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The $$\frac{G'}{G}$$ method and 1-soliton solution of the Davey-Stewartson equation. (English) Zbl 1217.35171
Summary: This paper studies the Davey-Stewartson equation. The $$\frac{G'}{G}$$ method is applied to carry out the integration of this equation. Subsequently, using the ansatz method this equation is integrated in $$(1+2)$$ dimensions with power law nonlinearity.

##### MSC:
 35Q55 NLS equations (nonlinear Schrödinger equations) 35C08 Soliton solutions
##### Keywords:
evolution equation; integrability; solitons
Full Text:
##### References:
 [1] Bekir, A.; Cevikel, A.C., New solitons and periodic solutions for nonlinear physical models in mathematical physics, Nonlinear analysis: real world applications, 11, 4, 3275-3285, (2010) · Zbl 1196.35178 [2] Caixia, S.; Boling, G., Ill-posedness for the nonlinear davey – stewartson equation, Acta Mathematica scientia, 28, 1, 117-127, (2008) · Zbl 1150.35068 [3] Eden, A.; Erbay, H.A.; Muslu, G.M., Two remarks on a generalized davey – stewartson system, Nonlinear analysis: theory, methods and applications, 64, 5, 979-986, (2006) · Zbl 1091.35088 [4] Eden, A.; Erbay, H.A.; Muslu, G.M., Closing the gap in the purely elliptic generalized davey – stewartson system, Nonlinear analysis: theory, methods and applications, 69, 8, 2575-2582, (2008) · Zbl 1152.35492 [5] Eden, A.; Topaloglu, I.A., Standing waves for a generalized davey – stewartson system: revisited, Applied mathematics letters, 21, 4, 342-347, (2008) · Zbl 1165.35458 [6] Guo, C.; Cui, S., A note on the Cauchy problem of the generalized davey – stewartson equations, Applied mathematics and computation, 215, 6, 2262-2268, (2009) · Zbl 1181.35261 [7] Jun, Z.; Bo-Ling, G.; Shou-Feng, S., Homoclinic orbits of the davey – stewartson equation, Applied mathematics and mechanics, 26, 2, 139-141, (2005) · Zbl 1144.76306 [8] Taimanov, I.A., Surfaces in the four-space and the davey – stewartson equations, Journal of geometry and physics, 56, 8, 1235-1256, (2006) · Zbl 1103.53031 [9] Wang, Y., The Cauchy problem for the elliptic – hyperbolic davey – stewartson system in Sobolev space, Journal of mathematical analysis and applications, 367, 1, 174-192, (2010) · Zbl 1196.35017 [10] Zhao, X., Self-similar solutions to a generalized davey – stewartson system, Mathematical and computer modelling, 50, 9-10, 1394-1399, (2009) · Zbl 1185.35272
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zbMATH — the first resource for mathematics

Bandle, Catherine

Compute Distance To:
 Author ID: bandle.catherine Published as: Bandle, C.; Bandle, Catherina; Bandle, Catherine External Links: MGP · Math-Net.Ru · Wikidata · dblp · GND
 Documents Indexed: 172 Publications since 1967, including 11 Books Reviewing Activity: 59 Reviews
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Co-Authors

 58 single-authored 20 Marcus, Moshe M. 9 Wagner, Alfred 8 Chipot, Michel 8 Pozio, Maria Assunta 6 Reichel, Wolfgang 6 Stakgold, Ivar 5 Shafrir, Itai 5 Tesei, Alberto 4 Bemelmans, Josef 4 Flucher, Martin 4 Kabeya, Yoshitsugu 4 Levine, Howard Allen 4 Peletier, Lambertus Adrianus 4 Saint Jean Paulin, Jeannine 3 Brillard, Alain 3 Losonczi, László 3 Moroz, Vitaly 3 Punzo, Fabio 3 Sperb, Rene P. 2 Amann, Herbert 2 Brauner, Claude-Michel 2 Brunner, Hermann 2 Conrad, Francis 2 Diaz Diaz, Jesus Ildefonso 2 Dozzi, Marco E. 2 Essén, Matts Raguel 2 Gilányi, Attila 2 Grüter, Michael 2 Hersch, Joseph 2 Monticelli, Dario Daniele 2 Mossino, Jacqueline 2 Ninomiya, Hirokazu 2 Plum, Michael 2 Porru, Giovanni 2 Stingelin, Simon 2 von Below, Joachim 2 Wei, Juncheng 1 Benguria, Rafael D. 1 Berestycki, Henri 1 Bordag, Ljudmila A. 1 Brighi, Bernard 1 Buonocore, Pasquale 1 Coffman, Charles V. 1 Coron, Jean-Michel 1 de Thélin, François 1 Diaz, Gregorio 1 Everitt, William Norrie 1 Fleckinger, Jacqueline 1 Fontelos López, Marco Antonio 1 Giarrusso, Ester 1 González, María del Mar 1 Greco, Antonio 1 Klötzler, Rolf 1 Kwong, Man Kam 1 Leutwiler, Heinz 1 Mastrolia, Paolo 1 Nanbu, Tokumori 1 Páles, Zsolt 1 Philippin, Gérard A. 1 Sbordone, Carlo 1 Scarpellini, Bruno 1 Schmidt-Lainé, Claudine 1 Schott, René 1 Valente, Vanda 1 Vergara Caffarelli, Giorgio 1 Vernier-Piro, Stella 1 Walter, Wolfgang 1 Wolanski, Noemi I. 1 Zemp, Beat 1 Zhang, Qi-Shuhuason
all top 5

Serials

 11 ZAMP. Zeitschrift für angewandte Mathematik und Physik 8 Journal of Mathematical Analysis and Applications 8 SIAM Journal on Mathematical Analysis 8 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 7 Comptes Rendus de l’Académie des Sciences. Série I 5 Journal of Differential Equations 4 Transactions of the American Mathematical Society 4 Nonlinear Analysis. Theory, Methods & Applications 3 Archive for Rational Mechanics and Analysis 3 Journal d’Analyse Mathématique 3 Commentarii Mathematici Helvetici 3 Mathematische Zeitschrift 3 ISNM. International Series of Numerical Mathematics 3 Advances in Nonlinear Analysis 2 Applicable Analysis 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Mathematische Annalen 2 Mathematische Nachrichten 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Pacific Journal of Mathematics 2 Proceedings of the American Mathematical Society 2 Zeitschrift für Analysis und ihre Anwendungen 2 Differential and Integral Equations 2 Communications in Partial Differential Equations 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 SIAM Journal on Applied Mathematics 2 Journal of Convex Analysis 1 Israel Journal of Mathematics 1 Mathematical Methods in the Applied Sciences 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Funkcialaj Ekvacioj. Serio Internacia 1 Journal of Computational and Applied Mathematics 1 Journal of the London Mathematical Society. Second Series 1 Journal of Optimization Theory and Applications 1 Journal für die Reine und Angewandte Mathematik 1 Ricerche di Matematica 1 SIAM Journal on Numerical Analysis 1 Delft Progress Report 1 Complex Variables. Theory and Application 1 Stochastic Analysis and Applications 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 1 Aequationes Mathematicae 1 Mitteilungen der Mathematischen Gesellschaft in Hamburg 1 Nova Acta Leopoldina. Neue Folge 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales de Madrid 1 SIAM Review 1 Expositiones Mathematicae 1 Notices of the American Mathematical Society 1 Bollettino della Unione Matemàtica Italiana. Serie VII. B 1 Advances in Mathematical Sciences and Applications 1 Calculus of Variations and Partial Differential Equations 1 St. Petersburg Mathematical Journal 1 Analele Universităţii din Craiova. Seria Matematică Informatică 1 Advances in Differential Equations 1 Journal of the European Mathematical Society (JEMS) 1 Communications on Pure and Applied Analysis 1 Banach Journal of Mathematical Analysis 1 Progress in Nonlinear Differential Equations and Their Applications
all top 5

Fields

 143 Partial differential equations (35-XX) 29 Calculus of variations and optimal control; optimization (49-XX) 12 Convex and discrete geometry (52-XX) 11 Ordinary differential equations (34-XX) 9 General and overarching topics; collections (00-XX) 9 Operator theory (47-XX) 9 Global analysis, analysis on manifolds (58-XX) 8 Numerical analysis (65-XX) 7 Differential geometry (53-XX) 6 Real functions (26-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Functions of a complex variable (30-XX) 4 History and biography (01-XX) 4 Fluid mechanics (76-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Potential theory (31-XX) 3 Functional analysis (46-XX) 2 Integral equations (45-XX) 2 Geometry (51-XX) 2 Probability theory and stochastic processes (60-XX) 2 Mechanics of deformable solids (74-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Measure and integration (28-XX) 1 Special functions (33-XX) 1 Difference and functional equations (39-XX) 1 Algebraic topology (55-XX) 1 Astronomy and astrophysics (85-XX)

