Identifying the distinct features of geometric structures for hole trapping to generate radicals on rutile TiO2(110) in photooxidation using density functional theory calculations with hybrid functional

Using density functional theory calculations with HSE 06 functional, we obtained the structures of spin-polarized radicals on rutile TiO2(110), which is crucial to understand the photooxidation at the atomic level, and further calculate the thermodynamic stabilities of these radicals. By analyzing the results, we identify the structural features for hole trapping in the system, and reveal the mutual effects among the geometric structures, the energy levels of trapped hole states and their hole trapping capacities. Furthermore, the results from HSE 06 functional are compared to those from DFT + U and the stability trend of radicals against the number of slabs is tested. The effect of trapped holes on two important steps of the oxygen evolution reaction, i.e. water dissociation and the oxygen removal, is investigated and discussed.

Einstein-like geometric structures on surfaces

An AH (affine hypersurface) structure is a pair comprising a projective equivalence class of torsion-free connections and a conformal structure satisfying a compatibility condition which is automatic in two dimensions. They generalize Weyl structures, and a pair of AH structures is induced on a co-oriented non-degenerate immersed hypersurface in flat affine space. The author has defined for AH structures Einstein equations, which specialize on the one hand to the usual Einstein Weyl equations and, on the other hand, to the equations for affine hyperspheres. Here these equations are solved for Riemannian signature AH structures on compact orientable surfaces, the deformation spaces of solutions are described, and some aspects of the geometry of these structures are related. Every such structure is either Einstein Weyl (in the sense defined for surfaces by Calderbank) or is determined by a pair comprising a conformal structure and a cubic holomorphic differential, and so by a convex flat real projective structure. In the latter case it can be identified with a solution of the Abelian vortex equations on an appropriate power of the canonical bundle. On the cone over a surface of genus at least two carrying an Einstein AH structure there are Monge-Amp`ere metrics of Lorentzian and Riemannian signature and a Riemannian Einstein K"ahler affine metric. A mean curvature zero spacelike immersed Lagrangian submanifold of a para-K"ahler four-manifold with constant para-holomorphic sectional curvature inherits an Einstein AH structure, and this is used to deduce some restrictions on such immersions.

A Geometric Algorithm for Learning Oblique Decision Trees

In this paper we present a novel algorithm for learning oblique decision trees. Most of the current decision tree algorithms rely on impurity measures to assess goodness of hyperplanes at each node. These impurity measures do not properly capture the geometric structures in the data. Motivated by this, our algorithm uses a strategy, based on some recent variants of SVM, to assess the hyperplanes in such a way that the geometric structure in the data is taken into account. We show through empirical studies that our method is effective.

Geometric Decision Tree

In this paper, we present a new algorithm for learning oblique decision trees. Most of the current decision tree algorithms rely on impurity measures to assess the goodness of hyperplanes at each node while learning a decision tree in top-down fashion. These impurity measures do not properly capture the geometric structures in the data. Motivated by this, our algorithm uses a strategy for assessing the hyperplanes in such a way that the geometric structure in the data is taken into account. At each node of the decision tree, we find the clustering hyperplanes for both the classes and use their angle bisectors as the split rule at that node. We show through empirical studies that this idea leads to small decision trees and better performance. We also present some analysis to show that the angle bisectors of clustering hyperplanes that we use as the split rules at each node are solutions of an interesting optimization problem and hence argue that this is a principled method of learning a decision tree.

Geometric quantization and foliation reduction

A standard question in the study of geometric quantization is whether symplectic reduction interacts nicely with the quantized theory, and in particular whether “quantization commutes with reduction.” Guillemin and Sternberg first proposed this question, and answered it in the affirmative for the case of a free action of a compact Lie group on a compact Kähler manifold. Subsequent work has focused mainly on extending their proof to non-free actions and non-Kähler manifolds. For realistic physical examples, however, it is desirable to have a proof which also applies to non-compact symplectic manifolds.

In this thesis we give a proof of the quantization-reduction problem for general symplectic manifolds. This is accomplished by working in a particular wavefunction representation, associated with a polarization that is in some sense compatible with reduction. While the polarized sections described by Guillemin and Sternberg are nonzero on a dense subset of the Kähler manifold, the ones considered here are distributional, having support only on regions of the phase space associated with certain quantized, or “admissible”, values of momentum.

