We introduce the concept of maximal orthogonal subcategories over artin algebras and orders, and develop higher Auslander-Reiten theory on them. Auslander-Reiten theory, especially the concept of almost split sequences and their existence theorem, is fundamental to study categories which appear in representation theory, for example, modules over artin algebras [ARS][GR][Ri], their functorially ...

In the title mol-ecule, C(17)H(11)N(11), the five rings are almost coplanar [maxium deviation 0.1949 (1) Å]. The dihedral angles between the two pyrazine rings and the two triazole rings are 1.52 (4) and 2.51 (5)°, respectively. The central pyridine ring forms dihedral angles of 5.57 (1) and 1.71 (1)° with the two triazole rings. The crystal packing consists of a three-dimensional network struc...

We present an oracle factorisation algorithm, which in polynomial deterministic time, finds a nontrivial factor of almost all positive integers n based on the knowledge number points certain elliptic curves residue rings modulo n.

We introduce the concept of maximal orthogonal subcategories over artin algebras and orders, and develop higher Auslander-Reiten theory on them. Auslander-Reiten theory, especially the concept of almost split sequences and their existence theorem, is fundamental to study categories which appear in representation theory, for example, modules over artin algebras [ARS][GR][Ri], their functorially ...

In the title mol-ecule, C(15)H(14)N(2)O(4), the dihedral angle between the two benzene rings is 29.52 (8)°. The nitro and two meth-oxy substituents are almost coplanar with their respective benzene rings. The crystal structure is stabilized by inter-molecular C-H⋯O inter-actions.

We empirically analyze and compare two distributed, low-overhead policies for scheduling dynamic treestructured computations on rings of identical PEs. Our experiments show that both policies give significant parallel speedup on large classes of computations, and that one yields almost optimal speedup on moderate size rings. We believe that our methodology of experiment design and analysis will...

In the title compound, [Fe(C5H5)(C9H6ClN2)], the two cyclo-penta-dienyl rings are almost parallel, subtending a dihedral angle of 3.01 (5)°. The dihedral angle between the substituted cyclo-penta-dienyl ring and the pyrimidinyl ring is 12.02 (1)°. The conformation of the two cyclopentadienyl rings in the ferrocenyl moiety is eclipsed.