Interfaces for 1-D degenerate Keller–Segel systems

Let us consider the Keller–Segel system of degenerate type (KS) _m with m >1 below. We prove the property of finite speed of propagation for weak solutions u with a certain regularity. Moreover, we investigate the interface curve which separates the regions and . Concretely, we characterize the interface curve as the solution of a certain ordinary differential equation associated with (KS) _m .     

Certified reference material for quantification of polycyclic aromatic hydrocarbons in sediment from the National Metrology Institute of Japan

The National Metrology Institute of Japan has issued a certified reference material (CRM) of freshwater lake sediment for polycyclic aromatic hydrocarbon (PAHs) analyses. The certification used three extraction techniques: pressurized liquid extraction (PLE) with toluene, PLE with dichloromethane/ethyl acetate (1:1 by volume), and alkaline extraction (1 M KOH in methanol) in combination with microwave-assisted extraction. Both gas chromatography/mass spectrometry (GC/MS) and liquid chromatography/dopant-assisted atmospheric pressure photoionization/MS (LC/DA-APPI/MS) analyses were used. Certified values are provided for 18 PAHs at 1–25 μg kg⁻¹ except for perylene (2.08 × 10³ μg kg⁻¹), and information values are provided for two. Since the values of PAHs in the CRM are much lower than those in other CRMs and are comparable to those found at sites with little human influence, the CRM is suitable for PAH monitoring in sediment and soil samples.     

Densely Packed CO2 Aids Charge,Spin, and Lattice Ordering Partially Fluctuated in a Porous Metal–Organic Framework Magnet

Partial charge fluctuations in the charge-ordered state of a material, often triggered by structural disorders and/or defects, can significantly alter its physical characteristics, such as magnetic long-range ordering. However, it is difficult to post-chemically fix such accidental partial fluctuations to reconstruct a uniform charge-ordered state. Herein, we report CO₂-aided charge ordering demonstrated in a CO₂-post-captured layered magnet, [{Ru₂(o-ClPhCO₂)₄}₂{TCNQ(OMe)₂}] ⋅ CO₂ ( 1⊃CO₂ ; o-ClPhCO₂⁻=ortho-chlorobenzoate; TNCQ(OMe)₂=2,5-dimethoxy-7,7,8,8-tetracyanoquinodimethane). Pristine porous layered magnet 1 had a partially charge-fluctuated ordered state, which provided ferrimagnetic ordering at T_C=65 K. Upon loading CO₂, 1 adsorbed one mole of CO₂, forming 1⊃CO₂ , and raising T_C to 100 K. This was because of the vanishing charge fluctuations without significantly changing the framework structure. This research illustrates the post-accessible host–guest chemistry delicately combined with charge, spin, and lattice ordering in a spongy magnet. Furthermore, it highlights how this innovative approach opens up new possibilities for technology and nanoscale magnetism manipulation.