recollement(T′,T,T′′,i*,i_*,i~!,j!,j*,j*),where T′,T,T′′are triangulated categories with small coproducts and T is compactly generated.First,the authors show that the BB...The aim of this paper is two-fold.Given a recollement(T′,T,T′′,i*,i_*,i~!,j!,j*,j*),where T′,T,T′′are triangulated categories with small coproducts and T is compactly generated.First,the authors show that the BBD-induction of compactly generated t-structures is compactly generated when i*preserves compact objects.As a consequence,given a ladder(T′,T,T′′,T,T′) of height 2,then the certain BBD-induction of compactly generated t-structures is compactly generated.The authors apply them to the recollements induced by homological ring epimorphisms.This is the first part of their work.Given a recollement(D(B-Mod),D(A-Mod),D(C-Mod),i*,i_*,i~!,j!,j*,j_*) induced by a homological ring epimorphism,the last aim of this work is to show that if A is Gorenstein,AB has finite projective dimension and j! restricts to D^b(C-mod),then this recollement induces an unbounded ladder(B-Gproj,A-Gproj,C-Gproj) of stable categories of finitely generated Gorenstein-projective modules.Some examples are described.展开更多
With the wide application of the fifth-generation mobile communication system(5G)technology,wireless communication equipment tends to develop in miniaturization,high frequency,and low loss.In this paper,a surface acou...With the wide application of the fifth-generation mobile communication system(5G)technology,wireless communication equipment tends to develop in miniaturization,high frequency,and low loss.In this paper,a surface acoustic wave(SAW)filter with a center frequency of 3.5 GHz was designed.Firstly,the acoustic waveguide structure of the longitudinal leaky SAW(LLSAW)excitation is determined,and the two-dimensional(2D)theoretical model of the device is established by COMSOL Multiphysics.Secondly,the influence of electrode parameters on the performance of the device is studied,and the electrode parameters are optimized on this basis.By setting the device structure parameters reasonably,the spurious in the passband can be effectively suppressed.Finally,the center frequency of the mirror T-structure LLSAW filter is 3.536 GHz,the insertion loss is-1.414 dB,the bandwidth of-3 dB is 276 MHz,and the out-of-band rejection is greater than-30 dB.展开更多
The concept of Koszulity for differential graded (DG, for short) modules is introduced. It is shown that any bounded below DG module with bounded Ext-group to the trivial module over a Koszul DG algebra has a Koszul D...The concept of Koszulity for differential graded (DG, for short) modules is introduced. It is shown that any bounded below DG module with bounded Ext-group to the trivial module over a Koszul DG algebra has a Koszul DG submodule (up to a shift and truncation), moreover such a DG module can be approximated by Koszul DG modules (Theorem 3.6). Let A be a Koszul DG algebra, and Dc(A) be the full triangulated subcategory of the derived category of DG A-modules generated by the object AA. If the trivial DG module kA lies in Dc(A), then the heart of the standard t-structure on Dc(A) is anti-equivalent to the category of finitely generated modules over some finite dimensional algebra. As a corollary, Dc(A) is equivalent to the bounded derived category of its heart as triangulated categories.展开更多
This paper investigates the structure of the"missing part"from the category of coherent sheaves over a weighted projective line of weight type(2,2,n)to the category of finitely generated right modules on the...This paper investigates the structure of the"missing part"from the category of coherent sheaves over a weighted projective line of weight type(2,2,n)to the category of finitely generated right modules on the associated canonical algebra.By constructing a t-structure in the stable category of the vector bundle category,we show that the"missing part"is equivalent to the heart of the t-structure,hence it is abelian.Moreover,it is equivalent to the category of finitely generated modules on the path algebra of type An-1.展开更多
We introduce diagrams for m-cluster categories which we call "horizontal" and "vertical" mutation fans. These are analogous to the mutation fans(also known as "semi-invariant pictures" or...We introduce diagrams for m-cluster categories which we call "horizontal" and "vertical" mutation fans. These are analogous to the mutation fans(also known as "semi-invariant pictures" or "scattering diagrams") for the standard(m = 1) cluster case, which are dual to the poset of finitely generated torsion classes. The purpose of these diagrams is to visualize mutations and analogues of maximal green sequences in the m-cluster category with special emphasis on the c-vectors(the "brick" labels).展开更多
基金supported in part by the fund of 2023 Guangdong Province Science and Technology Innovation Strategy Special Project“Construction of Industrial Data and Intelligent Application Innovation Platform”(2023A011),2024 Shanwei New Generation Electronic Information Industry Talent Revitalization Plan,and the project“Research on the Impact and Countermeasures of Large Scale Charging Facility Access on Guangdong Power Grid Planning and Construction.”。
文摘University courses should have both breadth and depth.However,most courses in universities only focus on the breadth construction,while neglecting the depth construction,resulting in students being unable to apply the knowledge they have learned to conduct research or solve real-world application problems.The students’high-level abilities are insufficient and not well-trained.Therefore,in this paper,we propose a T-structured course design method to ensure both breadth and depth of a course.The proposed T-structured course design method includes four aspects:T-structured course contents,T-structured teaching activities,T-structured examination formats,and T-structured homework difficulty.By applying our proposed T-structured course design strategy to the course Optimization Algorithms and Intelligent Computing,good results are achieved,demonstrating the applicability of our proposed strategy.
