Alexei Iantchenko - Academia.edu (original) (raw)
Papers by Alexei Iantchenko
arXiv (Cornell University), Feb 3, 2012
Ultrasound wave propagation in a nonhomogeneous linearly elastic layer of constant thickness is c... more Ultrasound wave propagation in a nonhomogeneous linearly elastic layer of constant thickness is considered. The resonances for the corresponding acoustic propagator are studied. It is shown that the distribution of the resonances depends on the smoothness of the coefficients. Namely, if the coefficients have jump discontinuities at the boundaries, then the resonances are asymptotically distributed along a straight line parallel to the real axis on the unphysical sheet of the complex frequency plane. In the contrary, if the coefficients are continuous, then it is shown that the resonances are asymptotically distributed along a logarithmic curve. The spacing between two successive resonances turns out to be sensitive to articular cartilage degeneration. The application of the obtained results to ultrasound testing of articular cartilage is discussed.
arXiv (Cornell University), Jan 21, 2002
Mechanics Research Communications, 2019
A simple mathematical model for free vibrations of an elastically clamped beam is suggested to in... more A simple mathematical model for free vibrations of an elastically clamped beam is suggested to interpret the results of the resonance frequency analysis developed for implant stability measurements in terms of the Implant Stability Quotient (ISQ) units. It is shown that the resonance frequency substantially depends on the lateral compliance of the implant/bone system. Based on the notion of the lateral stiffness of the implant/bone system, a new measure of the implant stability is introduced in the form similar to the ISQ scale and is called the Implant Clamping Quotient (ICQ), because it characterizes the jawbone's clamp of the implant. By definition, the ICQ unit is equal to a percentage of the original scale for the lateral stiffness of the implant/bone system.
Journal of Mathematical Analysis and Applications, Apr 1, 2012
We describe the spectral properties of the Jacobi operator (Hy) n = a n−1 y n−1 +a n y n+1 + b n ... more We describe the spectral properties of the Jacobi operator (Hy) n = a n−1 y n−1 +a n y n+1 + b n y n , n ∈ Z, with a n = a 0 n + u n , b n = b 0 n + v n , where sequences a 0 n > 0, b 0 n ∈ R are periodic with period q, and sequences u n , v n have compact support. In the case u n ≡ 0 we obtain the asymptotics of the spectrum in the limit of small perturbations v n .
Journal of Mathematical Physics, 2022
Journal of Mathematical Physics, 2022
We analyze an inverse problem associated with the time-harmonic Rayleigh system on a flat elastic... more We analyze an inverse problem associated with the time-harmonic Rayleigh system on a flat elastic half-space concerning the recovery of Lamé parameters in a slab beneath a traction-free surface. We employ the Markushevich substitution, while the data are captured in a Jost function, and we point out parallels with a corresponding problem for the Schrödinger equation. The Jost function can be identified with spectral data. We derive a Gel’fand-Levitan type equation and obtain uniqueness with two distinct frequencies.
We consider a periodic Jacobi operator H with finitely supported perturbations on Z. We solve the... more We consider a periodic Jacobi operator H with finitely supported perturbations on Z. We solve the inverse resonance problem: we prove that the mapping from finitely supported perturbations to the scattering data, the inverse of the transmission coefficient and the Jost function on the right half-axis, is one-to-one and onto. We consider the problem of reconstruction of the scattering data from all eigenvalues, resonances and the set of zeros of R − (λ) + 1, where R − is the reflection coefficient.
Abstract: The electron density of the neutral atoms at the distances Z−γ, γ 2 (1=3; 1) from the n... more Abstract: The electron density of the neutral atoms at the distances Z−γ, γ 2 (1=3; 1) from the nucleus in the limit when the charge of the nucleus Z tends to infinity is well approximated by the function constZ 32 jxj − 32, which is a common limiting value for both the Thomas-Fermi density at the origin and the hydrogen density at infinity. This conjecture by Lieb is proved in some weak sense by using the Ivrii and Sigal method. 1.