We first propose a reduction procedure for the prequantum geometric structures that “covers” symplectic reduction, and demonstrate how both symplectic and prequantum reduction can be viewed as examples of foliation reduction. Consistency of prequantum reduction imposes the above-mentioned admissibility conditions on the quantized momenta, which can be seen as analogues of the Bohr-Wilson-Sommerfeld conditions for completely integrable systems.

We then describe our reduction-compatible polarization, and demonstrate a one-to-one correspondence between polarized sections on the unreduced and reduced spaces.

Finally, we describe a factorization of the reduced prequantum bundle, suggested by the structure of the underlying reduced symplectic manifold. This in turn induces a factorization of the space of polarized sections that agrees with its usual decomposition by irreducible representations, and so proves that quantization and reduction do indeed commute in this context.

A significant omission from the proof is the construction of an inner product on the space of polarized sections, and a discussion of its behavior under reduction. In the concluding chapter of the thesis, we suggest some ideas for future work in this direction.

Electronic structures of 3d-metal mononitrides

Bond distances, vibrational frequencies, electron affinities, ionization potentials, and dissociation energies of the title molecules in neutral, positively, and negatively charged ions were studied by use of density functional methods B3LYP, BLYP, BHLYP, BPW91, and B3PW91. The calculated results are compared with experiments and previous theoretical studies. It was found that the calculated properties are highly dependent on the functionals employed, in particular for the dissociation energy and vibrational frequency. For neutral species, pure density functional methods BLYP and BPW91 have relatively good performance in reproducing the experimental bond distance and vibrational frequency. For cations, hybrid exchange functional methods B3LYP and B3PW91 are good in predicting the dissociation energy. For both neutral and charged species, BHLYP tends to give smaller dissociation energy.

Applications of Fractal Based Structures in Radar Cross Section Reduction

This thesis presents the Radar Cross Section measurements of different geometric structures such as flat plate,cylinder, corner reflector and circular cone loaded with fractal based metallo dielectric structures.Use of different fractal geometris,metallizations of different shapes as well as the frequency tanability is investigated for TE and TM polarization of the incident electromagnetic field.Application of fractal based metallo-dielectric structures results in RCS reduction over a wide range of frequency bands.RCS enhancement of dihedral corner is observed at certain acute and obtuse corner angles.The experimental results are validated using electromagnetic simulation softwares.

Thinking in three dimensions: Exploring students' geometric thinking and spatial ability with the Geometer's Sketchpad

Current reform initiatives recommend that geometry instruction include the study of three-dimensional geometric objects and provide students with opportunities to use spatial skills in problem-solving tasks. Geometer's Sketchpad (GSP) is a dynamic and interactive computer program that enables the user to investigate and explore geometric concepts and manipulate geometric structures. Research using GSP as an instructional tool has focused primarily on teaching and learning two-dimensional geometry. This study explored the effect of a GSP based instructional environment on students' geometric thinking and three-dimensional spatial ability as they used GSP to learn three-dimensional geometry. For 10 weeks, 18 tenth-grade students from an urban school district used GSP to construct and analyze dynamic, two-dimensional representations of three-dimensional objects in a classroom environment that encouraged exploration, discussion, conjecture, and verification. The data were collected primarily from participant observations and clinical interviews and analyzed using qualitative methods of analysis. In addition, pretest and posttest measures of three-dimensional spatial ability and van Hiele level of geometric thinking were obtained. Spatial ability measures were analyzed using standard t-test analysis. ^ The data from this study indicate that GSP is a viable tool to teach students about three-dimensional geometric objects. A comparison of students' pretest and posttest van Hiele levels showed an improvement in geometric thinking, especially for students on lower levels of the van Hiele theory. Evidence at the p < .05 level indicated that students' spatial ability improved significantly. Specifically, the GSP dynamic, visual environment supported students' visualization and reasoning processes as students attempted to solve challenging tasks about three-dimensional geometric objects. The GSP instructional activities also provided students with an experiential base and an intuitive understanding about three-dimensional objects from which more formal work in geometry could be pursued. This study demonstrates that by designing appropriate GSP based instructional environments, it is possible to help students improve their spatial skills, develop more coherent and accurate intuitions about three-dimensional geometric objects, and progress through the levels of geometric thinking proposed by van Hiele. ^

