A Generalization of the Doubling Construction for Sums of Squares Identities

The doubling construction is a fast and important way to generate new solutions to the Hurwitz problem on sums of squares identities from any known ones. In this short note, we generalize the doubling construction and obtain from any given admissible triple $[r,s,n]$ a series of new ones $[r+\rho(2^{m-1}),2^ms,2^mn]$ for all positive integer $m$, where $\rho$ is the Hurwitz-Radon function

AGGREGATE STABILITY AND WATER RETENTION NEAR SATURATION CHARACTERISTICS AS AFFECTED BY SOIL TEXTURE, AGGREGATE SIZE AND POLYACRYLAMIDE APPLICATION

Understanding the effects of soil intrinsic properties and extrinsic conditions on aggregate stability is essential for the development of effective soil and water conservation practices. Our objective was to evaluate the combined role of soil texture, aggregate size and application of a stabilizing agent on aggregate and structure stability indices (composite structure index [SI], the and n parameters of the VG model and the S-index) by employing the high energy (0-5.0 J kg(-1)) moisture characteristic (HEMC) method. We used aggregates of three sizes (0.25-0.5, 0.5-1.0 and 1.0-2.0 mm) from four semi-arid soils treated with polyacrylamide (PAM). An increase in SI was associated with the increase in clay content, aggregate size and PAM application. The value of increased with the increase in aggregate size and with PAM application but was not affected by soil texture. For each aggregate size, a unique exponential type relationship existed between SI and . The value of n and the S-index tended, generally, to decrease with the increase in PAM application; however, an increase in aggregate size had an inconsistent effect on these two indices. The relationship between SI and n or the S-index could not be generalized. Our results suggest that (i) the effects of PAM on aggregate stability are not trivial, and its application as a soil conservation tool should consider field soil condition, and (ii), n and S-index cannot replace the SI as a solid measure for aggregate stability and soil structure firmness when assessing soil conservation practices

Extreme Precipitation Events over East Asia: Evaluating the CMIP5 Model

Extreme hydrological events are a direct threat to society and the environment, and their study within the framework of global climate change remains crucial. However, forecasts present numerous uncertainties

Surface roughness effects on runoff and soil erosion rates under simulated rainfall

Soil surface roughness is identified as one of the controlling factors governing runoff and soil loss. Yet, most studies pay little attention to soil surface roughness. In this study, we analyzed the influence of surface roughness on runoff and soil erosion rates. Bulk samples of a silt loam soil were collected and sieved to 4 aggregate sizes: 0.003-0.012, 0.012-0.02, 0.02-0.045, 0.045-0.1 m. The aggregates were packed in a 0.60 by 1.2 m soil tray, which was set at a slope of 5%. Rainfall simulations using an oscillating nozzle simulator were executed for 90 min at intensity of 50.2 mm.h-1. The surface microtopography was digitized by an instantaneous profile laser scanner before and after the rainfall application. From the laser scanner data, a digital elevation model was produced and a roughness factor extracted. The data revealed longer times to runoff with increasing soil surface roughness as surface depressions first had to be filled before runoff could take place. Once channels were interconnected, runoff velocity and runoff amount increased as aggregates were broken down and depressions were filled. Rough surfaces were smoothed throughout the rainfall event, diminishing the effect on runoff. Final wash rates were comparable for all different applications. The simulations reveal that the significance of soil surface roughness effect is the delay in runoff for rougher surfaces rather than the decrease of soil erosion amount

Harrison center and products of sums of powers

This paper is mainly concerned with identities like $$(x_1^d + x_2^d + \cdots + x_r^d) (y_1^d + y_2^d + \cdots y_n^d) = z_1^d + z_2^d + \cdots + z_n^d$$ where $d>2,$ $x=(x_1, x_2, \dots, x_r)$ and $y=(y_1, y_2, \dots, y_n)$ are systems of indeterminates and each $z_k$ is a linear form in $y$ with coefficients in the rational function field \k (x) over any field \k of characteristic $0$ or greater than $d.$ These identities are higher degree analogue of the well-known composition formulas of sums of squares of Hurwitz, Radon and Pfister. We show that such composition identities of sums of powers of degree at least $3$ are trivial, i.e., if $d>2,$ then $r=1.$ Our proof is simple and elementary, in which the crux is Harrison's center theory of homogeneous polynomials.Comment: 6 page

Kappa-alpha plot derived structural alphabet and BLOSUM-like substitution matrix for rapid search of protein structure database

3D BLAST, a novel protein structure database search tool, is a useful tool for analysing novel structures, capable of returning a list of aligned structures ordered according to E-values