Citations contained in zbMATH

133 Publications have been cited 1,963 times in 1,365 Documents Cited by Year
Isoperimetric inequalities and applications. Zbl 0436.35063
Bandle, Catherine
1980
‘Large’ solutions of semilinear elliptic equations: Existence, uniqueness and asymptotic behaviour. Zbl 0802.35038
Bandle, Catherine; Marcus, Moshe
1992
Blowup in diffusion equations: A survey. Zbl 0932.65098
Bandle, Catherine; Brunner, Hermann
1998
On the existence and nonexistence of global solutions of reaction- diffusion equations in sectorial domains. Zbl 0693.35081
Bandle, Catherine; Levine, Howard A.
1989
Nonlinear elliptic problems in annular domains. Zbl 0618.35043
Bandle, C.; Coffman, C. V.; Marcus, M.
1987
Asymptotic behaviour of solutions and their derivatives, for semilinear elliptic problems with blowup on the boundary. Zbl 0840.35033
Bandle, Catherine; Marcus, Moshe
1995
Boundary blow up for semilinear elliptic equations with nonlinear gradient terms. Zbl 0840.35034
Bandle, Catherine; Giarrusso, Ester
1996
On second-order effects in the boundary behaviour of large solutions of semilinear elliptic problems. Zbl 1042.35535
Bandle, Catherine; Marcus, Moshe
1998
Semilinear elliptic problems in annular domains. Zbl 0687.35036
Bandle, C.; Kwong, Man Kam
1989
Harmonic radius and concentration of energy; hyperbolic radius and Liouville’s equations $$\Delta U=e^ U$$ and $$\Delta U=U^{n+2\over n-2}$$. Zbl 0857.35034
Bandle, C.; Flucher, M.
1996
Existence theorems, qualitative results and priori bounds for a class of non-linear Dirichlet problems. Zbl 0335.35046
Bandle, Catherine
1975
The formation of the dead core in parabolic reaction-diffusion problems. Zbl 0519.35042
Bandle, Catherine; Stakgold, Ivar
1984
Diffusion and reaction with monotone kinetics. Zbl 0545.35011
Bandle, C.; Sperb, R. P.; Stakgold, I.
1984
Existence and uniqueness of solutions of nonlinear Neumann problems. Zbl 0633.35042
Bandle, C.; Pozio, M. A.; Tesei, A.
1988
On the solutions of quasilinear elliptic problems with boundary blow-up. Zbl 0806.35045
Bandle, Catherine; Essén, Matts
1994
Sur les solutions maximales de problèmes elliptiques nonlinéaires: Bornes isopérimétriques et comportement asymptotique. (Maximal solutions in nonlinear elliptic problems: Isoperimetric estimates and asymptotic behaviour). Zbl 0726.35041
Bandle, Catherine; Marcus, Moshe
1990
Dependence of blowup rate of large solutions of semilinear elliptic equations, on the curvature of the boundary. Zbl 1129.35312
Bandle, Catherine; Marcus, Moshe
2004
Asymptotic behaviour of large solutions of quasilinear elliptic problems. Zbl 1099.35505
Bandle, C.
2003
The asymptotic behavior of the solutions of degenerate parabolic equations. Zbl 0633.35041
Bandle, Catherine; Pozio, M. A.; Tesei, Alberto
1987
Critical exponents of Fujita type for inhomogeneous parabolic equations and systems. Zbl 0968.35019
Bandle, C.; Levine, H. A.; Zhang, Qi S.
2000
On positive solutions of Emden equations in cone-like domains. Zbl 0727.35051
Bandle, Catherine; Essén, Matts
1990
On symmetrizations in parabolic equations. Zbl 0331.35036
Bandle, Catherine
1976
The Brézis-Nirenberg problem on $$\mathbb{S}^3$$. Zbl 0995.35027
Bandle, Catherine; Benguria, Rafael
2002
‘Boundary blowup’ type sub-solutions to semilinear elliptic equations with Hardy potential. Zbl 1141.35022
Bandle, Catherine; Moroz, Vitaly; Reichel, Wolfgang
2008
Green’s function, harmonic transplantation, and best Sobolev constant in spaces of constant curvature. Zbl 0912.35065
Bandle, C.; Brillard, A.; Flucher, M.
1998
Best Sobolev constants and Emden equations for the critical exponent in $$S^3$$. Zbl 0932.49023
Bandle, C.; Peletier, L. A.
1999
The Fujita exponent for the Cauchy problem in the hyperbolic space. Zbl 1227.35052
Bandle, Catherine; Pozio, Maria Assunta; Tesei, Alberto
2011
Numerical analysis of semilinear parabolic problems with blow-up solutions. Zbl 0862.65053
Bandle, C.; Brunner, H.
1994
The positive radial solutions of a class of semilinear elliptic equations. Zbl 0676.35033
Bandle, Catherine; Marcus, Moshe
1989
Parabolic problems with dynamical boundary conditions: eigenvalue expansions and blow up. Zbl 1223.35187
Bandle, Catherine; von Below, Joachim; Reichel, Wolfgang
2006
Asymptotic behavior of large solutions of elliptic equations. Zbl 1120.35014
Bandle, Catherine
2005
Large solutions of quasilinear elliptic equations: Existence and qualitative properties. Zbl 0887.35056
Bandle, Catherine; Greco, Antonio; Porru, Giovanni
1997
Konstruktion isoperimetrischer Ungleichungen der mathematischen Physik aus solchen der Geometrie. Zbl 0219.52008
Bandle, C.
1971
Existence and nonexistence of patterns on Riemannian manifolds. Zbl 1245.58010
Bandle, Catherine; Punzo, Fabio; Tesei, Alberto
2012
Nonlinear elliptic problems with critical exponent in shrinking annuli. Zbl 0619.35044
Bandle, C.; Peletier, L. A.
1988
Second domain variation for problems with Robin boundary conditions. Zbl 1329.49082
Bandle, Catherine; Wagner, Alfred
2015
On the positive, “radial” solutions of a semilinear elliptic equation in $$\mathbb {H}^N$$. Zbl 1277.35147
Bandle, Catherine; Kabeya, Yoshitsugu
2012
Large solutions to semilinear elliptic equations with Hardy potential and exponential nonlinearity. Zbl 1187.35080
Bandle, Catherine; Moroz, Vitaly; Reichel, Wolfgang
2010
Solutions of quasilinear second-order elliptic boundary value problems via degree theory. Zbl 1129.35367
Bandle, Catherine; Reichel, Wolfgang
2004
Fujita type results for convective-like reaction diffusion equations in exterior domains. Zbl 0697.76099
Bandle, Catherine; Levine, Howard A.
1989
Über das Stekloffsche Eigenwertproblem: Isoperimetrische Ungleichungen für symmetrische Gebiete. Zbl 0157.42802
Bandle, C.
1968
Multiple clustered layer solutions for semilinear elliptic problems on S$$^n$$. Zbl 1196.35107
Bandle, Catherine; Wei, Juncheng
2008
Porous medium equation with absorption. Zbl 0935.35083
Bandle, Catherine; Nanbu, Tokumori; Stakgold, Ivar
1998
On a quasilinear elliptic equation and a Riemannian metric invariant under Möbius transformations. Zbl 0763.35033
Bandle, Catherine; Leutwiler, Heinz
1991
A priori estimates and the boundary values of solutions for a problem arising in plasma physics. Zbl 0509.35032
Bandle, Catherine; Marcus, Moshe
1983
Bounds for the solutions of boundary value problems. Zbl 0327.35007
Bandle, Catherine
1976
Applications of Rellich’s perturbation theory to a classical boundary and eigenvalue problem. Zbl 0278.35069
Bandle, Catherine; Sperb, Rene P.
1973
On the stability of solutions of semilinear elliptic equations with Robin boundary conditions on Riemannian manifolds. Zbl 1338.35175
Bandle, C.; Mastrolia, P.; Monticelli, D. D.; Punzo, F.
2016
Non-radial clustered spike solutions for semilinear elliptic problems on $$S^N$$. Zbl 1132.35363
Bandle, Catherine; Wei, Juncheng
2007
A linear parabolic problem with non-dissipative dynamical boundary conditions. Zbl 1141.35386
Bandle, C.; Reichel, W.
2006
Table of inequalities in elliptic boundary value problems. Zbl 0914.35042
Bandle, C.; Flucher, M.
1998
Solutions of reaction-diffusion equations blowing up on the parabolic boundary. Zbl 0802.35076
Bandle, Catherine; Díaz, Gregorio; Díaz, Jesús Ildefonso
1994
Fujita type phenomena for reaction-diffusion equations with convection like terms. Zbl 0811.35044
Bandle, Catherine; Levine, Howard A.
1994
On isoperimetric gradient bounds for Poisson problems and problems of torsional creep. Zbl 0436.35026
Bandle, Catherine
1979
Boundary singularities of solutions of semilinear elliptic equations in the half-space with a Hardy potential. Zbl 1381.35045
Bandle, Catherine; Marcus, Moshe; Moroz, Vitaly
2017
Rayleigh-Faber-Krahn inequalities and quasilinear elliptic boundary value problems. Zbl 1162.35363
Bandle, Catherine
2003
Estimates for solutions of quasilinear problems with dead cores. Zbl 1039.35031
Bandle, Catherina; Vernier-Piro, Stella
2003
On a differential inequality and its applications to geometry. Zbl 0316.35009
Bandle, Catherine
1976
Extremaleigenschaften von Kreissektoren und Halbkugeln. (Extremal properties of sectors of a circle and hemispheres). Zbl 0221.52006
Bandle, Catherine
1971
Isoperimetric inequalities for the principal eigenvalue of a membrane and the energy of problems with Robin boundary conditions. Zbl 1328.49041
Bandle, Catherine; Wagner, Alfred
2015
Sublinear elliptic problems with a Hardy potential. Zbl 1318.35049
Bandle, Catherine; Pozio, Maria Assunta
2015
Imperfect bifurcations in nonlinear elliptic equations on spherical caps. Zbl 1202.35096
Bandle, Catherine; Kabeya, Yoshitsugu; Ninomiya, Hirokazu
2010
Equivalence classes for Emden equations. Zbl 1011.34037
Bandle, Catherine; Bordag, Ljudmila A.
2002
Extremal problems for eigenvalues of the Sturm-Liouville type. Zbl 0638.34019
Bandle, Catherine
1987
Comparison theorems for a class of nonlinear Dirichlet problems. Zbl 0362.35034
Bandle, Catherine; Marcus, Moshe
1977
Isoperimetric inequalities for a class of nonlinear parabolic equations. Zbl 0324.35051
Bandle, Catherine
1976
Problèmes de Dirichlet non linéaires: une condition suffisante isoperimetrique pour l’existence d’une solution. Zbl 0298.35026
Bandle, Catherine; Hersch, Joseph
1975
Bounds for the solutions of Poisson problems and applications to nonlinear eigenvalue problems. Zbl 0291.35024
Bandle, Catherine
1975
Mean value theorems for functions satisfying the inequality $$\Delta u +Ke^u \geq 0$$. Zbl 0257.35039
Bandle, Catherine
1973
Radial averaging transformations with various metrics. Zbl 0256.53048
Bandle, Catherine; Marcus, Moshe
1973
Isoperimetric inequality for some eigenvalues of an inhomogeneous, free membrane. Zbl 0237.35069
Bandle, Catherine
1972
Extensions of an inequality by Pólya and Schiffer for vibrating membranes. Zbl 0217.13301
Bandle, C.
1972
Large solutions of semilinear elliptic equations with ‘singular’ coefficients. Zbl 0795.35023
Bandle, C.; Marcus, M.
1992
Singular perturbation method in a parabolic problem with free boundary. Zbl 0674.35041
Bandle, Catherine; Brauner, Claude-Michel
1986
Problèmes de Dirichlet non-linéaires dans des anneaux. (Nonlinear Dirichlet problems in annuli). Zbl 0608.35019
1986
Qualitative behavior and bounds in a nonlinear plasma problem. Zbl 0519.35030
Bandle, Catherine; Sperb, Rene P.
1983
On the boundary values of solutions of a problem arising in plasma physics. Zbl 0509.35031
Bandle, Catherine; Marcus, Moshe
1982
Un théorème de comparaison pour un problème elliptique avec une non- linearite singuliere. Zbl 0402.35010
Bandle, Catherine; Marcus, Moshe
1978
Estimates for the Green’s functions of elliptic operators. Zbl 0401.35005
Bandle, Catherine
1978
Isoperimetric inequalities for a nonlinear eigenvalue problem. Zbl 0326.35004
Bandle, Catherine
1976
Radial averaging transformations and generalized capacities. Zbl 0308.31003
Bandle, Catherine; Marcus, Moshe
1975
Symetrisation et équations paraboliques. Zbl 0299.35051
Bandle, Catherine
1975
Sur un problème de Dirichlet non linéaire. Zbl 0249.35031
Bandle, Catherine
1973
Shape optimization for an elliptic operator with infinitely many positive and negative eigenvalues. Zbl 1385.49011
Bandle, Catherine; Wagner, Alfred
2018
Domain perturbations for elliptic problems with Robin boundary conditions of opposite sign. Zbl 1360.35126
Bandle, C.; Wagner, A.
2017
Domain derivatives for energy functionals with boundary integrals. Zbl 1253.49030
Bandle, Catherine; Wagner, Alfred
2012
A Rayleigh-Faber-Krahn inequality and some monotonicity properties for eigenvalue problems with mixed boundary conditions. Zbl 1266.35118
Bandle, Catherine
2009
Positivity and anti-maximum principles for elliptic operators with mixed boundary conditions. Zbl 1167.35012
Bandle, C.; von Below, J.; Reichel, W.
2008
Optimization problems for weighted Sobolev constants. Zbl 1118.49004
Bandle, Catherine; Wagner, Alfred
2007
Nonlinear elliptic equations involving critical Sobolev exponents: Asymptotic analysis via methods of epi-convergence. Zbl 0808.35031
Bandle, C.; Brillard, A.
1994
Solutions of semilinear elliptic problems in shrinking annuli. Zbl 0702.35088
Bandle, Catherine; Marcus, Moshe
1990
Blow up in exterior domains. Zbl 0699.35120
Bandle, C.
1989
Nonlinear parabolic equations with sinks and sources. Zbl 0685.35058
Bandle, Catherine; Pozio, Maria Assunta
1988
Reaction-diffusion and dead cores. Zbl 0594.35058
Bandle, C.; Stakgold, I.
1985
A note on optimal domains in a reaction-diffusion problem. Zbl 0578.35046
Bandle, C.
1985
Rearrangement in variational inequalities. Zbl 0563.49005
Bandle, C.; Mossino, J.
1984
Application du réarrangement à une inéquation variationnelle. Zbl 0534.49006
Bandle, Catherine; Mossino, Jacqueline
1983
Remarks on plasma problems with nonmonotone nonlinearities. Zbl 0509.35033
Bandle, Catherine; Marcus, Moshe
1983
On the size of the plasma region. Zbl 0494.35040
Bandle, Catherine; Marcus, Moshe
1983
Abschätzung der Randwerte bei nichtlinearen elliptischen Gleichungen aus der Plasmaphysik. Zbl 0469.76115
Bandle, Catherine
1981
Shape optimization for an elliptic operator with infinitely many positive and negative eigenvalues. Zbl 1385.49011
