THERMODYNAMIC STUDY OF ADSORPTION OF PHENOLIC COMPOUNDS FROM AQUEOUS SOLUTION BY A WATER-COMPATIBLE HYPERCROSSLINKED POLYMERIC ADSORBENT

Equilibrium data for the adsorption of phenolic compounds, i.e., phenol, p-cresol, p-chlorophenol and p-nitrophenol from aqueous solutions by a water-compatible hypercrosslinked polymeric adsorbent (NJ-8) within temperature range of 283-323 K were obtained and correlated with a Freundlich-type of isotherm equation, so that equilibrium constants KF and n were obtained. The capacities of equilibrium adsorption for all the four phenolic compounds on the NJ-8 from aqueous solutions are around 2 times as high as those of Amberlite XAD-4, which may be attributed to the unusual micropore structure and the partial polarity on the network. The values of the enthalpy (always negative) are indicative of an exothermic process, which manifests the adsorption of all the four phenolic compounds on the two polymeric adsorbents to be a process of physical adsorption. The negative values of free energy change show that the solute is more concentrated on the adsorbent than in the bulk solution. The absolute free energy values of adsorption for NJ-8 are always higher than those for Amberlite XAD-4, which indicates that phenolic compounds are preferentially adsorbed on NJ-8. The negative values of the adsorption entropy are consistent with the restricted mobilities of adsorbed molecules of phenolic compounds as compared with the molecules in solution. The adsorption entropy values of phenolic compounds for NJ-8 are lower than those for Amberlite XAD-4, which means the micropores of NJ-8 require more orderly arranged adsorbate.     

Global Existence of Solutions and Lower Bound Estimate of Blow-Up Time for the Keller-Segel Chemotaxis Model北大核心CSCD

A macroscopic nonlinear Keller-Segel model for chemotactic cell migration was considered, where the existence region of the model is a bounded convex one on Ω ⊂ RN(N≥2). The global existence of the solution on Ω ⊂ R3 was obtained by means of the energy estimate method. The lower bound of the blow-up time was proved for N = 3 and N = 2. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Lower semicontinuous solutions of the Bellman equation for the minimum time problem

The minimum time problem associated with a nonlinear control system is considered, and the unicity of the lower semicontinuous solution of the corresponding Bellman equation is investigated. A main tool in our approach is the Kruzkov transformation that enables us to work on ⁿ –{0}, where {0} is the target set, instead of the unknown reachable set.This research was carried out while the first author was visiting the Department of Mathematics, University of Genova, Genova, Italy.     

The occupation time of Brownian motion in a ball

LetW be a Wiener process of dimensiond3, starting from 0, and letX(t) be the total time spent byW in the ball centered at 0 with radiust. We give an affirmative answer to a conjecture of Taylor and Tricot⁽¹⁶⁾ on the tail distribution ofX(t). Lévy's lower functions ofX(t) are characterized by an integral test.     

硝酸钆低水合物的制备及表征

本文用两种方法制得硝酸钆的低水合物Gd(NO_3)_3·5H_2O、Gd(NO_3)_3·3.5H_2O,其中Gd(NO_3)_3·3.5H_2O是文献中尚未报道的 ,给出了它们的M.P.和X-衍射特征值。     

Heterogeneous Catalytic Partial Oxidation of C3-C4 Alkanes with Nitrogen Monoxide

The possibility of making products of partial oxidation, alcohols and acids in particular, by the reaction of C₃-C₄ alkanes with nitrogen monoxide over oxide and zeolite catalysts is demonstrated. The most effective catalysts are CeO₂ and Fe-TsVK. The dependence of the rate and selectivity of the process on the reaction conditions has been established.     

Asymptotic Behavior of the t Expansion

The asymptotic behavior of a system's ground-state energy from the t expansion of Horn and Weinstein has been suggested to have the form E ₁(t)=E ₁+exp(–a _n t+b _n ). In the limit of very large t, this becomes E ₁(t)=E ₁+exp(–a ₁ t+b ₁). A simple analysis shows that the parameters are a ₁=E ₂–E ₁ and b ₁=ln[(E ₂–E ₁)|c ₂|²/|c ₁|²]. Functions are introduced which allow determination of a ₁, b ₁ and lower bounds to E ₁.     

Topological degree of a family of convex functions and localization of nash equilibrium points

We define the degree of a family of convex functionsf _x, wherex , and prove that, if this degree is different from zero, one has at least one Nash equilibrium point in . This is a criterion of localization of such equilibrium points.     

Average electron momenta in many-electron atoms

In many-electron atoms, the average electron momentum p represents the mean momentum of a single electron when all the electron motions are averaged. If any two electrons are considered simultaneously, however, the average momentum p splits into two different momenta, low momentum p_< and high momentum p_>. For the 102 atoms He through Lr in their ground states, the momenta p_< and p_> are systematically examined at the Hartree–Fock limit level. It is also shown that the sum p_>+p_< and the difference p_>–p_< of the two momenta constitute upper and lower bounds to the electron-pair relative momentum p₁₂=|p₁–p₂| and to the electron-pair center-of-mass momentum P=|p₁+p₂|/2. The tightness of the bounds is discussed for the 102 atoms.     

CT联合血清HCY、β2-M在下肢动脉狭窄闭塞性疾病中的诊断价值

本文对CT联合血清同型半胱氨酸（HCY）、β2-微球蛋白（β2-M）在下肢动脉狭窄闭塞性疾病中的诊断价值进行分析。选取上海市金山区中西医结合医院收治的120例疑似下肢动脉狭窄闭塞性疾病患者进行研究，选取同期健康体检者120例作为对照组，对患者进行CT检查、血清HCY和β2-M水平检查，并比较了CT诊断下肢动脉狭窄闭塞情况、两组患者血清HCY和β2-M水平，以明确CT、HCY、β2-M诊断价值及误诊率、漏诊率。结果显示，120例疑似患者中，CT检测出646节段病变血管，其中轻度狭窄155节段，中度狭窄257节段，重度狭窄143节段，血管完全闭塞91节段；研究组患者血清HCY、β2-M水平明显高于对照组，两组比较差异有统计学意义（P<0.05）；HCY的AUC为0.863，截断值>21.75（μmol/L），诊断敏感性为79.00%，特异性为80.00%，β2-M的AUC为0.837，截断值>2.98（μmol/mL），诊断敏感性为75.25%，特异性为65.21%；CT诊断阳性率为67.50%，HCY诊断阳性率为69.17%，β2-M诊断阳性率为67.50%，三者联合诊断阳性率为82.50%，联合诊断阳性率高于CT、HCY、β2-M单独诊断阳性率（P<0.05）；CT、HCY、β2-M单一检测对下肢动脉狭窄闭塞性疾病均有较高灵敏度、特异性及准确度，但三者联合诊断灵敏度、特异性及准确度最高，误诊率、漏诊率最低。本文证实了采用CT联合血清HCY、β2-M诊断下肢动脉狭窄闭塞性疾病诊断灵敏度、特异性及准确度高，误诊率、漏诊率低。