Unique solvability and exponential stability of differential hemivariational inequalities

ABSTRACT

In this paper, we study a differential hemivariational inequality (DHVI, for short) in the framework of reflexive Banach spaces. Our aim is three fold. The first one is to investigate the existence and the uniqueness of mild solution, by applying a general fixed-point principle. The second one is to study its exponential stability, by employing the formula for the variation of parameters and inequality techniques. Finally, the third aim is to illustrate an application of our abstract results in the study of an initial and boundary value problem which describes the contact of an elastic rod with an obstacle.     

Partition coefficients of ω-phenylalkanols between water and liposome membranes of phospholipids

For the liposome of two types of phospholipids (zwitterionic dipalmitoyl-phosphatidylcholine (DPPC) and anionic dimyristoylphosphatidic acid (DMPA)), the partition coefficient K _X for partition of homologous v32/xxlarge969.gif" alt="ohgr" align="BASELINE" BORDER="0">-phenylalkanols (C₆H₅(CH₂) _mp OH; m _p =0–8) between bulk water and the liposome membrane was determined on the basis of the gel to liquid crystalline phase transition temperature T _m of the liposome membrane. The plot of log K _X vs. m _p gave a break at m _p =7 for both phospholipids, and a second break at m _p =4 was observed for DPPC. The local polarity of the surface region and the orderliness of phospholipid molecules in the liposome membrane were estimated from ESR spectra of two spin probes solubilized in the membrane. The results suggest that the hydration of DPPC liposome membrane is relatively restricted to its surface region, but for DMPA the hydration spreads not only along the surface but also to the inside of the membrane. The main factor controlling the partitioning of the alkanols is the local polarity. The higher alkanols (m _p =7, 8) are solubilized not only in the liquid crystalline phase but also in the gel phase, although the other lower alkanols are solubilized in the liquid phase only.     

A one-step oxidative synthesis of trimethylantimony(v) diacylates

Trimethylantimony(v) diacylates Me₃Sb(OCOR)₂ (R = H, Me, Ph) have been obtained in 72–75 % yield by the interaction of trimethylantimony withtert-butylhydroperoxide and carboxylic acids at the ratio of 1 1 2 in benzene (20 °C, 20 h) in the presence of sodium sulfate.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 537–538, March, 1994.     

Combined high-resolution electron microscopy and computer modeling of a Σ=5 (210) [001] tilt boundary in AuCu3

Combined high-resolution electron microscopy, computer modeling, and image simulations are used to study the structure of the v32q1323t201560q/xxlarge931.gif" alt="Sgr" align="BASELINE" BORDER="0">=5 (210) [001] tilt boundary in the ordered compound AuCu₃. On the experimental side, we have prepared thin samples cut in a bulk bicrystal containing an interface close to the above (v32q1323t201560q/xxlarge952.gif" alt="theta" align="BASELINE" BORDER="0">_tilt v32q1323t201560q/xxlarge8776.gif" alt="ap" align="MIDDLE" BORDER="0"> 37°). The high-resolution images obtained at 400 kV along the [001] tilt axis show that among possible configurations, the boundary adopted predominantly a symmetrical one. Theoretically, using the standard geometrical approach, we derived possible atomic configurations of the boundary and we identified some of the defects allowing for the coexistence between these variants. Finally, we performed energy minimizations using these geometrical models and an n-body potential adapted to this compound. In agreement with the experiment, one of the two possible symmetrical variants is associated to the lowest excess energy. Moreover, the computations show that large variations affect the spacing of (210) atomic planes near the boundary.     

Incorporation of silver into soda-lime silicate glass by a classical staining process

Silver was introduced into soda-lime silicate glass by a classical staining process under varying conditions of temperature and time. The spectroscopic features of the stained glasses were investigated by studying absorption, photoluminescence and electron paramagnetic resonance properties. The diffusion parameters (diffusion coefficient and diffusion activation energy) of silver ions were calculated based on elemental analysis data from inductively coupled plasma (ICP) spectrometry, and line scan profiles from energy dispersion X-ray analysis (EDX).     

Structure of bis(O,O′-diisopropyldithiophosphato-S,S′) (1,10-phenanthroline-N1,N10)zinc(II) complex, [Zn(phen)(S2P(OiPr)2)2]

The crystal and molecular structure of [Zn(phen)(S₂P(OiPr)₂)₂] (Phen = 1,10-phenanthroline) has been determined by X-ray crystallography. It crystallizes in the Monoclinic system, space group C2/c, with lattice parameters a = 19.315(4), b = 10.438(2), c = 16.567(3)Å, v4q7/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0"> = 102.89 (3)°, and Z = 4. The complex has C₂ symmetry. The coordination geometry of each Zn atom, by two S atoms from two (O,Ov4q7/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-diisopropyldithiophosphato) anions and by two N atoms from phenanthroline ligand, is that of a slightly distorted tetrahedron [Zn—S 2.2914(8)Å Zn—N 2.111(2)Å]. The Zn···S distances to the noncoordinated S atoms are long: 3.5276 Å, which are indicated that there are much weaker interactions between them.     

集合论在拟仿紧性中的应用

1977年,刘应明引进拟仿紧性并证明了下述集论拓扑学的结果：在假设$2^{\omega_1}>2^{\omega}$下每一个可分正规的拟仿紧空间是仿紧空间.我们进一步证明假设$2^{\omega_1}>2^{\omega}$等价于每一个可分正规的拟仿紧空间是仿紧空间,获得了拟仿紧性的一个独立性结果.     

Selectivity of the nucleon-induced deuteron breakup and relativistic effects

Theoretical predictions for the nucleon-induced deuteron breakup process based on solutions of the three-nucleon Faddeev equation including such relativistic features as the relativistic kinematics and boost effects are presented. Large changes of the breakup cross section in some complete configurations are found at higher energies. The predicted relativistic effects, which are mostly of dynamical origin, seem to be supported by existing data.     

A new way to look at DIS

We discuss inclusive scattering of electrons from composite systems. In particular, we consider the examples of quasi-elastic electron-nucleus scattering and deep-inelastic electron-nucleon scattering, DIS, processes that have much in common. The study of DIS in a way analogous to past studies of quasi-elastic scattering provides new insight, in particular in what concerns the role of final-state interaction and the importance of binding of the constituents.