Bandle, Catherine; Wagner, Alfred
2018
A nonlocal diffusion problem on manifolds. Zbl 1405.35066
Bandle, Catherine; del Mar González, María; Fontelos, Marco A.; Wolanski, Noemi
2018
Boundary singularities of solutions of semilinear elliptic equations in the half-space with a Hardy potential. Zbl 1381.35045
Bandle, Catherine; Marcus, Moshe; Moroz, Vitaly
2017
Domain perturbations for elliptic problems with Robin boundary conditions of opposite sign. Zbl 1360.35126
Bandle, C.; Wagner, A.
2017
Dido’s problem and its impact on modern mathematics. Zbl 1395.01010
Bandle, Catherine
2017
On the stability of solutions of semilinear elliptic equations with Robin boundary conditions on Riemannian manifolds. Zbl 1338.35175
Bandle, C.; Mastrolia, P.; Monticelli, D. D.; Punzo, F.
2016
Second domain variation for problems with Robin boundary conditions. Zbl 1329.49082
Bandle, Catherine; Wagner, Alfred
2015
Isoperimetric inequalities for the principal eigenvalue of a membrane and the energy of problems with Robin boundary conditions. Zbl 1328.49041
Bandle, Catherine; Wagner, Alfred
2015
Sublinear elliptic problems with a Hardy potential. Zbl 1318.35049
Bandle, Catherine; Pozio, Maria Assunta
2015
Large solutions in cylindrical domains. Zbl 1304.35032
Bandle, Catherine; Chipot, Michel
2013
Erratum: “On the positive, ‘radial’ solutions of a semilinear elliptic equation in $$\mathbb H^N$$”. Zbl 1277.35146
Bandle, Catherine; Kabeya, Yoshitsugu
2013
Existence and nonexistence of patterns on Riemannian manifolds. Zbl 1245.58010
Bandle, Catherine; Punzo, Fabio; Tesei, Alberto
2012
On the positive, “radial” solutions of a semilinear elliptic equation in $$\mathbb {H}^N$$. Zbl 1277.35147
Bandle, Catherine; Kabeya, Yoshitsugu
2012
Domain derivatives for energy functionals with boundary integrals. Zbl 1253.49030
Bandle, Catherine; Wagner, Alfred
2012
The Fujita exponent for the Cauchy problem in the hyperbolic space. Zbl 1227.35052
Bandle, Catherine; Pozio, Maria Assunta; Tesei, Alberto
2011
Large solutions to semilinear elliptic equations with Hardy potential and exponential nonlinearity. Zbl 1187.35080
Bandle, Catherine; Moroz, Vitaly; Reichel, Wolfgang
2010
Imperfect bifurcations in nonlinear elliptic equations on spherical caps. Zbl 1202.35096
Bandle, Catherine; Kabeya, Yoshitsugu; Ninomiya, Hirokazu
2010
A Rayleigh-Faber-Krahn inequality and some monotonicity properties for eigenvalue problems with mixed boundary conditions. Zbl 1266.35118
Bandle, Catherine
2009
Optimization problems for an energy functional with mass constraint revisited. Zbl 1158.49042
Bandle, Catherine; Wagner, Alfred
2009
‘Boundary blowup’ type sub-solutions to semilinear elliptic equations with Hardy potential. Zbl 1141.35022
Bandle, Catherine; Moroz, Vitaly; Reichel, Wolfgang
2008
Multiple clustered layer solutions for semilinear elliptic problems on S$$^n$$. Zbl 1196.35107
Bandle, Catherine; Wei, Juncheng
2008
Positivity and anti-maximum principles for elliptic operators with mixed boundary conditions. Zbl 1167.35012
Bandle, C.; von Below, J.; Reichel, W.
2008
An eigenvalue problem with mixed boundary conditions and trace theorems. Zbl 1141.35040
Bandle, Catherine
2008
Non-radial clustered spike solutions for semilinear elliptic problems on $$S^N$$. Zbl 1132.35363
Bandle, Catherine; Wei, Juncheng
2007
Optimization problems for weighted Sobolev constants. Zbl 1118.49004
Bandle, Catherine; Wagner, Alfred
2007
Parabolic problems with dynamical boundary conditions: eigenvalue expansions and blow up. Zbl 1223.35187
Bandle, Catherine; von Below, Joachim; Reichel, Wolfgang
2006
A linear parabolic problem with non-dissipative dynamical boundary conditions. Zbl 1141.35386
Bandle, C.; Reichel, W.
2006
Sobolev constants in disconnected domains. Zbl 1366.49006
Bandle, Catherine; Wagner, Alfred
2006
Asymptotic behavior of large solutions of elliptic equations. Zbl 1120.35014
Bandle, Catherine
2005
Best Sobolev constants and quasi-linear elliptic equations with critical growth on spheres. Zbl 1330.35166
Bandle, C.; Peletier, L. A.; Stingelin, S.
2005
Dependence of blowup rate of large solutions of semilinear elliptic equations, on the curvature of the boundary. Zbl 1129.35312
Bandle, Catherine; Marcus, Moshe
2004
Solutions of quasilinear second-order elliptic boundary value problems via degree theory. Zbl 1129.35367
Bandle, Catherine; Reichel, Wolfgang
2004
Asymptotic behaviour of large solutions of quasilinear elliptic problems. Zbl 1099.35505
Bandle, C.
2003
Rayleigh-Faber-Krahn inequalities and quasilinear elliptic boundary value problems. Zbl 1162.35363
Bandle, Catherine
2003
Estimates for solutions of quasilinear problems with dead cores. Zbl 1039.35031
Bandle, Catherina; Vernier-Piro, Stella
2003
The Brézis-Nirenberg problem on $$\mathbb{S}^3$$. Zbl 0995.35027
Bandle, Catherine; Benguria, Rafael
2002
Equivalence classes for Emden equations. Zbl 1011.34037
Bandle, Catherine; Bordag, Ljudmila A.
2002
Boundary value problems for the $$q$$-Laplacian on $$\mathbb{S}^N$$. Zbl 1002.35034
Bandle, C.; Fleckinger, J.; de Thélin, F.
2001
Critical exponents of Fujita type for inhomogeneous parabolic equations and systems. Zbl 0968.35019
Bandle, C.; Levine, H. A.; Zhang, Qi S.
2000
Best Sobolev constants and Emden equations for the critical exponent in $$S^3$$. Zbl 0932.49023
Bandle, C.; Peletier, L. A.
1999
Blowup in diffusion equations: A survey. Zbl 0932.65098
Bandle, Catherine; Brunner, Hermann
1998
On second-order effects in the boundary behaviour of large solutions of semilinear elliptic problems. Zbl 1042.35535
Bandle, Catherine; Marcus, Moshe
1998
Green’s function, harmonic transplantation, and best Sobolev constant in spaces of constant curvature. Zbl 0912.35065
Bandle, C.; Brillard, A.; Flucher, M.
1998
Porous medium equation with absorption. Zbl 0935.35083
Bandle, Catherine; Nanbu, Tokumori; Stakgold, Ivar
1998
Table of inequalities in elliptic boundary value problems. Zbl 0914.35042
Bandle, C.; Flucher, M.
1998
Large solutions of quasilinear elliptic equations: Existence and qualitative properties. Zbl 0887.35056
Bandle, Catherine; Greco, Antonio; Porru, Giovanni
1997
Boundary blow up for semilinear elliptic equations with nonlinear gradient terms. Zbl 0840.35034
Bandle, Catherine; Giarrusso, Ester
1996
Harmonic radius and concentration of energy; hyperbolic radius and Liouville’s equations $$\Delta U=e^ U$$ and $$\Delta U=U^{n+2\over n-2}$$. Zbl 0857.35034
Bandle, C.; Flucher, M.
1996
Blow up behaviour of a stochastic partial differential equation of reaction-diffusion type. Zbl 0866.60052
Bandle, C.; Dozzi, M.; Schott, R.
1996
Asymptotic behaviour of solutions and their derivatives, for semilinear elliptic problems with blowup on the boundary. Zbl 0840.35033
Bandle, Catherine; Marcus, Moshe
1995
On the solutions of quasilinear elliptic problems with boundary blow-up. Zbl 0806.35045
Bandle, Catherine; Essén, Matts
1994
Numerical analysis of semilinear parabolic problems with blow-up solutions. Zbl 0862.65053
Bandle, C.; Brunner, H.
1994
Solutions of reaction-diffusion equations blowing up on the parabolic boundary. Zbl 0802.35076
Bandle, Catherine; Díaz, Gregorio; Díaz, Jesús Ildefonso
1994
Fujita type phenomena for reaction-diffusion equations with convection like terms. Zbl 0811.35044
Bandle, Catherine; Levine, Howard A.
1994
Nonlinear elliptic equations involving critical Sobolev exponents: Asymptotic analysis via methods of epi-convergence. Zbl 0808.35031
Bandle, C.; Brillard, A.
1994
Comparison theorems for stochastic differential inequalities and an application to reaction-diffusion equations with random sources. Zbl 0796.60063
Bandle, Catherine; Dozzi, Marco
1994
‘Large’ solutions of semilinear elliptic equations: Existence, uniqueness and asymptotic behaviour. Zbl 0802.35038
Bandle, Catherine; Marcus, Moshe
1992
Large solutions of semilinear elliptic equations with ‘singular’ coefficients. Zbl 0795.35023
Bandle, C.; Marcus, M.
1992
Positive solutions of Emden equations in cone-like domains. Zbl 0795.35029
Bandle, Catherine
1992
A stability analysis for semilinear Neumann problems with concave non- linearities. Zbl 0801.35055
Bandle, C.; Brauner, C. M.; Schmidt-Lainé, C.
1992
On a quasilinear elliptic equation and a Riemannian metric invariant under Möbius transformations. Zbl 0763.35033
Bandle, Catherine; Leutwiler, Heinz
1991
Sur les solutions maximales de problèmes elliptiques nonlinéaires: Bornes isopérimétriques et comportement asymptotique. (Maximal solutions in nonlinear elliptic problems: Isoperimetric estimates and asymptotic behaviour). Zbl 0726.35041
Bandle, Catherine; Marcus, Moshe
1990
On positive solutions of Emden equations in cone-like domains. Zbl 0727.35051
Bandle, Catherine; Essén, Matts
1990
Solutions of semilinear elliptic problems in shrinking annuli. Zbl 0702.35088
Bandle, Catherine; Marcus, Moshe
1990
On the existence and nonexistence of global solutions of reaction- diffusion equations in sectorial domains. Zbl 0693.35081
Bandle, Catherine; Levine, Howard A.
1989
Semilinear elliptic problems in annular domains. Zbl 0687.35036
Bandle, C.; Kwong, Man Kam
1989
The positive radial solutions of a class of semilinear elliptic equations. Zbl 0676.35033
Bandle, Catherine; Marcus, Moshe
1989
Fujita type results for convective-like reaction diffusion equations in exterior domains. Zbl 0697.76099
Bandle, Catherine; Levine, Howard A.
1989
Blow up in exterior domains. Zbl 0699.35120
Bandle, C.
1989
Existence and uniqueness of solutions of nonlinear Neumann problems. Zbl 0633.35042
Bandle, C.; Pozio, M. A.; Tesei, A.
1988
Nonlinear elliptic problems with critical exponent in shrinking annuli. Zbl 0619.35044
Bandle, C.; Peletier, L. A.
1988
Nonlinear parabolic equations with sinks and sources. Zbl 0685.35058
Bandle, Catherine; Pozio, Maria Assunta
1988
Nonlinear elliptic problems in annular domains. Zbl 0618.35043
Bandle, C.; Coffman, C. V.; Marcus, M.
1987
The asymptotic behavior of the solutions of degenerate parabolic equations. Zbl 0633.35041
Bandle, Catherine; Pozio, M. A.; Tesei, Alberto
1987
Extremal problems for eigenvalues of the Sturm-Liouville type. Zbl 0638.34019
Bandle, Catherine
1987
On a reaction-diffusion problem with a dead core. Zbl 0661.35049
Bandle, C.
1987
Problème de Neumann non linéaires de types elliptique et parabolique. (Nonlinear Neumann problems of elliptic and parabolic type). Zbl 0638.35033
Bandle, Catherine; Pozio, Maria A.; Tesei, Alberto
1987
Singular perturbation method in a parabolic problem with free boundary. Zbl 0674.35041
Bandle, Catherine; Brauner, Claude-Michel
1986
Problèmes de Dirichlet non-linéaires dans des anneaux. (Nonlinear Dirichlet problems in annuli). Zbl 0608.35019
1986
Reaction-diffusion and dead cores. Zbl 0594.35058
Bandle, C.; Stakgold, I.
1985
A note on optimal domains in a reaction-diffusion problem. Zbl 0578.35046
Bandle, C.
1985
Nonlinear boundary value problems in annular domains. Zbl 0608.35018
Bandle, Catherine
1985
The formation of the dead core in parabolic reaction-diffusion problems. Zbl 0519.35042
Bandle, Catherine; Stakgold, Ivar
1984
Diffusion and reaction with monotone kinetics. Zbl 0545.35011
Bandle, C.; Sperb, R. P.; Stakgold, I.
1984
Rearrangement in variational inequalities. Zbl 0563.49005
Bandle, C.; Mossino, J.
1984
Isoperimetric inequality for the effectiveness in semilinear parabolic problems. Zbl 0592.35069
Bandle, Catherine; Stakgold, Ivar
1984
The formation of the dead core in parabolic reaction-diffusion problems. Zbl 0526.35045
Stakgold, Ivar; Bandle, Catherine
1984
A priori estimates and the boundary values of solutions for a problem arising in plasma physics. Zbl 0509.35032
Bandle, Catherine; Marcus, Moshe
1983
Qualitative behavior and bounds in a nonlinear plasma problem. Zbl 0519.35030
Bandle, Catherine; Sperb, Rene P.
1983
Application du réarrangement à une inéquation variationnelle. Zbl 0534.49006
Bandle, Catherine; Mossino, Jacqueline
1983
Remarks on plasma problems with nonmonotone nonlinearities. Zbl 0509.35033
Bandle, Catherine; Marcus, Moshe
1983
On the size of the plasma region. Zbl 0494.35040
Bandle, Catherine; Marcus, Moshe
1983
Isoperimetric inequalities. Zbl 0519.53037
Bandle, Catherine
1983
On the boundary values of solutions of a problem arising in plasma physics. Zbl 0509.35031
Bandle, Catherine; Marcus, Moshe
1982
Estimates for the boundary values of the solutions of certain nonlinear elliptic equations. Zbl 0502.35042
Bandle, Catherine
1982
Abschätzung der Randwerte bei nichtlinearen elliptischen Gleichungen aus der Plasmaphysik. Zbl 0469.76115
Bandle, Catherine
1981
Sur une classe de problèmes apparaissant en physique des plasmas. Zbl 0484.35036
Bandle, Catherine; Marcus, Moshe
1981
A priori bounds for a class of nonlinear elliptic equations and applications to physical problems. Zbl 0454.35020
Bandle, Catherine
1981
Isoperimetric inequalities and applications. Zbl 0436.35063
Bandle, Catherine
1980
On isoperimetric gradient bounds for Poisson problems and problems of torsional creep. Zbl 0436.35026
Bandle, Catherine
1979
...and 33 more Documents
all top 5

