A note on finite determinacy for corank 2 map germs from surfaces to 3-space

We study properties of finitely determined corank 2 quasihomogeneous map germs f: (C(2), 0) -> (C(3), 0). Examples and counter examples of such map germs are presented.

A FREE BOUNDARY ISOPERIMETRIC PROBLEM IN HYPERBOLIC 3-SPACE BETWEEN PARALLEL HOROSPHERES

We investigate the isoperimetric problem of finding the regions of prescribed volume with minimal boundary area between two parallel horospheres in hyperbolic 3-space (the part of the boundary contained in the horospheres is not included). We reduce the problem to the study of rotationally invariant regions and obtain the possible isoperimetric solutions by studying the behavior of the profile curves of the rotational surfaces with constant mean curvature in hyperbolic 3-space. We also classify all the connected compact rotational surfaces M of constant mean curvature that are contained in the region between two horospheres, have boundary partial derivative M either empty or lying on the horospheres, and meet the horospheres perpendicularly along their boundary.

3-D kinematical conservation laws (KCL): Evolution of a surface in R-3 - in particular propagation of a nonlinear wavefront

3-D KCL are equations of evolution of a propagating surface (or a wavefront) Omega(t), in 3-space dimensions and were first derived by Giles, Prasad and Ravindran in 1995 assuming the motion of the surface to be isotropic. Here we discuss various properties of these 3-D KCL.These are the most general equations in conservation form, governing the evolution of Omega(t) with singularities which we call kinks and which are curves across which the normal n to Omega(t) and amplitude won Omega(t) are discontinuous. From KCL we derive a system of six differential equations and show that the KCL system is equivalent to the ray equations of 2, The six independent equations and an energy transport equation (for small amplitude waves in a polytropic gas) involving an amplitude w (which is related to the normal velocity m of Omega(t)) form a completely determined system of seven equations. We have determined eigenvalues of the system by a very novel method and find that the system has two distinct nonzero eigenvalues and five zero eigenvalues and the dimension of the eigenspace associated with the multiple eigenvalue 0 is only 4. For an appropriately defined m, the two nonzero eigenvalues are real when m > 1 and pure imaginary when m < 1. Finally we give some examples of evolution of weakly nonlinear wavefronts.

Space, authenticity and utopia in the hip-hop teen dance film

The dance film flourished in the 2000s in the form of the hip-hop teen dance film. Such films as Save the Last Dance (Thomas Carter, 2001), Honey (Billy Woodruff, 2002) and Step Up (Anne Fletcher, 2006) drew on hip-hop’s dominance of the mainstream music industry and combined the teen film’s pre-existing social problem and musical narratives. Yet various tension were created by their interweaving of representations of post-industrial city youth with the utopian sensibilities of the classical Hollywood musical. Their narratives celebrated hip-hop performance, and depicted dance’s ability to bridge cultural boundaries and bring together couples and communities. These films used hip-hop to define space and identity yet often constructed divisions within their soundscapes, limiting hip-hop’s expressive potential. This article explores the cycle’s celebration of, yet struggle with, hip-hop through examining select films’ interactions between soundscape, narrative and form. It will engage with these films’ attempts to marry the representational, narrative and aesthetic meanings of hip-hop culture with the form and ideologies of the musical genre, particularly the tensions and continuities that arise from their engagement with the genre’s utopian qualities identified by Richard Dyer (1985). Yet whilst these films illustrate the tensions and challenges of combining hip-hop culture and the musical genre, they also demonstrate an effective integration of hip-hop soundscape and the dancing body in their depiction of dance, highlighting both form’s aesthetics of layering, rupture and flow (Rose, 1994: 22).

Total absolute horospherical curvature of submanifolds in hyperbolic space

We study the horospherical geometry of submanifolds in hyperbolic space. The main result is a formula for the total absolute horospherical curvature of M, which implies, for the horospherical geometry, the analogues of classical inequalities of the Euclidean Geometry. We prove the horospherical Chern-Lashof inequality for surfaces in 3-space and the horospherical Fenchel and Fary-Milnor`s theorems.

Horo-tight spheres in hyperbolic space

We study horo-tight immersions of manifolds into hyperbolic spaces. The main result gives several characterizations of horo-tightness of spheres, answering a question proposed by Cecil and Ryan. For instance, we prove that a sphere is horo-tight if and only if it is tight in the hyperbolic sense. For codimension bigger than one, it follows that horo-tight spheres in hyperbolic space are metric spheres. We also prove that horo-tight hyperspheres are characterized by the property that both of its total absolute horospherical curvatures attend their minimum value. We also introduce the notion of weak horo-tightness: an immersion is weak horo-tight if only one of its total absolute curvature attends its minimum. We prove a characterization theorem for weak horo-tight hyperspheres.