Spectral Theory and Mathematical Physics, 2020
The theoretical existence of elastic surface waves, that is, propagating wave solutions which dec... more The theoretical existence of elastic surface waves, that is, propagating wave solutions which decay exponentially away from the boundary of a homogeneous elastic half-space, was first discovered in 1885 by Rayleigh [17]. In 1911 Love [14] was the first to argue that surface-wave dispersion is responsible for the oscillatory character of the main shock of an earthquake tremor, following the "primary" and "secondary" arrivals. Rayleigh and Love waves can be identified with Earth's free oscillations n S l and n T l with n l/4 assuming spherical symmetry. We study the linear elastic wave equation in the half space IR 3 − = IR 2 x ×(−∞, 0] z , with coordinates (x, z), x = (x 1 , x 2) ∈ IR 2 , z ∈ IR − = (−∞, 0]. ∂ 2 u ∂t 2 = div σ (u) ρ , where u is displacement vector, σ (u) is the stress tensor given by Hooke's law σ (u) = Cε(u). Here, ε(u) is strain tensor, C is the fourth-order stiffness tensor with components c ij kl , ρ is the density of mass. In [4] we give the semiclassical description of surface waves in a general elastic medium stratified near the boundary in full generality. This semiclassical framework was first formulated by Colin
arXiv: Spectral Theory, 2015
We provide the full asymptotic description of the quasi-normal modes in any strip of fixed width ... more We provide the full asymptotic description of the quasi-normal modes in any strip of fixed width for massless Dirac fields in slowly rotating Kerr-Newman-de Sitter black holes. The method is based on the extension to the Dirac operators of techniques applied by Dyatlov 2012 to the (uncharged) Kerr-de Sitter black holes.
arXiv: Analysis of PDEs, 2017
In this paper, we present a semiclassical description of surface waves or modes in an elastic med... more In this paper, we present a semiclassical description of surface waves or modes in an elastic medium near a boundary, in spatial dimension three. The medium is assumed to be essentially stratified near the boundary at some scale comparable to the wave length. Such a medium can also be thought of as a surficial layer (which can be thick) overlying a half space. The analysis is based on the work of Colin de Verdiere on acoustic surface waves. The description is geometric in the boundary and locally spectral "beneath" it. Effective Hamiltonians of surface waves correspond with eigenvalues of ordinary differential operators, which, to leading order, define their phase velocities. Using these Hamiltonians, we obtain pseudodifferential surface wave equations. We then construct a parametrix. Finally, we discuss Weyl's formulas for counting surface modes, and the decoupling into two classes of surface waves, that is, Rayleigh and Love waves, under appropriate symmetry conditions.
Inverse Problems, 2020
Introduction: Several studies have demonstrated better outcomes for carotid endarterectomy (CEA) ... more Introduction: Several studies have demonstrated better outcomes for carotid endarterectomy (CEA) at high-volume hospitals and providers. However, only a few studies have reported the effect of surgeons' specialty and volume on the perioperative outcome of CEA. Methods: This is a retrospective analysis of prospectively collected CEA data during a recent 2-year period. Surgeons' specialties were classified according to their board specialties into general surgeons (GS), cardiothoracic (CT), and vascular surgeons (VS). Surgeons' annual volume was categorized into low volume (Ͻ10 CEAs), medium volume (10 to Ͻ30 CEAs), and high volume (Ն30 CEAs). The primary outcome was 30-day perioperative stroke or death, or both. Other perioperative complications were analyzed. Univariate and multivariate analyses were done to predict the effect of specialty/volume and any other patient risk factors on stroke outcome. Results: A total of 953 CEAs were performed by 24 surgeons: 122 by 7 GS, 383 by 13 CT, and 448 by 4 VS. Patients' demographics and clinical JOURNAL OF VASCULAR SURGERY
Analysis and Applications, 2018
We provide the full asymptotic description of the quasi-normal modes (resonances) in any strip of... more We provide the full asymptotic description of the quasi-normal modes (resonances) in any strip of fixed width for Dirac fields in slowly rotating Kerr–Newman–de Sitter black holes. The resonances split in a way similar to the Zeeman effect. The method is based on the extension to Dirac operators of techniques applied by Dyatlov in [Quasi-normal modes and exponential energy decay for the Kerr–de Sitter black hole, Commun. Math. Phys. 306(1) (2011) 119–163; Asymptotic distribution of quasi-normal modes for Kerr–de Sitter black holes, Ann. Henri Poincaré 13(5) (2012) 1101–1166] to the (uncharged) Kerr–de Sitter black holes. We show that the mass of the Dirac field does not have an effect on the two leading terms in the expansions of resonances. We give an expansion of the solution of the evolution equation for the Dirac fields in the outer region of the slowly rotating Kerr–Newman–de Sitter black hole which implies the exponential decay of the local energy. Moreover, using the [Formula...
