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- Pattern Formation and Solitons (5)
- Nonlinear Schrödinger equation (3)
- Solitons (3)
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- Bright soliton (1)
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- Discrete solitons (1)
- Dissipative Gross-Pitaevskii equation. (1)
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Articles 31 - 60 of 65
Full-Text Articles in Physical Sciences and Mathematics
Positive And Negative Mass Solitons In Spin-Orbit Coupled Bose-Einstein Condensates, V. Achilleos, D.J. Frantzeskakis, P. G. Kevrekidis, P. Schmelcher, J. Stockhofe
Positive And Negative Mass Solitons In Spin-Orbit Coupled Bose-Einstein Condensates, V. Achilleos, D.J. Frantzeskakis, P. G. Kevrekidis, P. Schmelcher, J. Stockhofe
Mathematics and Statistics Department Faculty Publication Series
We present a unified description of different types of matter-wave solitons that can emerge in quasi one-dimensional spin-orbit coupled (SOC) Bose-Einstein condensates (BECs). This description relies on the reduction of the original two-component Gross-Pitaevskii SOC-BEC model to a single nonlinear Schrödinger equation, via a multiscale expansion method. This way, we find approximate bright and dark soliton solutions, for attractive and repulsive interatomic interactions respectively, for different regimes of the SOC interactions. Beyond this, our approach also reveals “negative mass” regimes, where corresponding “negative mass” bright or dark solitons can exist for repulsive or attractive interactions, respectively. Such a unique opportunity …
Traveling Waves For The Mass In Mass Model Of Granular Chains, Panayotis G. Kevrekidis, Atanas G. Stefanov, Haitao Xu
Traveling Waves For The Mass In Mass Model Of Granular Chains, Panayotis G. Kevrekidis, Atanas G. Stefanov, Haitao Xu
Mathematics and Statistics Department Faculty Publication Series
In the present work, we consider the mass in mass (or mass with mass) system of granular chains, namely a granular chain involving additionally an internal resonator. For these chains, we rigorously establish that under suitable “anti-resonance” conditions connecting the mass of the resonator and the speed of the wave, bell-shaped traveling wave solutions continue to exist in the system, in a way reminiscent of the results proven for the standard granular chain of elastic Hertzian contacts. We also numerically touch upon settings where the conditions do not hold, illustrating, in line also with recent experimental work, that non-monotonic waves …
Nonlinear Resonances And Antiresonances Of A Forced Sonic Vacuum, D. Pozharskiy, Y. Zhang, M. O. Williams, D. M. Mcfarland, P. G. Kevrekidis, A. F. Vakakis, I. G. Kevrekidis
Nonlinear Resonances And Antiresonances Of A Forced Sonic Vacuum, D. Pozharskiy, Y. Zhang, M. O. Williams, D. M. Mcfarland, P. G. Kevrekidis, A. F. Vakakis, I. G. Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We consider a harmonically driven acoustic medium in the form of a (finite length) highly nonlinear granular crystal with an amplitude- and frequency-dependent boundary drive. Despite the absence of a linear spectrum in the system, we identify resonant periodic propagation whereby the crystal responds at integer multiples of the drive period and observe that this can lead to local maxima of transmitted force at its fixed boundary. In addition, we identify and discuss minima of the transmitted force (“antiresonances”) between these resonances. Representative one-parameter complex bifurcation diagrams involve period doublings and Neimark-Sacker bifurcations as well as multiple isolas (e.g., of …
Conical Wave Propagation And Diffraction In 2d Hexagonally Packed Granular Lattices, C. Chong, P. G. Kevrekidis, M. J. Ablowitz, Yi-Ping Ma
Conical Wave Propagation And Diffraction In 2d Hexagonally Packed Granular Lattices, C. Chong, P. G. Kevrekidis, M. J. Ablowitz, Yi-Ping Ma
Mathematics and Statistics Department Faculty Publication Series
Linear and nonlinear mechanisms for conical wave propagation in two-dimensional lattices are explored in the realm of phononic crystals. As a prototypical example, a statically compressed granular lattice of spherical particles arranged in a hexagonal packing configuration is analyzed. Upon identifying the dispersion relation of the underlying linear problem, the resulting diffraction properties are considered. Analysis both via a heuristic argument for the linear propagation of a wavepacket, as well as via asymptotic analysis leading to the derivation of a Dirac system suggests the occurrence of conical diffraction. This analysis is valid for strong precompression i.e., near the linear regime. …
