The Dirichlet generating functions for the number of sublattices fixed under each symmetry operation of the parent Patterson group may be combined to count the number of crystallographically nonequivalent sublattices, in total, by sublattice point group and by colour lattice group type. The combinatorial formulae used imply the existence of various congruences among the corresponding arithmetic functions.

Download full-text PDF

Source
http://dx.doi.org/10.1107/S010876730804333XDOI Listing

Publication Analysis

Top Keywords

parent patterson
8
colour lattice
8
lattice group
8
group type
8
sublattice enumeration
4
enumeration equivalence
4
equivalence classes
4
classes plane
4
plane sublattices
4
sublattices parent
4

Similar Publications

Sexual and gender minority young adult (SGM YA) populations use tobacco at higher rates than their non-SGM YA peers. Prior studies have identified significant correlations between interpersonal stigma and tobacco use, yet structural stigma may also influence tobacco use among SGM YA. This study aimed to assess the indirect effects of structural stigma on current tobacco use among SGM YA and non-SGM YA via depletion of economic resources, interpersonal discrimination, and perceived psychological stress.

View Article and Find Full Text PDF

Purpose: Swedish adolescents' free and added sugars intake exceeds recommended levels. This poses potential health problems; however, little is known about dietary sources within the Swedish population. This study investigated dietary sources of sugars among Swedish adolescents, as well as timing and location of free sugars intake.

View Article and Find Full Text PDF

Importance: Classification of persons with long COVID (LC) or post-COVID-19 condition must encompass the complexity and heterogeneity of the condition. Iterative refinement of the classification index for research is needed to incorporate newly available data as the field rapidly evolves.

Objective: To update the 2023 research index for adults with LC using additional participant data from the Researching COVID to Enhance Recovery (RECOVER-Adult) study and an expanded symptom list based on input from patient communities.

View Article and Find Full Text PDF

A natural history study of pediatric patients with early onset of GM1 gangliosidosis, GM2 gangliosidoses, or gaucher disease type 2 (RETRIEVE).

Orphanet J Rare Dis

December 2024

Division of Metabolism and Children's Research Center, Reference Center for Inborn Errors of Metabolism, University Children's Hospital of Zurich, University of Zurich, Zurich, Switzerland.

Article Synopsis
  • RETRIEVE is a natural history study focused on the survival and disease progression of early-onset GM1, GM2, and type 2 Gaucher disease (GD2).
  • The study gathered data from 185 patients retrospectively and 40 patients prospectively, revealing varying median survival rates: GM1 (19 months), GM2 (44 months), and GD2 (14 months).
  • The findings noted that hypotonia was widespread among GM1 patients (94.4%), with additional symptoms like strabismus and splenomegaly specifically observed in GD2 patients, confirming known patterns of these rare lysosomal storage disorders.
View Article and Find Full Text PDF

Background: Each year 1.5 million children receive childcare subsidized under the Child Care and Development Fund, which supports working parents with low income in affording childcare; such policies hold promise for reducing child neglect.

Objective: The current study sought to examine how receiving childcare subsidies might reduce emotional neglect by supporting working parents' self-efficacy.

View Article and Find Full Text PDF

Want AI Summaries of new PubMed Abstracts delivered to your In-box?

Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!