Normal Lattice Research Articles

Pseudocomplementation in (Normal) Subgroup Lattices

The goal of this article is to study finite groups admitting a pseudocomplemented subgroup lattice (PK-groups) or a pseudocomplemented normal subgroup lattice (PKN-groups). In particular, we obtain a complete classification of finite PK-groups and of finite nilpotent PKN-groups. We also study groups with a Stone normal subgroup lattice, and we classify finite groups for which every subgroup has a Stone normal subgroup lattice. Finally, we obtain a complete classification of finite groups for which every subgroup is monolithic.

Textural, structural, and morphological characterizations and catalytic activity of nanosized CeO 2–MO x (M = Mg 2+, Al 3+, Si 4+) mixed oxides for CO oxidation

The present work focuses on the combination of ceria with another oxide of different ionic valences from period 3 (Mg 2+, Al 3+, and Si 4+) using coprecipitation method, followed by calcination at 450 and 750 °C, respectively. The textural, structural, morphological and redox properties of nanosized ceria–magnesia, ceria–alumina and ceria–silica mixed oxides have been investigated by means of N 2 physisorption, XRD, Raman, HRTEM, DRS, FT-IR, and H 2-TPR technologies. XRD results of these mixed oxides reveal that only nanocrystalline ceria ( ca. 3–6 nm for the 450 °C calcined samples) could be observed. The grain size of ceria increases with the increasing calcination temperature from 450 to 750 °C due to sintering effect. The highest specific surface area is obtained at CeO 2–Al 2O 3 mixed oxides when calcination temperature reaches 750 °C. Raman spectra display the cubic fluorite structure of ceria and the existence of oxygen vacancies, and displacement of oxygen ions from their normal lattice positions in the ceria-based mixed oxides. DRS measurements confirm that the smaller the grain size of the ceria, the higher indirect band gap energy. H 2-TPR results suggest that the reductions of surface and bulk oxygen of ceria were predominant at low and high calcination temperature, respectively. Finally, CO oxidation were performed over these ceria-based mixed oxides, and the combination of CeO 2–Al 2O 3 exhibited highest activity irrespective of calcination temperature, which may due to excellent textural/structural properties, good homogeneity, and redox abilities.

Percutaneous Collagen Induction Therapy as a Novel Therapeutic Option for Striae Distensae

Sir: The occurrence of striae distensae is a well-recognized, common skin condition that rarely causes any significant medical problems but is often a significant source of distress to those affected. Striae are atrophic linear plaques, most often found on the breasts, abdomen, hips, and thighs in the dermal layer. This disruption of collagen-elastic matrix may develop in a variety of circumstances, such as during adolescent growth spurts, and during hormonal changes, such as Cushing syndrome. Striae gravidarum are widely known to occur in pregnancy and, aesthetically, they can be a cause of great concern for many women. Maternal age, body mass index, weight gain, and neonatal birth weight were independently associated with the occurrence of striae gravidarum.1 It appears that the group at highest risk of developing severe striae are teenagers. Treatment is often anecdotical. To date, no therapeutic option offers complete treatment.2 Cocoa butter was recently studied in a randomized controlled trial for prevention of striae gravidarum but failed to be effective.3 Percutaneous collagen induction therapy is capable of dermal rejuvenation by smoothing of the skin by thickening the epidermal layers and expression of genes and proteins relevant for dermal regeneration without the risk of dyspigmentation.4,5 Percutaneous collagen induction works best in combination with a scientific skin care program. In contrast to ablative laser therapy, the epidermis remains intact. Thus, the procedure can be repeated safely if needed, and it is also applicable to regions where laser treatments or deep peelings cannot be performed. Twenty-two female patients with stretch marks underwent single percutaneous collagen induction therapy in an outpatient setting. All patients had conventional tumescence anesthesia. The procedure took a mean time of 30 minutes, without any immediate adverse effects, such as abdominal perforation or infection. Follow-up assessment was performed 6 months after the intervention. Assessment of the result revealed improved skin texture, skin tightening, dermal neovascularization, and no change of pigmentation (Fig. 1). Biopsy specimens obtained 6 months after the intervention revealed an increase of collagen I and elastin (Fig. 2). Collagen III was not affected at all.Fig. 1.: Preoperative (above) and postoperative (6 months after treatment) (below) clinical images.Fig. 2.: Preoperative (above) and postoperative (6 months after treatment) (below) histologic photomicrographs of striae distensae showing a considerable normalization of the collagen/elastin matrix in the reticular dermis and an increase in collagen deposition at 6 months postoperatively. The collagen appears not to have been laid down in parallel bundles but is rather in the normal lattice pattern. Masson's trichrome staining. Scale bar = 50 μm (representative example).Given this preliminary clinical observation of percutaneous collagen induction therapy in striae distensae, we strongly believe that further large-scale and possibly randomized controlled trials are mandatory to elucidate the value of this promising technique. DISCLOSURE Dr. Aust is a medical consultant for Care Concept, distributors for Environ Skin Care Products and Roll-CitR in Germany. Neither of the other authors has any financial information to disclose. Matthias C. Aust, M.D. Karsten Knobloch, M.D., Ph.D. Peter M. Vogt, M.D., Ph.D. Plastic, Hand, and Reconstructive Surgery Hannover Medical School Hannover, Germany

