Geometry and computing

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  • Parametrized surfaces of low degrees are very useful in applications, especially in Computer Aided Geometric Design and Geometric Modeling. The precise description of their geometry is not easy in general. Here we study some of the corresponding projective complex surfaces of low implicit degree (i.e. smaller than 12). We show that, generically up to linear changes of coordinates, they are classified by a few number of continuous parameters (called moduli).

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  • Nanoclusters have been emerging as potential building blocks for advanced nanostructured materials with desired catalytic, magnetic, and electronic properties. However, determining the structure of doped atomic clusters encounters many difficulties. A powerful approach to assign the ground state geometries of atomic clusters has been the comparison the recorded vibrational infrared spectra with the corresponding computed ones.

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  • UV-Vis absorption data of p-nitrophenyl azo resorcinol (Magneson I) and its 2 Fe(III) and Cr(III) complexes were investigated both experimentally and theoretically. The geometries were optimized at BP86/TZVP level. The most stable spin states were computed as doublet and quartet for Fe(magneson) 3 and Cr(magneson) 3 complexes, respectively. Time-dependent density functional theory (TDDFT) was employed to explore the absorption spectra properties, whereas the solvent effects were taken into account using the polarizable continuum model (PCM).

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  • The compounds were characterized by analytical and spectral methods. In addition, X-ray diffraction was performed to characterize and obtain detailed information about the structure of 3. The fully optimized geometries of compounds 3 and 4 were calculated at different basis sets by using the Gaussian09 (G09) software to investigate their 3D geometries and electronic structures. Comparisons between the calculated and experimental data including molecular structures, fundamental vibrational modes, and electronic properties were made.

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  • Then we successfully prepared the poly(methyl methacrylate) (PMMA)/ZnPc/Al nanocomposite films by incorporating Al nanoparticles into a transparent PMMA/ZnPc matrix. The structure and morphology of nanocomposite films were studied using X-ray diffraction and scanning electron microscopy. The optical absorption spectra of PMMA/ZnPc/Al nanocomposite films showed red shifting in the Q-band in the polymeric matrix. The geometrical structure of two phthalocyanines was investigated at the RHF/3-21G* computational level.

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  • In this paper we present theory and algorithms enabling classes of Artificial Intelligence (AI) systems to continuously and incrementally improve with a priori quantifiable guarantees – or more specifically remove classification errors – over time.

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  • Glucose oxidase was covalently immobilized to a porous electrode, which was developed by using ferrocene functionalized polyethyleneimine, multiwall carbon nanotubes, and carbon cloth for biofuel cell applications in our recent studies. The kinetics parameters (i.e. kM, Vmax) and other parameters required for the modeling study were determined experimentally. Fuel cell flow channel geometry was analyzed by a computational fluid dynamics modeling approach. Substrate flow rate and mass transfer for each proposed channel type were considered in the simulations.

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  • Lecture Calculus - Chapter 2: Velocity and tangents. After studying this section will help you understand: the answer to both questions involves the same mathematical concept and computation,...

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  • The distal radius is the most common osteoporotic fracture site occurring in postmenopausal women. Finite element (FE) modeling is a non-invasive mathematical technique that can estimate bone strength using inputted geometry/micro-architecture and tissue material properties from computed tomographic images.

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  • Conventional topology optimization approaches are implemented in an implicit manner with a very large number of design variables, requiring large storage and computation costs. In this study, an explicit topology optimization approach is proposed by moving polygonal morphable voids whose geometry parameters are considered as design variables.

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  • Tumorigenesis is an evolutionary process by which tumor cells acquire mutations through successive diversification and differentiation. There is much interest in reconstructing this process of evolution due to its relevance to identifying drivers of mutation and predicting future prognosis and drug response.

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  • This paper deals with a geometrically nonlinear finite element formulation for the analysis of torsional behaviour of RC members. Using the corotational framework, the formulation is developed for the inclusion of nonlinear geometry effects in a multi-fiber finite element beam model. The assumption of small strains but large displacements and rotations is adopted. The principle is an element-independent algorithm, where the element formulation is computed in a local reference frame which is uncoupled from the rigid body motions (translations and rotations) of the reference frame.

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  • (BQ) Every once in a while, a book is published that significantly advances scholarship. Thus, I am not going to be apologetic for beginning this review by stating boldly that Ron Eglash’s African Fractals is bound to be regarded as one of the greatest books on African studies produced in this century.

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  • (BQ) The book is divided into three parts with 14 chapters. The first part introduces fractal geometry for people without any mathematics background, fractals in African settlement architecture, fractals in cross-cultural comparison, and intention and invention in design. The second part discusses geometric algorithms, scaling, numeric systems, recursion, infinity, and complexity. The third part focuses on theoretical frameworks in cultural studies of knowledge, the politics of African fractals, fractals in European history of mathematics, and futures for African fractals.

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  • (BQ) In this context, there are many designers claiming to use the computer to design. But are they really creating a new design? Or are they just rearranging existing information within a domain set by the programmers? If it is the programmer who is considering all possible solutions to a design environment beforehand, who is really setting the parameters and the outcome of a design solution? We saw already the I-Generation (Internet-Generation) risen out of the information age.

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  • After studying this chapter you will be able to understand: Inverse perspective transformation, imaging geometry where the world coordinate system and the camera coordinate system, what are the transformations steps involved in a generalized imaging setup, illustrate the concept with the help of an example.

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  • The following will be discussed in this chapter: Principles of cellular networks, cellular geometries, frequency reuse, increasing capacity, macrocell and microcell, operation of cellular system, call stages, design factors, impairments, ist generation cellular networks, 2nd generation cellular networks.

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  • The current study measures the mechanical behavior of both natural and the monobloc elastomeric disc prosthesis (CadiscTM-L) by employing a finite element method (FEM) to study the fiber-reinforced constitutive formulation provided in the literature. The three-dimensional geometry was created by computed tomography (CT) scan imaging technique.

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  • In this paper a molecular dynamics simulation of nano-metric cutting of copper with a diamond tool is presented. MD simulations require the determination of the interaction of the involved atoms through a function of potential for the materials involved in the analysis and the accurate topography of the studied area, leading to high demand of computational time.

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  • Interests in Cu-Cr sub-nanometer systems have been increasing due to the recentlyfound icosahedral Cu12Cr cluster as a superatomic molecule, where the 3d-Cr and 4s-Cu electrons can phenomenologically form the 18-e molecular shell (1S2 1P6 1D10) of Cu12Cr. In this report, we set out to investigate the energetically-preferred geometries and stabilities of CunCr (n = 9÷11) clusters using the density-functional-theory calculations.

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