Mechanics Research Communications, 2018
A simple mathematical model for free vibrations of an elastically clamped beam is suggested to in... more A simple mathematical model for free vibrations of an elastically clamped beam is suggested to interpret the results of the resonance frequency analysis developed for implant stability measurements in terms of the Implant Stability Quotient (ISQ) units. It is shown that the resonance frequency substantially depends on the lateral compliance of the implant/bone system. Based on the notion of the lateral stiffness of the implant/bone system, a new measure of the implant stability is introduced in the form similar to the ISQ scale and is called the Implant Clamping Quotient (ICQ), because it characterizes the jawbone's clamp of the implant. By definition, the ICQ unit is equal to a percentage of the original scale for the lateral stiffness of the implant/bone system.
Continuum Mechanics and Thermodynamics, 2017
A large amplitude oscillatory shear (LAOS) is considered in the strain-controlled regime, and the... more A large amplitude oscillatory shear (LAOS) is considered in the strain-controlled regime, and the interrelation between the Fourier transform (FT) and the stress decomposition (SD) approaches is established. Several definitions of the generalized storage and loss moduli are examined in a unified conceptual scheme based on the Lissajous-Bowditch plots. An illustrative example of evaluating the generalized moduli from a LAOS flow is given.
Mathematical Research Letters, 2017
The quasi-normal modes for black holes are the resonances for the scattering of incoming waves by... more The quasi-normal modes for black holes are the resonances for the scattering of incoming waves by black holes. Here we consider scattering of massless uncharged Dirac fields propagating in the outer region of de Sitter-Reissner-Nordström black hole, which is spherically symmetric charged exact solution of the Einstein-Maxwell equations. Using the spherical symmetry of the equation and restricting to a fixed harmonic the problem is reduced to a scattering problem for the 1D massless Dirac operator on the line. The resonances for the problem are related to the resonances for a certain semiclassical Schrödinger operator with exponentially decreasing positive potential. We give exact relation between the sets of Dirac and Schrödinger resonances. The asymptotic distribution of the resonances is close to the lattice of pseudopoles associated to the non-degenerate maxima of the potentials. Using the techniques of quantum Birkhoff normal form we give the complete asymptotic formulas for the resonances. In particular, we calculate the first three leading terms in the expansion. Moreover, similar results are obtained for the de Sitter-Schwarzschild quasi-normal modes, thus improving the result of Sá Barreto and Zworski in [2].
Journal of Mathematical Analysis and Applications, 2017
We give an expansion of the solution of the evolution equation for the massless Dirac fields in t... more We give an expansion of the solution of the evolution equation for the massless Dirac fields in the outer region of de Sitter-Reissner-Nordström black hole in terms of resonances. By means of this method we describe the decay of local energy for compactly supported data. The proof uses the cutoff resolvent estimates for the semiclassical Schrödinger operators from [4]. The method extends to the Dirac operators on spherically symmetric asymptotically hyperbolic manifolds.
To study the location of poles for the acoustic scattering matrix for two strictly convex obstacl... more To study the location of poles for the acoustic scattering matrix for two strictly convex obstacles with smooth boundaries, one uses an approximation of the quantized billiard operator M along the trapped ray between the two obstacles. Assuming that the boundaries are analytic and the eigenvalues of Poincar´e map are non-resonant we use the Birkhoff normal form for M to get the complete asymptotic expansions for the poles in any logarithmic neighborhood of real axis
Matematiken ar internationell och det matematiska spraket, symbolerna, ar samma overallt i varlde... more Matematiken ar internationell och det matematiska spraket, symbolerna, ar samma overallt i varlden. Manga olika kulturer har bidragit till matematikens utveckling. I denna forelasningspresentation diskuteras matematikutveckling i olika lander och matematiker av olika ursprung. Begransning tidsperiod:1800-1900.
