We obtain some methods to construct a (strongly) proper resolution (resp. coproper coresolution) of one end term in a short exact sequence from that of the other two terms. By using this method, we prove that for a left and right Noetherian ring R, RR satisfies the Auslander condition if and only if so does every flat left R-module, if and only if the injective dimension of the ith term in a mi...

Let L be a two component link in S, an embedding of two disjoint circles which is topologically locally flat, that is, which extends to an embedding of two solid tori. The link has Alexander polynomial one, if, and only if, the first homology of the universal abelian cover of the complement of the link vanishes. If the link has Alexander polynomial one, then the linking number of the two compon...

We consider several natural fragments of the alternating-time temporal logics ATL* and ATL with restrictions on the nesting between temporal operators and strategic quantifiers. We develop optimal decision procedures for satisfiability in these fragments, showing that they have much lower complexities than the full languages. In particular, we prove that the satisfiability problem for state for...

A recent variation of the classical geodetic problem, the strong geodetic problem, is defined as follows. If G is a graph, then sg(G) is the cardinality of a smallest vertex subset S, such that one can assign a fixed geodesic to each pair {x, y} ⊆ S so that these (|S| 2 ) geodesics cover all the vertices of G. In this paper, the strong geodetic problem is studied on Cartesian product graphs. A ...

As wildland fire frequency increases around the globe, a better understanding of the patterns of plant community recovery in burned landscapes is needed to improve rehabilitation efforts. We measured establishment of seeded species, colonization of Bromus tectorum and other nonnative annual plants, and recovery of nonseeded native species in topographically distinct areas within five fires that...

We provide examples of flat Laguerre planes of Kleinewillinghöfer type E, thus completing the classification of flat Laguerre planes with respect to Laguerre translations in B. Polster and G.F. Steinke, Results Maths. (2004). These planes are obtained by a method for constructing a new flat Laguerre plane from three given Laguerre planes devised in B. Polster and G. Steinke, Canad. Math. Bull. ...

Let $T=\biggl(\begin{matrix} A&0\\U&B\end{matrix}\biggr)$ be a formal triangular matrix ring, where $A$ and $B$ are rings $U$ is $(B, A)$-bimodule. We first give some computing formulas of projective, injective, flat $FP$-injective dimensions special left $T$-modules. Then we establish (weak) global $T$. It proven that (1) If $U_{A}$ $_{B}U$ $lD(A)\neq lD(B)$, then $lD(T)={\rm m...

This paper examines the relationship of C-band radar backscatter from the Advanced Synthetic Aperture Radar on board the ENVISAT satellite with the local angle of incidence, whose influence on the received signal is significant, particularly in the modes of sensor operation that use the full swath of the orbit track. Linear regression is carried out for each pixel throughout a large time series...

Aim: The aim of this is to evaluate the effects on vitrectomy with inverted internal limiting membrane (ILM) flap technique versus complete ILM peeling (standard macular hole surgery) for large diameter greater than 400 micron.Design: A prospective, randomized clinical trialParticipants: patients holes larger micron were included. In group A,75 eyes 75 underwent standard surgery peeling. in B,7...