Synthesis, Characterization, and Electronic Structure of New Type of Heterometallic Boride Clusters

The reaction of [Cp*TaCl(4)], 1 (Cp* = eta(5)-C(5)Me(5)), with [LiBH(4)center dot THF] at -78 degrees C, followed by thermolysis in the presence of excess [BH(3)center dot THF], results in the formation of the oxatantalaborane cluster [(Cp*Ta)(2)B(4)H(10)O], 2 in moderate yield. Compound 2 is a notable example of an oxatantalaborane cluster where oxygen is contiguously bound to both the metal and boron. Upon availability of 2, a room temperature reaction was performed with [Fe(2)(CO)(9)], which led to the isolation of [(Cp*Ta)(2)B(2)H(4)O{H(2)Fe(2)(CO)(6)BH} ] 3. Compound 3 is an unusual heterometallic boride cluster in which the [Ta(2)Fe(2)] atoms define a butterfly framework with one boron atom lying in a semi-interstitial position. Likewise, the diselenamolybdaborane, [(Cp*Mo)(2)B(4)H(4)Se(2)], 4 was treated with an excess of [Fe(2)(CO)(9)] to afford the heterometallic boride cluster [(Cp*MoSe)(2)Fe(6)(CO)(13)B(2)(BH)(2)], 5. The cluster core of 5 consists of a cubane [Mo(2)Se(2)Fe(2)B(2)] and a tricapped trigonal prism [Fe(6)B(3)] fused together with four atoms held in common between the two subclusters. In the tricapped trigonal prism subunit, one of the boron atoms is completely encapsulated and bonded to six iron and two boron atoms. Compounds 2, 3, and 5 have been characterized by mass spectrometry, IR, (1)H, (11)B, (13)C NMR spectroscopy, and the geometric structures were unequivocally established by crystallographic analysis. The density functional theory calculations yielded geometries that are in close agreement with the observed structures. Furthermore, the calculated (11)B NMR chemical shifts also support the structural characterization of the compounds. Natural bond order analysis and Wiberg bond indices are used to gain insight into the bonding patterns of the observed geometries of 2, 3, and 5.

Weak Zone Related Seismic Cycles in Progressive Failure Leading to Collapse in Brittle Crust

Until quite recently our understanding of the basic mechanical process responsible for earthquakes and faulting was not well known. It can be argued that this was partly a consequence of the complex nature of fracture in crust and in part because evidence of brittle phenomena in the natural laboratory of the earth is often obliterated or obscured by other geological processes. While it is well understood that the spatial and temporal complexity of earthquakes and the fault structures emerge from geometrical and material built-in heterogeneities, one important open question is how the shearing becomes localized into a band of intense fractures. Here the authors address these questions through a numerical approach of a tectonic plate by considering rockmass heterogeneity both in microscopic scale and in mesoscopic scale. Numerical simulations of the progressive failure leading to collapse under long-range slow driving forces in the far-field show earthquake-like rupture behavior. $En Echelon$ crack-arrays are reproduced in the numerical simulation. It is demonstrated that the underlying fracturing induced acoustic emissions (or seismic events) display self-organized criticality------from disorder to order. The seismic cycles and the geometric structures of the fracture faces, which are found greatly depending on the material heterogeneity (especially on the macroscopic scale), agree with that observed experimentally in real brittle materials. It is concluded that in order to predict a main shock, one must have extremely detailed knowledge on very minor features of the earth's crust far from the place where the earthquake originated. If correct, the model proposed here seemingly provides an explanation as to why earthquakes to date are not predicted so successfully. The reason is not that the authors do not understand earthquake mechanisms very well but that they still know little about our earth's crust.