文摘In this paper, we study the homotopy category of unbounded complexes of strongly copure projective modules with bounded relative homologies K;（SCP）.We show that the existence of a right recollement of K;（SCP） with respect to K;（SCP）, K;（SCP） and K;（SCP） has the homotopy category of strongly copure projective acyclic complexes as a triangulated subcategory in some case.
文摘The aim of this paper is two-fold.Given a recollement(T′,T,T′′,i*,i_*,i~!,j!,j*,j*),where T′,T,T′′are triangulated categories with small coproducts and T is compactly generated.First,the authors show that the BBD-induction of compactly generated t-structures is compactly generated when i*preserves compact objects.As a consequence,given a ladder(T′,T,T′′,T,T′) of height 2,then the certain BBD-induction of compactly generated t-structures is compactly generated.The authors apply them to the recollements induced by homological ring epimorphisms.This is the first part of their work.Given a recollement(D(B-Mod),D(A-Mod),D(C-Mod),i*,i_*,i~!,j!,j*,j_*) induced by a homological ring epimorphism,the last aim of this work is to show that if A is Gorenstein,AB has finite projective dimension and j! restricts to D^b(C-mod),then this recollement induces an unbounded ladder(B-Gproj,A-Gproj,C-Gproj) of stable categories of finitely generated Gorenstein-projective modules.Some examples are described.
文摘With the wide application of the fifth-generation mobile communication system(5G)technology,wireless communication equipment tends to develop in miniaturization,high frequency,and low loss.In this paper,a surface acoustic wave(SAW)filter with a center frequency of 3.5 GHz was designed.Firstly,the acoustic waveguide structure of the longitudinal leaky SAW(LLSAW)excitation is determined,and the two-dimensional(2D)theoretical model of the device is established by COMSOL Multiphysics.Secondly,the influence of electrode parameters on the performance of the device is studied,and the electrode parameters are optimized on this basis.By setting the device structure parameters reasonably,the spurious in the passband can be effectively suppressed.Finally,the center frequency of the mirror T-structure LLSAW filter is 3.536 GHz,the insertion loss is-1.414 dB,the bandwidth of-3 dB is 276 MHz,and the out-of-band rejection is greater than-30 dB.
基金supported by National Natural Science Foundation of China (Grant No.10801099)Doctorate Foundation of Ministry of Education of China (Grant No.20060246003)Foundation of Zhejiang Province's Educational Committee (Grant No.20070501)
文摘The concept of Koszulity for differential graded (DG, for short) modules is introduced. It is shown that any bounded below DG module with bounded Ext-group to the trivial module over a Koszul DG algebra has a Koszul DG submodule (up to a shift and truncation), moreover such a DG module can be approximated by Koszul DG modules (Theorem 3.6). Let A be a Koszul DG algebra, and Dc(A) be the full triangulated subcategory of the derived category of DG A-modules generated by the object AA. If the trivial DG module kA lies in Dc(A), then the heart of the standard t-structure on Dc(A) is anti-equivalent to the category of finitely generated modules over some finite dimensional algebra. As a corollary, Dc(A) is equivalent to the bounded derived category of its heart as triangulated categories.
基金supported by National Natural Science Foundation of China(Grant Nos.11201386,10931006,11071040 and 11201388)the Natural Science Foundation of Fujian Province of China(Grant No.2012J05009)
文摘This paper investigates the structure of the"missing part"from the category of coherent sheaves over a weighted projective line of weight type(2,2,n)to the category of finitely generated right modules on the associated canonical algebra.By constructing a t-structure in the stable category of the vector bundle category,we show that the"missing part"is equivalent to the heart of the t-structure,hence it is abelian.Moreover,it is equivalent to the category of finitely generated modules on the path algebra of type An-1.
文摘We introduce diagrams for m-cluster categories which we call "horizontal" and "vertical" mutation fans. These are analogous to the mutation fans(also known as "semi-invariant pictures" or "scattering diagrams") for the standard(m = 1) cluster case, which are dual to the poset of finitely generated torsion classes. The purpose of these diagrams is to visualize mutations and analogues of maximal green sequences in the m-cluster category with special emphasis on the c-vectors(the "brick" labels).