Cited by 1,305 Authors

 55 Bandle, Catherine 28 Marcus, Moshe M. 26 García-Melián, Jorge 22 Rossi, Julio Daniel 22 Zhang, Zhijun 17 Payne, Lawrence Edward 15 Agarwal, Ravi P. 15 Véron, Laurent 14 López-Gómez, Julián 12 Diaz Diaz, Jesus Ildefonso 12 Porru, Giovanni 12 Sperb, Rene P. 12 Wang, Mingxin 12 Wong, Patricia J. Y. 11 Brock, Friedemann 11 Chiacchio, Francesco 11 Ferone, Vincenzo 11 Laugesen, Richard Snyder 11 Levine, Howard Allen 11 Mohammed, Ahmed 11 Philippin, Gérard A. 11 Siudeja, Bartłomiej Andrzej 11 Vazquez, Juan Luis 10 Boscaggin, Alberto 10 Guo, Zongming 10 Quaas, Alexander 10 Sabina-de-Lis, José Claudio 10 Wei, Juncheng 10 Wong, Fu-Hsiang 9 Avkhadiev, Farit Gabidinovich 9 Bartolucci, Daniele 9 Benguria, Rafael D. 9 Giarrusso, Ester 9 Groisman, Pablo 9 Henderson, Johnny 9 Huang, Shuibo 9 Punzo, Fabio 9 Samet, Bessem 9 Zheng, Sining 8 Alvino, Angelo 8 Bobisud, Larry E. 8 Ding, Juntang 8 Grossi, Massimo 8 Jleli, Mohamed 8 Lin, Chang-Shou 8 Lions, Pierre-Louis 8 Rădulescu, Vicenţiu D. 8 Ramos Quoirin, Humberto 8 Tian, Qiaoyu 8 Umezu, Kenichiro 8 Volzone, Bruno 8 Yang, Zuodong 7 Alarcón, Salomón 7 Bañuelos, Rodrigo 7 Chen, Yujuan 7 Cîrstea, Florica-Corina Şt. 7 Kawohl, Bernd 7 Mercaldo, Anna 7 Nguyen Phuoc Tai 7 Posteraro, Maria Rosaria 7 Rakotoson, Jean-Michel 7 Reichel, Wolfgang 7 Salakhudinov, Rustem Gumerovich 7 Wagner, Alfred 7 Wang, Haiyan 7 Zanolin, Fabio 6 Cosner, Chris 6 Feltrin, Guglielmo 6 Kaufmann, Uriel 6 Li, Fengjie 6 Lin, Song-Sun 6 Liu, Bingchen 6 Peletier, Lambertus Adrianus 6 Pinsky, Ross George 6 Pozio, Maria Assunta 6 Schmitt, Klaus 6 Sirakov, Boyan Slavchev 6 Tarantello, Gabriella 6 Trombetti, Guido 6 Wei, Lei 5 Ashbaugh, Mark S. 5 Brandolini, Barbara 5 Brunner, Hermann 5 Chu, Chieping 5 Di Blasio, Giuseppina 5 Dittmar, Bodo 5 Fang, Zhongbo 5 Lin, Changhao 5 Liu, Chunlian 5 Lorca, Sebastian Antonio 5 Lucia, Marcello 5 Ma, Jingtang 5 Maire, Luis 5 Mi, Ling 5 O’Regan, Donal 5 Orpel, Aleksandra 5 Pistoia, Angela 5 Schaefer, Philip W. 5 Stakgold, Ivar 5 Suzuki, Takashi ...and 1,205 more Authors
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Cited in 224 Serials

 134 Journal of Mathematical Analysis and Applications 109 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 101 Journal of Differential Equations 48 ZAMP. Zeitschrift für angewandte Mathematik und Physik 45 Nonlinear Analysis. Theory, Methods & Applications 32 Proceedings of the American Mathematical Society 32 Calculus of Variations and Partial Differential Equations 30 Journal of Functional Analysis 29 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 24 Applicable Analysis 24 Archive for Rational Mechanics and Analysis 23 Applied Mathematics and Computation 21 Journal d’Analyse Mathématique 21 Transactions of the American Mathematical Society 20 Communications in Partial Differential Equations 19 Computers & Mathematics with Applications 18 Mathematische Annalen 17 Annali di Matematica Pura ed Applicata. Serie Quarta 17 Journal of Computational and Applied Mathematics 16 Journal de Mathématiques Pures et Appliquées. Neuvième Série 15 Applied Mathematics Letters 15 Communications in Contemporary Mathematics 15 Advanced Nonlinear Studies 13 Nonlinear Analysis. Real World Applications 12 Mathematical Methods in the Applied Sciences 12 Rocky Mountain Journal of Mathematics 12 Advances in Mathematics 11 Zeitschrift für Analysis und ihre Anwendungen 11 NoDEA. Nonlinear Differential Equations and Applications 11 Discrete and Continuous Dynamical Systems 11 Boundary Value Problems 10 Journal of Mathematical Physics 9 Israel Journal of Mathematics 9 Duke Mathematical Journal 9 Mathematische Zeitschrift 9 Mathematical and Computer Modelling 8 Numerische Mathematik 8 Journal of Mathematical Sciences (New York) 8 Comptes Rendus. Mathématique. Académie des Sciences, Paris 8 Advances in Nonlinear Analysis 7 Mathematische Nachrichten 7 Monatshefte für Mathematik 7 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 7 Journal of Evolution Equations 6 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 5 Communications in Mathematical Physics 5 Mathematical Notes 5 Archiv der Mathematik 5 Manuscripta Mathematica 5 The Journal of Geometric Analysis 5 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 5 Journal of Dynamics and Differential Equations 5 Potential Analysis 5 Abstract and Applied Analysis 5 Journal of the European Mathematical Society (JEMS) 5 Acta Mathematica Sinica. English Series 5 Communications on Pure and Applied Analysis 4 Journal of Computational Physics 4 Proceedings of the Edinburgh Mathematical Society. Series II 4 Ricerche di Matematica 4 Russian Mathematics 4 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 4 Lobachevskii Journal of Mathematics 4 Annales Henri Poincaré 4 Complex Variables and Elliptic Equations 3 Journal of Engineering Mathematics 3 Journal of Optimization Theory and Applications 3 Kodai Mathematical Journal 3 Quarterly of Applied Mathematics 3 Results in Mathematics 3 Studies in Applied Mathematics 3 Tohoku Mathematical Journal. Second Series 3 Physica D 3 Acta Mathematicae Applicatae Sinica. English Series 3 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 3 Japan Journal of Industrial and Applied Mathematics 3 Computational Mathematics and Mathematical Physics 3 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 3 Electronic Journal of Differential Equations (EJDE) 3 Mathematical Problems in Engineering 3 Computational Methods and Function Theory 3 Advances in Difference Equations 3 Journal of Spectral Theory 2 Journal of Statistical Physics 2 Nonlinearity 2 Ukrainian Mathematical Journal 2 Annales de l’Institut Fourier 2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 2 Applied Mathematics and Optimization 2 Computing 2 Journal of Geometry 2 Journal of the London Mathematical Society. Second Series 2 Numerical Functional Analysis and Optimization 2 Pacific Journal of Mathematics 2 Proceedings of the Japan Academy. Series A 2 Proceedings of the London Mathematical Society. Third Series 2 Chinese Annals of Mathematics. Series B 2 Acta Mathematica Hungarica 2 Probability Theory and Related Fields 2 Journal of Complexity ...and 124 more Serials
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Cited in 46 Fields

