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Uniqueness And Stability In Determining A Rigid Inclusion In An Elastic Body
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Book Synopsis Uniqueness and Stability in Determining a Rigid Inclusion in an Elastic Body by : Antonino Morassi
Download or read book Uniqueness and Stability in Determining a Rigid Inclusion in an Elastic Body written by Antonino Morassi and published by American Mathematical Society(RI). This book was released on 2014-09-11 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Uniqueness and Stability in Determining a Rigid Inclusion in an Elastic Body by : Antonino Morassi
Download or read book Uniqueness and Stability in Determining a Rigid Inclusion in an Elastic Body written by Antonino Morassi and published by American Mathematical Soc.. This book was released on with total page 75 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Uniqueness and Stability in Determining a Rigid Inclusion in an Elastic Body by : Antonino Morassi
Download or read book Uniqueness and Stability in Determining a Rigid Inclusion in an Elastic Body written by Antonino Morassi and published by American Mathematical Soc.. This book was released on 2009-06-05 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider the inverse problem of determining a rigid inclusion inside an isotropic elastic body $\Omega$, from a single measurement of traction and displacement taken on the boundary of $\Omega$. For this severely ill-posed problem they prove uniqueness and a conditional stability estimate of log-log type.
Book Synopsis An Elastic Model for Volcanology by : Andrea Aspri
Download or read book An Elastic Model for Volcanology written by Andrea Aspri and published by Springer Nature. This book was released on 2019-11-08 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a rigorous mathematical framework for a linear elastic model arising from volcanology that explains deformation effects generated by inflating or deflating magma chambers in the Earth’s interior. From a mathematical perspective, these modeling assumptions manifest as a boundary value problem that has long been known by researchers in volcanology, but has not, until now, been given a thorough mathematical treatment. This mathematical study gives an explicit formula for the solution of the boundary value problem which generalizes the few well-known, explicit solutions found in geophysics literature. Using two distinct analytical approaches—one involving weighted Sobolev spaces, and the other using single and double layer potentials—the well-posedness of the elastic model is proven. An Elastic Model for Volcanology will be of particular interest to mathematicians researching inverse problems, as well as geophysicists studying volcanology.
Book Synopsis Systems, Control, Modeling and Optimization by : F. Ceragioli
Download or read book Systems, Control, Modeling and Optimization written by F. Ceragioli and published by Springer. This book was released on 2006-10-31 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This constitutes the Proceedings of the 22nd IFIP TC7 Conference held in July 2005, in Torino, Italy, and dedicated to Camillo Possio, on the 60th anniversary of his death during the last air raid over Torino. The papers in this volume concern primarily stochastic and distributed systems, their control/optimization, and inverse problems. These proceedings also explore applications of optimization techniques and computational methods in fields such as medicine, biology and economics.
Book Synopsis Spectral Geometry and Inverse Scattering Theory by : Huaian Diao
Download or read book Spectral Geometry and Inverse Scattering Theory written by Huaian Diao and published by Springer Nature. This book was released on 2023-10-31 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse scattering problems are a vital subject for both theoretical and experimental studies and remain an active field of research in applied mathematics. This book provides a detailed presentation of typical setup of inverse scattering problems for time-harmonic acoustic, electromagnetic and elastic waves. Moreover, it provides systematical and in-depth discussion on an important class of geometrical inverse scattering problems, where the inverse problem aims at recovering the shape and location of a scatterer independent of its medium properties. Readers of this book will be exposed to a unified framework for analyzing a variety of geometrical inverse scattering problems from a spectral geometric perspective. This book contains both overviews of classical results and update-to-date information on latest developments from both a practical and theoretical point of view. It can be used as an advanced graduate textbook in universities or as a reference source for researchers in acquiring the state-of-the-art results in inverse scattering theory and their potential applications.
Book Synopsis Twisted Pseudodifferential Calculus and Application to the Quantum Evolution of Molecules by : Andr Martinez
Download or read book Twisted Pseudodifferential Calculus and Application to the Quantum Evolution of Molecules written by Andr Martinez and published by American Mathematical Soc.. This book was released on 2009-06-05 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors construct an abstract pseudodifferential calculus with operator-valued symbol, suitable for the treatment of Coulomb-type interactions, and they apply it to the study of the quantum evolution of molecules in the Born-Oppenheimer approximation, in the case of the electronic Hamiltonian admitting a local gap in its spectrum. In particular, they show that the molecular evolution can be reduced to the one of a system of smooth semiclassical operators, the symbol of which can be computed explicitely. In addition, they study the propagation of certain wave packets up to long time values of Ehrenfest order.