Syfte med denna forelasning ar att introducera begreppet “resonans” och att overtyga er om att re... more Syfte med denna forelasning ar att introducera begreppet “resonans” och att overtyga er om att resonanser ar en del av var verklighet. Jag ska ocksa ge exempel som visar hur resonanser kan anvandas for att studera var varld. Forelasning ska vara begriplig for alla. I forelasningen introduceras begreppet “resonans” pa grundlaggande niva. Exempel ges pa hur renosanser kan anvandas for att studera var varld. Renosanser ar en del av var verklighet - genom att mata resonanser kan man skapa en bild av det verkliga objektet. Presentationen anvandes vid Alexei Iantchenkos docentforelasning den 1 april 2005.
arXiv (Cornell University), Feb 3, 2012
Ultrasound wave propagation in a nonhomogeneous linearly elastic layer of constant thickness is c... more Ultrasound wave propagation in a nonhomogeneous linearly elastic layer of constant thickness is considered. The resonances for the corresponding acoustic propagator are studied. It is shown that the distribution of the resonances depends on the smoothness of the coefficients. Namely, if the coefficients have jump discontinuities at the boundaries, then the resonances are asymptotically distributed along a straight line parallel to the real axis on the unphysical sheet of the complex frequency plane. In the contrary, if the coefficients are continuous, then it is shown that the resonances are asymptotically distributed along a logarithmic curve. The spacing between two successive resonances turns out to be sensitive to articular cartilage degeneration. The application of the obtained results to ultrasound testing of articular cartilage is discussed.
arXiv (Cornell University), Jan 21, 2002
Mechanics Research Communications, 2019
A simple mathematical model for free vibrations of an elastically clamped beam is suggested to in... more A simple mathematical model for free vibrations of an elastically clamped beam is suggested to interpret the results of the resonance frequency analysis developed for implant stability measurements in terms of the Implant Stability Quotient (ISQ) units. It is shown that the resonance frequency substantially depends on the lateral compliance of the implant/bone system. Based on the notion of the lateral stiffness of the implant/bone system, a new measure of the implant stability is introduced in the form similar to the ISQ scale and is called the Implant Clamping Quotient (ICQ), because it characterizes the jawbone's clamp of the implant. By definition, the ICQ unit is equal to a percentage of the original scale for the lateral stiffness of the implant/bone system.
Journal of Mathematical Analysis and Applications, Apr 1, 2012
We describe the spectral properties of the Jacobi operator (Hy) n = a n−1 y n−1 +a n y n+1 + b n ... more We describe the spectral properties of the Jacobi operator (Hy) n = a n−1 y n−1 +a n y n+1 + b n y n , n ∈ Z, with a n = a 0 n + u n , b n = b 0 n + v n , where sequences a 0 n > 0, b 0 n ∈ R are periodic with period q, and sequences u n , v n have compact support. In the case u n ≡ 0 we obtain the asymptotics of the spectrum in the limit of small perturbations v n .
Journal of Mathematical Physics, 2022
Journal of Mathematical Physics, 2022
We analyze an inverse problem associated with the time-harmonic Rayleigh system on a flat elastic... more We analyze an inverse problem associated with the time-harmonic Rayleigh system on a flat elastic half-space concerning the recovery of Lamé parameters in a slab beneath a traction-free surface. We employ the Markushevich substitution, while the data are captured in a Jost function, and we point out parallels with a corresponding problem for the Schrödinger equation. The Jost function can be identified with spectral data. We derive a Gel’fand-Levitan type equation and obtain uniqueness with two distinct frequencies.
We consider a periodic Jacobi operator H with finitely supported perturbations on Z. We solve the... more We consider a periodic Jacobi operator H with finitely supported perturbations on Z. We solve the inverse resonance problem: we prove that the mapping from finitely supported perturbations to the scattering data, the inverse of the transmission coefficient and the Jost function on the right half-axis, is one-to-one and onto. We consider the problem of reconstruction of the scattering data from all eigenvalues, resonances and the set of zeros of R − (λ) + 1, where R − is the reflection coefficient.
Abstract: The electron density of the neutral atoms at the distances Z−γ, γ 2 (1=3; 1) from the n... more Abstract: The electron density of the neutral atoms at the distances Z−γ, γ 2 (1=3; 1) from the nucleus in the limit when the charge of the nucleus Z tends to infinity is well approximated by the function constZ 32 jxj − 32, which is a common limiting value for both the Thomas-Fermi density at the origin and the hydrogen density at infinity. This conjecture by Lieb is proved in some weak sense by using the Ivrii and Sigal method. 1.
