Chirality is of primary importance in many areas of chemistry and has been extensively investigated since its discovery. We introduce here a description of central chirality for tetrahedral molecules using a geometrical approach based on complex numbers. According to this representation, for a molecule having n chiral centers it is possible to define an "index of chirality chi." Consequently, a "chirality selection rule" has been derived which allows the characterization of a molecule as achiral, enantiomer, or diastereoisomer.
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.1002/chir.10191 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Lowering Linker Symmetry to Access Zirconium Metal-Organic Frameworks for Inverse Alkane/Alkene Separations.
Angew Chem Int Ed Engl
January 2025
Northwestern University, Department of Chemistry, UNITED STATES OF AMERICA.
Enriching the structural diversity of metal-organic frameworks (MOFs) is of great importance in developing functional porous materials with specific properties. New MOF structures can be accessed through the rational design of organic linkers with diverse geometric conformations, and their structural complexity can be enhanced by choosing linkers with reduced symmetry. Herein, a series of Zr-based MOFs with unprecedented topologies were developed through a linker desymmetrization and conformation engineering approach.
View Article and Find Full Text PDFAbdominal synthetic CT generation for MR-only radiotherapy using structure-conserving loss and transformer-based cycle-GAN.
Front Oncol
January 2025
Department of Radiation Oncology, Yonsei Cancer Center, Heavy Ion Therapy Research Institute, Yonsei University College of Medicine, Seoul, Republic of Korea.
Purpose: Recent deep-learning based synthetic computed tomography (sCT) generation using magnetic resonance (MR) images have shown promising results. However, generating sCT for the abdominal region poses challenges due to the patient motion, including respiration and peristalsis. To address these challenges, this study investigated an unsupervised learning approach using a transformer-based cycle-GAN with structure-preserving loss for abdominal cancer patients.
View Article and Find Full Text PDFOn the directional asymptotic approach in optimization theory.
Math Program
July 2024
Department of Mathematics and Computer Science, Philipps-Universität Marburg, 35032 Marburg, Germany.
As a starting point of our research, we show that, for a fixed order , each local minimizer of a rather general nonsmooth optimization problem in Euclidean spaces is either M-stationary in the classical sense (corresponding to stationarity of order 1), satisfies stationarity conditions in terms of a coderivative construction of order , or is asymptotically stationary with respect to a critical direction as well as order in a certain sense. By ruling out the latter case with a constraint qualification not stronger than directional metric subregularity, we end up with new necessary optimality conditions comprising a mixture of limiting variational tools of orders 1 and . These abstract findings are carved out for the broad class of geometric constraints and , and visualized by examples from complementarity-constrained and nonlinear semidefinite optimization.
View Article and Find Full Text PDFScan/rescan reliability of magnetic resonance imaging (MRI).
Eur Spine J
January 2025
Department of Industrial and Systems Engineering, Auburn University, 3301 Shelby Center, Auburn, AL, 36849-5346, USA.
Background: Magnetic resonance imaging (MRI) is increasingly used to estimate the geometric dimensions of lower lumbar vertebrae. While MRI-based measurements have demonstrated good reliability with interclass correlation coefficients (ICCs) of 0.80 or higher, many evaluations focus solely on the comparison of identical MRI images.
View Article and Find Full Text PDFA Method that Maintains Accuracy in the Prediction of Vitamin A Total Body Stores when Population-Based Modeling of a Limited Number of Theoretical Subjects Is Used with Retinol Isotope Dilution.
J Nutr
January 2025
Department of Nutritional Sciences, The Pennsylvania State University, University Park, PA, USA.
Background: Retinol isotope dilution (RID) equations are used to predict vitamin A total body stores (TBS). Including population-based ("super-subject") modeling with RID provides group-specific values for the equation coefficients.
Objectives: Objective was to test an approach that would accommodate a limited super-subject sample size without compromising accuracy in RID predictions of TBS.
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!