Edge-vertex domination and total edge domination in trees

An edge e is an element of E(G) dominates a vertex v is an element of V (G) if e is incident with v or e is incident with a vertex adjacent to v. An edge-vertex dominating set of a graph G is a set D of edges of G such that every vertex of G is edge-vertex dominated by an edge of D. The edge-vertex domination number of a graph G is the minimum cardinality of an edge-vertex dominating set of G. A subset D subset of E(G) is a total edge dominating set of G if every edge of G has a neighbor in D. The total edge domination number of G is the minimum cardinality of a total edge dominating set of G. We characterize all trees with total edge domination number equal to edge-vertex domination number.The second author is supported by DST-SERB (MATRICS), India -grant MTR/2018/000234.Publisher's Versio

DOMINATION AND EDGE DOMINATION IN TREES

Let $G=(V,E)$ be a simple graph. A set $S\subseteq V$ is a dominating set if every vertex in $V \setminus S$ is adjacent to a vertex in $S$. The domination number of a graph $G$, denoted by $\gamma(G)$ is the minimum cardinality of a dominating set of $G$. A set $D \subseteq E$ is an edge dominating set if every edge in $E\setminus D$ is adjacent to an edge in $D$. The edge domination number of a graph $G$, denoted by $\gamma'(G)$ is the minimum cardinality of an edge dominating set of $G$. We characterize trees with  domination number equal to twice edge domination number

Fire and forage quality: Postfire regrowth quality and pyric herbivory in subtropical grasslands of Nepal

Fire is rampant throughout subtropical South and Southeast Asian grasslands. However, very little is known about the role of fire and pyric herbivory on the functioning of highly productive subtropical monsoon grasslands lying within the Cwa climatic region. We assessed the temporal effect of fire on postfire regrowth quality and associated pyric-herbivory in the subtropical monsoon grasslands of Bardia National Park, Nepal. Every year, grasslands are burned as a management intervention in the park, especially between March and May. Within a week after fire, at the end of March 2020, we established 60 m x 60 m plots within patches of burned grassland in the core area of the Park. We collected grass samples from the plots and determined physical and chemical properties of the vegetation at regular 30-day intervals from April to July 2020, starting from 30 days after fire to assess postfire regrowth forage quality. We counted pellet groups of cervids that are abundant in the area for the same four months from 2 m x 2 m quadrats that were permanently marked with pegs along the diagonal of each 60 m x 60 m plot to estimate intensity of use by deer to the progression of postfire regrowth. We observed strong and significant reductions in crude protein (mean value 9.1 to 4.1 [55% decrease]) and phosphorus (mean value 0.2 to 0.11 [45% decrease]) in forage collected during different time intervals, that is, from 30 days to 120 days after fire. Deer utilized the burned areas extensively for a short period, that is, up to two months after fire when the burned areas contained short grasses with a higher level of crude protein and phosphorus. The level of use of postfire regrowth by chital (Axis axis) differed significantly over time since fire, with higher intensity of use at 30 days after fire. The level of use of postfire regrowth by swamp deer (Rucervus duvaucelii) did not differ significantly until 90 days after fire, however, decreased significantly after 90 days since fire. Large-scale single event fires, thus, may not fulfil nutritional requirements of all species in the deer assemblage in these subtropical monsoon grasslands. This is likely because the nutritional requirements of herbivores differ due to differences in body size and physiological needs-maintenance, reproduction, and lactation. We recommend a spatiotemporal manipulation of fire to reinforce grazing feedback and to yield forage of high quality for the longest possible period for a sustainable high number of deer to maintain a viable tiger population within the park

Diffractive triangulation of radiative point sources

We describe a general method to determine the location of a point source of waves relative to a twodimensional single-crystalline active pixel detector. Based on the inherent structural sensitivity of crystalline sensor materials, characteristic detector diffraction patterns can be used to triangulate the location of a wave emitter. The principle described here can be applied to various types of waves, provided that the detector elements are suitably structured. As a prototypical practical application of the general detection principle, a digital hybrid pixel detector is used to localize a source of electrons for Kikuchi diffraction pattern measurements in the scanning electron microscope. This approach provides a promising alternative method to calibrate Kikuchi patterns for accurate measurements of microstructural crystal orientations, strains, and phase distributions

Hygroscopic growth of water soluble organic carbon isolated from atmospheric aerosol collected at US national parks and Storm Peak Laboratory

Due to the atmospheric abundance and chemical complexity of water soluble organic carbon (WSOC), its contribution to the hydration behavior of atmospheric aerosol is both significant and difficult to assess. For the present study, the hygroscopicity and CCN activity of isolated atmospheric WSOC particulate matter was measured without the compounding effects of common, soluble inorganic aerosol constituents. WSOC was extracted with high purity water from daily high-volume PM2.5 filter samples and separated from water soluble inorganic constituents using solid-phase extraction. The WSOC filter extracts were concentrated and combined to provide sufficient mass for continuous generation of the WSOC-only aerosol over the combined measurement time of the tandem differential mobility analyzer and coupled scanning mobility particle sizer–CCN counter used for the analysis. Aerosol samples were taken at Great Smoky Mountains National Park during the summer of 2006 and fall–winter of 2007–2008; Mount Rainier National Park during the summer of 2009; Storm Peak Laboratory (SPL) near Steamboat Springs, Colorado, during the summer of 2010; and Acadia National Park during the summer of 2011. Across all sampling locations and seasons, the hygroscopic growth of WSOC samples at 90 % RH, expressed in terms of the hygroscopicity parameter, κ, ranged from 0.05 to 0.15. Comparisons between the hygroscopicity of WSOC and that of samples containing all soluble materials extracted from the filters implied a significant modification of the hydration behavior of inorganic components, including decreased hysteresis separating efflorescence and deliquescence and enhanced water uptake between 30 and 70 % RH