Association schemes in which the thin residue is a finite cyclic group

In this article, we investigate association schemes S (on finite sets) in which each element s satisfies s s ⁎ s = { s } . It is shown that these schemes are schurian if the partially ordered set of the intersections of the closed subsets s ⁎ s of S with s ∈ S is distributive. (A scheme is said to be schurian if it arises (in a well-understood way) from a transitive permutation group.) It is also shown that, if these schemes are schurian, the transitive permutation group from which they arise have subnormal one-point stabilizers. As a consequence of the first result one obtains that schemes are schurian if their thin residue is thin and has a distributive normal closed subset lattice (normal subgroup lattice). This implies, for instance, that schemes are schurian if their thin residue is a cyclic group.

Thermodynamic and transport properties of M3CeBr6 compounds (M = K, Rb, Cs)

Systematic trends in the thermodynamic properties of congruently melting M3CeBr6 compounds (molar enthalpies of the solid–solid phase transitions, molar heat capacity) following those found for another M3LnX6 compounds (Ln = lanthanide; X = halide, M = Li, Na, K, Rb, Cs) were evidenced. These data were complemented by electrical conductivity measurements over the wide temperature range. The results obtained clearly show that the M3CeBr6 compounds can be divided into two groups. The first one with K3CeBr6 compound having a single high temperature modification of cubic, elpasolite-type, crystal structure, and the second one with Rb3CeBr6 and Cs3CeBr6 compounds having both low- (monoclinic, Cs3BiCl6-type) and high-temperature (cubic, elpasolite-type) modifications. Transition from low- to high-temperature modification of these compounds is non-reconstructive phase transition. Within the two groups, the thermodynamic and transport properties of M3CeBr6 compounds are well correlated with their crystal structure. These results suggest different order–disorder mechanisms of the alkali metal cations whereas the CeBr6 octahedra, forming anionic sublattice, retain their normal lattice positions.

Stoichiometry and doping effects on cation ordering in LiNbO3 crystals

The cation disorder in stoichiometric and congruent lithium niobate crystals and also in congruent crystals doped with Y3+ or Gd3+ has been studied by X-ray diffraction and Raman scattering spectroscopy using vacancy models. The results indicate that the structural disordering induced by doping with Y3+, revealed by both X-ray diffraction and Raman spectroscopy, can be understood in terms of the mechanism of yttrium incorporation into the cation sublattice of the crystal. Yttrium substitution for Nb5+ on its normal lattice site causes Nb5+ to occupy vacant octahedra, thereby increasing the cation and vacancy disorder along the polar axis and distorting the octahedra because the ionic radius of Y3+ exceeds that of Nb5+.

Commutativity Criterions Using Normal Subgroup Lattices

We prove that a group G is Abelian whenever (1) it is nilpotent and the lattice of normal subgroups of G is isomorphic to the subgroup lattice of an Abelian group or (2) there exists a non-torsion Abelian group B such that the normal subgroup lattice of B × G is isomorphic to the subgroup lattice of an Abelian group. Using (2), it is proved that an Abelian group A can be determined in the class of all groups by the lattice of all normal subgroups of some groups, e.g. if A is an Abelian group and G is a group such that \mathbb Z × A and \mathbb Z × G have isomorphic normal subgroup lattices then A and G are isomorphic groups.