Weakly Nonlinear Analysis Of Vortex Formation In A Dissipative Variant Of The Gross-Pitaevskii Equation, J. C. Tzou, P. G. Kevrekidis, T. Kolokolnikov, R. Carretero-González
Weakly Nonlinear Analysis Of Vortex Formation In A Dissipative Variant Of The Gross-Pitaevskii Equation, J. C. Tzou, P. G. Kevrekidis, T. Kolokolnikov, R. Carretero-González
Mathematics and Statistics Department Faculty Publication Series
For a dissipative variant of the two-dimensional Gross-Pitaevskii equation with a parabolic trap under rotation, we study a symmetry breaking process that leads to the formation of vortices. The first symmetry breaking leads to the formation of many small vortices distributed uniformly near the Thomas-Fermi radius. The instability occurs as a result of a linear instability of a vortex-free steady state as the rotation is increased above a critical threshold. We focus on the second subsequent symmetry breaking, which occurs in the weakly nonlinear regime. At slightly above threshold, we derive a one dimensional amplitude equation that describes the slow …
Generating And Manipulating Quantized Vortices On-Demand In A Bose-Einstein Condensate: A Numerical Study, B. Gertjerenken, P. G. Kevrekidis, R. Carretero-González, B. P. Anderson
Generating And Manipulating Quantized Vortices On-Demand In A Bose-Einstein Condensate: A Numerical Study, B. Gertjerenken, P. G. Kevrekidis, R. Carretero-González, B. P. Anderson
Mathematics and Statistics Department Faculty Publication Series
We numerically investigate an experimentally viable method, that we will refer to as the “chopsticks method”, for generating and manipulating on-demand several vortices in a highly oblate atomic Bose-Einstein condensate (BEC) in order to initialize complex vortex distributions for studies of vortex dynamics. The method utilizes moving laser beams (the “chopsticks”) to generate, capture and transport vortices inside and outside the BEC. We examine in detail this methodology and show a wide parameter range of applicability for the prototypical two-vortex case, and show case examples of producing and manipulating several vortices for which there is no net circulation, equal numbers …
Pt Meets Supersymmetry And Nonlinearity: An Analytically Tractable Case Example, P. G. Kevrekidis, Jesús Cuevas–Maraver, Avadh Saxena, Fred Cooper, Avinash Khare
Pt Meets Supersymmetry And Nonlinearity: An Analytically Tractable Case Example, P. G. Kevrekidis, Jesús Cuevas–Maraver, Avadh Saxena, Fred Cooper, Avinash Khare
Mathematics and Statistics Department Faculty Publication Series
In the present work, we combine the notion of PT -symmetry with that of super-symmetry (SUSY) for a prototypical case example with a complex potential that is related by SUSY to the so-called Pöschl-Teller potential which is real. Not only are we able to identify and numerically confirm the eigenvalues of the relevant problem, but we also show that the corresponding nonlinear problem, in the presence of an arbitrary power law nonlinearity, has an exact bright soliton solution that can be analytically identified and has intriguing stability properties, such as an oscillatory instability, which the corresponding solution of the regular …
Bright Discrete Solitons In Spatially Modulated Dnls Systems, Panayotis G. Kevrekidis, R. L. Horne, N. Whitaker, Q. E. Hoq, D. Kip
Bright Discrete Solitons In Spatially Modulated Dnls Systems, Panayotis G. Kevrekidis, R. L. Horne, N. Whitaker, Q. E. Hoq, D. Kip
Mathematics and Statistics Department Faculty Publication Series
In the present work, we revisit the highly active research area of inhomogeneously nonlinear defocusing media and consider the existence, spectral stability and nonlinear dynamics of bright solitary waves in them. We use the anti-continuum limit of vanishing coupling as the starting point of our analysis, enabling in this way a systematic characterization of the branches of solutions. Our stability findings and bifurcation characteristics reveal the enhanced robustness and wider existence intervals of solutions with a broader support, culminating in the “extended” solution in which all sites are excited. Our eigenvalue predictions are corroborated by numerical linear stability analysis. Finally, …
Staggered Parity-Time-Symmetric Ladders With Cubic Nonlinearity, Jennie D'Ambroise, Panayotis G. Kevrekidis, B. A. Malomed
Staggered Parity-Time-Symmetric Ladders With Cubic Nonlinearity, Jennie D'Ambroise, Panayotis G. Kevrekidis, B. A. Malomed