Spectral Theory and Mathematical Physics, 2020
The theoretical existence of elastic surface waves, that is, propagating wave solutions which dec... more The theoretical existence of elastic surface waves, that is, propagating wave solutions which decay exponentially away from the boundary of a homogeneous elastic half-space, was first discovered in 1885 by Rayleigh [17]. In 1911 Love [14] was the first to argue that surface-wave dispersion is responsible for the oscillatory character of the main shock of an earthquake tremor, following the "primary" and "secondary" arrivals. Rayleigh and Love waves can be identified with Earth's free oscillations n S l and n T l with n l/4 assuming spherical symmetry. We study the linear elastic wave equation in the half space IR 3 − = IR 2 x ×(−∞, 0] z , with coordinates (x, z), x = (x 1 , x 2) ∈ IR 2 , z ∈ IR − = (−∞, 0]. ∂ 2 u ∂t 2 = div σ (u) ρ , where u is displacement vector, σ (u) is the stress tensor given by Hooke's law σ (u) = Cε(u). Here, ε(u) is strain tensor, C is the fourth-order stiffness tensor with components c ij kl , ρ is the density of mass. In [4] we give the semiclassical description of surface waves in a general elastic medium stratified near the boundary in full generality. This semiclassical framework was first formulated by Colin
arXiv: Spectral Theory, 2015
We provide the full asymptotic description of the quasi-normal modes in any strip of fixed width ... more We provide the full asymptotic description of the quasi-normal modes in any strip of fixed width for massless Dirac fields in slowly rotating Kerr-Newman-de Sitter black holes. The method is based on the extension to the Dirac operators of techniques applied by Dyatlov 2012 to the (uncharged) Kerr-de Sitter black holes.
arXiv: Analysis of PDEs, 2017
In this paper, we present a semiclassical description of surface waves or modes in an elastic med... more In this paper, we present a semiclassical description of surface waves or modes in an elastic medium near a boundary, in spatial dimension three. The medium is assumed to be essentially stratified near the boundary at some scale comparable to the wave length. Such a medium can also be thought of as a surficial layer (which can be thick) overlying a half space. The analysis is based on the work of Colin de Verdiere on acoustic surface waves. The description is geometric in the boundary and locally spectral "beneath" it. Effective Hamiltonians of surface waves correspond with eigenvalues of ordinary differential operators, which, to leading order, define their phase velocities. Using these Hamiltonians, we obtain pseudodifferential surface wave equations. We then construct a parametrix. Finally, we discuss Weyl's formulas for counting surface modes, and the decoupling into two classes of surface waves, that is, Rayleigh and Love waves, under appropriate symmetry conditions.
Inverse Problems, 2020
Introduction: Several studies have demonstrated better outcomes for carotid endarterectomy (CEA) ... more Introduction: Several studies have demonstrated better outcomes for carotid endarterectomy (CEA) at high-volume hospitals and providers. However, only a few studies have reported the effect of surgeons' specialty and volume on the perioperative outcome of CEA. Methods: This is a retrospective analysis of prospectively collected CEA data during a recent 2-year period. Surgeons' specialties were classified according to their board specialties into general surgeons (GS), cardiothoracic (CT), and vascular surgeons (VS). Surgeons' annual volume was categorized into low volume (Ͻ10 CEAs), medium volume (10 to Ͻ30 CEAs), and high volume (Ն30 CEAs). The primary outcome was 30-day perioperative stroke or death, or both. Other perioperative complications were analyzed. Univariate and multivariate analyses were done to predict the effect of specialty/volume and any other patient risk factors on stroke outcome. Results: A total of 953 CEAs were performed by 24 surgeons: 122 by 7 GS, 383 by 13 CT, and 448 by 4 VS. Patients' demographics and clinical JOURNAL OF VASCULAR SURGERY
Analysis and Applications, 2018
We provide the full asymptotic description of the quasi-normal modes (resonances) in any strip of... more We provide the full asymptotic description of the quasi-normal modes (resonances) in any strip of fixed width for Dirac fields in slowly rotating Kerr–Newman–de Sitter black holes. The resonances split in a way similar to the Zeeman effect. The method is based on the extension to Dirac operators of techniques applied by Dyatlov in [Quasi-normal modes and exponential energy decay for the Kerr–de Sitter black hole, Commun. Math. Phys. 306(1) (2011) 119–163; Asymptotic distribution of quasi-normal modes for Kerr–de Sitter black holes, Ann. Henri Poincaré 13(5) (2012) 1101–1166] to the (uncharged) Kerr–de Sitter black holes. We show that the mass of the Dirac field does not have an effect on the two leading terms in the expansions of resonances. We give an expansion of the solution of the evolution equation for the Dirac fields in the outer region of the slowly rotating Kerr–Newman–de Sitter black hole which implies the exponential decay of the local energy. Moreover, using the [Formula...
