Finite generation of the cohomology rings for the extension algebras of monomial algebras

We describe the cohomology ring of a monomial algebra in the language of dimension tree or minimal resolution graph and in this context we study the finite generation of the cohomology rings of the extension algebras, showing among others that the cohomology ring [Formula: see text] is finitely generated [Formula: see text] is [Formula: see text] is, where [Formula: see text] is the dual extension of a monomial algebra [Formula: see text] and [Formula: see text] is the opposite algebra of [Formula: see text].

Hypercomplex Algebras and Calculi Derived from Generalized Kinematics

The paper provides a study of the commutative algebras generated by iteration of the cross products in $\mathbb{C}^3$. Focusing on particular real forms we also consider the analytical properties of the corresponding rings of functions and relate them to different physical problems. Familiar results from the theory of holomorphic and bi-holomorphic functions appear naturally in this context, but new types of hypercomplex calculi emerge as well. The parallel transport along smooth curves in $\mathbb{E}^3$ and the associated Maurer-Cartan form are also studied with examples from kinematics and electrodynamics. Finally, the dual extension is discussed in the context of screw calculus and Galilean mechanics; a similar construction is studied also in the multi-dimensional real and complex cases.

Jordan derivations of generalized one point extensions

For a generalized one-point extension algebra, it is proved that under certain conditions, each Jordan derivation is the sum of a derivation and an anti-derivation. Moreover, we prove that every Jordan derivation of a dual extension algebra is a derivation.

Design Application of LQS20000 Column Strength Test Bench

Analyzed the trend of the development of hydraulic powered support and column, this paper designs a column strength test bench with 20000KN working resistance which combined with the new release of GB25974.2-2010 for coal mine hydraulic support and jack technical conditions of Part 2 standard requirements. Through the practical application, it turned out that the test bench has reasonable structure, stable performance and it can meet all of the following Ф630 bore hydraulic support column factory test requirements. The trend of the mine-used hydraulic support column and the performed new criterion demands manufacturers to enhance the ability of test equipment. In this situation, the 20000KN column strength test bench our company designed and manufactured not only do the loading test, but also apply external load at columns by simulating the actual working conditions, which is essential to Inspection and testing of dual-extension hydraulic columns middle cylinder strength.