Systematics of Bromelioideae (Bromeliaceae)—Evidence from Molecular and Anatomical Studies

A reconstruction of the phylogeny of Bromeliaceae based on sequence data from three noncoding chloroplast DNA markers (trnL intron, trnT–trnL, and trnT–trnF intergenic spacer [IGS]) is presented, including 26 genera and 33 species. Relationships of Bromelioideae and phylogeny within this subfamily were analyzed in more detail on the basis of two of these markers (trnL intron and trnL–trnF IGS) using a set of 37 genera/74 species of Bromeliaceae, including 28 genera/60 species of Bromelioideae. Sister group relationships of Bromelioideae were not resolved with sufficient reliability, but the most likely candidates are the genera Fosterella and Puya. The basal phylogeny of Bromelioideae also was not resolved. Greigia, Ochagavia/Fascicularia/Fernseea, Deinacanthon, Bromelia, and a ‘‘core group’’ of the remaining Bromelioideae formed a basal polytomy. Within Bromelioideae, the AFLP technique was applied to assess relationships among selected groups of genera. In the Ochagavia/Fascicularia group (5 species and subspecies/16 accessions), AFLP data fully confirmed the systematic relationships based on morphological and anatomical characters. Investigation of 30 Aechmea species (33 accessions), including all subgenera and one species each from the related genera Ursulaea, Portea, Chevaliera, and Streptocalyx produced no resolution for several of the species. Clades that received good bootstrap support generally did not correspond with the delimitation of subgenera of Aechmea. Additionally, leaf blade anatomy of these species was investigated. The results corresponded partly with those of the AFLP analysis. Generic rank for Ursulaea and Portea was not supported

Almost Symmetric Schur Functions

We introduce and study a generalization $s_{(\mu|\lambda)}$ of the Schur functions called the almost symmetric Schur functions. These functions simultaneously generalize the finite variable key polynomials and the infinite variable Schur functions. They form a homogeneous basis for the space of almost symmetric functions and are defined using a family of recurrences involving the isobaric divided difference operators and limits of Weyl symmetrization operators. The $s_{(\mu|\lambda)}$ are the $q=t=0$ specialization of the stable limit non-symmetric Macdonald functions $\widetilde{E}_{(\mu|\lambda)}$ defined by the author in previous work. We find a combinatorial formula for these functions simultaneously generalizing well known formulas for the Schur functions and the key polynomials. Further, we prove positivity results for the coefficients of the almost symmetric Schur functions expanded into the monomial basis and into the monomial-Schur basis of the space of almost symmetric functions. The latter positivity result follows after realizing the almost symmetric Schur functions $s_{(\mu|\lambda)}$ as limits of characters of representations of parabolic subgroups in type $GL.$Comment: 23 page

Crossroads: Outcomes of Egalitarian and Traditional Gender Ideology on Abortion Attitudes

What is the relationship between gender ideology and abortion attitudes? For decades now, abortion has remained one of the most controversial topics in the modern world. A greater understanding of the motivations behind abortion attitudes could be useful to predict changes in abortion policy within a variety of cultures. This study analyzes data from the 2021 General Social Survey (GSS). Multivariate regression was used to investigate the effect of gender ideology on abortion attitudes. The independent variable was tested with two models. In Model A, four conditions for gender ideology were analyzed separately, and in Model B, the four conditions were combined into an index variable. The findings from the study reveal that overall, egalitarian gender ideology is a significant predictor of supportive abortion attitudes. Some significance was also found for religiosity and level of education as alternate predictors of abortion attitudes. No significant relationship was found between sex and abortion attitudes. Overall, the findings suggest a significant positive relationship between egalitarian gender ideology and supportive abortion attitudes

Murnaghan-Type Representations for the Positive Elliptic Hall Algebra

We construct a new family of graded representations $\widetilde{W}_{\lambda}$ for the positive elliptic Hall algebra $\mathcal{E}^{+}$ indexed by Young diagrams $\lambda$ which generalize the standard $\mathcal{E}^{+}$ action on symmetric functions. These representations have homogeneous bases of eigenvectors for the action of the Macdonald element $P_{0,1} \in \mathcal{E}^{+}$ with distinct $\mathbb{Q}(q,t)$-rational spectrum generalizing the symmetric Macdonald functions. The analysis of the structure of these representations exhibits interesting combinatorics arising from the stable limits of periodic standard Young tableaux. We find an explicit combinatorial rule for the action of the multiplication operators $e_r[X]^{\bullet}$ generalizing the Pieri rule for symmetric Macdonald functions. We will also naturally obtain a family of interesting $(q,t)$ product-series identities which come from keeping track of certain combinatorial statistics associated to periodic standard Young tableaux.Comment: This is the complete version of the author's accepted FPSAC24 extended abstract arXiv:2310.10249; 52 page

