Three equivalence relations are considered on the set of n x n matrices with elements in Fo' an · abelian group with absorbing zero adjoined. They are the relations of diagonal similarity, diagonal equivalence, and restricted diagonal equivalence. These relations are usually considered for matrices with elements in a field, but only multiplication is involved. Thus our formulation in terms of a...

It is a well-known phenomenon in set theory that problems in infinite combinatorics involving singular cardinals and their successors tend to be harder than the parallel problems for regular cardinals. Examples include the behaviour of cardinal exponentiation, the extent of the tree property, the extent of stationary reflection, and the existence of non-free almost-free abelian groups. The expl...

The main objective of this paper is to analyze the geometry of the modular diagonal quotient surface ZN,ε = ∆ε\(X(N) × X(N)) which classifies pairs of elliptic curves E1 and E2 together with an isomorphism of “determinant ε” between their associated modular representations mod N . In particular, we calculate some of the numerical invariants of its minimal desingularization Z̃N,ε such as its Bett...

Bacteria transduce signals across the membrane using two-component systems, consisting of a membranespanning sensor histidine kinase and a cytoplasmic response regulator. The histidine kinase, PhoQ, serves as a master regulator of virulence response in S. typhimurium and E. coli. It also is inhibited by divalent cations, particularly Mg2+. While the periplasmic sensor domain of this protein has...

Interior point methods solve small to medium sized problems to high accuracy in a reasonable amount of time. However, for larger problems as well as stochastic problems, one needs to use first-order methods such as stochastic gradient descent (SGD), the alternating direction method of multipliers (ADMM), and conjugate gradient (CG) in order to attain a modest accuracy in a reasonable number of ...

Notes: 1) The modular diagonal quotient surfaces as defined above may be viewed as a special case of the general diagonal quotient surfaces studied in Kani/Schanz[7]. 2) The inclusions of subsgroups {1} ≤ ∆αε ≤ G × G induce finite morphisms (both of degree m = |G|) YN Φ → ZN,ε Ψ → Y1 ' P × P. Moreover, by using Shimura’s canonical model X(N)/Q, it can be shown that all these varieties have cano...

We introduce the notion of signed diagonal flips on signed surface tri-angulations. We then formulate the conjecture that any two triangulations (without interior vertices) of a given polygon may be transformed into each other by a signable sequence of diagonal flips. Finally, we explain how this conjecture implies the four color theorem.

A diagonal cycle is a cycle of length 2n together with one edge between two vertices at distance n in the cycle. For example, /{4 e is a cycle of length fonr with one extra edge between two vertices at distance two in the cycle. Methods for decomposing the complete graph Kv into diagonal cycles are given when v == 0 (mod 2n + 1) if n is odel, and when v == 1 (mod 2n + 1), if n 3 (mod 4); in the...

computer model of the patellofemoral joint was developed and the effects on the anterior displacement of the tibial tuberosity were investigated. the input geometrical and verification data for the model were obtained form an experimental study on a cadaver knee, mounted in an instron machine. the computer program found the configuration of the patellofemoral joint which satified both the geome...

This paper presents a physical approach to simulate image represented objects’ behaviour. The Finite Element Method (FEM) is employed to physically model the given objects, then modal analysis is used to match some objects’ nodes (by solving the related eigenvalue/vector problem and analysing each node displacement in the respective modal space (Sclaroff, Tavares)), and finally the dynamic equi...