scholarly journals ON THE EXISTENCE OF A DERIVED EQUIVALENCE BETWEEN A KOSZUL ALGEBRA AND ITS YONEDA ALGEBRA

2014 ◽  
Vol 13 (04) ◽  
pp. 1350136
Author(s):  
R. M. AQUINO ◽  
E. N. MARCOS ◽  
S. TREPODE
Keyword(s):  
Sufficient Conditions ◽  
Derived Categories ◽  
Koszul Algebras ◽  
Derived Equivalence ◽  
Koszul Algebra ◽  
Yoneda Algebra ◽  
Hereditary Algebras ◽  
Yoneda Algebras ◽  
Necessary And Sufficient ◽  
Simply Connected

In this paper, we study the derived categories of a Koszul algebra and its Yoneda algebra to determine when those categories are triangularly equivalent. We prove that the simply connected Koszul algebras are derived equivalent to their Yoneda algebras. We have considered discrete Koszul algebras and we gave necessary and sufficient conditions for those Koszul algebras to be derived equivalent to their Yoneda algebras. We also study the class of Koszul algebras which are derived equivalent to hereditary algebras. For the case where the hereditary algebra is tame, we characterized the derived equivalence between those Koszul algebras and their Yoneda algebras.

scholarly journals On dimensions supporting a rational projective plane

2019 ◽  
Vol 11 (03) ◽  
pp. 535-555 ◽  
Author(s):  
Lee Kennard ◽  
Zhixu Su
Keyword(s):  
Projective Plane ◽  
Open Problem ◽  
Sufficient Conditions ◽  
Quadratic Residue ◽  
Bernoulli Numbers ◽  
Existence Results ◽  
Necessary And Sufficient ◽  
Simply Connected ◽  
Existence Question ◽  
Smooth Closed Manifold

A rational projective plane ([Formula: see text]) is a simply connected, smooth, closed manifold [Formula: see text] such that [Formula: see text]. An open problem is to classify the dimensions at which such a manifold exists. The Barge–Sullivan rational surgery realization theorem provides necessary and sufficient conditions that include the Hattori–Stong integrality conditions on the Pontryagin numbers. In this paper, we simplify these conditions and combine them with the signature equation to give a single quadratic residue equation that determines whether a given dimension supports a [Formula: see text]. We then confirm the existence of a [Formula: see text] in two new dimensions and prove several non-existence results using factorization of the numerators of the divided Bernoulli numbers. We also resolve the existence question in the Spin case, and we discuss existence results for the more general class of rational projective spaces.

An Inverse Eigenvalue Problem for Spring-Mass Systems with Partial Mass Connected to the Ground

2013 ◽  
Vol 353-356 ◽  
pp. 3308-3311
Author(s):  
Xia Tian ◽  
Chuan Xiao Li
Keyword(s):  
Total Mass ◽  
Sufficient Conditions ◽  
Inverse Eigenvalue Problem ◽  
Spring Stiffness ◽  
Positive Mass ◽  
Mass System ◽  
Inverse Eigenvalue ◽  
Physical Elements ◽  
Necessary And Sufficient ◽  
Simply Connected

Consider the simply connected spring-mass system with partial mass connected to the ground. The inverse mode problem of constructing the physical elements of the system from two eigenpairs, the grounding spring stiffness and total mass of the system is considered. The necessary and sufficient conditions for constructing a physical realizable system with positive mass and stiffness elements are established. If these conditions are satisfied, the grounding spring-mass system may be constructed uniquely. The numerical methods and examples are given finally.

An Inverse Mode Problem for the Rod on Elastic Foundation

2013 ◽  
Vol 353-356 ◽  
pp. 3198-3201
Author(s):  
Xia Tian ◽  
Chuan Xiao Li
Keyword(s):  
Numerical Methods ◽  
Elastic Foundation ◽  
Discrete Model ◽  
Sufficient Conditions ◽  
Spring Stiffness ◽  
Positive Mass ◽  
Mass System ◽  
Physical Elements ◽  
Necessary And Sufficient ◽  
Simply Connected

Consider the rod on elastic foundation. Its discrete model is the simply connected spring-mass system with partial mass connected to the ground. The inverse mode problem of constructing the physical elements of the system from two eigenpairs, the spring stiffness of the system is considered. The necessary and sufficient conditions for constructing a physical realizable system with positive mass and stiffness elements are established. If these conditions are satisfied, the rod on the elastic foundation may be constructed uniquely. The numerical methods and examples are given finally.

