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"differential analysis"
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Gromov’s Theory of Multicomplexes with Applications to Bounded Cohomology and Simplicial Volume
The simplicial volume is a homotopy invariant of manifolds introduced by Gromov in his pioneering paper
The first aim of this paper is to lay the foundation of the theory of
multicomplexes. After setting the main definitions, we construct the singular multicomplex
In the second part of this work we apply the theory of multicomplexes to the study of the bounded
cohomology of topological spaces. Our constructions and arguments culminate in the complete proofs of Gromov’s Mapping Theorem (which
implies in particular that the bounded cohomology of a space only depends on its fundamental group) and of Gromov’s Vanishing Theorem,
which ensures the vanishing of the simplicial volume of closed manifolds admitting an amenable cover of small multiplicity.
The
third and last part of the paper is devoted to the study of locally finite chains on non-compact spaces, hence to the simplicial volume
of open manifolds. We expand some ideas of Gromov to provide detailed proofs of a criterion for the vanishing and a criterion for the
finiteness of the simplicial volume of open manifolds. As a by-product of these results, we prove a criterion for the
eBook
Advanced numerical methods with Matlab 2 : resolution of nonlinear, differential and partial differential equations
The purpose of this book is to introduce and study numerical methods basic and advanced ones for scientific computing. This last refers to the implementation of appropriate approaches to the treatment of a scientific problem arising from physics (meteorology, pollution, etc.) or of engineering (mechanics of structures, mechanics of fluids, treatment signal, etc.). Each chapter of this book recalls the essence of the different methods resolution and presents several applications in the field of engineering as well as programs developed under Matlab software.
Book
The Regularity of the Linear Drift in Negatively Curved Spaces
We show that the linear drift of the Brownian motion on the universal cover of a closed connected smooth Riemannian manifold is
eBook
The shape of a life : one mathematician's search for the universe's hidden geometry
\"Harvard geometer and Fields medalist Shing-Tung Yau has provided a mathematical foundation for string theory, offered new insights into black holes, and mathematically demonstrated the stability of our universe. In this autobiography, Yau reflects on his improbable journey to becoming one of the world's most distinguished mathematicians. Beginning with an impoverished childhood in China and Hong Kong, Yau takes readers through his doctoral studies at Berkeley during the height of the Vietnam War protests, his Fields Medal-winning proof of the Calabi conjecture, his return to China, and his pioneering work in geometric analysis. This new branch of geometry, which Yau built up with his friends and colleagues, has paved the way for solutions to several important and previously intransigent problems. With complicated ideas explained for a broad audience, this book offers readers not only insights into the life of an eminent mathematician, but also an accessible way to understand advanced and highly abstract concepts in mathematics and theoretical physics\"--Publisher's website.
Book
The Yang-Mills heat equation with finite action in three dimensions
The existence and uniqueness of solutions to the Yang-Mills heat equation is proven over
eBook
XRD and TG-DTA Study of New Alkali Activated Materials Based on Fly Ash with Sand and Glass Powder
In this paper, the effect on thermal behavior and compounds mineralogy of replacing different percentages of fly ash with compact particles was studied. A total of 30% of fly ash was replaced with mass powder glass (PG), 70% with mass natural aggregates (S), and 85% with mass PG and S. According to this study, the obtained fly ash based geopolymer exhibits a 20% mass loss in the 25–300 °C temperature range due to the free or physically bound water removal. However, the mass loss is closely related to the particle percentage. Multiple endothermic peaks exhibit the dihydroxylation of β-FeOOH (goethite) at close to 320 °C, the Ca(OH)2 (Portlandite) transformation to CaCO3 (calcite) occurs at close to 490 °C, and Al(OH)3 decomposition occurs at close to 570 °C. Moreover, above 600 °C, the curves show only very small peaks which may correspond to Ti or Mg hydroxides decomposition. Also, the X-ray diffraction (XRD) pattern confirms the presence of sodalite after fly ash alkaline activation, whose content highly depends on the compact particles percentage. These results highlight the thermal stability of geopolymers in the 25–1000 °C temperature range through the use of thermogravimetric analysis, differential thermal analysis, and XRD.
Journal Article
Characterization of Five Collagenous Biomaterials by SEM Observations, TG-DTA, Collagenase Dissolution Tests and Subcutaneous Implantation Tests
Collagenous biomaterials that are clinically applied in dentistry have dermis-type and membrane-type, both of which are materials for promoting bone and soft tissue formation. The properties of materials supplied with different types could affect their biodegradation periods. The purpose of this study was to characterize five of these products by four different methods: scanning electron microscopy (SEM) observation, thermogravimetry-differential thermal analysis (TG-DTA), 0.01 wt% collagenase dissolution test, and subcutaneous implantation test in vivo. SEM micrographs revealed that both dermis and membranous materials were fibrous and porous. The membranous materials had higher specific derivative thermal gravimetry (DTG) peak temperatures in TG-DTA at around 320 °C, longer collagenase dissolution time ranging from about 300 to 500 min, and more longevity in mice exceeding 9 weeks than the dermis materials. There existed a correlation between the peak temperature in TG-DTA and the collagenase dissolution time. It was considered that higher cross-link degree among collagen fibrils of the membrane-type collagenous materials might account for these phenomena. The experimental protocol and numerical results obtained could be helpful for selection and future development of fibrous collagenous biomaterials in clinical use.
Journal Article
XRD and TG-DTA Study of New Phosphate-Based Geopolymers with Coal Ash or Metakaolin as Aluminosilicate Source and Mine Tailings Addition
Coal ash-based geopolymers with mine tailings addition activated with phosphate acid were synthesized for the first time at room temperature. In addition, three types of aluminosilicate sources were used as single raw materials or in a 1/1 wt. ratio to obtain five types of geopolymers activated with H3PO4. The thermal behaviour of the obtained geopolymers was studied between room temperature and 600 °C by Thermogravimetry-Differential Thermal Analysis (TG-DTA) and the phase composition after 28 days of curing at room temperature was analysed by X-ray diffraction (XRD). During heating, the acid-activated geopolymers exhibited similar behaviour to alkali-activated geopolymers. All of the samples showed endothermic peaks up to 300 °C due to water evaporation, while the samples with mine tailings showed two significant exothermic peaks above 400 °C due to oxidation reactions. The phase analysis confirmed the dissolution of the aluminosilicate sources in the presence of H3PO4 by significant changes in the XRD patterns of the raw materials and by the broadening of the peaks because of typically amorphous silicophosphate (Si–P), aluminophosphate (Al–P) or silico-alumino-phosphate (Si–Al–P) formation. The phases resulted from geopolymerisation are berlinite (AlPO4), brushite (CaHPO4∙2H2O), anhydrite (CaSO4) or ettringite as AFt and AFm phases.
Journal Article
Aspects of Thermal Analysis of Ceramics
During differential thermal analysis (DTA) of ceramic samples, it is advisable to take into account the dimensions and the shape of the samples, the variation of temperature at the center of the sample, the temperature difference between the center and surface of the sample as well as between the centers of the samples, the density, and the mass of the samples as a function of time. It was revealed that the thermal effect in the material is more accurately reflected by the curve showing the change in the sample mass change with time than by the differential thermogravimetric analysis (DTGA) curve. Enthalpy change of the process should be determined taking into account only the part of the DTA curve between the horizontal through the process start point, and the vertical through the minimum or maximum of the DTA curve, rather than the entire area under or above the peak of the curve. The rest of the curve describes the behavior of the sample as it transitions into the regular mode at the end of the chemical or phase (recrystallization) process.
Journal Article