Two regularization methods for backward heat problems with new error estimates

We introduce two new methods for solving a backward heat conduction problem. For these two methods, we give a stability analysis with new error estimates. Meanwhile, we investigate the roles of the regularization parameters in these two methods. Numerical results show that our algorithm is effective.     

Local hydrodynamic investigation of the aeration in a submerged hollow fibre membranes cassette

The better understanding of the effective air distribution inside a membrane cassette is a particular challenge in submerged membrane bioreactor. The present study is the first one that investigates the hydrodynamics of the coarse bubbles flow inside a hollow fibre membranes cassette. The experimental investigations were carried out in a reactor equipped with commercial modules from ZENON ZeeWeed^® 500d. A bi-optical probe was used to measure the bubble size, the bubble velocity and the gas hold-up at different locations between the modules and for three different gas flow rates. These local measurements gave significant information about the lateral distribution of the air and its evolution with the height on the surface of the membrane modules, which can impact on the filtration performance and are the first step to an optimisation of the aeration system and module geometry.     

Dependence of photoemission efficiency on the pulsed laser cleaning of Tungsten photocathodes, part 1: Experimental

3+ :YAG laser with 5^th harmonic generator, generating 16 ps duration pulses at 213 nm, with energies up to 0.5 mJ. Experimental results concerning the action of laser pulses, as well as the effects of residual pressure on the cleanliness of the photocathodes surface are presented and discussed. Influence of laser pulses and residual pressure on the work function of the metal are also investigated. Received: 15 April 1996/Accepted: 5 November 1996     

Low-temperature photoluminescence spectra of highly excited quantum wires

Optical spectra of highly excited quantum wires at low temperatures have been studied within the dynamical screening approximation. We found a strong Fermi-edge singularity (FES) in the photoluminescence spectra. The spectral shape and FES intensity strongly depend on temperature in agreement with recent experimental results.     

Graphs with prescribed mean curvature on hyperbolic spaces

We study a quasilinear elliptic equation in the unit ball ofℝ ^m . Using this result we get the existence of graphs with prescribed curvature on hyperbolic spacesℍ ^m inℍ ^m ×ℝ.     

Morse-Palais lemma for nonsmooth functionals on normed spaces

Using elementary differential calculus we get a version of the Morse-Palais lemma. Since we do not use powerful tools in functional analysis such as the implicit theorem or flows and deformations in Banach spaces, our result does not require the -smoothness of functions nor the completeness of spaces. Therefore it is stronger than the classical one but its proof is very simple.

     

Hydrogenated Graphene and Hydrogenated Silicene: Computational Insights

Density functional calculations are performed to study the energetic, structural, and electronic properties of graphene and silicene functionalized with hydrogen. Our calculations predict that H atoms bind much more strongly to silicene than to graphene. The adsorbed H atoms tend to cooperatively stabilize each other leading to a two‐dimensional nucleation and growth mechanism. The different structural and electronic modifications induced by H in fully functionalized graphene and silicene (known as graphane and silicane) are also explained. Finally, the electronic properties of defective graphane with multiple hydrogen vacancies are investigated. Engineering the vacancies in graphane offers a way to modify the electronic properties of this material.     

Syntheses,Crystal Structures,and Properties of the Isotypic Pair [Cr(H2O)6]2[B12H12]3·15H2O and [In(H2O)6]2[B12H12]3·15H2O

Single crystals of [Cr(H₂O)₆]₂[B₁₂H₁₂]₃ · 15H₂O and [In(H₂O)₆]₂[B₁₂H₁₂]₃ · 15H₂O were obtained by reactions of aqueous solutions of the acid (H₃O)₂[B₁₂H₁₂] with chromium(III) hydroxide and indium metal shot, respectively. The title compounds crystallize isotypically in the trigonal system with space group R$\bar{3}$ c (a = 1157.62(3), c = 6730.48(9) pm for the chromium, a = 1171.71(3), c = 6740.04(9) pm for the indium compound, Z = 6). The arrangement of the quasi‐icosahedral [B₁₂H₁₂]^2– dianions can be considered as stacking of two times nine layers with the sequence …ABCCABBCA… and the metal trications arrange in a cubic closest packed …abc… stacking sequence. The metal trications are octahedrally coordinated by six water molecules of hydration, while another fifteen H₂O molecules fill up the structures as zeolitic crystal water or second‐sphere hydrating species. Between these free and the metal‐bonded water molecules, bridging hydrogen bonds are found. Furthermore, there is also evidence of hydrogen bonding between the anionic [B₁₂H₁₂]^2– clusters and the free zeolitic water molecules according to B–H^δ– ··· ^δ+H–O interactions. Vibrational spectroscopy studies prove the presence of these hydrogen bonds and also show slight distortions of the dodecahydro‐closo‐dodecaborate anions from their ideal icosahedral symmetry (I_h). Thermal decomposition studies for the example of [Cr(H₂O)₆]₂[B₁₂H₁₂]₃ · 15H₂O gave no hints for just a simple multi‐stepwise dehydration process.     

Bounds on the Elastic Moduli of Completely Random Two-Dimensional Polycrystals

Explicit bounds on the elastic moduli of completely random planar polycrystals, the shape and crystalline orientations of the constituent grains of which are uncorrelated, are derived and calculated for a number of crystals of general two-dimensional anisotropy. The bounds on the elastic two-dimensional bulk modulus happen to coincide with the simple third order (in anisotropy contrast) bounds for the subclass of idealistic circular cell polycrystals. The bounds on the shear modulus are close to the much simpler bounds for circular cell polycrystals, which approximate aggregates of equiaxed grains.