MODULES WITH PURE RESOLUTIONS OVER KOSZUL ALGEBRAS

2014 ◽  
Vol 13 (05) ◽  
pp. 1350159 ◽  
Author(s):  
JIAFENG LÜ
Keyword(s):  
Jacobson Radical ◽  
Koszul Algebras ◽  
Finitely Generated ◽  
Koszul Algebra ◽  
Yoneda Algebra

Let A be a Koszul algebra and M a finitely generated graded A-module. Suppose that M is generated in degree 0 and has a pure resolution. We prove that, if rℰ(M) ≠ 0 then M is Koszul; and if in addition M is not projective, then the converse is true as well, where r denotes the graded Jacobson radical of the Yoneda algebra [Formula: see text] of A, and [Formula: see text] denotes the Ext module of M.

An Inverse Mode Problems for Simply Connected Central Symmetric Spring-Mass Systems

2012 ◽  
Vol 166-169 ◽  
pp. 3399-3402
Author(s):  
Xia Tian ◽  
Chuan Xiao Li
Keyword(s):  
Numerical Methods ◽  
Total Mass ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Positive Mass ◽  
Mass System ◽  
Physical Elements ◽  
Necessary And Sufficient ◽  
Simply Connected

Given the odd /even degree eigenpair and the even degree eigenpair of a simply connected central symmetric spring-mass system respectively. The inverse mode problem of constructing the physical elements of the system from two eigenpairs and the total mass of the system is considered. The necessary and sufficient conditions for constructing of a physical realizable system with positive mass and stiffness elements are established. If these conditions are satisfied, the simply connected central symmetric spring-mass system may be constructed uniquely. The numerical methods and examples are given finally.

scholarly journals Some Conditions on Trans-Sasakian Manifolds to Be Homothetic to Sasakian Manifolds

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1887
Author(s):  
Sharief Deshmukh ◽  
Amira Ishan ◽  
Olga Belova ◽  
Suha B. Al-Shaikh
Keyword(s):  
Sufficient Conditions ◽  
Sasakian Manifold ◽  
Necessary And Sufficient Conditions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Sasakian Manifolds ◽  
3 Dimensional ◽  
Necessary And Sufficient ◽  
Simply Connected

In this paper, we study 3-dimensional compact and connected trans-Sasakian manifolds and find necessary and sufficient conditions under which these manifolds are homothetic to Sasakian manifolds. First, four results in this paper deal with finding necessary and sufficient conditions on a compact and connected trans-Sasakian manifold to be homothetic to a compact and connected Sasakian manifold, and the fifth result deals with finding necessary and sufficient condition on a connected trans-Sasakian manifold to be homothetic to a connected Sasakian manifold. Finally, we find necessary and sufficient conditions on a compact and simply connected trans-Sasakian manifold to be homothetic to a compact and simply connected Einstein Sasakian manifold.

The moments of the number of exits from a simply connected region

1998 ◽  
Vol 30 (1) ◽  
pp. 167-180 ◽  
Author(s):  
Robert Illsley
Keyword(s):  
Integral Formula ◽  
Sufficient Conditions ◽  
Moment Matrix ◽  
Expected Number ◽  
Factorial Moments ◽  
Gaussian Case ◽  
Simply Connected Region ◽  
Necessary And Sufficient ◽  
Simply Connected ◽  
Stationary Vector

We generalise the work of Cramér and Leadbetter, Ylvisaker and Ito on the level crossings of a stationary Gaussian process to multivariate processes. Necessary and sufficient conditions for the existence of the expected number of crossings E(C) of the boundary of a region of ℝp by a stationary vector stochastic process are obtained, along with an explicit formula for E(C) in the Gaussian case. A rigorous proof of Belyaev's integral formula for the factorial moments of the number of exits from a region of ℝp is given for a class of processes which includes Gaussian processes having a finite second order spectral moment matrix. Applications to χ2 processes are briefly considered.

Modules with pure resolutions over Koszul algebras revisited

2015 ◽  
Vol 15 (02) ◽  
pp. 1650035 ◽  
Author(s):  
Thomas Cassidy
Keyword(s):  
Jacobson Radical ◽  
Koszul Algebras ◽  
Finitely Generated ◽  
Koszul Algebra ◽  
Yoneda Algebra ◽  
Koszul Module

I construct a Koszul algebra A and a finitely generated graded A-module M that together form a counterexample to a recently published claim. M is generated in degree 0 and has a pure resolution, and the graded Jacobson radical of the Yoneda algebra of A does not annihilate the Ext module of M, but nonetheless M is not a Koszul module.

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