Essentially Retractable Modules Relative To A Submodule And Some Generalizations

R is a ring with unity, and all modules are unitary right R-modules. The concept of compressible modules was introduced in 1981 by Zelmanowitz, where module M is called compressible if it can be embedded in any nonzero submodule A of M . In other words, M is a compressible module if for each nonzero submodule A of M, f 2 Hom(M;A) exists, such that f is monomorphism. Retractable modules were introduced in 1979 Khuri, where module M is retractable if Hom(M, A ) 6= 0 for every nonzero submodule A of M . We define a new notion, namely, essentially retractable module relative to a submodule. In addition, new generalizations of compressible modules relative to a submodule are introduced, where module M is called compressible module relative to a submodule N of M . If for all nonzero submodule K of M contains N , then a monomorphism f 2 Hom(M, K) exists. Some basic properties are studied and many relationships between these classes and other related concepts are presented and studied. We also introduce another generalization of retractable module, which is called small kernel retractable module

A Study on Rupture Resistance of Groundnut (cv. SAMNUT 22) Kernel

This study was done to assess the influence of compression loading rate and kernel size on the rupture resistance of groundnut (cv. SAMNUT 22) kernel. These groundnut kernel mechanical parameters (rupture force, deformation at rupture, rupture power, firmness and toughness) were evaluated under three loading rates (15 mm min-1, 20 mm min-1 and 25 mm min-1), and three size categories (small, medium and large). The groundnut kernels were harvested at peak maturity stage, and tested in accordance to ASTM International standards. Results obtained from the tests showed that the rupture resistance of SAMNUT 22 kernel was highly dependent on its size and the loading rate. Generally, as the loading rate increases, the mechanical parameters values declined significantly (p ≤ 0.05). Rupture force, deformation at rupture point, rupture power and the firmness increased as the kernel size increases; but in contrast, the kernel toughness decreases as its size increased. An average force of 57.96 N ruptured the large kernel, while a lower force of 27.35 N ruptured the small kernel. Moreover, the large kernel recorded the highest firmness (59.03 N mm-1), when compared to the medium (51.69 N mm-1) and small (44.98 N mm-1) size kernel. In terms of rupture power, the small kernel power ranged from 0.1002 W (15 mm min-1) to 0.084 W (25 mm min-1); medium size kernel ranged from 0.115 W (15 mm min-1) to 0.074 W (25 mm min- 1); while the large size kernel ranged from 0.135 W (15 mm min-1) to 0.104 W (25 mm min-1). These results portrayed importance of sorting of the groundnut kernels before processing unit operation, as it will help to conserve power and energy during the processing operation.

Maize YSL2 is required for iron distribution and development in kernels

Iron (Fe) is an essential micronutrient and plays an irreplaceable role in plant growth and development. Although its uptake and translocation are important biological processes, little is known about the molecular mechanism of Fe translocation within seed. Here, we characterized a novel small kernel mutant yellow stripe like 2 (ysl2) in maize (Zea mays). ZmYSL2 was predominantly expressed in developing endosperm and was found to encode a plasma membrane-localized metal–nicotianamine (NA) transporter ZmYSL2. Analysis of transporter activity revealed ZmYSL2-mediated Fe transport from endosperm to embryo during kernel development. Dysfunction of ZmYSL2 resulted in the imbalance of Fe homeostasis and abnormality of protein accumulation and starch deposition in the kernel. Significant changes of nitric oxide accumulation, mitochondrial Fe–S cluster content, and mitochondrial morphology indicated that the proper function of mitochondria was also affected in ysl2. Collectively, our study demonstrated that ZmYSL2 had a pivotal role in mediating Fe distribution within the kernel and kernel development in maize.

