Some properties of autocentral automorphisms of a group

Let G be a group, Aut(G) and L(G) denote the full automorphisms group and absolute centre of G, respectively. The automorphism \({\alpha\in Aut(G)}\) is called autocentral if \({g^{-1}\alpha(g)\in L(G)}\), for all \({g\in G}\). In the present paper, we investigate the properties of such automorphisms.     

Synthesis and characterization of new polymer systems containing very bulky tris(trimethylsilyl)methyl substituents as side chains

The 4-chloromethyl styrene (CMS) was copolymerized with different styrenic monomers such as methyl styrene, 4-methoxy styrene and α-methyl styrene by free radical polymerization method at 70 ± 1 °C using α,α^′-azobis(isobutyronitrile) (AIBN) as an initiator and the copolymers I, II and III collected respectively. The very bulky tris(trimethylsilyl)methyl {trisyl} substituents were covalently attached to the obtained copolymers with replacement of all the chlorine atoms in CMS units. The polymers, obtained in quantitative yields, were characterized by FT-IR, ¹H NMR and ¹³C NMR spectroscopy; differential scanning calorimetry (DSC) and GPC studies. All the polymers containing trisyl groups showed a high glass transition temperature (in the range 150-190 °C) in comparison with copolymers I-III (in the range 90-95 °C). The increase of the glass transition temperature reflects the substantial increase in rigidity of new polymers bearing very bulky substituents in side chains.     

The effect of capping layers on low-angle Bragg peaks from copper-cobalt multilayers

Using simulations based on the Parratt theory for grazing incidence X-ray specular reflectivity, we show that small variations in the thickness of the gold cap used to prevent oxidation in Co/Cu multilayers can have a dramatic effect on the height and position of the low-order Bragg peaks from these multilayers. The height of the specular Bragg peak cannot be used as a measured of interface roughness nor its position used to determine multilayer period unless the cap thickness is known or determined precisely by simulation.     

Adsorption of Acid Blue 193 from aqueous solutions onto Na-bentonite and DTMA-bentonite

Dodecyltrimethylammonium bromide-modified bentonite (DTMA-bentonite) was prepared and tested as an adsorbent for an acid dye (Acid Blue 193, AB193) removal from aqueous solution in comparison with Na-bentonite. The effect of various experimental parameters was investigated using a batch adsorption technique. In this manner, the adsorption isotherms, adsorption kinetics, and temperature and pH effects upon Acid Blue 193 adsorption on Na-bentonite and DTMA-bentonite were thoroughly examined. Results show that a pH value of 1.5 is favorable for the adsorption of Acid Blue 193. The isothermal data could be well described by the Freundlich equation. The dynamical data fit well with the pseudo-second-order kinetic model. The adsorption capacity of DTMA-bentonite (740.5 mg g(-1)) was found to be around 11 times higher than that of Na-bentonite (67.1 mg g(-1)) at 20 degrees C. Thermodynamic parameters such as activation energy (E(a)) and change in the free energy (DeltaG(0)), the enthalpy (DeltaH(0)), and the entropy (DeltaS(0)) were also evaluated. The overall adsorption process was exothermic but it is only spontaneous at 20 degrees C. The results indicate that Na-bentonite and DTMA-bentonite could be employed as low-cost alternatives to activated carbon in wastewater treatment for the removal of color which comes from textile dyes.     

Thermolysis of [tris(trimethylsilyl)methyl](diphenyl)fluorosilane. Isomerization of a sila-olefin intermediate