Double Dyck Path Algebra Representations From DAHA

The double Dyck path algebra $\mathbb{A}_{q,t}$ was introduced by Carlsson-Mellit in their proof of the Shuffle Theorem. A variant of this algebra, $\mathbb{B}_{q,t}$, was introduced by Carlsson-Gorsky-Mellit in their study of the parabolic flag Hilbert schemes of points in $\mathbb{C}^2$ showing that $\mathbb{B}_{q,t}$ acts naturally on the equivariant $K$-theory of these spaces. The algebraic relations defining $\mathbb{B}_{q,t}$ appear superficially similar to those of the positive double affine Hecke algebras (DAHA) in type $GL$, $\mathscr{D}_n^{+}$, introduced by Cherednik. In this paper we provide a general method for constructing $\mathbb{B}_{q,t}$ representations from DAHA representations. In particular, every $\mathscr{D}_n^{+}$ module yields a representation of a subalgebra $\mathbb{B}_{q,t}^{(n)}$ of $\mathbb{B}_{q,t}$ and special families of compatible DAHA representations give representations of $\mathbb{B}_{q,t}$. These constructions are functorial. Lastly, we will construct a large family of $\mathbb{B}_{q,t}$ representations indexed by partitions using this method related to the Murnaghan-type representations of the positive elliptic Hall algebra introduced previously by the author.Comment: 17 page

Isolation and characterization of nine microsatellite loci for the tropical understory tree Miconia affinis Wurdack (Melastomataceae)

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75161/1/j.1755-0998.2008.02428.x.pd

Влияние интенсивности механической активации на структуру гексагонального нитрида бора

Изучено влияние интенсивности механической активации на микроструктуру и свойства гексагонального нитрида бора (hBN).Вивчено вплив інтенсивності механічної активації на мікроструктуру і властивості гексагонального нітриду бору (hBN).The mechanical activation intensity effect on the microstructure and properties of hexagonal boron nitride (hBN) has been studied

Stable-Limit Cherednik Theory

This thesis is centered around extending families of representation theoretic objects corresponding to finite rank GL to the setting of infinite rank GL. Specifically, we study representations of the double affine Hecke algebras in type GL, the elliptic Hall algebra, and the double Dyck path algebra. Throughout this thesis we will develop new methods for constructing representation theoretic objects from families of finite rank classical objects and ways to understand these representations.In the first chapter, we give an overview of the background information regarding Macdonald theory and Cherednik theory and of recent results in the area including the Shuffle Theorem. This chapter contains a review of the necessary algebraic, combinatorial, and representation theoretic definitions which will be used throughout the thesis. In Chapter 2, we investigate limits of non-symmetric Macdonald polynomials and their place in the theory of almost symmetric functions. We will construct a basis of simultaneous eigenvectors for the limit Cherednik operators of Ion-Wu and investigate many of their properties. Further, we construct new operators on the space of almost symmetric functions generalizing the higher delta operators in Macdonald theory. Lastly, we explicitly compute q,t specializations of this basis to find a generalization of Schur functions to the almost symmetric functions with interesting combinatorial and representation theoretic properties.Chapter 3 revolves around a family of modules called the Murnaghan-type representations for the elliptic Hall algebra generated using a stable-limit procedure from the vector-valued polynomial DAHA representations of Dunkl-Luque. This family of modules is indexed by partitions and generalizes the standard polynomial representation of EHA. We will construct a special family of generalized symmetric Macdonald functions as simultaneous eigenvectors for a generalized Macdonald operator and investigate their properties. Lastly, in Chapter 4 we will construct new representations of the double Dyck path algebra built from compatible families of DAHA representations. We will use this general procedure to define Murnaghan-type representations using the EHA representations in Chapter 2