Mathematics and Statistics Department Faculty Publication Series
We introduce a ladder-shaped chain with each rung carrying a parity-time- (PT -) symmetric gain-loss dimer. The polarity of the dimers is staggered along the chain, meaning alternation of gain-loss and loss-gain rungs. This structure, which can be implemented as an optical waveguide array, is the simplest one which renders the system PT -symmetric in both horizontal and vertical directions. The system is governed by a pair of linearly coupled discrete nonlinear Schrödinger equations with self-focusing or defocusing cubic onsite nonlinearity. Starting from ¨ the analytically tractable anticontinuum limit of uncoupled rungs and using the Newton’s method for continuation of …
Bifurcation And Stability Of Single And Multiple Vortex Rings In Three-Dimensional Bose-Einstein Condensates, R. N. Bisset, Wenlong Wang, C. Ticknor, R. Carretero-González, D. J. Frantzeskakis, L. A. Collins, P. G. Kevrekidis
Bifurcation And Stability Of Single And Multiple Vortex Rings In Three-Dimensional Bose-Einstein Condensates, R. N. Bisset, Wenlong Wang, C. Ticknor, R. Carretero-González, D. J. Frantzeskakis, L. A. Collins, P. G. Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
In the present work, we investigate how single- and multi-vortex-ring states can emerge from a planar dark soliton in three-dimensional (3D) Bose-Einstein condensates (confined in isotropic or anisotropic traps) through bifurcations. We characterize such bifurcations quantitatively using a Galerkin-type approach and find good qualitative and quantitative agreement with our Bogoliubov–de Gennes (BdG) analysis. We also systematically characterize the BdG spectrum of the dark solitons, using perturbation theory, and obtain a quantitative match with our 3D BdG numerical calculations. We then turn our attention to the emergence of single- and multi-vortexring states. We systematically capture these as stationary states of the …
Vortex Nucleation In A Dissipative Variant Of The Nonlinear Schrödinger Equation Under Rotation, R. Carretero-González, Panayotis G. Kevrekidis, T. Kolokolnikov
Vortex Nucleation In A Dissipative Variant Of The Nonlinear Schrödinger Equation Under Rotation, R. Carretero-González, Panayotis G. Kevrekidis, T. Kolokolnikov
Mathematics and Statistics Department Faculty Publication Series
In the present work, we motivate and explore the dynamics of a dissipative variant of the nonlinear Schrödinger equation under the impact of external rotation. As in the well established Hamiltonian case, the rotation gives rise to the formation of vortices. We show, however, that the most unstable mode leading to this instability scales with an appropriate power of the chemical potential μ of the system, increasing proportionally toμ2/3. The precise form of the relevant formula, obtained through our asymptotic analysis, provides the most unstable mode as a function of the atomic density and the trap strength. We …
Time- And Space-Variant Wave Transmission In Helicoidal Phononic Crystals, F. Li, C. Chong, Panayotis G. Kevrekidis, C Daraio
Time- And Space-Variant Wave Transmission In Helicoidal Phononic Crystals, F. Li, C. Chong, Panayotis G. Kevrekidis, C Daraio
Mathematics and Statistics Department Faculty Publication Series
We present a dynamically tunable mechanism of wave transmission in 1D helicoidal phononic crystals in a shape similar to DNA structures. These helicoidal architectures allow slanted nonlinear contact among cylindrical constituents, and the relative torsional movements can dynamically tune the contact stiffness between neighboring cylinders. This results in cross-talking between in-plane torsional and out-of-plane longitudinal waves. We numerically demonstrate their versatile wave mixing and controllable dispersion behavior in both wavenumber and frequency domains. Based on this principle, a suggestion towards an acoustic configuration bearing parallels to a transistor is further proposed, in which longitudinal waves can be switched on/off through …
Interaction Of Sine-Gordon Kinks And Breathers With A Parity-Time-Symmetric Defect, Danial Saadatmand, Sergey V. Dmitriev, Denis I. Borisov, Panayotis G. Kevrekidis
Interaction Of Sine-Gordon Kinks And Breathers With A Parity-Time-Symmetric Defect, Danial Saadatmand, Sergey V. Dmitriev, Denis I. Borisov, Panayotis G. Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