Surface and structure characteristics of carbon-supported Pd 3Pt 1 bimetallic nanoparticles for methanol-tolerant oxygen reduction reaction

Surface and structure of carbon-supported Pd 3Pt 1 (Pd 3Pt 1/C) bimetallic nanoparticles of small particle size can be tuned during synthesis through the use or nonuse of trisodium citrate (TC) as the complexing agent. The addition of TC during the synthesis results in Pd enrichment on the surface layers of the Pd 3Pt 1/C catalysts and to an abnormal lattice expansion as compared to that of pure Pd/C and Pt/C. However, without the addition of TC, a normal lattice constant and Pt enrichment on the surface layers of the catalysts are obtained. Among the prepared catalysts, the maximum activity for the oxygen reduction reaction (ORR) occurs for Pd 3Pt 1/C catalyst with Pt surface enrichment. Importantly, the Pd 3Pt 1/C catalysts with Pd surface enrichment exhibited substantially higher methanol tolerance during the ORR than both the Pd 3Pt 1/C catalyst with Pt surface enrichment and the Pt/C catalyst. Thus, Pd 3Pt 1/C catalysts may represent a methanol-tolerant ORR cathode catalyst.

Electric center of gravity of overlap charge distribution in impurity-doped ionic crystals

The electric center of gravity (ECG) of the first-neighbor or second-neighbor overlap charge distribution in several alkali-halide crystals doped with monovalent impurity ions is calculated including its dependence on the internuclear distance. The Madelung potentials at this ECG due to the point charges on the normal lattice sites are computed except the contributions from the overlapping ions nearest to the ECG, in order to exclude the two-body potentials. These Madelung potentials are used in the calculation of the three-body potentials in the Ra-Abarenkov-Antonova model.

Electronic and transport properties of CuCl

In this article we present a set of fully self-consistent studies of the energy bands' defect and/or impurity levels in CuCl. These studies are performed as a function of lattice constant and uniaxial compression along the (001) direction. The methods employed are the self-consistent Hartree-Fock plus correlation corrections method. Calculations are performed for the normal lattice constant, 3% volume reduction, and 15% volume reduction, and for a 2% reduction in lattice constant along the (001) direction. The defect and/or impurity systems studied include F centers, H− centers, OH− centers, O2− plus anion vacancy centers, and S2− plus anion vacancy centers. We find the upper valence band is largely Cu 3d in origin and that for normal lattice constant the band gap is direct, at T, and is about 4.0 eV. Under uniaxial stress or hydrostatic pressure, a weak indirect gap may be generated of insufficient width to agree with Abrikosov's hypothesis. We find, however, that defects or impurities produce electrons near the conduction band. We speculate about the role of these electrons as they may pertain to recent CuCl experiments.

Classifying smooth lattice polytopes via toric fibrations

We show that any smooth Q -normal lattice polytope P of dimension n and degree d is a strict Cayley polytope if n ⩾ 2 d + 1 . This gives a sharp answer, for this class of polytopes, to a question raised by V.V. Batyrev and B. Nill.

Ground-state properties of fermions in double-well optical lattices

We investigate the ground-state properties of fermions trapped in a one-dimensional double-well optical lattice by means of the density-matrix renormalization group method. A weak harmonic confinement potential inherent in real experiments, which makes the system inhomogeneous, is also considered. Under certain conditions for interactions, we find that two kinds of insulating regions coexist at half-filling and three-quarters filling due to the double-well structure and the system inhomogeneity. We further study the dynamical properties of the system by employing the adaptive time-dependent density-matrix renormalization group method. When the double-well lattice is suddenly changed into a normal single-well lattice, the two insulating regions gradually disappear under time evolution, which is accompanied by oscillating behavior of the local density characteristic of many-body fermionic systems.

Characterization of Capsicum annuum Recombinant α- and β-Tubulin

There are several conditions which might modulate polymerization to produce polymers having normal lattice structure. In the absence of 1 mM MgCl(2) the assembly was reduced by 36% in Capsicum annuum tubulin (CAnm tubulin). There was no significant difference in the final assembly formation in the presence of 5% to 10% glycerol. However, nucleation rate was slow and apparent study state was achieved lately in the presence of 10% glycerol. Taxol at 100 microM concentration increased 23% tubulin assembly. One millimolar CaCl(2), >or=1% dimethyl sulfoxide (DMSO) and physiologically low temperature reduced CAnm tubulin assembly. A value of 0.089 mg/ml was obtained as critical concentration for polymerization. Benomyl significantly reduced the number of cysteine residues accessible to 5,5'-dithiobis-(2-nitrobenzoic acid); there were 4.77 +/- 0.21 and 3.49 +/- 0.35 residues accessible per tubulin dimer in the presence of 50 and 100 microM benomyl respectively.

