We call a module M , quasi-catenary if for each pair of quasi-prime submodules K and L of M with K L all saturated chains of quasi-prime submodules of M from K to L have a common finite length. We show that any homomorphic image of a quasi-catenary module is quasi-catenary. We prove that if M   is a module with following properties: (i) Every quasi-prime submodule of M has finite quasi-height;...

The main theorem says that any module-finite (but not necessarily commutative) algebra Λ over a commutative Noetherian universally catenary ring R is catenary. Hence the ring Λ is catenary if R is Cohen-Macaulay. When R is local and Λ is a Cohen-Macaulay R-module, we have that Λ is a catenary ring, dim Λ = dimΛ/Q + htΛQ for any Q ∈ Spec Λ, and the equality n = htΛQ− htΛP holds true for any pair...

Let R be a universally catenary locally equidimensional Noetherian ring. We give a multiplicity based criterion for an arbitrary finitely generated R-module to be integral over a submodule. Our proof is self-contained and implies the previously known numerical criteria for integral dependence of ideals and modules.

Let A be a Noetherian local domain, N be a finitely generated torsion-free module, and M a proper submodule that is generically equal to N . Let A[N ] be an arbitrary graded overdomain of A generated as an A-algebra by N placed in degree 1. Let A[M ] be the subalgebra generated by M . Set C := Proj(A[M ]) and r := dimC. Form the (closed) subset W of Spec(A) of primes p where A[N ]p is not a fin...

Dynamic pantograph-catenary interaction is one of the most critical aspects to consider in catenary design, especially in high-speed rails. It is essential to maintain a constant power transmission in order to achieve high speeds and avoid the production of electric arcs, which damage the wires. This paper shows a tool, called InDiCa 3D, based on a three-dimensional model to solve the dynamic p...

Let NA be the monoid generated byA = {a1, . . . ,an} ⊆ Z.We introduce the homogeneous catenary degree of NA as the smallest N ∈ N with the following property: for each a ∈ NA and any two factorizations u,v of a, there exists factorizations u = w1, . . . ,wt = v of a such that, for every k, d(wk,wk+1) ≤ N, where d is the usual distance between factorizations, and the length of wk, |wk|, is less ...

Pantograph current collectors, especially for high-speed trains, need to ensure safe contact with the catenary under stringent requirements on the dynamic contact force. A novel, high-dynamic pantograph test rig with accurate virtual catenary emulation is presented that allows for efficient, realistic, and reproducible testing. The complex dynamics of the pantograph/catenary interaction is mode...

The notion of the Cousin complex of a module was given by Sharp in 1969. It wasn’t known whether its cohomologies are finitely generated until recently. In 2001, Dibaei and Tousi showed that the Cousin cohomologies of a finitely generated A-module M are finitely generated if the base ring A is local, has a dualizing complex, M satisfies Serre’s (S2)-condition and is equidimensional. In the pres...

The dynamic simulation system of a pantograph and a catenary has been built by using the finite element method, in which the pantograph is equivalent to a threemass-damper-stiffness system and the catenary contains only cable and beam elements. Considering droppers as nonlinear elements only stressed by tension, a sliding contact model of the pantograph and catenary is coupled by penalty functi...

An ultrasonic planar horn with a Bézier profile is developed. The first longitudinal displacement mode of the horn is exploited for high displacement amplification in order to reduce the penetration force required to enter and cut materials. The displacement amplification and stress distribution characteristics of the Bézier horn and the commonly used catenary horn are examined. The penetration...