On Sums of SL(3,Z) Kloosterman Sums

We show that sums of the SL(3,Z) long element Kloosterman sum against a smooth weight function have cancellation due to the variation in argument of the Kloosterman sums, when each modulus is at least the square root of the other. Our main tool is Li's generalization of the Kuznetsov formula on SL(3,R), which has to date been prohibitively difficult to apply. We first obtain analytic expressions for the weight functions on the Kloosterman sum side by converting them to Mellin-Barnes integral form. This allows us to relax the conditions on the test function and to produce a partial inversion formula suitable for studying sums of the long-element SL(3,Z) Kloosterman sums.Comment: 44 pages, 1 figure, Revised version accepted by the Ramanujan Journa

Analogue Modelling of Inverted Oblique Rift Systems

The geometric evolution of brittle fault systems in inverted oblique and offset rift systems has been simulated using scaled sandbox analogue models. Dry fine-grained quartz sand was used to represent the brittle upper crust. Extensional faults geometries in the models were governed by the geometry and orientation of a stretching zone at the base of the models. Oblique rift models were characterized by segmented en-echelon border fault systems trending parallel to the rift axis and the underlying zone of basement stretching. Offset rift models promoted highly-segmented border faults as well as offset sub-basins within the rift. In both types of models, intra-rift fault arrays were oriented sub-perpendicular to the extension direction. Inversion of the oblique and offset extensional models was achieved by horizontal shortening. This resulted in partial inversion of the border and intra-rift faults as well as the formation of new reverse faults. The geometries, distribution, orientations and number of these new reverse faults were strongly controlled by the earlier-formed fault extensional architectures. At the margins of the rift zone, shortening was mainly accommodated by partial inversion of the border faults together with the formation of hanging-wall bypass faults and footwall shortcut thrusts. Inversion of the offset rift models produced reactivation of the extensional accommodation zones as soft-linked transfer zones between new thrust faults. The analogue model results have been compared with natural inversion structures in the Atlas Mountains of Morocco and the Ukrainian Donbas fold belt. The analogue modelling results suggest that the High Atlas formed as the result of oblique inversion of an oblique rift system, and the contractional structures in the Ukranian Donbas belt were generated by partial inversion of the earlier-formed Donbas extensional graben via two major newly developed short-cuts that uplifted and exhumed the basin

catena-Poly[[(2,2′-bipyridine-κ2 N,N′)nickel(II)]-μ-oxalato-κ4 O 1,O 2:O 1′,O 2′]

The title compound, [Ni(C2O4)(C10H8N2)]n, is isostructural with its MnII, FeII, CuII and ZnII analogues. Each NiII atom is chelated by two oxalate ligands and one 2,2′-bipyridine, forming a slightly distorted octa­hedral geometry. Oxlate acts as a bridge to link neighbouring pairs of NiII cations, forming a one-dimensional wave-like chain. The crystal showed partial inversion twinning

Graphical Markov models, unifying results and their interpretation

Graphical Markov models combine conditional independence constraints with graphical representations of stepwise data generating processes.The models started to be formulated about 40 years ago and vigorous development is ongoing. Longitudinal observational studies as well as intervention studies are best modeled via a subclass called regression graph models and, especially traceable regressions. Regression graphs include two types of undirected graph and directed acyclic graphs in ordered sequences of joint responses. Response components may correspond to discrete or continuous random variables and may depend exclusively on variables which have been generated earlier. These aspects are essential when causal hypothesis are the motivation for the planning of empirical studies. To turn the graphs into useful tools for tracing developmental pathways and for predicting structure in alternative models, the generated distributions have to mimic some properties of joint Gaussian distributions. Here, relevant results concerning these aspects are spelled out and illustrated by examples. With regression graph models, it becomes feasible, for the first time, to derive structural effects of (1) ignoring some of the variables, of (2) selecting subpopulations via fixed levels of some other variables or of (3) changing the order in which the variables might get generated. Thus, the most important future applications of these models will aim at the best possible integration of knowledge from related studies.Comment: 34 Pages, 11 figures, 1 tabl

A quaternary germanium(II) phosphate, Na[Ge4(PO4)3]

A new germanium(II) phosphate, sodium tetra­germanium tris­(phosphate), Na[Ge4(PO4)3], has been synthesized by a solid-state reaction. The compound is isotypic with A[Sn4(PO4)3] (A = Na, K, NH4). It features a [Ge4(PO4)3]− framework made up of GeO3 pyramids and PO4 tetra­hedra, which are linked by shared corners, yielding a three-dimensional structure. The crystal studied showed partial inversion twinning