Book Synopsis Small Divisor Problem in the Theory of Three-Dimensional Water Gravity Waves by : Grard Iooss
Download or read book Small Divisor Problem in the Theory of Three-Dimensional Water Gravity Waves written by Grard Iooss and published by American Mathematical Soc.. This book was released on 2009-06-05 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider doubly-periodic travelling waves at the surface of an infinitely deep perfect fluid, only subjected to gravity $g$ and resulting from the nonlinear interaction of two simply periodic travelling waves making an angle $2\theta$ between them. Denoting by $\mu =gL/c^{2}$ the dimensionless bifurcation parameter ( $L$ is the wave length along the direction of the travelling wave and $c$ is the velocity of the wave), bifurcation occurs for $\mu = \cos \theta$. For non-resonant cases, we first give a large family of formal three-dimensional gravity travelling waves, in the form of an expansion in powers of the amplitudes of two basic travelling waves. ``Diamond waves'' are a particular case of such waves, when they are symmetric with respect to the direction of propagation. The main object of the paper is the proof of existence of such symmetric waves having the above mentioned asymptotic expansion. Due to the occurence of small divisors, the main difficulty is the inversion of the linearized operator at a non trivial point, for applying the Nash Moser theorem. This operator is the sum of a second order differentiation along a certain direction, and an integro-differential operator of first order, both depending periodically of coordinates. It is shown that for almost all angles $\theta$, the 3-dimensional travelling waves bifurcate for a set of ``good'' values of the bifurcation parameter having asymptotically a full measure near the bifurcation curve in the parameter plane $(\theta,\mu ).$
Book Synopsis Unitary Invariants in Multivariable Operator Theory by : Gelu Popescu
Download or read book Unitary Invariants in Multivariable Operator Theory written by Gelu Popescu and published by American Mathematical Soc.. This book was released on 2009-06-05 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper concerns unitary invariants for $n$-tuples $T:=(T_1,\ldots, T_n)$ of (not necessarily commuting) bounded linear operators on Hilbert spaces. The author introduces a notion of joint numerical radius and works out its basic properties. Multivariable versions of Berger's dilation theorem, Berger-Kato-Stampfli mapping theorem, and Schwarz's lemma from complex analysis are obtained. The author studies the joint (spatial) numerical range of $T$ in connection with several unitary invariants for $n$-tuples of operators such as: right joint spectrum, joint numerical radius, euclidean operator radius, and joint spectral radius. He also proves an analogue of Toeplitz-Hausdorff theorem on the convexity of the spatial numerical range of an operator on a Hilbert space, for the joint numerical range of operators in the noncommutative analytic Toeplitz algebra $F_n^\infty$.
Book Synopsis The Minimal Polynomials of Unipotent Elements in Irreducible Representations of the Classical Groups in Odd Characteristic by : Irina D. Suprunenko
Download or read book The Minimal Polynomials of Unipotent Elements in Irreducible Representations of the Classical Groups in Odd Characteristic written by Irina D. Suprunenko and published by American Mathematical Soc.. This book was released on 2009-06-05 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: The minimal polynomials of the images of unipotent elements in irreducible rational representations of the classical algebraic groups over fields of odd characteristic are found. These polynomials have the form $(t-1)^d$ and hence are completely determined by their degrees. In positive characteristic the degree of such polynomial cannot exceed the order of a relevant element. It occurs that for each unipotent element the degree of its minimal polynomial in an irreducible representation is equal to the order of this element provided the highest weight of the representation is large enough with respect to the ground field characteristic. On the other hand, classes of unipotent elements for which in every nontrivial representation the degree of the minimal polynomial is equal to the order of the element are indicated. In the general case the problem of computing the minimal polynomial of the image of a given element of order $p^s$ in a fixed irreducible representation of a classical group over a field of characteristic $p>2$ can be reduced to a similar problem for certain $s$ unipotent elements and a certain irreducible representation of some semisimple group over the field of complex numbers. For the latter problem an explicit algorithm is given. Results of explicit computations for groups of small ranks are contained in Tables I-XII. The article may be regarded as a contribution to the programme of extending the fundamental results of Hall and Higman (1956) on the minimal polynomials from $p$-solvable linear groups to semisimple groups.
Book Synopsis Lyapunov Exponents and Invariant Manifolds for Random Dynamical Systems in a Banach Space by : Zeng Lian
Download or read book Lyapunov Exponents and Invariant Manifolds for Random Dynamical Systems in a Banach Space written by Zeng Lian and published by American Mathematical Soc.. This book was released on 2010 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study the Lyapunov exponents and their associated invariant subspaces for infinite dimensional random dynamical systems in a Banach space, which are generated by, for example, stochastic or random partial differential equations. The authors prove a multiplicative ergodic theorem and then use this theorem to establish the stable and unstable manifold theorem for nonuniformly hyperbolic random invariant sets.
