9,273 research outputs found
Chains of large gaps between primes
Let denote the -th prime, and for any and sufficiently
large , define the quantity which measures the occurrence of
chains of consecutive large gaps of primes. Recently, with Green and
Konyagin, the authors showed that for sufficiently large . In this
note, we combine the arguments in that paper with the Maier matrix method to
show that for any fixed and sufficiently large . The
implied constant is effective and independent of .Comment: 16 pages, no figure
Gravity gradient preliminary investigations on exhibit ''A'' Final report
Quartz microbalance gravity gradiometer performance test
Fluid inclusion study on carbonatite dyke and associated quartzite in Bayan Obo, Inner Mongolia, China
Improved laboratory gradiometer can be a field survey instrument
Improvements made to quartz gradiometer minimize or eliminate disturbing effects from known error sources and permit sensitivity of + or - 1 times 10 to the minus 9th power/sec sq or better and measuring accuracy of + or - 5 times 10 to the minus 9th power/sec sq
The gas-phase structure of the hexasilsesquioxane Si<sub>6</sub>O<sub>9</sub>(OSiMe<sub>3</sub>)<sub>6</sub>
Solutions of the Generic Non-Compact Weyl Equation
In this paper, solutions of the generic non-compact Weyl equation are
obtained. In particular, by identifying a suitable similarity transformation
and introducing a non-trivial change of variables we are able to implement
azimuthal dependence on the solutions of the diagonal non-compact Weyl
equation. We also discuss some open questions related to the construction of
infinite BPS monopole configurations.Comment: 12 pages, Latex. Few extra comments and a reference adde
Musculoskeletal modelling of an ostrich (Struthio camelus) pelvic limb: influence of limb orientation on muscular capacity during locomotion
We developed a three-dimensional, biomechanical computer model of the 36 major pelvic limb muscle groups in an ostrich (Struthio camelus) to investigate muscle function in this, the largest of extant birds and model organism for many studies of locomotor mechanics, body size, anatomy and evolution. Combined with experimental data, we use this model to test two main hypotheses. We first query whether ostriches use limb orientations (joint angles) that optimize the moment-generating capacities of their muscles during walking or running. Next, we test whether ostriches use limb orientations at mid-stance that keep their extensor muscles near maximal, and flexor muscles near minimal, moment arms. Our two hypotheses relate to the control priorities that a large bipedal animal might evolve under biomechanical constraints to achieve more effective static weight support. We find that ostriches do not use limb orientations to optimize the moment-generating capacities or moment arms of their muscles. We infer that dynamic properties of muscles or tendons might be better candidates for locomotor optimization. Regardless, general principles explaining why species choose particular joint orientations during locomotion are lacking, raising the question of whether such general principles exist or if clades evolve different patterns (e.g., weighting of muscle force–length or force–velocity properties in selecting postures). This leaves theoretical studies of muscle moment arms estimated for extinct animals at an impasse until studies of extant taxa answer these questions. Finally, we compare our model’s results against those of two prior studies of ostrich limb muscle moment arms, finding general agreement for many muscles. Some flexor and extensor muscles exhibit self-stabilization patterns (posture-dependent switches between flexor/extensor action) that ostriches may use to coordinate their locomotion. However, some conspicuous areas of disagreement in our results illustrate some cautionary principles. Importantly, tendon-travel empirical measurements of muscle moment arms must be carefully designed to preserve 3D muscle geometry lest their accuracy suffer relative to that of anatomically realistic models. The dearth of accurate experimental measurements of 3D moment arms of muscles in birds leaves uncertainty regarding the relative accuracy of different modelling or experimental datasets such as in ostriches. Our model, however, provides a comprehensive set of 3D estimates of muscle actions in ostriches for the first time, emphasizing that avian limb mechanics are highly three-dimensional and complex, and how no muscles act purely in the sagittal plane. A comparative synthesis of experiments and models such as ours could provide powerful synthesis into how anatomy, mechanics and control interact during locomotion and how these interactions evolve. Such a framework could remove obstacles impeding the analysis of muscle function in extinct taxa
Identification of some Fe-bearing daughter minerals in fluid inclusions using raman spectroscopy
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