 1,103 Partial differential equations (35-XX) 142 Ordinary differential equations (34-XX) 89 Calculus of variations and optimal control; optimization (49-XX) 83 Global analysis, analysis on manifolds (58-XX) 78 Numerical analysis (65-XX) 75 Operator theory (47-XX) 49 Differential geometry (53-XX) 47 Fluid mechanics (76-XX) 34 Functions of a complex variable (30-XX) 33 Real functions (26-XX) 31 Functional analysis (46-XX) 30 Probability theory and stochastic processes (60-XX) 30 Biology and other natural sciences (92-XX) 29 Potential theory (31-XX) 29 Mechanics of deformable solids (74-XX) 25 Integral equations (45-XX) 23 Convex and discrete geometry (52-XX) 21 Statistical mechanics, structure of matter (82-XX) 13 Difference and functional equations (39-XX) 13 Classical thermodynamics, heat transfer (80-XX) 12 Measure and integration (28-XX) 10 Dynamical systems and ergodic theory (37-XX) 10 Quantum theory (81-XX) 6 Special functions (33-XX) 6 Geometry (51-XX) 3 Combinatorics (05-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Manifolds and cell complexes (57-XX) 3 Computer science (68-XX) 3 Astronomy and astrophysics (85-XX) 3 Systems theory; control (93-XX) 2 Approximations and expansions (41-XX) 2 Mechanics of particles and systems (70-XX) 2 Operations research, mathematical programming (90-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Number theory (11-XX) 1 Field theory and polynomials (12-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Abstract harmonic analysis (43-XX) 1 Statistics (62-XX) 1 Relativity and gravitational theory (83-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Information and communication theory, circuits (94-XX)

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A $\text{TEM}$ wave is incident normally upon a perfect conductor. The $\mathrm{E}$ and $\mathrm{H}$ fields at the boundary will be, respectively,

1. minimum and minimum
2. maximum and maximum
3. minimum and maximum
4. maximum and minimum


text:
# Tag Info

15

Conventionally $a^{b^c}$ means $a^{(b^c)}$. The other way of parsing it, $(a^b)^c$, yields a result equal to $a^{bc}$. In particular $(2^3)^4 = 2^{3\times 4} = 2^{12} = 4096$.

12

Fix $x\in\mathbf R$. By Bernoulli's inequality (here $n$ has to be large enough, so that $a_n x/n>-1$), $$\Bigl(1+\frac{a_nx}{n}\Bigr)^n\geq 1+a_n x.$$ On the other hand, since $$\Bigl(1+\frac{a}{n}\Bigr)^n\leq e^a$$ for all $a\in\mathbf R$, $$\Bigl(1+\frac{a_nx}{n}\Bigr)^n\leq e^{a_n x}.$$ Now use the sandwich theorem.

10

If one first defines $$e:=\lim\limits_{n\to\infty} \left(1+\frac 1n\right)^n$$ and then goes on defining a real-valued function $$\exp:\mathbb R\rightarrow\mathbb R,~x\mapsto\exp(x):=e^x,$$ one has $e^x=\exp(x)$ by definition but then has to show $\displaystyle e^x=\sum\limits_{k=0}^\infty \frac{x^k}{k!}$. This involves finding the derivative of $\exp$ ...

9

The next step is $$\left(2^x\right)^2-10\cdot2^x+16=0$$ wich is a quadratic equation in $2^x$. Then $2^x=5\pm3$ and $$x=1\text{ or }x=3.$$

9

Hint. One may recall that $$e^{-x}=\frac1{e^x}$$

8

The guiding question goes like this: What happens when you divide $1$ by a really, really large number?

8

$x=\dfrac{\log7}{\log25}$ $y=\dfrac{\log 125}{\log 7}$ $\implies xy = \dfrac{\log 125}{\log 25}= \dfrac{\log 5^3}{\log 5^2} = \boxed {\dfrac{3}{2}}$

7

Look closer at your graph! (I am going to use $k$ and $n$ here.) I get e.g. $$\frac{1}{100000}\left(\sum_{k=1}^{100000}\ln(k)\right)\approx \ln(100000)-0.999933$$ This suggests an asymptotic of $\ln(n)-1$. Indeed: $$\begin{array}{ll} \displaystyle \frac{1}{n}\sum_{k=1}^n\ln(k) & \displaystyle =\ln(n)+\frac{1}{n}\sum_{k=1}^n \big(\ln(k)-\ln(n)\big) \\ ... 7 There are a number of type-setting situations with algebraic expressions that cause problems when you try to enter them into a one-line input calculator. For example$$\frac{2+3}{4+5}$$must be entered into a calculator as$$(2+3)/(4+5)$$The horizontal line in the fraction implies brackets around the expression in the numerator and denominator. Similarly, ... 6 Elaborating on what Jack said, assume we have an nth root instead of a square root:$$y = \sqrt[n]{\log_x{\exp{\sqrt[n]{\log_x{\exp{\sqrt[n]{\log_x{\exp{\cdots}}}}}}}}}$$Then$$y = \sqrt[n]{\log_x{\exp\left(y\right)}}y = \sqrt[n]{y\log_x{e}}y^n = y\log_x{e}y^{n-1} = \log_xe$$Obviously, with n = 2, n-1 = 1, meaning y itself ... 6$$y=\sqrt{\log_x{\exp{\sqrt{\log_x{\exp{\sqrt{\log_x{\exp{\cdots}}}}}}}}}\implies y=\sqrt{\log_x\exp(y)}=\sqrt{y\log_xe}\\ \therefore y=\log_xe$$6 The complex exponential function needs some definition. There are several ways one could define it: Power series As a solution to a differential equation As the unique holomorphic extension of the real exponential function to the whole plane Via the limit definition \lim_{n \to \infty} (1+\frac{z}{n})^n Via Euler's formula ... One can take any one of ... 6 x^{2n}=(x^2)^n=\frac{1}{2^n}. So if n\neq 0, for x\in \mathbb{R} you have x^2=\frac{1}{2} then x=\frac{1}{\sqrt{2}} or x=-\frac{1}{\sqrt{2}}. 5 Usually one defines \exp x=\displaystyle \sum_{n=0}^\infty \dfrac{x^n}{n!}. It is easy to show it converges for all x (even for complex values) and it satisfies the differential equation with initial condition:$$y'=y,\quad y(0)=1.$$Now this differential equation implies the functional ralation:$$\exp(x+y)=\exp x\cdot\exp y$$which in turn implies ... 5 By Taylor series with Lagrange remainder$$ e^x=\sum\limits_{k=0}^{2n-1}\frac{x^k}{k!}+\frac{(e^x)^{(2n)}|_t}{2n!}x^{2n}=\sum\limits_{k=0}^{2n-1}\frac{x^k}{k!}+\frac{e^t}{2n!}x^{2n} $$where |t|<|x|. And$$ ...

5

This can be proved purely combinatorially using nothing more than the binomial theorem. In fact, I claim that the polynomial $P_n(x)=\left(\sum\limits_{k=0}^{2n-1} \frac{x^k}{k!}\right)\left(\sum\limits_{\ell=0}^{2n-1}(-1)^\ell \frac{x^\ell}{\ell!}\right)-1$ is even, has no constant term, and has no positive coefficients, which is sufficient to show that it ...

4

Set $z=2^x$ to obtain $z^2-10z+16=0$ and solve the quadratic

4

I'm looking at integral (1) and seeing a Laplace transform convolution integral. Note that $$\int_0^t dt' \, f(t') g(t-t') = \frac1{i 2 \pi} \int_{c-i \infty}^{c+i \infty} ds \, F(s) G(s) e^{s t}$$ where $$F(s) = \int_0^{\infty} dt \, f(t) e^{-s t}$$ $$G(s) = \int_0^{\infty} dt \, g(t) e^{-s t}$$ In this case, we may define $$f_1(t) = t^{-3/2} ... 4 In order to eliminate e-function, it can be done as follows$$B=A\cdot (1-e^{-x})(1-e^{-x})=\frac{B}{A} (1-e^{-x})=\frac{B}{A} e^{-x}=1-\frac{B}{A}e^{-x}=\frac{A-B}{A}$$Now, taking logarithm as follows$$\ln e^{-x}=\ln\left|\frac{A-B}{A}\right|-x\ln e=\ln\left|\frac{A-B}{A}\right|x=-\ln\left|\frac{A-B}{A}\right|$$... 3 To solve an expression like x^{2n}=\frac{1}{2n} for x, you need to use logarithms. As was quite rightly pointed out, if n\neq 0 and x\in\mathbb{R}, then$$(x^2)^n=\frac{1}{2^n}\Rightarrow x^2=\frac{1}{2}\Rightarrow x=\frac{1}{\sqrt{2}}.$$If n=0, then we have a blow-up singularity. Hence we will need to travel in an arbitrarily small circuit ... 3 Notice,$$\lim_{n\to \infty}\left(1+a_n\frac{x}{n}\right)^n$$Using binomial expansion of \left(1+a_n\frac{x}{n}\right)^n & neglecting higher power terms, we get$$=\lim_{n\to \infty}\left(1+na_n\frac{x}{n}\right)=\lim_{n\to \infty}\left(1+a_n x\right)=\lim_{n\to \infty} 1+x\lim_{n\to \infty}a_n = 1+x(0)=1 $$3 In standard mathematics the notation A \mathrel{^\wedge} B is not used; one does A^B instead. In some computer science (programming) applications the infix circumflex operator notation A \mathrel{^\wedge} B is used (or rather the ASCII version A^B). What you point out is that this operator \mathrel{^\wedge} is not associative. So does A ... 3 HINT : Let (e^x)^2=e^{2x}=t. Then, you'll have$$t^2-4t=-3$$3 no just consider the 1 by 1 case. i.e. real numbers. Let X=10 and the series doesn't converge. 3 I assume that the integral of interest I is$$I=\int_0^{\infty}e^{-\left(u^2+\frac{\alpha^2}{16tu^2}\right)}du$$First, we let a^2=\frac{\alpha^2}{16t} and write$$\begin{align} I&=\int_0^{\infty} e^{-a\left(\frac{u^2}{a}+\frac{a}{u^2}\right)}du\\\\ &=e^{-2a}\int_0^{\infty} e^{-a\left(\frac{u}{\sqrt{a}}-\frac{\sqrt{a}}{u}\right)^2}du\tag 1 ...

