Odonata Diversity in Thadiyankudisai, Palni Hills of Western Ghats, Tamil Nadu

A total of 419 individuals under 5 families, 8 genera and 10 species of Odonata were recorded in the present study. Among them family Libellulidae had 6 species followed by Chlorocyphidae (2 species), and Coenagrionidae and Euphaeidae had1 species. The dominance order of Odonata was Pantala flavescens (44.40%) > Diplacodes trivialis (22.70%) > Orthetrum chrysis (7.40%) while rest of the fauna ranged from (1.40 to 6.90%). Pantala flavescens was maximum during NEM (50.0%) followed by summer and winter (43.8% each) and minimum during SWM (38.5%). Margalef Index of Species Richness was highest (2.00) during winter. Simpson Index of Diversity was highest (0.75) during SWM while Shannon-Wiener Index of Dominance was highest (1.75) during summer. The species were evenly distributed during summer with Pielou’s Evenness Index value of 0.76. The community change was 80.00 per cent change during January, 2018 and had a steep fall in February and April, 2018 and reached a peak of 66.67 per cent during March and November, 2018.

Asymptotic Bounds on Graphical Partitions and Partition Comparability

An integer partition is called graphical if it is the degree sequence of a simple graph. We prove that the probability that a uniformly chosen partition of size $n$ is graphical decreases to zero faster than $n^{-.003}$, answering a question of Pittel. A lower bound of $n^{-1/2}$ was proven by Erd̋s and Richmond, meaning our work demonstrates that the probability decreases polynomially. Our proof also implies a polynomial upper bound for the probability that two randomly chosen partitions are comparable in the dominance order.

Chemical Characteristics of the Karmanasha River Water and Its Appropriateness for Irrigational Usage

Water is a prime natural resource and precious national asset and one of the chief constituents of the environment. The chemical characteristics play a key role in terms of ecological and economic perspectives in the river water. The characterization and evaluation of river water quality in the Karmanasha River is necessary due to its immense importance in the livelihood of the people in the core urban areas of Kathmandu valley, Nepal. In this study, the surface water samples were collected from 16 sites with a 0.5 km interval to characterize and evaluate the water quality mainly from the perspective of its irrigational usage. The assessment was carried out by applying electrical conductivity (EC), sodium percentage (Na%), sodium adsorption ratio (SAR), permeability index (PI), Kelly’s ratio (KR), magnesium adsorption ratio (MAR), cation ratio of soil structural stability (CROSS), Wilcox diagram and water quality index (WQI) including the general hydrochemistry. The general hydrochemistry of river water indicates slightly alkaline in nature with mean pH value 8.07, and the dominance order of major ions follows the pattern of Ca2+>Mg2+>Na+>K+ for cations, and HCO3->Cl->NO3- for anions. Furthermore, the results revealed that the water is safe for irrigation purposes based on EC, Na%, SAR, KR, MAR, CROSS, and Wilcox diagram. The results also specified that no severe degradation in water, however, the low DO, and high BOD and COD values than that of the standard value prescribed by Nepal Drinking Water Quality Standard, signify the anthropogenic signature in the river water. This study provides the baseline information about the WQI and suitability of irrigation water quality, and further in-depth studies are required at spatiotemporal levels to get in-depth insights about the ecological health of the river.

Two Partial Orders for Standard Young Tableaux

In this manuscript we show that two partial orders defined on the set of standard Young tableaux of shape $\alpha$ are equivalent. In fact, we give two proofs for the equivalence of the box order and the dominance order for tableaux. Both are algorithmic. The first of these proofs emphasizes links to the Bruhat order for the symmetric group and the second provides a more straightforward construction of the cover relations. This work is motivated by the known result that the equivalence of the two combinatorial orders leads to a description of the geometry of the representation space of invariant subspaces of nilpotent linear operators.

The Queen of the Paper Wasp Polistes jokahamae (Vespidae: Polistinae) Is Not Aggressive but Maintains Her Reproductive Priority

The behaviors performed on the nest by the foundress queen and workers of the paper wasp Polistes jokahamae were observed in three colonies in the field and one colony in a cage set in the field. Each queen was rarely ranked top in the dominance hierarchy determined by the pairwise dominance–subordinate interactions and did not display more frequent direct aggression toward the top-ranked worker than toward other workers. Furthermore, the queen exhibited aggression less frequently than did the most aggressive workers in all four colonies. The dominance order among the workers was positively correlated with the emergence order, with older workers being more dominant. The queen laid eggs in a dominant or monopolized way; some dominant workers laid eggs in three colonies. These observations suggest that the queen maintained her queen status, including her reproductive priority, using signals rather than aggression. Lateral vibrations (rapidly laterally vibrating the abdomen) and abdominal rubbing (rubbing the abdomen onto the comb) appeared to be candidate signals of the fertility or reproductive potential of the performer. Lateral vibrations were performed only by the queen, and their frequency was positively correlated with the frequency of ovipositing. The queen and some dominant workers performed abdominal rubbing; the frequency was higher for the queen than for any of the dominant workers early in the colony’s development, but not later. Although performers of abdominal rubbing were more likely to lay eggs than non-performers, the frequency of abdominal rubbing was not a predictor of the frequency of ovipositing.

Schur $P$-positivity and Involution Stanley Symmetric Functions

The involution Stanley symmetric functions$\hat{F}_y$ are the stable limits of the analogs of Schubert polynomials for the orbits of the orthogonal group in the flag variety. These symmetric functions are also generating functions for involution words and are indexed by the involutions in the symmetric group. By construction, each $\hat{F}_y$ is a sum of Stanley symmetric functions and therefore Schur positive. We prove the stronger fact that these power series are Schur $P$-positive. We give an algorithm to efficiently compute the decomposition of $\hat{F}_y$ into Schur $P$-summands and prove that this decomposition is triangular with respect to the dominance order on partitions. As an application, we derive pattern avoidance conditions which characterize the involution Stanley symmetric functions which are equal to Schur $P$-functions. We deduce as a corollary that the involution Stanley symmetric function of the reverse permutation is a Schur $P$-function indexed by a shifted staircase shape. These results lead to alternate proofs of theorems of Ardila–Serrano and DeWitt on skew Schur functions which are Schur $P$-functions. We also prove new Pfaffian formulas for certain related involution Schubert polynomials.

Dominance order on signed integer partitions

In 1973 Brylawski introduced and studied in detail the dominance partial order on the set