SEPARATION PROPERTY OF POSITIVE RADIAL SOLUTIONS FOR A GENERAL SEMILINEAR ELLIPTIC EQUATION

The asymptotic behavior at infinity and an estimate of positive radial solutions of the equation △u ＋ sum from i=1 to k cirli upi = 0, x ∈ Rn,（0.1）are obtained and the structure of separation property of positive radial solutions of Eq. （0.1） with different initial data α is discussed.

Remarks on the Riesz Separation Property of the Linear Span of Positive Compact Operators

It is proven that there exists a Dedekind complete Banach lattice E such that the linear spans/f （E） and IV （E） of positive compact and positive weakly compact operators on E fails to possess the Riesz separation property.

SINGULAR POSITIVE RADIAL SOLUTIONS FOR A GENERAL SEMILINEAR ELLIPTIC EQUATION

The existence and uniqueness of singular solutions decaying like r^-m（see （1.4）） of the equation △u＋k∑i=1ci｜x｜liupi=0,x∈R^N are obtained, wheren≥3, ci 〉0, li〉-2, i=1,2,..,k, pi〉 1, i=l,2,-..,kandthe separation structure of singular solutions decaying like r^-（n-2） of eq. （0.1） are discussed. moreover, we obtain the explicit critical exponent ps （l） （see （1.9））.

QUASI-WEAK CONVERGENCE WITH APPLICATIONS IN ORDERED BANACH SPACE

In the paper quasi_weak convergence is introduced in ordered Banach space and it is weaker than weak convergence. Besed on it, the fixed point existence theorem of increasing operator is proved without the suppose of continuity and compactness in the sense of norm and weak compactness and is applied to the Hammerstein nonlinear intergal equation.

A Functional Comparison of Marital Debts in Common Law Jurisdictions:Lessons from the Model Not Accepting the Common Property Regime

Traditionally,the Common Law System exercises a legal separation of marital property regime between husband and wife;this regime still has interpretation theory value for functional comparison to that of China.The husband-wife personality integration in the early days of the Common Law System goes back to the original agency of necessity similar to that of the daily family agency of the Civil Law System;the aim was to strengthen marital coherence rather than protect creditors.The“daily family needs”should beidentifiedwithoutexcluding the husband-and-wife separation period,and be based on the consumption level during the time that a couple have lived together.The current mainstream mode of the Common Law System starts from the“Consensual Approach”under the legal regime of separation of property between husband and wife,and limits the“Purpose Theory”to cases of insufficient consensual evidence.Moreover,thismainstream mode is supplemented by the“Presumption Theory”that only exists as a method of proof,and is similar to the current Chinese position of co-debt and co-signing.When a nondebtor consents a debtor to borrow money in the name of husband and wife,this consent can be used as a yardstick to determine their marital community debt and to identify the nature of various debts in the context of marital community debt.

Highly Stable sp^(2) Carbon-Conjugated Porous Organic Cages

The high-yield synthesis of ultrastable porous organic cages(POCs)by facile methods is highly desirable but challenging.Inspired by highly stable sp^(2) carbon-conjugated(C=C)covalent organic frameworks,we used rational design and synthesized the first family of sp^(2) carbon-linked POCs(sp^(2)c-POCs)with triangular prism shapes by a one-step Knoevenagel reaction that is a high yield[2+3]condensation reaction.The stability of sp^(2)c-POC was demonstrated under strenuous conditions involving for example concentrated HCl or saturated NaOH solution.sp^(2)c-POC was used as a robust adsorbent for efficient separation of CO_(2)/CH_(4) or CO_(2)/N_(2) mixtures.In view of their facile synthesis and unique properties,we expect widespread use of these sp^(2) C=C linkages in the development of POC materials.

The preparation of a novel polydopamine-graft-poly(2-methyl-2-oxazoline) protein-resistant coating and its applications in protein separation

A novel polydopamine-graft-poly（2-methyl-2-oxazoline） （PDA-g-PMOXA） coating was prepared by immobilizing poly（2-methyl-2-oxazoline） （PMOXA） onto material surfaces through polydopamine （PDA） anchored coating for the first time. And then, the chemical composition, hydrophilicity, and protein-resistant properties of the PDA-g-PMOXA coating were studied using X-ray photoelectron spectroscopy （XPS）, contact angel （CA） test, surface plasmon resonance （SPR）, and quartz crystal microbalance with dissipation （QCM-D） measurement. Finally, the coating was applied to the capillary inner surface for protein separation by capillary electrophoresis （CE）.