Removal of Small Kernels Reduces the Content of Fusarium Mycotoxins in Oat Grain

Cereal grain contaminated by Fusarium mycotoxins is undesirable in food and feed because of the harmful health effects of the mycotoxins in humans and animals. Reduction of mycotoxin content in grain by cleaning and size sorting has mainly been studied in wheat. We investigated whether the removal of small kernels by size sorting could be a method to reduce the content of mycotoxins in oat grain. Samples from 24 Norwegian mycotoxin-contaminated grain lots (14 from 2015 and 10 from 2018) were sorted by a laboratory sieve (sieve size 2.2 mm) into large and small kernel fractions and, in addition to unsorted grain samples, analyzed with LC-MS-MS for quantification of 10 mycotoxins. By removing the small kernel fraction (on average 15% and 21% of the weight of the samples from the two years, respectively), the mean concentrations of HT-2+T-2 toxins were reduced by 56% (from 745 to 328 µg/kg) in the 2015 samples and by 32% (from 178 to 121 µg/kg) in the 2018 samples. Deoxynivalenol (DON) was reduced by 24% (from 191 to 145 µg/kg) in the 2018 samples, and enniatin B (EnnB) by 44% (from 1059 to 594 µg/kg) in the 2015 samples. Despite low levels, our analyses showed a trend towards reduced content of DON, ADON, NIV, EnnA, EnnA1, EnnB1 and BEA after removing the small kernel fraction in samples from 2015. For several of the mycotoxins, the concentrations were considerably higher in the small kernel fraction compared to unsorted grain. Our results demonstrate that the level of mycotoxins in unprocessed oat grain can be reduced by removing small kernels. We assume that our study is the first report on the effect of size sorting on the content of enniatins (Enns), NIV and BEA in oat grains.

A Kernel-Width Adaption Diffusion Maximum Correntropy Algorithm

In this paper, a diffusion maximum correntropy criterion (DMCC) algorithm with adaption kernel width is proposed, denoting as DMCC$_{\rm adapt}$ algorithm, to find out a solution for dynamically choosing the kernel width. The DMCC$_{\rm adapt}$ algorithm chooses small kernel width at initial stage to improve its convergence speed rate, and uses large kernel width at completion stage to reduce its steady-state error. To render the proposed DMCC$_{\rm adapt}$ algorithm suitable for sparse system identifications, the DMCC$_{\rm adapt}$ algorithm based on proportional coefficient adjustment is realized and named as diffusion proportional maximum correntropy criterion (DPMCC$_{\rm adapt}$). The theoretical analysis and simulation results are presented to show that the DPMCC$_{\rm adapt}$ and DMCC$_{\rm adapt}$ algorithms have better convergence than the traditional diffusion AF algorithms under impulse noise and sparse systems.

A Kernel-Width Adaption Diffusion Maximum Correntropy Algorithm

In this paper, a diffusion maximum correntropy criterion (DMCC) algorithm with adaption kernel width is proposed, denoting as DMCC$_{\rm adapt}$ algorithm, to find out a solution for dynamically choosing the kernel width. The DMCC$_{\rm adapt}$ algorithm chooses small kernel width at initial stage to improve its convergence speed rate, and uses large kernel width at completion stage to reduce its steady-state error. To render the proposed DMCC$_{\rm adapt}$ algorithm suitable for sparse system identifications, the DMCC$_{\rm adapt}$ algorithm based on proportional coefficient adjustment is realized and named as diffusion proportional maximum correntropy criterion (DPMCC$_{\rm adapt}$). The theoretical analysis and simulation results are presented to show that the DPMCC$_{\rm adapt}$ and DMCC$_{\rm adapt}$ algorithms have better convergence than the traditional diffusion AF algorithms under impulse noise and sparse systems.

Hysteretic behavior of spatially coupled phase-oscillators

Motivated by phenomena related to biological systems such as the synchronously flashing swarms of fireflies, we investigate a network of phase oscillators evolving under the generalized Kuramoto model with inertia. A distance-dependent, spatial coupling between the oscillators is considered. Zeroth and first order kernel functions with finite kernel radii were chosen to investigate the effect of local interactions. The hysteretic dynamics of the synchronization depending on the coupling parameter was analyzed for different kernel radii. Numerical investigations demonstrate that (1) locally locked clusters develop for small coupling strength values, (2) the hysteretic behavior vanishes for small kernel radii, (3) the ratio of the kernel radius and the maximal distance between the oscillators characterizes the behavior of the network.