EXTREMAL VALUES ON THE MODIFIED SOMBOR INDEX OF TREES AND UNICYCLIC GRAPHS

Let $G=(V,E)$ be a simple connected graph. The modified Sombor index denoted by $mSo(G)$ is defined as $$mSo(G)=\sum_{uv\in E}\frac{1}{\sqrt{d^2_u+d^2_v}},$$ where $d_v$ denotes the degree of vertex $v$. In this paper we present extremal values of modified Sombor index  over the set of trees and unicyclic graphs

Wide variability in the ICRISAT germplasm collections as a source for genetic enhancement of crop cultivars

Sustained gains in plant breeding rely on variation in crop gene pool. Therefore, it is essential to conserve crops’ diversity in situ and ex situ. Globally over 7.4 million germplasm accessions have been conserved in about 1750 genebanks. The greater use of germplasm diversity in crop improvement programmes could potentially broaden genetic base of crop cultivars. The ICRISAT genebank conserves over 128,000 germplasm accessions of six mandate crops (sorghum, pearl millet, finger millet, chickpea, groundnut, pigeonpea) and five small millets (foxtail millet, proso millet, barnyard millet, little millet and kodo millet). The collection is dominated with cultivated germplasm (97.7%) while wild and weedy relatives represent only 2.3%. Large variability was reported in the germplasm collections conserved at ICRISAT genebank, as revealed by characterization and evaluation of small subsets of total collection. However, large-scale evaluation to uncover hidden untapped potential is required to identify and introduce novel variability in to the crop improvement program

PKMζ is essential for spinal plasticity underlying the maintenance of persistent pain

<p>Abstract</p> <p>Background</p> <p>Chronic pain occurs when normally protective acute pain becomes pathologically persistent. We examined here whether an isoform of protein kinase C (PKC), PKMζ, that underlies long-term memory storage in various brain regions, also sustains nociceptive plasticity in spinal cord dorsal horn (SCDH) mediating persistent pain.</p> <p>Results</p> <p>Cutaneous injury or spinal stimulation produced persistent increases of PKMζ, but not other atypical PKCs in SCDH. Inhibiting spinal PKMζ, but not full-length PKCs, reversed plasticity-dependent persistent painful responses to hind paw formalin and secondary mechanical hypersensitivity and SCDH neuron sensitization after hind paw capsaicin, without affecting peripheral sensitization-dependent primary heat hypersensitivity after hind paw capsaicin. Inhibiting spinal PKMζ, but not full-length PKCs, also reversed mechanical hypersensitivity in the rat hind paw induced by spinal stimulation with intrathecal dihydroxyphenylglycine. Spinal PKMζ inhibition also alleviated allodynia 3 weeks after ischemic injury in rats with chronic post-ischemia pain (CPIP), at a point when allodynia depends on spinal changes. In contrast, spinal PKMζ inhibition did not affect allodynia in rats with chronic contriction injury (CCI) of the sciatic nerve, or CPIP rats early after ischemic injury, when allodynia depends on ongoing peripheral inputs.</p> <p>Conclusions</p> <p>These results suggest spinal PKMζ is essential for the maintenance of persistent pain by sustaining spinal nociceptive plasticity.</p

Probing coke formation during the methanol-to-hydrocarbon reaction on zeolite ZSM-5 catalyst at the nanoscale using tip-enhanced fluorescence microscopy

The deactivation mechanism of the widely used zeolite ZSM-5 catalysts remains unclear to date due to the lack of analytical techniques with sufficient sensitivity and/or spatial resolution. Herein, a combination of hyperspectral confocal fluorescence microscopy (CFM) and tip-enhanced fluorescence (TEFL) microscopy is used to study the formation of different coke (precursor) species involved in the deactivation of zeolite ZSM-5 during the methanol-to-hydrocarbon (MTH) reaction. CFM submicron-scale imaging shows a preferential formation of graphite-like coke species at the edges of zeolite ZSM-5 crystals within 10 min of the MTH reaction ( i.e., working catalyst), whilst the amount of graphite-like coke species uniformly increased over the entire zeolite ZSM-5 surface after 90 min ( i.e., deactivated catalyst). Furthermore, TEFL nanoscale imaging with ∼35 nm spatial resolution revealed that formation of coke species on the zeolite ZSM-5 surface is non-uniform and a relatively larger amount of coke is formed at the crystal steps, indicating a higher initial catalytic activity

Genetic variability, character association and diversity studies in brinjal (Solanum melongena L.)

An experiment was conducted to assess the existing variability in brinjal germplasm based on Mahalanobis’s D2 statistic based on nine quantitative traits. The germplasm accessions were classified into six clusters, in which the highest inter-cluster distance was recorded between clusters III and IV. Cluster I exhibited a low mean estimate for days to 50% flowering; cluster VI showed high estimates of the mean for plant height, the number of primary branches per plant, average fruit weight, and 1000 seed weight. Cluster V recorded the highest number of fruits and fruit yields per plant. Principal component analysis revealed total variability of 53.09 per cent, contributed by PC 1 (30.83 %) and PC 2 (23.07 %). Traits viz., days to 50% flowering, plant height, an average number of branches per plant, fruit length, and 1000 seed weight contributed positive significant component loadings for the first two PCs. High heritability and high GAM were also recorded for a number of fruits per plant, fruit yield per plant, fruit length, fruit girth, fruit weight, and 1000 seed weight. Fruit yield and the number of fruits per plant were positively and significantly associated with each other. Hence, simultaneous selection of these traits is advised for the genetic improvement in the brinjal breeding program