Concerted regulation on vertical orientation and film quality of two-dimensional ruddlesden-popper perovskite layer for efficient solar cells

Recently,the two-dimensional(2D)ruddlesden-popper(RPP)perovskite has been successfully attracting great attention owing to their excellent electronic property and superior ambient stability.But 2D perovskite solar cells(PVSCs)with insulating large cations show a worse performance than three-dimensional(3D)PVSCs in general because of the worse charge transportation.In this work,dimethyl sulfoxide(DMSO)and KI were incorporated simultaneously to produce a synergistic effect on both film quality and orientation of 2D perovskite.With this strategy,a cavity-free 2D perovskite film was formed with vertically oriented crystal,and high quality film was obtained with decreased defects and increased crystallinity.Besides,profitable multiple phases were obtained for better spontaneous carrier separation and transportation.The 2D PVSCs based on(PEA)2(MA)n−1PbnI3n+1(n=5)delivered a higher power conversion efficiency(PCE)of 13.4%.In addition,the perovskite with KI and DMSO contained more stable low-dimension phase at the bottom of perovskite film,which could act as a barrier to prevent moisture from further eroding internal perovskites.The optimized 2D PVSCs remained 90%of the PCE after being exposed in air(50%–60%humidity,room temperature)with a continuous illumination for 300 h.

A Note on Weighted Korn Inequality

In this note, we show that, for domains satisfying the separation property, certain weighted Korn inequality is equivalent to the John condition. Our result generalizes previous result from Jiang Kauranen [Calc. Vat. Partial Differential Equations, 56, Art. 109, （2017）] to weighted settings.

Thermal properties of polyurethane elastomer with different flexible molecular chain based on para-phenylene diisocyanate

This work focuses on the relationship between flexibility of molecular chains and thermal properties of polyurethane elastomer（PUE）, which laid the foundation of further research about how to improve thermal properties of PUE. A series of PUE samples with different flexibility of molecular chains was prepared by using 1,4-butanediol（1,4-BDO）/bisphenol-a（BPA） blends with different mole ratios including9/1, 8/2, 7/3, 6/4 and 5/5. As comparison, PUE extended with pure 1,4-BDO and BPA was also synthesized.These samples were characterized by differential scanning calorimetry（DSC）, thermogravimetric analysis（TGA）, dynamic mechanical analysis（DMA）, etc. The results showed that with the decrease in flexibility of molecular chains the glass transition temperature（Tg） increased and low-temperature properties became worse. Besides, all samples had a certain degree of microphase separation, and soft segments in some samples were crystallized, i.e. the decreasing flexibility of molecular chains led to the impossibility of chains tightly packing and crystalline domains forming so that the degree of microphase separation decreased and the thermal properties became worse.

Controllable magnetic properties of cobalt ferrite particles derived from layered double hydroxide precursors

Cobalt ferrite CoxNi1-xFe2O4 （x = 0, 0.5, 1 ） particles with controllable magnetic properties have been prepared by calcination of co-substituted NiFe^2＋Fe^3＋ -layered double hydroxide （NiFe^2＋Fe^3＋-LDH） precursors prepared via a scalable method involving separate nucleation and aging steps （SNAS）. Their structural and magnetic characteristics were investigated by powder X-ray diffraction （XRD）, scanning electron microscopy （SEM） and vibrating sample magnetometry （VSM）. Measurements of magnetic properties show that the saturation magnetization （Ms） and coercivity （He） of the calcined products increased with increasing cobalt content. The LDH precursor-based product obtained by calcination of a mixture of CoFe^2＋Fe3^＋-LDH and NiFe^2＋Fe^3＋ -LDH powders with a Co/Ni molar ratio of 1：1, exhibits a moderate value of Ms and an increased value of He compared to the corresponding values for an Ni0.5Co0.5Fe2O4 material prepared by calcination of a Co0.5Ni0.5Fe^2＋Fe^3＋-LDH precursor, and a physical mixture of CoFe2O4 and NiFe2O4 with a Co/Ni molar ratio of 1 ： 1. These results may provide a way to regulate magnetic anisotropy of ferrite spinels by varying the composition of the LDH precursors.