The compound (Me₃Si)₃CSiPh₂F loses Me₃SiF under reflux or on passage through a tube at 450°C to give three products, A, B, and C, in approximately 20/20/60 ratio. Products A and B, which are solids, were shown by X-ray crystallographic analysis to be the diastereoisomeric forms of 1-dimethylsila-2-trimethylsilyl-3-[(methyl)(phenyl)sila]indane. From its mass and ¹H NMR spectra, C (a liquid) was tentatively identified as 1,3-bis(dimethylsila)-2-[(dimethyl)(phenyl)silyl]indane. All three products are isomers of the sila-olefin (Me₃Si)₂CSiPh₂, and it is suggested that the latter is first formed by loss of Me₃SiF from (MeSi)₃CSiPh₂F, and the equilibrium (Me₃Si)₂CSiPh₂ ? (Me₃Si)(Ph₂MeSi)CSiMe₂ ? (Me₃Si)(PhMe₂Si)CSiMePh ? (Me₂PhSi)₂CSiMe₂ is then rapidly established; internal cyclizations involving addition of aryl CH bonds across SiC bonds then occur to give the observed products. Consistent with this is the observation that a mixture of silicon alkoxides, thought to be (Me₃Si)₂CHSiPh₂OMe and its isomers (which would be formed by addition of methanol across the SiC bonds of the four sila-olefins) is produced when methanol is passed through the hot tube with the (Me₃Si)₃CSiPh₂F.Full structural details are given for compounds A and B. Some features of interest are: (a) the conformation of the 5-membered ring is different in the two diastereoisomers; (b) the exocyclic SiCSiMe₃ bond angles, of ca. 120° are unusually large; and (c) there is a little distortion of the fused benzene ring, which is attributed to the effect of silicon substituents on the hybridization of carbon atoms to which they are attached.     

Observation of magnetic domain wall movements by X-ray topography using synchrotron radiation

Antiferromagnetic domain wall movements in KNiF₃ have been observed directly by X-ray topography using synchrotron radiation. Topographs were taken in fields up to 1.3 T at a temperature of 77 K. In contrast to X-ray topography using conventional sources, the apparatus is simple and it is possible to obtain good resolution topographs despite the geometrical limitations imposed by the cryostat and electromagnet. Exposure times were typically 8 seconds when recording on Ilford L4 Nuclear Emulsion plates.     

Integrating thermal-concentration smoothed profile with lattice Boltzmann methods for simulating sedimentation of nonisothermal circular particles

A thermal-concentration smoothed profile-lattice Boltzmann method is proposed to study the effect of the concentration field on the dynamic behavior of nonisothermal cylindrical particles during the sedimentation process. The velocity, temperature, and concentration equations are solved using the lattice Boltzmann method. Moreover, the smoothed profile method is employed to enforce the nonslip boundary condition as well as constant temperature and constant concentration boundary conditions at the particles surfaces. Moreover, the Boussinesq approximation is used to couple the velocities, temperatures, and concentrations fields. The proposed combined method is validated by comparing the present numerical results with those found in the literature, showing good consistency. Then, the effect of the concentration buoyancy on the behavior of nonisothermal particles is discussed. In addition, the effect of Prandtl, Schmidt, and thermal Grashof numbers on the settling process is investigated. The results show that, by adding the effect of concentration, the maximum settling velocity of hot particles is reduced more relative to the cold ones; accordingly, the cold particles are settled faster than the hot ones. Finally, the sedimentation of two particles in a container at high thermal Grashof is investigated. It is shown that, at high thermal Grashof, there is an intense competition between the buoyancy force and gravity for the hot particles. The buoyancy flow generated leads to the reversal of the drafting-kissing-tumbling motion of the hot particles, making the particles move upward.     

A survey of optimization models on cancer chemotherapy treatment planning

While chemotherapy is an effective method for treating cancers such as colorectal cancer, its effectiveness may be dampened by the drug resistance and it may have significant side effects due to the destruction of normal cells during the treatment. As a result, there is a need for research on choosing an optimal chemotherapy treatment plan that minimizes the number of cancerous cells while ensuring that the total toxicity is below an allowable limit. In this paper, we summarize the mathematical models applied to the optimal design of the cancer chemotherapy. We first elaborate on a typical optimization model and classify relevant literature with respect to modeling methods: Optimal control model (OCM) and others. We further classify the OCM models with respect to the solution method used. We discuss the limitations of the existing research and provide several directions for further research in optimizing chemotherapy treatment planning.