Kondo Lattice and Magnetic Properties in Strongly Correlated Electron Systems

We review here the magnetic properties of some strongly correlated electron systems and especially cerium and uranium compounds. The normal Kondo lattice model with a localized S = 1=2 spin can account for the Kondo-magnetism competition observed in cerium or ytterbium systems, while the underscreened Kondo lattice model with a localized S = 1 spin can well account for the ferromagnetism | Kondo coexistence observed in some uranium compounds such as UTe. Then, we discuss the spin glass-Kondo competition and present the resulting phase diagrams showing spin glass, Kondo and magnetically ordered phases observed in disordered heavy fermion cerium alloys such as CeNixCu1ix alloys.

Elastic properties of aspirin in its crystalline and glassy phases studied by micro-Brillouin scattering

The acoustic waves propagating along the direction perpendicular to the (1 0 0) cleavage plane of aspirin crystal were investigated using micro-Brillouin spectroscopy from which C 11 , C 55 and C 66 were obtained. The temperature dependence of the longitudinal acoustic waves could be explained by normal anharmonic lattice models, while the transverse acoustic waves showed an abnormal increase in the hypersonic attenuation at low temperatures indicating their coupling to local remnant dynamics. The sound velocity as well as the attenuation of the longitudinal acoustic waves of glassy aspirin showed a substantial change at ∼235 K confirming a transition from glassy to supercooled liquid state in vitreous aspirin.

Characterization of anisotropic relaxation rate of SGOI (110) substrates

In this report, both normal and lateral lattice parameters of partially-relaxed (110) surface Silicon–Germanium-on-Insulator (SGOI) layers are precisely determined by using asymmetric reflection XRD measurements. Moreover, relaxation rates of these SiGe layers are evaluated by using the values obtained from the XRD measurements. It is found, as a result, that anisotropic lattice relaxation between [− 110] and [001] directions occurs in the (110) SGOI layers and that it is much harder to relax the lattices along [− 110] direction than along [001] direction. This anisotropic lattice relaxation is attributable to the generation of twins on (111) glide planes.

The effect of the surface of SnO2 nanoribbons on their luminescence using x-ray absorption and luminescence spectroscopy

X-ray excited optical luminescence (XEOL) and x-ray absorption near-edge structure in total electron, x-ray fluorescence, and photoluminescence yields at Sn M5,4-, O K-, and Sn K-edges have been used to study the luminescence from SnO2 nanoribbons. The effect of the surface on the luminescence from SnO2 nanoribbons was studied by preferential excitation of the ions in the near-surface region and at the normal lattice positions, respectively. No noticeable change of luminescence from SnO2 nanoribbons was observed if the Sn ions in the near-surface region were excited selectively, while the luminescence intensity changes markedly when Sn or O ions at the normal lattice positions were excited across the corresponding edges. Based on the experimental results, we show that the luminescence from SnO2 nanoribbons is dominated by energy transfer from the excitation of the whole SnO2 lattice to the surface states. Surface site specificity is not observable due to its low concentration and weak absorption coefficient although the surface plays an important role in the emission as a luminescence center. The energy transfer and site specificity of the XEOL or the lack of the site specificity from a single-phase sample is discussed.

Catalytic Efficiency of Ceria–Zirconia and Ceria–Hafnia Nanocomposite Oxides for Soot Oxidation

The catalytic oxidation of soot particulates has been investigated over CeO2, CeO2–ZrO2 and CeO2–HfO2 nanocomposite oxides. These oxides were synthesized by a modified precipitation method employing dilute aqueous ammonia solution. The prepared catalysts were characterized by X-ray diffraction (XRD), transmission electron microscopy (TEM), Raman spectroscopy, UV-Vis diffuse reflectance spectroscopy (UV-Vis DRS) and BET surface area methods. The soot oxidation has been evaluated by a thermogravimetric method under ‘tight contact’ conditions. The XRD results revealed formation of cubic CeO2, Ce0.75Zr0.25O2 and Ce0.8Hf0.2O2 phases in case of CeO2, CeO2–ZrO2 and CeO2–HfO2 samples, respectively. TEM studies confirm the nanosized nature of the catalysts. Raman measurements suggest the presence of oxygen vacancies, lattice defects and oxide ion displacement from normal ceria lattice positions. UV-Vis DRS studies show presence of charge transfer transitions Ce3+←O2− and Ce4+←O2− respectively. The catalytic activity studies suggest that the oxidation of soot could be enhanced by incorporation of Zr4+ and Hf4+ into the CeO2 lattice. The CeO2–HfO2 combination catalyst exhibited better activity than the CeO2–ZrO2. The observed high activity has been related to the nanosized nature of the composite oxides and the oxygen vacancy created in the crystal lattice.