The scattering of kinks and low-frequency breathers of the nonlinear sine-Gordon (SG) equation on a spatially localized parity-time-symmetric perturbation (defect) with a balanced gain and loss is investigated numerically. It is demonstrated that if a kink passes the defect, it always restores its initial momentum and energy, and the only effect of the interaction with the defect is a phase shift of the kink. A kink approaching the defect from the gain side always passes, while in the opposite case it must have sufficiently large initial momentum to pass through the defect instead of being trapped in the loss region. …
Pt-Symmetric Dimer In A Generalized Model Of Coupled Nonlinear Oscillators, Jesús Cuevas–Maraver, Avinash Khare, Panayotis G. Kevrekidis, Haitao Xu, Avadh Saxena
Pt-Symmetric Dimer In A Generalized Model Of Coupled Nonlinear Oscillators, Jesús Cuevas–Maraver, Avinash Khare, Panayotis G. Kevrekidis, Haitao Xu, Avadh Saxena
Mathematics and Statistics Department Faculty Publication Series
Abstract In the present work, we explore the case of a general PT -symmetric dimer in the context of two both linearly and nonlinearly coupled cubic oscillators. To obtain an analytical handle on the system, we first explore the rotating wave approximation converting it into a discrete nonlinear Schrödinger type dimer. In the latter context, the stationary solutions and their stability are identified numerically but also wherever possible analytically. Solutions stemming from both symmetric and anti-symmetric special limits are identified. A number of special cases are explored regarding the ratio of coefficients of nonlinearity between oscillators over the intrinsic one …
Asymmetric Wave Propagation Through Saturable Nonlinear Oligomers, Daniel Law, Jennie D’Ambroise, Panayotis G. Kevrekidis, Detlef Kip
Asymmetric Wave Propagation Through Saturable Nonlinear Oligomers, Daniel Law, Jennie D’Ambroise, Panayotis G. Kevrekidis, Detlef Kip
Mathematics and Statistics Department Faculty Publication Series
In the present paper we consider nonlinear dimers and trimers (more generally, oligomers) embedded within a linear Schrödinger lattice where the nonlinear sites are of saturable type. We examine the stationary states of such chains in the form of plane waves, and analytically compute their reflection and transmission coefficients through the nonlinear oligomer, as well as the corresponding rectification factors which clearly illustrate the asymmetry between left and right propagation in such systems. We examine not only the existence but also the dynamical stability of the plane wave states. Lastly, we generalize our numerical considerations to the more physically relevant …
Capturing Data Uncertainty In Highvolume Stream Processing, Yanlei Diao, Boduo Li, Anna Liu, Liping Peng, Charles Sutton, Thanh Tran, Michael Zink
Capturing Data Uncertainty In Highvolume Stream Processing, Yanlei Diao, Boduo Li, Anna Liu, Liping Peng, Charles Sutton, Thanh Tran, Michael Zink
Mathematics and Statistics Department Faculty Publication Series
We present the design and development of a data stream system that captures data uncertainty from data collection to query processing to final result generation. Our system focuses on data that is naturally modeled as continuous random variables such as many types of sensor data. To provide an end-to-end solution, our system employs probabilistic modeling and inference to generate uncertainty description for raw data, and then a suite of statistical techniques to capture changes of uncertainty as data propagates through query operators. To cope with high-volume streams, we explore advanced approximation techniques for both space and time efficiency. We are …
Semiinfiniate Flags. Ii. Local And Global Intersection Cohomology Of Quasimaps' Spaces, Boris Feigin, Michael Finkelberg, Alexander Kuznetsov, Ivan Mirkoviæ
Semiinfiniate Flags. Ii. Local And Global Intersection Cohomology Of Quasimaps' Spaces, Boris Feigin, Michael Finkelberg, Alexander Kuznetsov, Ivan Mirkoviæ
Mathematics and Statistics Department Faculty Publication Series
No abstract provided.
Schrodinger Maps And Their Associated Frame Systems, Andrea Nahmod, Jalal Shatah, Luis Vega, Chongchun Zeng
Schrodinger Maps And Their Associated Frame Systems, Andrea Nahmod, Jalal Shatah, Luis Vega, Chongchun Zeng
Mathematics and Statistics Department Faculty Publication Series
In this paper we establish the equivalence of solutions between Schr¨odinger maps into S 2 or H 2 and their associated gauge invariant Schr¨odinger equations. We also establish the existence of global weak solutions into H 2 in two space dimensions. We extend these ideas for maps into compact hermitian symmetric manifolds with trivial first cohomology.