Coupling between elytra of some beetles: Mechanism, forces and effect of surface texture

Lightweight materials, structures and coupling mechanisms are very important for realizing advanced flight vehicles. Here, we obtained the geometric structures and morphologies of the elytra of beetles and ascertained its coupling zone by using the histological section technique and SEM. We set up a three-dimensional motion observing system to monitor the opening and closing behaviour of elytra in beetles and to determine the motion mechanism. We constructed a force measuring system to measure the coupling forces between elytra. The results show that elytra open and close by rotating about a single axle, where the coupling forces may be as high as 160 times its own bodyweight, the elytra coupling with the tenon and mortise mechanism, surface texture and opening angle between elytra heavily influence the coupling forces. These results may provide insights into the design mechanism and structure for future vehicles of flight.

Quantum dot superlattices and their conductance

The one-dimensional energy bands and corresponding conductivities of a T-shaped quantum-dot superlattice are studied in various cases: different periods, with potential barriers between dots, and in transverse electric fields. It is found that the conductivity of the superlattices has a similar energy relation to the conductance of a single quantum dot, but vanishes in the energy gap region. The energy band of a superlattice with periodically modulated conducting width in the perpendicular magnetic field is calculated for comparison with magneto-transport experiments. It is found that due to the edge state effect the electron has strong quantum transport features. The energy gaps change with the width of the channel, corresponding to the deep peaks in the conductance curve. This method of calculating the energy bands of quantum-dot superlattices is applicable to complex geometric structures without substantial difficulty. (C) 1997 American Institute of Physics.

Origin of extraordinarily high catalytic activity of Co3O4 and its morphological chemistry for CO oxidation at low temperature

Understanding and then designing efficient catalysts for CO oxidation at low temperature is one of the hottest topics in heterogeneous catalysis. Among the existing catalysts. Co3O4 is one of the most interesting systems: Morphology-controlled Co3O4 exhibits exceedingly high activity. In this study, by virtue of extensive density functional theory (OFT) calculations, the favored reaction mechanism in the system is identified. Through careful analyses on the energetics of elementary reactions on Co3O4(1 1 0)-A, Co3O4(1 1 0)-B, Co3O4(1 1 1) and Co3O4(1 0 0), which are the commonly exposed surfaces of Co3O4, we find the following regarding the relation between the activity and structure: (i) Co3+ is the active site rather than Co2+: and (ii) the three-coordinated surface oxygen bonded with three Co3+ may be slightly more reactive than the other two kinds of lattice oxygen, that is, the two-coordinated 0 bonded with one Co2+ and one Co3+ and the three-coordinated 0 bonded with one Co2+ and two Co3+. Following the results from Co3O4, we also extend the investigation to MnO2(1 1 0), Fe3O4(1 1 0), CuO(1 1 0) and CuO(1 1 1), which are the common metal oxide surfaces, aiming to understand the oxides in general. Three properties, such as the CO adsorption strength, the barrier of CO reacting with lattice 0 and the redox capacity, are identified to be the determining factors that can significantly affect the activity of oxides. Among these oxides, Co3O4 is found to be the most active one, stratifying all the three requirements. A new scheme to decompose barriers is introduced to understand the activity difference between lattice O-3c and O-2c on (1 1 0)-B surface. By utilizing the scheme, we demonstrate that the origin of activity variance lies in the geometric structures. (C) 2012 Elsevier Inc. All rights reserved.

Image Denoising Using Sure-Based Adaptive Thresholding In Directionlet Domain

The standard separable two dimensional wavelet transform has achieved a great success in image denoising applications due to its sparse representation of images. However it fails to capture efficiently the anisotropic geometric structures like edges and contours in images as they intersect too many wavelet basis functions and lead to a non-sparse representation. In this paper a novel de-noising scheme based on multi directional and anisotropic wavelet transform called directionlet is presented. The image denoising in wavelet domain has been extended to the directionlet domain to make the image features to concentrate on fewer coefficients so that more effective thresholding is possible. The image is first segmented and the dominant direction of each segment is identified to make a directional map. Then according to the directional map, the directionlet transform is taken along the dominant direction of the selected segment. The decomposed images with directional energy are used for scale dependent subband adaptive optimal threshold computation based on SURE risk. This threshold is then applied to the sub-bands except the LLL subband. The threshold corrected sub-bands with the unprocessed first sub-band (LLL) are given as input to the inverse directionlet algorithm for getting the de-noised image. Experimental results show that the proposed method outperforms the standard wavelet-based denoising methods in terms of numeric and visual quality