Double point curves for corank 2 map germs from C-2 to C-3

We characterize finite determinacy of map germs f : (C-2, 0) -> (C-3, 0) in terms of the Milnor number mu(D(f)) of the double point curve D(f) in (C-2, 0) and we provide an explicit description of the double point scheme in terms of elementary symmetric functions. Also we prove that the Whitney equisingularity of 1-parameter families of map germs f(t) : (C-2, 0) -> (C-3, 0) is equivalent to the constancy of both mu(D(f(t))) and mu(f(t)(C-2)boolean AND H) with respect to t, where H subset of C-3 is a generic plane. (C) 2011 Elsevier B.V. All rights reserved.

Geometry of the de-Sitter universe

By making use of the fact that the de-Sitter metric corresponds to a hyperquadric in a five-dimensional flat space, it is shown that the three Robertson-Walker metrics for empty spacetime and positive cosmological constant, corresponding to 3-space of positive, negative and zero curvative, are geometrically equivalent. The 3-spaces correspond to intersections of the hyperquadric by hyperplanes, and the time-like geodesics perpendicular to them correspond to intersections by planes, in all three cases.

成矿流体构造动力学研究—以冀西北后沟金矿和山东七宝山金矿为例

Tectonic dynamics of metallogenetic fluids is a new crossed subjects among fluid geology, mineral deposit geology and structural geology, and is one of the major current projects of geosciences. It is mainly focused on structures and tectonic dynamic induced by fluid motion, variation of physical condition of fluids (such as temperature and pressure), and interaction between chemical component of fluids and wall rocks in the crust. It takes features of deformation and metamorphysim, which formed during interaction between fluids and rocks and have been perserved in rocks, as basic research objects. After studying types, orders, distributions and fabrics of these features, and analyzing and testing physical and chemical information from these features by some techniques, it is intended to reconstruct moving process of fluids, dynamics of interaction between fluids and rocks, and dynamics of mineralizations. Three problems of tectonic dynamics of metallogenetic fluids, which have not been paid much attentions before, have been studied and discussed in this report. Three relative topics are including: 1)Double-fracturing induced by thermal stress and pressure of fluids and mineralization of Gold-copper in Breccia Pipe at the Qibaoshan in Shandong Province; 2)Parting structures induced by K-metasomatism in the Hougou area, northwestern Heibei province; 3)Migration mechanism of dissolved mass in Fe&S-rich fluids in Hougou gold deposit in Heibei province. After a synthetical study of two years, the author has made some new processes and progresses. The main new advances can be summaried as the following: 1)Thermal stress of fluids formed by temperature difference between fluids and country rock, during upword migration process of fluids with high temperature and pressure, can make rock to break, and some new fractures, which surfaces were uasally dry, formed. The breccia pipe at the Qibaoshan area in Shandong province has some distinct texture of fluidogenous tectonics, the breccia pipe is caused by double-fracturing induced by thermal stress and pressure, distribution of gold-corpper ore bodies are controlled powerfully by fluidogenous tectonics in the breccia pipe. 2)The author discovered a new kind of parting structures in K-alterated rocks in the northwestern part of Hebei province. The parting structures have some distinct geometry and fabrics, it is originated from the acting and reacting fores caused by K-metasomatism. Namely, the crystallizations of metasomatic K-feldspars are a volume expansion process, it would compress the relict fluid bodies, and the pressures in the relict fluid bodies gathered and increased, when the increased pressure of the fluid relict bodies is bigger than the strength of K-feldspars, the K-feldspars were broken with the strong compression, and the parting structures formed. 3)Space position replacing is a important transport pattern of dissolved mass in Fe&S-rich fluid. In addition, basing on views of tectonic dynamics of metallogenic fluids, and time-space texture of fluid-tectonic-lithogenetic-mineralization of the known gold-corpper mineral deposit and the subvolcanic complex at Qibaoshan area in Shandong province, this report does a detail prodict of position-shape-size of two concealed ore-bearing breccia pipe.