Complete Intersections In Toric Ideals, Eduardo Cattani, Raymond Curran, Alicia Dickenstein
Complete Intersections In Toric Ideals, Eduardo Cattani, Raymond Curran, Alicia Dickenstein
Mathematics and Statistics Department Faculty Publication Series
We present examples which show that in dimension higher than one or codimension higher than two, there exist toric ideals IA such that no binomial ideal contained in IA and of the same dimension is a complete intersection. This result has important implications in sparse elimination theory and in the study of the Horn system of partial differential equations.
Maximally Inflected Real Rational Curves, Viatcheslav Kharlamov, Frank Sottile
Maximally Inflected Real Rational Curves, Viatcheslav Kharlamov, Frank Sottile
Mathematics and Statistics Department Faculty Publication Series
We introduce and begin the topological study of real rational plane curves, all of whose inflection points are real. The existence of such curves is a corollary of results in the real Schubert calculus, and their study has consequences for the important Shapiro and Shapiro conjecture in the real Schubert calculus. We establish restrictions on the number of real nodes of such curves and construct curves realizing the extreme numbers of real nodes. These constructions imply the existence of real solutions to some problems in the Schubert calculus. We conclude with a discussion of maximally inflected curves of low degree.
On The Well-Posedness Of The Wave Map Problem In High Dimensions, Andrea Nahmod, Atanas Stefanov, Karen Uhlenbeck
On The Well-Posedness Of The Wave Map Problem In High Dimensions, Andrea Nahmod, Atanas Stefanov, Karen Uhlenbeck
Mathematics and Statistics Department Faculty Publication Series
We construct a gauge theoretic change of variables for the wave map from R × Rn into a compact group or Riemannian symmetric space, prove a new multiplication theorem for mixed Lebesgue-Besov spaces, and show the global well-posedness of a modified wave map equation - n ≥ 4 - for small critical initial data. We obtain global existence and uniqueness for the Cauchy problem of wave maps into compact Lie groups and symmetric spaces with small critical initial data and n ≥ 4.
On Schrodinger Maps, Andrea R. Nahmod, Atanas Stefanov, Karen Uhlenbeck
On Schrodinger Maps, Andrea R. Nahmod, Atanas Stefanov, Karen Uhlenbeck
Mathematics and Statistics Department Faculty Publication Series
We study the question of well-posedness of the Cauchy problem for Schr¨odinger maps from R 1 ×R 2 to the sphere S 2 or to H2 , the hyperbolic space. The idea is to choose an appropriate gauge change so that the derivatives of the map will satisfy a certain nonlinear Schr¨odinger system of equations and then study this modified Schr¨odinger map system (MSM). We then prove local well posedness of the Cauchy problem for the MSM with minimal regularity assumptions on the data and outline a method to derive well posedness of the Schr¨odinger map itself from it. In …
Analogues Of Weyl’S Formula For Reduced Enveloping Algebras, J. E. Humphreys
Analogues Of Weyl’S Formula For Reduced Enveloping Algebras, J. E. Humphreys
Mathematics and Statistics Department Faculty Publication Series
In this note we study simple modules for a reduced enveloping algebra Ux (g) in the critical case when X E 2 g^x is “nilpotent”. Some dimension formulas computed by Jantzen suggest modified versions of Weyl’s dimension formula, based on certain reflecting hyperplanes for the affine Weyl group which might be associated to Kazhdan–Lusztig cells.
Structure Of The Malvenuto-Reutenauer Hopf Algebra Of Permutations (Extended Abstract), Marcelo Aguiar, Frank Sottile
Structure Of The Malvenuto-Reutenauer Hopf Algebra Of Permutations (Extended Abstract), Marcelo Aguiar, Frank Sottile
Mathematics and Statistics Department Faculty Publication Series
We analyze the structure of the Malvenuto-Reutenauer Hopf algebra of permutations in detail. We give explicit formulas for its antipode, prove that it is a cofree coalgebra, determine its primitive elements and its coradical filtration and show that it decomposes as a crossed product over the Hopf algebra of quasi-symmetric functions. We also describe the structure constants of the multiplication as a certain number of facets of the permutahedron. Our results reveal a close relationship between the structure of this Hopf algebra and the weak order on the symmetric groups.
