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Chapter Three of the book "Classifying Spaces of Degenerating Polarized Hodge Structures," by Kazuya Kato and Sampei Usui is presented. It introduces several categories of various kinds of logarithmic generalized analytic spaces and consider relations between them. It considers logarithmic modifications of objects of a generalization of the modification in the toric geometry arising from subdivision of a fan which we will need to extend period maps to the boundary.

The weld bead geometry has been found to be a function of the parameter settings, such as welding speed and welding power, during fusion welding. Vibrations (both sonic and ultrasonic) applied to conventional casting and welding processes have changed the mechanical properties of many metals and alloys usually with a decrease in power requirements, processing temperature and time. Vibrations also affect the pool dynamics bringing along a change in the surface topology of the resultant solidified weld bead. Researchers have related the growth rate, cooling rate, thermal gradient and solidification rate to the weld bead geometry which is being disturbed by vibrations during ultrasound assisted welding. Mild steel plates were subjected to ultrasound of low acoustical power during "bead on plate" laser welding at different speeds. The mild steel plate was held at one end by the ultrasonic horn through which ultrasound was injected. A bead on plate weld of length 80 mm was then performed along the center of the plate using a CO2 laser (1 kW). After several trial tests, the following two welding speeds; 400 and 2000 mm per minute were used. The ultrasonic powers selected were 3W and 6W respectively for each welding speed as higher acoustical power was causing ejection of molten metal from the pool during welding. The surface topography of the weld beads have been affected by ultrasound and the effect is clearly dependent on both the welding speed and acoustical power. The welding speed affects the size of the molten pool while the acoustical power influences the magnitude of the forced vibration on the pool. The different layers in the molten pool are being pressed against each other and forced to move backwards on eth solidified weld bead in some cases. [ABSTRACT FROM AUTHOR]

As different tool materials are hard to machine by routine micromachining techniques, Focused Ion Beam (FIB) technique is used for fabrication of microtools. This paper aims to comprise a detailed review on microtools fabrication by FIB and a step by step procedure of fabricating microtools is explained. Operating parameters are briefly described to show their significance for microtools fabrication. The operating parameters of FIB machining presented here do not only give information about material removal rate but also helpful for achieving desired surface finish of microtools. In addition, new geometry of micro end mill cutter is also proposed. [ABSTRACT FROM AUTHOR]

Shape optimization is numerically a very demanding process, where several traditionally separate numerical processes meet together in a heterogeneous multidisciplinary environment. Typical elements involved are (1) the optimizer itself that implements the selected search strategy, (2) the parameterization procedure that provides the bidirectional mapping interface between the 3D geometric shape of the object and a limited number of parameters that control the parametric model of the geometry, (3) the simulation program that provides the results of the simulated interaction between the object and its environment (such as finite element analysis, FEA), and (4) control procedures that monitor the overall workflow and invoke mutual application calls (process flows and data flows) and handle data mining as well as acceptance or rejection of individual instances of candidate designs which are numerically generated and analyzed. In this paper, the set-up of this complex process, combined with evolutionary optimization, is developed with the objectives of numerical flexibility, computational efficiency in terms of combining sequential and parallel execution of individual applications, and low-cost implementation within an unmanaged computer cluster based on the Windows Communication Foundation, WCF. [ABSTRACT FROM AUTHOR]

Graded components are a resource-conserving alternative to today's composite materials. Functional gradation means a steady progress of the property values through the three spatial dimensions of the component. At the present time there is no methodology to specify the graded properties in the component description. Its starting point takes place in the conventional CAD-Models, based on Voxel models. The component geometry is reproduced with the aid of voxels. Each single Voxel is linked with the component properties. The effort of the description is reduced by the use of interpolation techniques. As a result, we have an enhanced component model which contains all the necessary information for the description of a functional graded component. This model constitutes the starting point of the process chain planning for the component production. [ABSTRACT FROM AUTHOR]

The article discusses several topics published in the book "The Princeton Companion to Mathematics" including what is mathematics, algebra versus geometry and number theory.

