FREE BOUNDARY PROBLEM ARISING FROM EVAPORATION FROM POROUS MEDIUM

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Banach空间值鞅不等式与弱大数定律

本文证明了Ｂａｎａｃｈ空间值鞅的一些不等式，讨论了Ｂａｎａｃｈ空间的凸性及光滑性与某些鞅不等的式的联系，给出了Ｈｉｌｂｅｒｔ空间的一个鞅不等式刻划，同时还讨论了一致Ｐ光滑空间中鞅的弱大数定律，本文的结论推广与改进了很多熟知的定理。     

STRONG DERIVATIVE AND ITS CONSEQUENCES

We introduce strong derivative, the corresponding Z-integrable and other related concepts. Also, we give an improved version of the fundamental theorem of calculus.     

含吡啶(噻唑)甲基的哌嗪类化合物的合成及生物活性

采用活性基团拼接原理, 分别以2-氯-5-氯甲基吡啶和2-氯-5-氯甲基噻唑为原料, 经过氮烷基化和加成反应, 得到系列含吡啶甲基或噻唑甲基的哌嗪类化合物. 初步测试结果表明: 部分化合物表现出较弱的除草活性和杀豆蚜活性, 但对孑孓显示出较高的的杀灭活性, 其中4f在50 mg/L的浓度下对孑孓的杀死率可达100%.     

Crystal structure of N-m-tolyl phthalimide

N-m-tolyl phthalimide, C₁₅NO₂H₁₁ crystallizes in the space group Cc with unit cell dimensions,a=8·54(1),b=19·89(2),c = 7·59(1)A, β=114·53(1)° andZ=4.V=1173(2)A³,D _m =1·35(1),D _c = 1·344 mg.m⁻³,M _r =237 λCoK_a=1·7903A. The structure was solved byMULTAN and refined to an R-factor of 0·116 for 632 counter reflections. The molecules are held together by van der Waal’s forces. The angle between the tolyl plane and the plane through the phthalimide group is 53·4(4)°. Contribution No. 607.     

Second-order linearity of the general signed-rank statistic

Let X₁,…, X_n be i.i.d. random variables symmetric about zero. Let R_i(t) be the rank of |X_i − tn^−1/2| among |X₁ − tn^−1/2|,…, |X_n − tn^−1/2| and T_n(t) = Σ_{i = 1}ⁿφ((n + 1)⁻¹R_i(t))sign(X_i − tn^−1/2). We show that there exists a sequence of random variables V_n such that sup_{0 ≤ t ≤ 1} |T_n(t) − T_n(0) − tV_n| → 0 in probability, as n → ∞. V_n is asymptotically normal.     

On Cesari's property (Q)

In the present paper, we generalize, within the family of convex-valued multifunctions, a selection theorem of Cole (Ref. 1). This then leads us to prove some new results concerning Cesari's property (Q) and to the introduction of the Cesari limit of sets, which is then compared to the Kuratowski-Mosco limit.This work was done while the author was a visiting professor at the University of Pavia, Pavia, Italy. Financial support was provided by CNR and by NSF Grant No. 84-03135.     

Analytical and approximate solutions of(2+1)-dimensional time-fractional Burgers-Kadomtsev-Petviashvili equation

In this paper, we applied the sub-equation method to obtain a new exact solution set for the extended version of the time-fractional Kadomtsev-Petviashvili equation, namely BurgersKadomtsev-Petviashvili equation(Burgers-K-P) that arises in shallow water waves.Furthermore, using the residual power series method(RPSM), approximate solutions of the equation were obtained with the help of the Mathematica symbolic computation package. We also presented a few graphical illustrations for some surfaces. The fractional derivatives were considered in the conformable sense. All of the obtained solutions were replaced back in the governing equation to check and ensure the reliability of the method. The numerical outcomes confirmed that both methods are simple, robust and effective to achieve exact and approximate solutions of nonlinear fractional differential equations.     

Entropic uncertainty relation of a qubit-qutrit Heisenberg spin model and its steering

We investigate the quantum-memory-assisted entropic uncertainty relation (QMA-EUR) in a Heisenberg XYZ mixed-spin (1/2, 1) model. Coupling strength, Dzyaloshinskii-Moriya (DM) interaction and inhomogeneous magnetic field, respectively, contributing to QMA-EUR by a thermal entanglement in the hybrid-spin model are studied in detail. Furthermore, we compare the uncertainty of the bipartite hybrid model with those of qubit-qubit and qutrit-qutrit systems. Meanwhile, the effects of local PT-symmetric operation and weak measurement on the steering of entropic uncertainty are analyzed. We find that the local PT-symmetric operation can reduce the entropic uncertainty, and the entropic uncertainty can also be decreased by weak measurement reversal.