Scattering Of A Solitary Pulse On A Local Defect Or Breather, Panayotis G. Kevrekidis, Boris A. Malomed, H. E. Nistazakis, Dimitri J. Frantzeskakis, A. Saxena, A. R. Bishop
Scattering Of A Solitary Pulse On A Local Defect Or Breather, Panayotis G. Kevrekidis, Boris A. Malomed, H. E. Nistazakis, Dimitri J. Frantzeskakis, A. Saxena, A. R. Bishop
Mathematics and Statistics Department Faculty Publication Series
A model is introduced to describe guided propagation of a linear or nonlinear pulse which encounters a localized nonlinear defect, that may be either static or breather-like one. The model with the static defect directly applies to an optical pulse in a long fiber link with an inserted additional section of a nonlinear fiber. A local breather which gives rise to the nonlinear defect affecting the propagation of a narrow optical pulse is possible in a molecular chain. In the case when the host waveguide is linear, the pulse has a Gaussian shape. In that case, an immediate result of …
A Polytope Combinatorics For Semisimple Groups, Jared E. Anderson
A Polytope Combinatorics For Semisimple Groups, Jared E. Anderson
Mathematics and Statistics Department Faculty Publication Series
Mirkovi and Vilonen discovered a canonical basis of algebraic cycles for the intersection homology of (the closures of the strata of) the loop Grassmannian. The moment map images of these varieties are a collection of polytopes, and they may be used to compute weight multiplicities and tensor product multiplicities for representations of a semisimple group. The polytopes are explicitly described for a few low rank groups.
Bilinear Operators With Non-Smooth Symbol, I, John E. Gilbert, Andrea R. Nahmod
Bilinear Operators With Non-Smooth Symbol, I, John E. Gilbert, Andrea R. Nahmod
Mathematics and Statistics Department Faculty Publication Series
This paper proves the Lp-boundedness of general bilinear operators associated to a symbol or multiplier which need not be smooth. The Main Theorem establishes a general result for multipliers that are allowed to have singularities along the edges of a cone as well as possibly at its vertex. It thus unifies ealier results of Coifman-Meyer for smooth multipliers and ones, such the Bilinear Hilbert transform of Lacey-Thiele, where the multiplier is not smooth. Using a Whitney decomposition in the Fourier plane a general bilinear operator is represented as infinite discrete sums of time-frequency paraproducts obtained by associating wave-packets with tiles …
An Excursion From Enumerative Geometry To Solving Systems Of Polynomial Equations With Macaulay 2, Frank Sottile
An Excursion From Enumerative Geometry To Solving Systems Of Polynomial Equations With Macaulay 2, Frank Sottile
Mathematics and Statistics Department Faculty Publication Series
Solving a system of polynomial equations is a ubiquitous problem in the applications of mathematics. Until recently, it has been hopeless to find explicit solutions to such systems, and mathematics has instead developed deep and powerful theories about the solutions to polynomial equations. Enumerative Geometry is concerned with counting the number of solutions when the polynomials come from a geometric situation and Intersection Theory gives methods to accomplish the enumeration. We use Macaulay 2 to investigate some problems from enumerative geometry, illustrating some applications of symbolic computation to this important problem of solving systems of polynomial equations. Besides enumerating solutions …
Boundedness Of Bilinear Operators With Nonsmooth Symbols, John Gilbert, Andrea Nahmod
Boundedness Of Bilinear Operators With Nonsmooth Symbols, John Gilbert, Andrea Nahmod
Mathematics and Statistics Department Faculty Publication Series
We announce the Lp-boundedness of general bilinear operators associated to a symbol or multiplier which need not be smooth. We establish a general result for multipliers that are allowed to have singularities along the edges of a cone as well as possibly at its vertex. It thus unifies ealier results of CoifmanMeyer for smooth multipliers and ones, such the Bilinear Hilbert transform of Lacey-Thiele, where the multiplier is not smooth.
The A-Hypergeometric System Associated With A Monomial Curve, Eduardo Cattani, Carlos D’Andrea, Alicia Dickenstein
The A-Hypergeometric System Associated With A Monomial Curve, Eduardo Cattani, Carlos D’Andrea, Alicia Dickenstein
Mathematics and Statistics Department Faculty Publication Series
No abstract provided.