A new method is presented to deal with shape optimization problems. In this method, the geometry is parameterized by B-spline shape functions with the control points of the B-spline curves becoming the design variables in the optimization scheme. The core idea of the method presented is to introduce the knot insertion algorithm which can keep the geometry unchanged whilst increasing the number of control points. Besides this core idea, the superreduced method and mesh re nement are also employed. The super-reduced method is used to get rid of the equality constraints. Hence a constrained optimization problem is converted into an unconstrained optimization problem with the constraints kept unchanged. We apply the method to two applications; rst a problem involving Poisson's equation, and second, an application of the method to an airfoil design problem based on the airfoil NACA 0012. In both of these applications, the new method is shown to be efficient compared with 'standard' methods. In particular, in the airfoil problem we obtain a CPU saving time of about 42% compared with the EXTREM method. [ABSTRACT FROM AUTHOR]

The paper presents a simplified mathematical model for a scroll-type air motor. Through air power/energy analysis, it has shown that a scroll-type air motor with a properly specified structure and suitable pressure of compressed air supply is able to achieve high energy efficiency and satisfies air power requirement. The features of a scroll-type air motor in geometry, mechanical structure, and pneumatic power transmission are studied in the paper. Differential geometry is used as the mathematical tool to parameterise the scroll. In this study, Matlab Symbolic Math Toolbox is found very efficient in finding analytic expressions of scroll chamber volumes and generalised torques. State shifting is employed to solve the dynamic system equations numerically. Energy efficiency of a scroll-type air motor is analysed based on the mathematical model. [ABSTRACT FROM AUTHOR]

The design and analysis of fully integrated Voltage Controlled Oscillators (VCO) for 20 6Hz low cost and low power communication system is presented in this paper. Our work is based mainly on the optimization of phase noise and buffer stage specitications. SiGeC hetero-junction bipolar transistors of ft=200 GHz have been used and produced with a monolithic BiCMOS technology. [ABSTRACT FROM AUTHOR]

Chapter 22 of the book "Spherical CR Geometry and Dehn Surgery," by Richard Evan Schwartz is presented. It examines more spherical CR geometry construction that is based on the parabolic element. It includes Loxodromic R-Cones, Loxodromic R-Spheres, and Loxodromic Elevation. Further it examines horotube group structure, and the Loxodromic normality condition.

Chapter 23 of the book "Spherical CR Geometry and Dehn Surgery," by Richard Evan Schwartz is presented. It examines the parameters of the complex hyperbolic ideal triangle group to prove various mathematical theory. It also focuses on the construction of Horotube Group Structure, and the Clifford Torus picture.

Chapter 21 of the book "Spherical CR Geometry and Dehn Surgery," by Richard Evan Schwartz is presented. It analyzes the topology of the domain and its side pairings. It uses combinatorial approach as it gives a global understanding of manifold. Further it describes a model for the fundamental domain.

Chapter 19 of the book "Spherical CR Geometry and Dehn Surgery," by Richard Evan Schwartz is presented. It examines the structure of ideal triangle groups. It introduced the hybrid cone construction to define hybrid spheres. Further it focuses on parabolic cospinal family that is a collection of spinal spheres.

Chapter 20 of the book "Spherical CR Geometry and Dehn Surgery," by Richard Evan Schwartz is presented. It examines the structure of golden triangle groups. It also builds topological models to prove the Horocusp Lemma. Further it uses various models to prove the Intersection Lemma, and the Monotone Lemma.

Chapter 9 of the book "Spherical CR Geometry and Dehn Surgery," by Richard Evan Schwartz is presented. It defines the horotube complex and control its geometry and topology . It deals with collections of horotubes and their functions. It also mentions that smaller horotubes that are used only for technical purposes.

Chapter 3 of the book "Dynamics in One Complex Variable," third edition, by John Milnor is presented. It explores the geometrically attracting points, their topological characterization and Koenings Linearization theorem. It discusses the superattracting fixed points, Böttcher's theorem and the polynomial dynamics with its proof of existence and uniqueness. A brief discussion on parabolic fix points, cremer points and siegel disks is also presented.

The article presents a paper which constructed a triangulated category DMeff- called the triangulated category of (effective) motivic complexes over k. According to the author, the minus sign suggests that they consider only complexes bounded from the above. As an introduction, it provided a basic construction of a triangulated category of DMeffgm(k) of effective geometrical motives over k.

This article presents an encyclopedia entry for force fields or molecular mechanics. They are empirical approaches to calculate molecular geometries and energies. The general aim of a force field calculation is to determine the conformation of three-dimensional structure of a molecule or complex with the minimal energy.