Dual Splitting Research Articles

Long-term effect of placement of fertilizer nitrogen and phosphorus on barley yields

An experiment that was established in 1990 to assess depth and method of placement of nitrogen (N) and phosphorus (P) fertilizer on the yield of continuous barley (with 1 yr interruption with canola in 1995) was continued to 2001. Annually, 80 kg N ha-1 were banded either at 7.5 to 10 or 15 to 17.5 cm depth alone or in combination with 40 kg P2O5 ha-1; the latter was either seedrow placed or banded with the N (dual banding), or split 1/2 in the seedrow and 1/2 in the band. An unfertilized control was maintained in all years. Temperature after seeding had a marked effect on the effectiveness of depth of N and P placement as well as the method of P placement. Shallow (7.5 to 10 cm depth) placement resulted in greater yields in 8 of the 11 yr that barley was grown and was never inferior to deeper placement (15 to 17.5 cm); this advantage was directly related to cooler-than-normal temperature after seeding. Cooler-than-normal temperatures also resulted in benefits from seedrow placed P; however, benefits were not as frequent as those obtained by either dual banding or splitting P between seedrow and the band. It would appear that overall benefits from banding P together with N (dual band), independently of the depth of banding, are greater than those from seedrow placing, as those benefits from the latter are less frequent and of considerably less magnitude. Key words: Band, dual band, seedrow, shallow, deep

Real-time optimal adaptation for planetary geometry and texture: 4-8 tile hierarchies

The real-time display of huge geometry and imagery databases involves view-dependent approximations, typically through the use of precomputed hierarchies that are selectively refined at runtime. A classic motivating problem is terrain visualization in which planetary databases involving billions of elevation and color values are displayed on PC graphics hardware at high frame rates. This paper introduces a new diamond data structure for the basic selective-refinement processing, which is a streamlined method of representing the well-known hierarchies of right triangles that have enjoyed much success in real-time, view-dependent terrain display. Regular-grid tiles are proposed as the payload data per diamond for both geometry and texture. The use of 4-8 grid refinement and coarsening schemes allows level-of-detail transitions that are twice as gradual as traditional quadtree-based hierarchies, as well as very high-quality low-pass filtering compared to subsampling-based hierarchies. An out-of-core storage organization is introduced based on Sierpinski indices per diamond, along with a tile preprocessing framework based on fine-to-coarse, same-level, and coarse-to-fine gathering operations. To attain optimal frame-to-frame coherence and processing-order priorities, dual split and merge queues are developed similar to the Realtime Optimally Adapting Meshes (ROAM) Algorithm, as well as an adaptation of the ROAM frustum culling technique. Example applications of lake-detection and procedural terrain generation demonstrate the flexibility of the tile processing framework.

Implementation of the fixed point method in contact problems with Coulomb friction based on a dual splitting type technique

The paper deals with the numerical solution of the quasi-variational inequality describing the equilibrium of an elastic body in contact with a rigid foundation under Coulomb friction. After a discretization of the problem by mixed finite elements, the duality approach is exploited to reduce the problem to a sequence of quadratic programming problems with box constraints, so that efficient recently proposed algorithms may be applied. A new variant of this method is presented. It combines fixed point with block Gauss–Seidel iterations. The method may be also considered as a new implementation of fixed point iterations for a sequence of problems with given friction. Results of numerical experiments are given showing that the resulting algorithm may be much faster than the original fixed point method and its efficiency is comparable with the solution of frictionless contact problems.

Blurring Boundaries: The Limits of "White Town" in Colonial Calcutta

Scholars assume colonial Calcutta was a dual city split into "black" and "white" towns. The critical aspect of colonial Calcutta, however, did not lie in such divisions, but in the blurring of boundaries between the two. The rhetorical categories of "white" and "black" towns were used to sustain the British desire to maintain difference in a city in which everyday life compromised such distinctions. The central argument of this essay rests on an analysis of a clearly distinguishable "pattern" of nineteenth-century colonial buildings that borrowed from indigenous as well as foreign sources. It is only by juxtaposing the spatial analysis with written and pictorial documentation that we can understand how these spaces operated in everyday practice. The attempt is to bridge the gap between rhetoric and practice, and to suggest that the spatial structure of Calcutta, from the building scale to the city scale, spoke of the hybrid conditions of colonial culture-a hybridity that did not simply reside in the native body and the native city, but one that the colonizers themselves inhabited.

Existence of bases and the dual splitting relation for Fréchet spaces

Existence of bases and the dual splitting relation for Fréchet spaces