3

The property that $(a^n)^m=(a^m)^n=a^{mn}$ is only defined for real numbers. But $\sqrt{-1}=i$ is a complex number.

2

I think computation via some kind of Jordan decomposition is pretty much the best you could do for calculation by hand. I suspect that you might make things slightly easier if you used something like Jordan real form, if you're comfortable exponentiating rotation matrices.

2

Looking here, there is an interesting expansion for large arguments $$E_1(x)=\frac{e^{-x}}{x}\sum_{k=0}^\infty \frac {k!}{(-x)^k}$$ For $x=25$, using $n$ terms, we have $$S_1=5.332970444146184 \times 10^{-13}$$ $$S_2=5.350747012293338 \times 10^{-13}$$ $$S_3=5.348613824115680 \times 10^{-13}$$ $$S_4=5.348955134224105 \times 10^{-13}$$ ...

2

Generally, power series representation is not a good choice for larger input, even if the radius of convergence if infinite. In this case, you need about 90 leading terms just simply to achieve the desired order of magnitude (and more terms for the accurate digits). Indeed, Mathematica 10.2 confirms that if we let  S_n = -\gamma - \log 25 - ...

2

Without seeing your code it is difficult. But I guess it is catastrophic cancellation. $E_1(25) \approx 5.3488997553\times 10^{-13}$ and the single terms are much larger, e.g. the for $n=10$ the value is $2628070.75729$ and for $n=24$ the term is $238585088.1445781!$ You will get similar problems is you compute $e^{-x}$ or $\sin(x)$ for $x=25$ using the ...

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text:
# nLab Haar measure

## Idea

If $G$ is a topological group, a Haar measure is a translation-invariant measure on the Borel sets of $G$. The archetypal example of Haar measure is the Lebesgue measure on the (additive group underlying) cartesian space ${ℝ}^{n}$.

## Definition

The proper generality in which to discuss Haar measure is where the topological group $G$ is assumed to be locally compact Hausdorff, and from here on we assume this. (For topological groups, the Hausdorff assumption is rather mild; it is equivalent to the ${T}_{0}$ separation condition. See the discussion at uniform space.)

Let ${C}_{c}\left(G\right)$ denote the vector space of continuous real-valued functionals with compact support on $G$. This is a locally convex topological vector space where the locally convex structure is specified by the family of seminorms

${\rho }_{K}\left(f\right)=\underset{x\in K}{\mathrm{sup}}\mid f\left(x\right)\mid ,$\rho_K(f) = \sup_{x \in K} |f(x)|,

$K$ ranging over compact subsets of $G$. Recall that a Radon measure on $G$ may be described as a continuous linear functional

$\mu :{C}_{c}\left(G\right)\to ℝ$\mu: C_c(G) \to \mathbb{R}

which is positive in the sense that $\mu \left(f\right)\ge 0$ whenever $f\ge 0$. This defines a measure $\stackrel{^}{\mu }$ on the $\sigma$-algebra of Borel sets in the usual sense of measure theory, where

$\stackrel{^}{\mu }\left(B\right)=\mathrm{sup}\left\{\mu \left(f\right):\mathrm{supp}\left(f\right)=K\subseteq B,{\rho }_{K}\left(f\right)=1\right\}$\hat{\mu}(B) = sup \{\mu(f): supp(f) = K \subseteq B, \rho_K(f) = 1\}

By abuse of notation, we generally conflate $\mu$ and $\stackrel{^}{\mu }$.

A left Haar measure on $G$ is a nonzero Radon measure $\mu$ such that

$\mu \left(gB\right)=\mu \left(B\right)$\mu(g B) = \mu(B)

for all $g\in G$ and all Borel sets $B$.

## Existence and Uniqueness

Any locally compact Hausdorff topological group $G$ admits a Haar mesaure that is unique up to scalar multiple. This result was first proven by Weil. A proof by be found in these online notes by Rubinstein-Salzedo.

### Left and Right Haar Measures that differ

The left and the right Haar measure may or may not coincide, groups for which they coincide are called unimodular. Consider the matrix subgroup

$G:=\left\{\phantom{\rule{thinmathspace}{0ex}}\left(\begin{array}{cc}y& x\\ 0& 1\end{array}\right)\phantom{\rule{thinmathspace}{0ex}}\mid \phantom{\rule{thinmathspace}{0ex}}x,y\in ℝ,y>0\right\}$G := \left\{ \left.\, \begin{pmatrix} y & x \\ 0 & 1 \end{pmatrix}\,\right|\, x, y \in \mathbb{R}, y \gt 0 \right\}

The left and right invariant measures are, respectively,

$d{\mu }_{L}={y}^{-2}\mathrm{dx}\mathrm{dy},\phantom{\rule{1em}{0ex}}d{\mu }_{R}={y}^{-1}\mathrm{dx}\mathrm{dy}$d\mu_L = y^{-2} dx dy,\quad d\mu_R = y^{-1} dx dy

and so G is not unimodular.

Revised on January 25, 2012 14:49:48 by Chris Waggoner? (67.158.6.115)


text:
Página 11 dos resultados de 435 itens digitais encontrados em 0.010 segundos

## ‣ Uso de ôndulas na compressão de operadores; Using wavelets for operator compression

Nunes, Ana Luísa da Silva
Relevância na Pesquisa
26.888838%

## ‣ Position Coding

Aboufadel, Edward; Armstrong, Timothy; Smietana, Elizabeth
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.985708%
A position coding pattern is an array of symbols in which subarrays of a certain fixed size appear at most once. So, each subarray uniquely identifies a location in the larger array, which means there is a bijection of some sort from this set of subarrays to a set of coordinates. The key to Fly Pentop Computer paper and other examples of position codes is a method to read the subarray and then convert it to coordinates. Position coding makes use of ideas from discrete mathematics and number theory. In this paper, we will describe the underlying mathematics of two position codes, one being the Anoto code that is the basis of "Fly paper". Then, we will present two new codes, one which uses binary wavelets as part of the bijection.; Comment: 14 pages, 7 figures

## ‣ Positive definite maps, representations and frames

Dutkay, Dorin Ervin
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
27.15793%
We present a unitary approach to the construction of representations and intertwining operators. We apply it to the $C^*$-algebras, groups, Gabor type unitary systems and wavelets. We give an application of our method to the theory of frames, and we prove a general dilation theorem which is in turn applied to specific cases, and we obtain in this way a dilation theorem for wavelets.

## ‣ Ergodic optimization of prevalent super-continuous functions

Bochi, Jairo; Zhang, Yiwei
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
26.985708%
Given a dynamical system, we say that a performance function has property P if its time averages along orbits are maximized at a periodic orbit. It is conjectured by several authors that for sufficiently hyperbolic dynamical systems, property P should be typical among sufficiently regular performance functions. In this paper we address this problem using a probabilistic notion of typicality that is suitable to infinite dimension: the concept of prevalence as introduced by Hunt, Sauer, and Yorke. For the one-sided shift on two symbols, we prove that property P is prevalent in spaces of functions with a strong modulus of regularity. Our proof uses Haar wavelets to approximate the ergodic optimization problem by a finite-dimensional one, which can be conveniently restated as a maximum cycle mean problem on a de Bruijin graph.; Comment: 23 pages, 4 figures. Final version, to appear in International Mathematics Research Notices (IMRN)

## ‣ Multiwavelet density estimation

Locke, Judson B.; Peter, Adrian M.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
27.15793%
Accurate density estimation methodologies play an integral role in a variety of scientific disciplines, with applications including simulation models, decision support tools, and exploratory data analysis. In the past, histograms and kernel density estimators have been the predominant tools of choice, primarily due to their ease of use and mathematical simplicity. More recently, the use of wavelets for density estimation has gained in popularity due to their ability to approximate a large class of functions, including those with localized, abrupt variations. However, a well-known attribute of wavelet bases is that they can not be simultaneously symmetric, orthogonal, and compactly supported. Multiwavelets-a more general, vector-valued, construction of wavelets-overcome this disadvantage, making them natural choices for estimating density functions, many of which exhibit local symmetries around features such as a mode. We extend the methodology of wavelet density estimation to use multiwavelet bases and illustrate several empirical results where multiwavelet estimators outperform their wavelet counterparts at coarser resolution levels.; Comment: Preprint

## ‣ Taylor Series as Wide-sense Biorthogonal Wavelet Decomposition

de Oliveira, H. M.; Lins, R. D.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
27.15793%
Pointwise-supported generalized wavelets are introduced, based on Dirac, doublet and further derivatives of delta. A generalized biorthogonal analysis leads to standard Taylor series and new Dual-Taylor series that may be interpreted as Laurent Schwartz distributions. A Parseval-like identity is also derived for Taylor series, showing that Taylor series support an energy theorem. New representations for signals called derivagrams are introduced, which are similar to spectrograms. This approach corroborates the impact of wavelets in modern signal analysis.; Comment: 6 pages, 4 figures. conference: XXII Simposio Brasileiro de Telecomunicacoes, SBrT'05, 2005, Campinas, SP, Brazil

## ‣ Phase retrieval for the Cauchy wavelet transform

Mallat, Stéphane; Waldspurger, Irène
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
27.15793%
We consider the phase retrieval problem in which one tries to reconstruct a function from the modulus of its wavelet transform. We study the unicity and stability of the reconstruction. In the case where the wavelets are Cauchy wavelets, we prove that the modulus of the wavelet transform uniquely determines the function up to a global phase. We show that the reconstruction operator is continuous but not uniformly continuous. We describe how to construct pairs of functions which are far away in $L^2$-norm but whose wavelet transforms are very close, in modulus. The principle is to modulate the wavelet transform of a fixed initial function by a phase which varies slowly in both time and frequency. This construction seems to cover all the instabilities that we observe in practice; we give a partial formal justification to this fact. Finally, we describe an exact reconstruction algorithm and use it to numerically confirm our analysis of the stability question.

## ‣ Some recent advances on the RBF

Chen, W
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
27.15793%
This paper aims to survey our recent work relating to the radial basis function (RBF) and its applications to numerical PDEs. We introduced the kernel RBF involving general pre-wavelets and scale-orthogonal wavelets RBF. A dimension-independent RBF error bound was also conjectured. The centrosymmetric structure of RBF interpolation matrix under symmetric sample knots was pointed out. On the other hand, we introduced the boundary knot method via nonsingular general solution and dual reciprocity principle and the boundary particle method via multiple reciprocity principle. By using the Green integral we developed a domain-type Hermite RBF scheme called the modified Kansa method, which significantly reduces calculation errors around boundary. To circumvent the Gibbs phenomenon, the least square RBF collocation scheme was presented. All above discretization schemes are meshfree, symmetric, spectral convergent, integration-free and mathematically very simple. The numerical validations are also briefly presented.

## ‣ Orthonormal dilations of non-tight frames

Bownik, Marcin; Jasper, John; Speegle, Darrin
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
27.15793%
We establish dilation theorems for non-tight frames with additional structure, i.e., frames generated by unitary groups of operators and projective unitary representations. This generalizes previous dilation results for Parseval frames due to Han and Larson and Gabardo and Han. We also extend the dilation theorem for Parseval wavelets, due to Dutkay, Han, Picioroaga, and Sun , by identifying the optimal class of frame wavelets for which dilation into an orthonormal wavelet is possible.

