A regularised boundary element formulation for contactless SAR evaluations within homogeneous and inhomogeneous head phantoms

This work presents a Boundary Element Method (BEM) formulation for contactless electromagnetic field assessments. The new scheme is based on a regularised BEM approach that requires the use of electric measurements only. The regularisation is obtained by leveraging on an extension of Calderón techniques to rectangular systems leading to well-conditioned problems independent of the discretisation density. This enables the use of highly discretized Huygens surfaces that can be consequently placed very near to the radiating source. In addition, the new regularised scheme is hybridised with both surfacic homogeneous and volumetric inhomogeneous forward BEM solvers accelerated with fast matrix–vector multiplication schemes. This allows for rapid and effective dosimetric assessments and permits the use of inhomogeneous and realistic head phantoms. Numerical results corroborate the theory and confirms the practical effectiveness of all newly proposed formulations.     

Visualization and In Situ Ablation of Intracellular Bacterial Pathogens through Metabolic Labeling

Protected by the host cells, the hidden intracellular bacteria are typically difficult to kill by common antibiotics and cannot be visualized without complex cellular pretreatments. Herein, we successfully developed a bacteria-metabolizable dual-functional probe TPEPy-d -Ala, which is based on d -alanine and a photosensitizer with aggregation-induced emission for fluorescence turn-on imaging of intracellular bacteria in living host cells and photodynamic ablation in situ. Once metabolically incorporated into bacterial peptidoglycan, the intramolecular motions of TPEPy-d -Ala are inhibited, leading to an enhanced fluorescent signal, which allows the clear visualization of the intracellular bacteria. Moreover, TPEPy-d -Ala can effectively ablate the labeled intracellular bacteria in situ owing to covalent ligation to peptidoglycan, yielding a low intracellular minimum inhibitory concentration (MIC) of 20±0.5 μg mL⁻¹, much more efficient than that of a commonly used antibiotic, vancomycin.     

安培环路定理的拓扑学描述

近年来拓扑学在量子力学中得到了广泛的运用.本文将安培环路定理积分式重新表达为一矢量场在轮胎参数面上的第一类陈数积分.数值模拟展示了该积分值为一整数即第一陈数,其代表矢量场的整体性质:当经历连续变换时,矢量场的局部数值发生改变但整体积分值即陈数仍保持不变;若陈数发生改变,则表明矢量场变换的连续性条件发生破坏,矢量场出现奇点.进一步通过高斯映射将该矢量场从参数轮胎面映射到单位球面上,并给出了第一陈数的直观几何意义.理论和数值结果揭示了安培环路定理的拓扑学本质,表明拓扑概念在经典物理学中也会有广泛应用.     

Conformally invariant Monge-Ampère equations: Global solutions

In this paper we will examine a class of fully nonlinear partial differential equations which are invariant under the conformal group . These equations are elliptic and variational. Using this structure and the conformal invariance, we will prove a global uniqueness theorem for solutions in with a quadratic growth condition at infinity.

     

Geometric properties of the sections of solutions to the Monge-Ampère equation

In this paper we establish several geometric properties of the cross sections of generalized solutions to the Monge-Ampère equation , when the measure satisfies a doubling property. A main result is a characterization of the doubling measures in terms of a geometric property of the cross sections of . This is used to obtain estimates of the shape and invariance properties of the cross sections that are valid under appropriate normalizations.