Central peaks, acoustic modes, and the dynamics of polar nanoregions inPb[(Zn1∕3Nb2∕3)xTi1−x]O3single crystals studied by Brillouin spectroscopy

Temperature dependence of acoustic behaviors and quasielastic central peaks (CPs) of $\mathrm{Pb}[{({\mathrm{Zn}}_{1∕3}{\mathrm{Nb}}_{2∕3})}_{x}{\mathrm{Ti}}_{1\ensuremath{-}x}]{\mathrm{O}}_{3}$ $(\mathrm{PZN}\text{\ensuremath{-}}x\mathrm{PT})$ single crystals with $x=4.5%$ and 9% have been investigated in a temperature range of $300\char21{}900\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ by using the Brillouin light scattering. The temperature dependence of the ${C}_{11}$ elastic constant of both crystals showed a deviation from normal lattice anharmonicity at the Burns temperature $({T}_{B})$ of about $730\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ upon cooling, indicating the onset of the electrostrictive coupling between the polar nanoregions (PNRs) and the longitudinal acoustic (LA) waves. Upon further cooling, depolarized CP began to appear at a certain temperature $({T}_{d})$ located in $500\char21{}550\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, which was accompanied by substantial softening of the ${C}_{44}$ elastic constant below this temperature suggesting anisotropic electrostrictive coupling between PNRs and the two acoustic waves. In addition, the onset of significant increase in the acoustic damping of both acoustic waves at ${T}_{d}$ could be seen from the temperature dependence of the linewidth of Brillouin doublets. These results suggested that electrostrictive coupling of the strain to the square of the local polarization of PNRs and the resultant order-parameter fluctuations are enhanced not at ${T}_{B}$ but at a much lower temperature of ${T}_{d}$, which may be ascribed to a local structural transformation occurring in PNRs at ${T}_{d}$. This suggestion is consistent with recent studies on $\mathrm{PZN}\text{\ensuremath{-}}x\mathrm{PT}$ single crystals reporting the appearance of strong acoustic emission signals [M. Roth et al., Phys. Rev. Lett. 98, 265701 (2007)] and substantial changes in the Raman spectrum [O. Svitelskiy, Phys. Rev. B 72, 172106 (2005)] at almost the same temperature. From the comparison of the present results to those of two typical relaxors, $\mathrm{Pb}({\mathrm{Mg}}_{1∕3}{\mathrm{Nb}}_{2∕3}){\mathrm{O}}_{3}$ and $\mathrm{Pb}({\mathrm{Mg}}_{1∕3}{\mathrm{Ta}}_{2∕3}){\mathrm{O}}_{3}$, it was suggested that the existence of an intermediate characteristic temperature ${T}_{d}$ below ${T}_{B}$ may be considered as a more common characteristic in the temperature evolution of PNRs of relaxor ferroelectrics.

Transient Hydrogen Diffusion-Elastoplastic Coupling Analysis near a Blunting Crack Tip

The effect of hydrogen on the metals is known as hydrogen embrittlement, which affects the structural integrity of a hydrogen energy system. Hydrogen atoms near a crack tip play an important role in the hydrogen embrittlement. In the present paper, we developed a computer program for an transient hydrogen diffusion-elastoplastic coupling analysis by combining an in-house finite element program for hydrogen diffusion analysis with a general purpose finite element computer program for stress analysis. In the hydrogen diffusion equation, we consider both the hydrogen concentration at the normal interstitial lattice sites and that at the trap sites, and also take account of hydrogen diffusion flux due to hydrostatic stress. We use a hypothesis that the hydrogen absorbed in the metal affects the yield stress of the metal. Therefore, the hydrogen diffusion problem is coupled with the elastoplastic stress problem. Using the computer program developed in the present study, we performed the transient hydrogen diffusion-elastoplastic coupling analysis of a cracked plate made of a bcc-metal, and obtained the hydrogen concentration, hydrostatic stress and plastic strain near the crack tip. In the present paper, we discuss the effects of the initial hydrogen concentration, the boundary condition of hydrogen on the free surface and the loading frequency. An important finding obtained from the present study is the fact that the hydrogen concentration near the crack tip depends greatly on the loading frequency. The fact indicates that the fatigue lives of the components in a hydrogen system depend not only on the number of loading cycles but also on the loading time.