Mechanics Research Communications, 2018
A simple mathematical model for free vibrations of an elastically clamped beam is suggested to in... more A simple mathematical model for free vibrations of an elastically clamped beam is suggested to interpret the results of the resonance frequency analysis developed for implant stability measurements in terms of the Implant Stability Quotient (ISQ) units. It is shown that the resonance frequency substantially depends on the lateral compliance of the implant/bone system. Based on the notion of the lateral stiffness of the implant/bone system, a new measure of the implant stability is introduced in the form similar to the ISQ scale and is called the Implant Clamping Quotient (ICQ), because it characterizes the jawbone's clamp of the implant. By definition, the ICQ unit is equal to a percentage of the original scale for the lateral stiffness of the implant/bone system.
Continuum Mechanics and Thermodynamics, 2017
A large amplitude oscillatory shear (LAOS) is considered in the strain-controlled regime, and the... more A large amplitude oscillatory shear (LAOS) is considered in the strain-controlled regime, and the interrelation between the Fourier transform (FT) and the stress decomposition (SD) approaches is established. Several definitions of the generalized storage and loss moduli are examined in a unified conceptual scheme based on the Lissajous-Bowditch plots. An illustrative example of evaluating the generalized moduli from a LAOS flow is given.
Mathematical Research Letters, 2017
The quasi-normal modes for black holes are the resonances for the scattering of incoming waves by... more The quasi-normal modes for black holes are the resonances for the scattering of incoming waves by black holes. Here we consider scattering of massless uncharged Dirac fields propagating in the outer region of de Sitter-Reissner-Nordström black hole, which is spherically symmetric charged exact solution of the Einstein-Maxwell equations. Using the spherical symmetry of the equation and restricting to a fixed harmonic the problem is reduced to a scattering problem for the 1D massless Dirac operator on the line. The resonances for the problem are related to the resonances for a certain semiclassical Schrödinger operator with exponentially decreasing positive potential. We give exact relation between the sets of Dirac and Schrödinger resonances. The asymptotic distribution of the resonances is close to the lattice of pseudopoles associated to the non-degenerate maxima of the potentials. Using the techniques of quantum Birkhoff normal form we give the complete asymptotic formulas for the resonances. In particular, we calculate the first three leading terms in the expansion. Moreover, similar results are obtained for the de Sitter-Schwarzschild quasi-normal modes, thus improving the result of Sá Barreto and Zworski in [2].
Journal of Mathematical Analysis and Applications, 2017
We give an expansion of the solution of the evolution equation for the massless Dirac fields in t... more We give an expansion of the solution of the evolution equation for the massless Dirac fields in the outer region of de Sitter-Reissner-Nordström black hole in terms of resonances. By means of this method we describe the decay of local energy for compactly supported data. The proof uses the cutoff resolvent estimates for the semiclassical Schrödinger operators from [4]. The method extends to the Dirac operators on spherically symmetric asymptotically hyperbolic manifolds.
To study the location of poles for the acoustic scattering matrix for two strictly convex obstacl... more To study the location of poles for the acoustic scattering matrix for two strictly convex obstacles with smooth boundaries, one uses an approximation of the quantized billiard operator M along the trapped ray between the two obstacles. Assuming that the boundaries are analytic and the eigenvalues of Poincar´e map are non-resonant we use the Birkhoff normal form for M to get the complete asymptotic expansions for the poles in any logarithmic neighborhood of real axis
Matematiken ar internationell och det matematiska spraket, symbolerna, ar samma overallt i varlde... more Matematiken ar internationell och det matematiska spraket, symbolerna, ar samma overallt i varlden. Manga olika kulturer har bidragit till matematikens utveckling. I denna forelasningspresentation diskuteras matematikutveckling i olika lander och matematiker av olika ursprung. Begransning tidsperiod:1800-1900.
Syfte med denna forelasning ar att introducera begreppet “resonans” och att overtyga er om att re... more Syfte med denna forelasning ar att introducera begreppet “resonans” och att overtyga er om att resonanser ar en del av var verklighet. Jag ska ocksa ge exempel som visar hur resonanser kan anvandas for att studera var varld. Forelasning ska vara begriplig for alla. I forelasningen introduceras begreppet “resonans” pa grundlaggande niva. Exempel ges pa hur renosanser kan anvandas for att studera var varld. Renosanser ar en del av var verklighet - genom att mata resonanser kan man skapa en bild av det verkliga objektet. Presentationen anvandes vid Alexei Iantchenkos docentforelasning den 1 april 2005.