## ‣ Stable and robust sampling strategies for compressive imaging

Krahmer, Felix; Ward, Rachel
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
27.15793%
In many signal processing applications, one wishes to acquire images that are sparse in transform domains such as spatial finite differences or wavelets using frequency domain samples. For such applications, overwhelming empirical evidence suggests that superior image reconstruction can be obtained through variable density sampling strategies that concentrate on lower frequencies. The wavelet and Fourier transform domains are not incoherent because low-order wavelets and low-order frequencies are correlated, so compressive sensing theory does not immediately imply sampling strategies and reconstruction guarantees. In this paper we turn to a more refined notion of coherence -- the so-called local coherence -- measuring for each sensing vector separately how correlated it is to the sparsity basis. For Fourier measurements and Haar wavelet sparsity, the local coherence can be controlled and bounded explicitly, so for matrices comprised of frequencies sampled from a suitable inverse square power-law density, we can prove the restricted isometry property with near-optimal embedding dimensions. Consequently, the variable-density sampling strategy we provide allows for image reconstructions that are stable to sparsity defects and robust to measurement noise. Our results cover both reconstruction by $\ell_1$-minimization and by total variation minimization. The local coherence framework developed in this paper should be of independent interest in sparse recovery problems more generally...

## ‣ Square Roots of -1 in Real Clifford Algebras

Hitzer, Eckhard; Helmstetter, Jacques; Ablamowicz, Rafal
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
26.985708%
It is well known that Clifford (geometric) algebra offers a geometric interpretation for square roots of -1 in the form of blades that square to minus 1. This extends to a geometric interpretation of quaternions as the side face bivectors of a unit cube. Systematic research has been done [32] on the biquaternion roots of -1, abandoning the restriction to blades. Biquaternions are isomorphic to the Clifford (geometric) algebra $Cl(3,0)$ of $\mathbb{R}^3$. Further research on general algebras $Cl(p,q)$ has explicitly derived the geometric roots of -1 for $p+q \leq 4$ [17]. The current research abandons this dimension limit and uses the Clifford algebra to matrix algebra isomorphisms in order to algebraically characterize the continuous manifolds of square roots of -1 found in the different types of Clifford algebras, depending on the type of associated ring ($\mathbb{R}$, $\mathbb{H}$, $\mathbb{R}^2$, $\mathbb{H}^2$, or $\mathbb{C}$). At the end of the paper explicit computer generated tables of representative square roots of -1 are given for all Clifford algebras with $n=5,7$, and $s=3 \, (mod 4)$ with the associated ring $\mathbb{C}$. This includes, e.g., $Cl(0,5)$ important in Clifford analysis, and $Cl(4,1)$ which in applications is at the foundation of conformal geometric algebra. All these roots of -1 are immediately useful in the construction of new types of geometric Clifford Fourier transformations.; Comment: 31 pages...

## ‣ Unitary systems and wavelet sets

Larson, David R.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
27.15793%
We give a detailed description of the local commutant approach to wavelet theory using operator algebraic methods. We include a new result on interpolation pairs of wavelet sets: Every pair in the generalized Journe family of wavelet sets is an interpolation pair. In the last section, we give a discussion of several open problems on wavelets and frame-wavelets.; Comment: This is a semi-expository article which was written by the author for the proceedings of the 4th International Conference on Wavelet Analysis and its Applications, Macau, China, December 2005 [WAA2005], as a keynote speaker; 30p

## ‣ Linear Stable Sampling Rate: Optimality of 2D Wavelet Reconstructions from Fourier Measurements

Adcock, Ben; Hansen, Anders C.; Kutyniok, Gitta; Ma, Jackie
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
27.15793%
In this paper we analyze two-dimensional wavelet reconstructions from Fourier samples within the framework of generalized sampling. For this, we consider both separable compactly-supported wavelets and boundary wavelets. We prove that the number of samples that must be acquired to ensure a stable and accurate reconstruction scales linearly with the number of reconstructing wavelet functions. We also provide numerical experiments that corroborate our theoretical results.

## ‣ A hypergeometric basis for the Alpert multiresolution analysis

Geronimo, Jeffrey S.; Iliev, Plamen
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
26.985708%
We construct an explicit orthonormal basis of piecewise ${}_{i+1}F_{i}$ hypergeometric polynomials for the Alpert multiresolution analysis. The Fourier transform of each basis function is written in terms of ${}_2F_3$ hypergeometric functions. Moreover, the entries in the matrix equation connecting the wavelets with the scaling functions are shown to be balanced ${}_4 F_3$ hypergeometric functions evaluated at $1$, which allows to compute them recursively via three-term recurrence relations. The above results lead to a variety of new interesting identities and orthogonality relations reminiscent to classical identities of higher-order hypergeometric functions and orthogonality relations of Wigner $6j$-symbols.

## ‣ The local trace function of shift invariant subspaces

Dutkay, Dorin Ervin
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
27.15793%
We define the local trace function for subspaces of $\ltworn$ which are invariant under integer translation. Our trace function contains the dimension function and the spectral function defined by Bownik and Rzeszotnik and completely characterizes the given translation invariant subspace. It has properties such as positivity, additivity, monotony and some form of continuity. It behaves nicely under dilations and modulations. We use the local trace function to deduce, using short and simple arguments, some fundamental facts about wavelets such as the characterizing equations, the equality between the dimension function and the multiplicity function and some new relations between scaling functions and wavelets.

## ‣ Prime Coset Sum: A Systematic Method for Designing Multi-D Wavelet Filter Banks with Fast Algorithms

Hur, Youngmi; Zheng, Fang
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
27.15793%
As constructing multi-D wavelets remains a challenging problem, we propose a new method called prime coset sum to construct multi-D wavelets. Our method provides a systematic way to construct multi-D non-separable wavelet filter banks from two 1-D lowpass filters, with one of whom being interpolatory. Our method has many important features including the following: 1) it works for any spatial dimension, and any prime scalar dilation, 2) the vanishing moments of the multi-D wavelet filter banks are guaranteed by certain properties of the initial 1-D lowpass filters, and furthermore, 3) the resulting multi-D wavelet filter banks are associated with fast algorithms that are faster than the existing fast tensor product algorithms.

## ‣ Reproducing subgroups of Sp(2,R). Part II: admissible vectors

Alberti, Giovanni S.; De Mari, Filippo; De Vito, Ernesto; Mantovani, Lucia
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
27.15793%
In part I we introduced the class ${\mathcal E}_2$ of Lie subgroups of $Sp(2,\R)$ and obtained a classification up to conjugation (Theorem 1.1). Here, we determine for which of these groups the restriction of the metaplectic representation gives rise to a reproducing formula. In all the positive cases we characterize the admissible vectors with a generalized Calder\'on equation. They include products of 1D-wavelets, directional wavelets, shearlets, and many new examples.; Comment: 37 pages, 3 figures

## ‣ On generic frequency decomposition. Part 1: vectorial decomposition

Vergara, Sossio
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
27.15793%
The famous Fourier theorem states that, under some restrictions, any periodic function (or real world signal) can be obtained as a sum of sinusoids, and hence, a technique exists for decomposing a signal into its sinusoidal components. From this theory an entire branch of research has flourished: from the Short-Time or Windowed Fourier Transform to the Wavelets, the Frames, and lately the Generic Frequency Analysis. The aim of this paper is to take the Frequency Analysis a step further. It will be shown that keeping the same reconstruction algorithm as the Fourier Theorem but changing to a new computing method for the analysis phase allows the generalization of the Fourier Theorem to a large class of nonorthogonal bases. New methods and algorithms can be employed in function decomposition on such generic bases. It will be shown that these algorithms are a generalization of the Fourier analysis, i.e. they are reduced to the familiar Fourier tools when using orthogonal bases. The differences between this tool and the wavelets and frames theories will be discussed. Examples of analysis and reconstruction of functions using the given algorithms and nonorthogonal bases will be given. In this first part the focus will be on vectorial decomposition...

## ‣ Asymptotic Analysis of Inpainting via Universal Shearlet Systems

Genzel, Martin; Kutyniok, Gitta
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
27.15793%
Recently introduced inpainting algorithms using a combination of applied harmonic analysis and compressed sensing have turned out to be very successful. One key ingredient is a carefully chosen representation system which provides (optimally) sparse approximations of the original image. Due to the common assumption that images are typically governed by anisotropic features, directional representation systems have often been utilized. One prominent example of this class are shearlets, which have the additional benefitallowing faithful implementations. Numerical results show that shearlets significantly outperform wavelets in inpainting tasks. One of those software packages, www.shearlab.org, even offers the flexibility of usingdifferent parameter for each scale, which is not yet covered by shearlet theory. In this paper, we first introduce universal shearlet systems which are associated with an arbitrary scaling sequence, thereby modeling the previously mentioned flexibility. In addition, this novel construction allows for a smooth transition between wavelets and shearlets and therefore enables us to analyze them in a uniform fashion. For a large class of such scaling sequences, we first prove that the associated universal shearlet systems form band-limited Parseval frames for $L^2(\mathbb{R}^2)$ consisting of Schwartz functions. Secondly...

## ‣ Wavelet filter functions, the matrix completion problem, and projective modules over $C(\mathbb T^n)$

Packer, Judith A.; Rieffel, Marc A.
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
26.985708%
We discuss how one can use certain filters from signal processing to describe isomorphisms between certain projective $C(\mathbb T^n)$-modules. Conversely, we show how cancellation properties for finitely generated projective modules over $C(\mathbb T^n)$ can often be used to prove the existence of continuous high pass filters, of the kind needed for multivariate wavelets, corresponding to a given continuous low-pass filter. However, we also give an example of a continuous low-pass filter for which it is impossible to find corresponding continuous high-pass filters. In this way we give another approach to the solution of the matrix completion problem for filters of the kind arising in wavelet theory.; Comment: 21 pages, various local improvements


text:
# Find the value of:(11 + 4) − 9 × 1 ÷ 3 of 4

This question was previously asked in
SSC GD Previous Paper 36 (Held On: 11 March 2019 Shift 2)_English
View all SSC GD Constable Papers >
1. $$\frac{{75}}{4}$$
2. $$\frac{{57}}{4}$$
3. 5
4. 3

Option 2 : $$\frac{{57}}{4}$$
Free
पर्यायवाची शब्द
143413
15 Questions 15 Marks 12 Mins

## Detailed Solution

Given:

(11 + 4) − 9 × 1 ÷ 3 of 4

Concept used:

Follow BODMAS rule to solve this question, as per the order given below,

Calculation:

(11 + 4) − 9 × 1 ÷ 3 of 4

⇒ 15 - 9 ÷ 12 = ?

⇒ 15 - 3/4 = ?

⇒ ? = 57/4

∴ The value of ? is 57/4.


text:
시간 제한메모리 제한제출정답맞힌 사람정답 비율
2 초 1024 MB0000.000%

## 문제

Quotdoku is a variant of the game Sudoku. As in Sudoku, the aim is to fill in a 9-by-9 grid with the digits 1 through 9 so that each digit 1 through 9 occurs exactly once in each row, exactly once in each column and exactly once in each of the 9 3-by-3 sub-squares subject to constraints on the choices. In Sudoku, the constraints are that certain squares must contain fixed values. In Quotdoku, the constraints are on the quotient of some of the adjacent squares within some 3-by-3 sub-squares. In each case, the larger of the two adjacent values is divided by the smaller to obtain the indicated quotient (any remainder is ignored). In the illustration below, the integers in the range 1 through 9 on the separating line indicate the desired quotient.