Book Synopsis Cohomological Invariants: Exceptional Groups and Spin Groups by : Skip Garibaldi
Download or read book Cohomological Invariants: Exceptional Groups and Spin Groups written by Skip Garibaldi and published by American Mathematical Soc.. This book was released on 2009-06-05 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume concerns invariants of $G$-torsors with values in mod $p$ Galois cohomology--in the sense of Serre's lectures in the book Cohomological invariants in Galois cohomology--for various simple algebraic groups $G$ and primes $p$. The author determines the invariants for the exceptional groups $F_4$ mod 3, simply connected $E_6$ mod 3, $E_7$ mod 3, and $E_8$ mod 5. He also determines the invariants of $\mathrm{Spin}_n$ mod 2 for $n \leq 12$ and constructs some invariants of $\mathrm{Spin}_{14}$. Along the way, the author proves that certain maps in nonabelian cohomology are surjective. These surjectivities give as corollaries Pfister's results on 10- and 12-dimensional quadratic forms and Rost's theorem on 14-dimensional quadratic forms. This material on quadratic forms and invariants of $\mathrm{Spin}_n$ is based on unpublished work of Markus Rost. An appendix by Detlev Hoffmann proves a generalization of the Common Slot Theorem for 2-Pfister quadratic forms.
Book Synopsis On the convergence of $\sum c_kf(n_kx)$ by : Istvan Berkes
Download or read book On the convergence of $\sum c_kf(n_kx)$ written by Istvan Berkes and published by American Mathematical Soc.. This book was released on 2009 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a general study of the convergence problem and intends to prove several fresh results and improve a number of old results in the field. This title studies the case when the nk are random and investigates the discrepancy the sequence (nkx) mod 1.
Book Synopsis Affine Insertion and Pieri Rules for the Affine Grassmannian by : Thomas Lam
Download or read book Affine Insertion and Pieri Rules for the Affine Grassmannian written by Thomas Lam and published by American Mathematical Soc.. This book was released on 2010 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study combinatorial aspects of the Schubert calculus of the affine Grassmannian ${\rm Gr}$ associated with $SL(n,\mathbb{C})$.Their main results are: Pieri rules for the Schubert bases of $H^*({\rm Gr})$ and $H_*({\rm Gr})$, which expresses the product of a special Schubert class and an arbitrary Schubert class in terms of Schubert classes. A new combinatorial definition for $k$-Schur functions, which represent the Schubert basis of $H_*({\rm Gr})$. A combinatorial interpretation of the pairing $H^*({\rm Gr})\times H_*({\rm Gr}) \rightarrow\mathbb Z$ induced by the cap product.
Book Synopsis Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups by : Drew Armstrong
Download or read book Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups written by Drew Armstrong and published by American Mathematical Soc.. This book was released on 2009-10-08 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir is a refinement of the author's PhD thesis -- written at Cornell University (2006). It is primarily a desription of new research but also includes a substantial amount of background material. At the heart of the memoir the author introduces and studies a poset $NC^{(k)}(W)$ for each finite Coxeter group $W$ and each positive integer $k$. When $k=1$, his definition coincides with the generalized noncrossing partitions introduced by Brady and Watt in $K(\pi, 1)$'s for Artin groups of finite type and Bessis in The dual braid monoid. When $W$ is the symmetric group, the author obtains the poset of classical $k$-divisible noncrossing partitions, first studied by Edelman in Chain enumeration and non-crossing partitions.
Book Synopsis Robin Functions for Complex Manifolds and Applications by : Kang-Tae Kim
Download or read book Robin Functions for Complex Manifolds and Applications written by Kang-Tae Kim and published by American Mathematical Soc.. This book was released on 2011 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Volume 209, number 984 (third of 5 numbers)."
Book Synopsis Operator Algebras for Multivariable Dynamics by : Kenneth R. Davidson
Download or read book Operator Algebras for Multivariable Dynamics written by Kenneth R. Davidson and published by American Mathematical Soc.. This book was released on 2011 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let $X$ be a locally compact Hausdorff space with $n$ proper continuous self maps $\sigma_i:X \to X$ for $1 \le i \le n$. To this the authors associate two conjugacy operator algebras which emerge as the natural candidates for the universal algebra of the system, the tensor algebra $\mathcal{A}(X,\tau)$ and the semicrossed product $\mathrm{C}_0(X)\times_\tau\mathbb{F}_n^+$. They develop the necessary dilation theory for both models. In particular, they exhibit an explicit family of boundary representations which determine the C*-envelope of the tensor algebra.|Let $X$ be a locally compact Hausdorff space with $n$ proper continuous self maps $\sigma_i:X \to X$ for $1 \le i \le n$. To this the authors associate two conjugacy operator algebras which emerge as the natural candidates for the universal algebra of the system, the tensor algebra $\mathcal{A}(X,\tau)$ and the semicrossed product $\mathrm{C}_0(X)\times_\tau\mathbb{F}_n^+$. They develop the necessary dilation theory for both models. In particular, they exhibit an explicit family of boundary representations which determine the C*-envelope of the tensor algebra.
