Geometric Permutations of Non-Overlapping Unit Balls Revisited

Given four congruent balls $A, B, C, D$ in $R^{d}$ that have disjoint interior and admit a line that intersects them in the order $ABCD$, we show that the distance between the centers of consecutive balls is smaller than the distance between the centers of $A$ and $D$. This allows us to give a new short proof that $n$ interior-disjoint congruent balls admit at most three geometric permutations, two if $n\ge 7$. We also make a conjecture that would imply that $n\geq 4$ such balls admit at most two geometric permutations, and show that if the conjecture is false, then there is a counter-example of a highly degenerate nature

First-round evaluation of the health demonstration project

노트 : Best available copy -- pages 6-11 missing, and broken and faded typ

Model Order Reduction for Determining Bubble Parameters to Attain a Desired Fluid Surface Shape

In this paper, a new methodology for predicting fluid free surface shape using Model Order Reduction (MOR) is presented. Proper Orthogonal Decomposition combined with a linear interpolation procedure for its coefficient is applied to a problem involving bubble dynamics near to a free surface. A model is developed to accurately and efficiently capture the variation of the free surface shape with different bubble parameters. In addition, a systematic approach is developed within the MOR framework to find the best initial locations and pressures for a set of bubbles beneath the quiescent free surface such that the resultant free surface attained is close to a desired shape. Predictions of the free surface in two-dimensions and three-dimensions are presented.Singapore-MIT Alliance (SMA

SENSING MECHANISM AND APPLICATION OF MECHANICAL STRAIN SENSOR: A MINI-REVIEW

This study reviews the potential of flexible strain sensors based on nanomaterials such as carbon nanotubes (CNTs), graphene, and metal nanowires (NWs). These nanomaterials have excellent flexibility, conductivity, and mechanical properties, which enable them to be integrated into clothing or attached to the skin for the real-time monitoring of various activities. However, the main challenge is balancing high stretchability and sensitivity. This paper explains the basic concept of strain sensors that can convert mechanical deformation into electrical signals. Moreover, this paper focuses on simple, flexible, and stretchable resistive and capacitive sensors. It also discusses the important factors in choosing materials and fabrication methods, emphasizing the crucial role of suitable polymers in high-performance strain sensing. This study reviews the fabrication processes, mechanisms, performance, and applications of stretchable strain sensors in detail. It analyzes key aspects, such as sensitivity, stretchability, linearity, response time, and durability. This review provides useful insights into the current status and prospects of stretchable strain sensors in wearable technology and human–machine interfaces

Catalytic Kinetic Resolution of a Dynamic Racemate: Highly Stereoselective β-Lactone Formation by N-Heterocyclic Carbene Catalysis

This study describes the combined experimental and computational elucidation of the mechanism and origins of stereoselectivities in the NHC-catalyzed dynamic kinetic resolution (DKR) of α-substituted-β-ketoesters. Density functional theory computations reveal that the NHC-catalyzed DKR proceeds by two mechanisms, depending on the stereochemistry around the forming bond: 1) a concerted, asynchronous formal (2+2) aldol-lactonization process, or 2) a stepwise spiro-lactonization mechanism where the alkoxide is trapped by the NHC-catalyst. These mechanisms contrast significantly from mechanisms found and postulated in other related transformations. Conjugative stabilization of the electrophile and non-classical hydrogen bonds are key in controlling the stereoselectivity. This reaction constitutes an interesting class of DKRs in which the catalyst is responsible for the kinetic resolution to selectively and irreversibly capture an enantiomer of a substrate undergoing rapid racemization with the help of an exogenous base

C–H···O Non-Classical Hydrogen Bonding in the Stereomechanics of Organic Transformations: Theory and Recognition

This manuscript describes the role of non-classical hydrogen bonds (NCHBs), specifically C–H···O interactions, in modern synthetic organic transformations. Our goal is to point out the seminal examples where C–H···O interactions have been invoked as a key stereocontrolling element and to provide predictive value in recognizing future and/or potential C–H···O interactions in modern transformations

Peroxiredoxin Catalysis at Atomic Resolution

Peroxiredoxins (Prxs) are ubiquitous cysteine-based peroxidases that guard cells against oxidative damage, are virulence factors for pathogens, and are involved in eukaryotic redox regulatory pathways. We have analyzed catalytically active crystals to capture atomic resolution snapshots of a PrxQ-subfamily enzyme (from Xanthomonas campestris) proceeding through thiolate, sulfenate, and sulfinate species. These analyses provide structures of unprecedented accuracy for seeding theoretical studies, and show novel conformational intermediates giving insight into the reaction pathway. Based on a highly non-standard geometry seen for the sulfenate intermediate, we infer that the sulfenate formation itself can strongly promote local unfolding of the active site to enhance productive catalysis. Further, these structures reveal that preventing local unfolding, in this case via crystal contacts, results in facile hyperoxidative inactivation even for Prxs normally resistant to such inactivation. This supports previous proposals that conformation-specific inhibitors may be useful for achieving selective inhibition of Prxs that are drug targets

Presentación

A reaction between imines and anhydrides has been developed with chiral disubstituted anhydrides and chiral imines. The synthesis of highly substituted γ-lactams with three stereogenic centers, including one quaternary center, proceeds at room temperature in high yield and with high diastereoselectivity in most cases. Enantiomerically pure alkyl-substituted anhydrides proceed with no epimerization, thus providing access to enantiomerically pure penta-substituted lactam products