Write a program to solve Quotdoku problems.

## 입력

The first line of input contains a single decimal integer K, (0 ≤ K ≤ 81), which is the number of pre-specified values.

The next 15 lines of input consist of the values from 0 to 9, separated by spaces. A value of 0 indicates that there is no constraint for the corresponding pair of values. Otherwise, the input value gives the quotient constraint. Rows 1, 3, 5, 6, 8, 10, 11, 13 and 15 contain 6 values corresponding to constraints on the quotient of dividing values to the left and right of the symbol. Rows 2, 4, 7, 9, 12 and 14 contain 9 values corresponding to constraints on the quotient of dividing values above and below the symbol.

The next K lines of input each consist of three decimal integers in the range 1 through 9, each separated by a space. The values give the row, column and value in that order of each pre-specified value.

## 출력

Your program should produce 9 lines of output where each line consists of 9 decimal digits separated by a single space. The value in the j th position in the i th line of the 9 output lines is the solution value in column j of row i.

## 예제 입력 1

0
1 1 0 0 1 2
1 1 1 0 0 0 6 1 2
1 1 0 0 7 3
2 6 1 0 0 0 3 1 2
2 7 0 0 3 1
0 0 1 4 0 0
0 0 0 3 3 2 0 0 0
0 0 1 1 0 0
0 0 0 1 6 1 0 0 0
0 0 7 5 0 0
1 3 0 0 1 1
1 2 2 0 0 0 4 1 6
2 1 0 0 2 4
8 1 1 0 0 0 3 1 9
4 1 0 0 2 3

## 예제 출력 1

3 5 9 2 7 1 6 8 4
4 6 8 5 3 9 1 7 2
2 1 7 4 8 6 3 9 5
5 9 1 3 2 8 4 6 7
7 2 3 9 6 4 5 1 8
6 8 4 7 1 5 9 2 3
9 7 2 1 4 3 8 5 6
8 3 5 6 9 7 2 4 1
1 4 6 8 5 2 7 3 9

## 예제 입력 2

3
2 4 0 0 1 1
1 3 9 0 0 0 1 1 1
1 6 0 0 1 3
1 1 3 0 0 0 1 9 1
1 2 0 0 5 2
0 0 1 9 0 0
0 0 0 2 2 5 0 0 0
0 0 1 1 0 0
0 0 0 2 2 1 0 0 0
0 0 3 4 0 0
4 1 0 0 4 1
2 1 1 0 0 0 4 2 1
1 2 0 0 2 1
4 2 1 0 0 0 9 1 1
1 1 0 0 3 1
1 6 7
6 9 9
4 3 7

## 예제 출력 2

5 2 9 1 3 7 8 6 4
4 6 1 8 5 2 7 9 3
7 8 3 4 6 9 5 1 2
3 5 7 6 9 1 4 2 8
8 9 2 3 4 5 6 7 1
6 1 4 7 2 8 3 5 9
1 4 5 9 7 3 2 8 6
2 3 8 5 1 6 9 4 7
9 7 6 2 8 4 1 3 5


text:
# Random Forest checklist

I am building a random forest model in R. Based on my research I (hope to) have come up with quite some understanding about how they work, and more importantly when they work.

I simply would like to see my understanding of RF-models cross-validated here.

So here we go (true or false?):

• scaling is not necessary in Random Forest models.
• when dealing with imbalanced data, one could downsample/upsample/use weights. In package randomForest however, the option classwt seems to be unreliable? Therefore I simply downsample my data (50/50) using package Unbalanced. In my final model I will downsample and build the forest K times and take the average of the predictions. Is this wise?
• Random Forests have little problems with highly correlated variables. I have many ideas for new features and would like to include all of them at once and based on importance (MeanDecreaseGini) optionally decide to leave some out. But the correlation between predictors will not influence performance? in other words: the model with extra features will perform at least similar to the one with less variables?
• @myself: downsampling in randomForest package happens much easier with: sampszize=rep(length(minorityClass,2) (in randomForest) The rest of the questions remain unanswered. – user3762631 Jun 28 '14 at 9:26

2. classwt is not reliable; RF and unbalanced data is long story, try browsing the site or ask a more detailed question.


text:
Definition of Lemma

A lemma is a little mathematical result that requires a proof.

Lemmas are not as important as theorems.

In fact, we often prove lemmas to help us prove theorems.

We use known facts to help us prove lemmas.

Description

The aim of this dictionary is to provide definitions to common mathematical terms. Students learn a new math skill every week at school, sometimes just before they start a new skill, if they want to look at what a specific term means, this is where this dictionary will become handy and a go-to guide for a student

Audience

Year 1 to Year 12 students

Learning Objectives

Learn common math terms starting with letter L

Author: Subject Coach
You must be logged in as Student to ask a Question.


text:
# Conformal/Biholomorphism equivalence classes in $\mathbb{C}^n$

Recently I have got interested in the topic of conformal equivalence classes of complex domains, mostly one-dimensional ones.

Here by conformal map $f: U \rightarrow V$ I mean a complex holomorphic bijection which is onto (where $U,V$ are open domains in $\mathbb{C}^n$). We call $U,V$ conformally equivallent if such a map exists; this is an equivalence relation.

My knowledge in this subject can be summarazied as follows:

• By Riemann's mapping theorem, Every simply connected domain is in the class of the unit disc $D=\{|z|<1\}$.

• Two annuli $\{r_1<|z|<r_2\},\{R_1<|z|<R_2\}$ are equivalent iff $\frac{R_2}{R_1}=\frac{r_2}{r_1}$. Moreover, different infinite annuli are not equivalent.

• Every one-dim. domain with single hole (=of genus 1) is equivalent to an annulus.

My general question is - What can be said about this classification? How many classes are there? Is there a full answer? Also, what if further restrictions are taken on the domains, such as connectivity (is this necessary in the general case)?

Another question is - what happens when $n>1$? I have read that the theory is poorer, but could not quite understand why. If so, can the notion of conformal equivalence be replaced by another (complex-analysis related) concept, with more theory (maybe some local conditions)?

Can someone give a brief summary, with relevant references (books/articles)?

As Mariono says in the comments, Liouville's theorem severely limits how interesting conformal equivalence is in more than $2$ real dimensions.


text:
6.5 SEATS decomposition

“SEATS” stands for “Seasonal Extraction in ARIMA Time Series” (ARIMA models are discussed in Chapter 8). This procedure was developed at the Bank of Spain, and is now widely used by government agencies around the world. The procedure works only with quarterly and monthly data. So seasonality of other kinds, such as daily data, or hourly data, or weekly data, require an alternative approach.

The details are beyond the scope of this book. However, a complete discussion of the method is available in Dagum & Bianconcini (2016). Here we will only demonstrate how to use it via the seasonal package.

library(seasonal)
elecequip %>% seas() %>%
autoplot() +
ggtitle("SEATS decomposition of electrical equipment index")

The result is quite similar to the X11 decomposition shown in Figure 6.9.

As with the X11 method, we can use the seasonal(), trendcycle() and remainder() functions to extract the individual components, and seasadj() to compute the seasonally adjusted time series.

The seasonal package has many options for handling variations of X11 and SEATS. See the package website for a detailed introduction to the options and features available.

Bibliography

Dagum, E. B., & Bianconcini, S. (2016). Seasonal adjustment methods and real time trend-cycle estimation. Springer. [Amazon]


text:
, 21.06.2019 23:30, jdenty3398

# The graph of the the function f(x) is given below. find $$\lim_{x \to 0\zero} f(x)$$ $$\lim_{x \to 1+\oneplus} f(x)$$ $$\lim_{x \to 0-\zeroneg} f(x)$$

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text:
# American Institute of Mathematical Sciences

2011, 2011(Special): 1111-1118. doi: 10.3934/proc.2011.2011.1111

## Oscillating solutions to a parabolic-elliptic system related to a chemotaxis model

 1 Department of Mathematics, Faculty of Sciences, Ehime University, Matsuyama, 790-8577, Japan 2 Faculty of Engineering, Kyushu Institute of Technology, Kitakyushu, 804-8550, Japan

Received  July 2010 Revised  January 2011 Published  October 2011

In this paper, we consider solutions to a Cauchy problem for a parabolic-elliptic system in two dimensional space. This system is a simpli ed version of a chemotaxis model, and is also a model of self-interacting particles. The behavior of solutions to the problem closely depends on the $L^1$-norm of the solutions. If the quantity is larger than 8$\pi$, the solution blows up in nite time. If the quantity is smaller than the critical mass, the solution exists globally in time. In the critical case, in nite blowup solutions are found. In the present paper, we direct our attention to radial solutions to the problem whose $L^1$-norm is equal to 8$\pi$ and nd oscillating solutions.
Citation: Yūki Naito, Takasi Senba. Oscillating solutions to a parabolic-elliptic system related to a chemotaxis model. Conference Publications, 2011, 2011 (Special) : 1111-1118. doi: 10.3934/proc.2011.2011.1111
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## ICFP 2009 Proceedings

Hi all,

I thought it might interest the LtU community that a few of the presentations from ICFP 2009 are avaialable for viewing. This particular link is to Guy Steele's talk Organizing Functional Code for Parallel Execution; or, foldl and foldr Considered Slightly Harmful but there are links to others and new ones seem to be getting added as well. I just stumbled on these and had nothing to do with actually making them available.

Enjoy.

## Comment viewing options

### Slides for Steele's talk

Organizing Functional Code for Parallel Execution

The first half is Scheme+cons, the second half is Fortress+conc.

### Proceedings

There was also a link to the proceedings on Reddit, with all papers apparently downloadable. Quite a few are PL-oriented.

### Coincidentally, I was just

Coincidentally, I was just reading Lammel's Google's MapReduce Programming Model -- Revisited, where he derives the parallelizable "map" and "reduce" functions used by MapReduce. So if traditional foldl and foldr are difficult to parallelize, Lammel's paper describes some slightly tweaked versions which parallelize quite easily.

### Well...

As I believe Laemmel notes, MapReduce's "reduce" is substantially different from FP's reduce/fold, so maybe "slightly tweaked" isn't quite right.


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HST/GHRS Studies of $\zeta$ Aurigae.\\ I. GHRS Observations of the 1993 Eclipse
Session 18 -- Stellar Spectra: Individual Objects
Display presentation, Wednesday, January 12, 9:30-6:45, Salons I/II Room (Crystal Gateway)

## [18.08] HST/GHRS Studies of $\zeta$ Aurigae.\\ I. GHRS Observations of the 1993 Eclipse

Alexander Brown, Jeffrey L. Linsky, Philip D. Bennett, Graham M. Harper (JILA, U. of Colorado \& NIST), Robert Baade, Thomas Kirsch, Dieter Reimers (Hamburg University, Germany)

The eclipsing binary $\zeta$ Aurigae (K4 Ib + B5 V) was observed using the Goddard High Resolution Spectrograph (GHRS) on Hubble Space Telescope (HST) at five epochs immediately preceeding and one following the April 1993 eclipse of the the hot B-type secondary by the K supergiant primary. A combination of Echelle-B and medium resolution G160M spectra were obtained at phases 0.78, 0.948, 0.957, 0.972, 0.978 and 1.13. These observations sample the absorption of the hot star's photospheric spectrum by the extended intervening cool star atmosphere. The GHRS spectra are presented and the circumstances of the individual observations are described. Fundamental parameters of the binary system derived from these data are discussed. \\ This work is supported by HST grant GO-3626.01-91A to the University of Colorado.