A Planning System for Robot Construction Tasks

This paper describes BUILD, a computer program which generates plans for building specified structures out of simple objects such as toy blocks. A powerful heuristic control structure enables BUILD to use a number of sophisticated construction techniques in its plans. Among these are the incorporation of pre-existing structure into the final design, pre-assembly of movable sub-structures on the table, and use of the extra blocks as temporary supports and counterweights in the course of construction. BUILD does its planning in a modeled 3-space in which blocks of various shapes and sizes can be represented in any orientation and location. The modeling system can maintain several world models at once, and contains modules for displaying states, testing them for inter-object contact and collision, and for checking the stability of complex structures involving frictional forces. Various alternative approaches are discussed, and suggestions are included for the extension of BUILD-like systems to other domains. Also discussed are the merits of BUILD's implementation language, CONNIVER, for this type of problem solving.

Material Management in Confined Site Construction

The objective of this paper is to identify various managerial issues encountered and resulting strategies adopted, with regards management of materials on confined construction site. This is achieved through classifying the various managerial burdens encountered with the numerous strategies adopted, for the successful management of such confined environments within the realm of materials management.


Through conducting an extensive literature review and detailed interviews, a comprehensive insight into the materials management concerns within a confined construction site environment is envisaged and portrayed. The following are the leading issues highlighted; (1)Lack of adequate storage space, (2)Work place becoming over-crowded, (3)Lack of adequate room for the effective handling of materials and (4)Difficult to transport materials around site. The leading managerial strategies to the management of materials on confined construction sites may be listed in order of importance, as follows; (1)Pre-fabrication and pre-assembly, (2)Providing adequate storage, (3)Space scheduling, (4)Just-In-Time delivery techniques, and (5)Effective design site layout.

Based on the research conducted, it can be concluded, that through effective management of the issues identified along with implementing the various strategies highlighted; successful materials management within a confined construction site environment is attainable.


Innovative Aspect of Paper: An empirical study of three different construction sites in three different countries (Ireland, England and USA) investigating the managerial issues and strategies relating to implementation of materials management in confined construction sites.

Dielectric properties of soft chemical method derived CaCu3Ti4O12 thin films onto Pt/TiO2/Si(100) substrates

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A dictionary of modular threefolds

The thesis deals with the modularity conjecture for three-dimensional Calabi-Yau varieties. This is a generalization of the work of A. Wiles and others on modularity of elliptic curves. Modularity connects the number of points on varieties with coefficients of certain modular forms. In chapter 1 we collect the basics on arithmetic on Calabi-Yau manifolds, including general modularity results and strategies for modularity proofs. In chapters 2, 3, 4 and 5 we investigate examples of modular Calabi-Yau threefolds, including all examples occurring in the literature and many new ones. Double octics, i.e. Double coverings of projective 3-space branched along an octic surface, are studied in detail. In chapter 6 we deal with examples connected with the same modular forms. According to the Tate conjecture there should be correspondences between them. Many correspondences are constructed explicitly. We finish by formulating conjectures on the occurring newforms, especially their levels. In the appendices we compile tables of coefficients of weight 2 and weight 4 newforms and many examples of double octics.

High-Pressure Behavior and Phase Stability of Al5BO9, a Mullite-Type Ceramic Material

Phase stability, elastic behavior, and pressure-induced structural evolution of synthetic boron-mullite Al5BO9 (a = 5.6780(7), b = 15.035(6), and c =7.698(3) Å, space group Cmc21, Z = 4) were investigated up to 25.6(1) GPa by in situ single-crystal synchrotron X-ray diffraction with a diamond anvil cell (DAC) under hydrostatic conditions. No evidence of phase transition was observed up to 21.7(1) GPa. At 25.6(1) GPa, the refined unit-cell parameters deviated significantly from the compressional trend, and the diffraction peaks appeared broader than at lower pressure. At 26.7(1) GPa, the diffraction pattern was not indexable, suggesting amorphization of the material or a phase transition to a high-pressure polymorph. Fitting the P–V data up to 21.7(1) GPa with a second-order Birch–Murnaghan Equation-of-State, we obtained a bulk modulus KT0 = 164(1) GPa. The axial compressibilities, here described as linearized bulk moduli, are as follows: KT0(a) = 244(9), KT0(b) = 120(4), and KT0(c) = 166(11) GPa (KT0(a):KT0(b):KT0(c) = 2.03:1:1.38). The structure refinements allowed a description of the main deformation mechanisms in response to the applied pressure. The stiffer crystallographic direction appears to be controlled by the infinite chains of edge-sharing octahedra running along [100], making the structure less compressible along the a-axis than along the b- and c-axis.

Design of underground installations in rock.

At head of title: Engineering and design.