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Physica. D, ISSN 0167-2789, 2002, Volume 162, Issue 1-2, pp. 9 - 33
The motion of plane curves in Klein geometry is studied. It is shown that the KdV, Harry–Dym, Sawada–Kotera, Burgers, the defocusing mKdV hierarchies, the... 
Klein geometry | Traveling wave | Lie algebra | Motion of plane curves | Integrable equations | traveling wave | MATHEMATICS, APPLIED | SYMMETRIES | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | SOLITONS | EVOLUTION | DYNAMICS | integrable equations | motion of plane curves | SPACE CURVES
Journal Article
Journal of differential geometry, ISSN 0022-040X, 2011, Volume 89, Issue 3, pp. 455 - 485
Contrast to the hyperbolic mean curvature flows studied in [HKL], [LS], and [KW], a new hyperbolic curvature flow is proposed for convex hypersurfaces. This... 
MATHEMATICS | EVOLUTION | MOTION | CONTRACTION | CONVEX HYPERSURFACES | STONES | PLANE-CURVES
Journal Article
Journal Article
1991, Translations of mathematical monographs, ISBN 0821845543, Volume 95., vii, 251
Book
Toxicology and applied pharmacology, ISSN 0041-008X, 2014, Volume 281, Issue 2, pp. 211 - 220
Epidemiological studies have reported associations between particulate matter (PM) and cardiovascular effects, and diabetes mellitus (DM) patients might be... 
Rats | Air pollution | Inflammation | Particulate matter | Diabetes mellitus | ENDOTHELIAL DYSFUNCTION | LONG-TERM EXPOSURE | SUBCLINICAL ATHEROSCLEROSIS | SYSTEMIC INFLAMMATION | AIR-POLLUTION EXPOSURE | INSULIN-RESISTANCE | CARDIOVASCULAR-DISEASE | FINE PARTICLES | PHARMACOLOGY & PHARMACY | SMOOTH-MUSCLE-CELLS | TOXICOLOGY | ASSOCIATION | Inflammation - chemically induced | Particulate Matter - toxicity | Myocarditis - chemically induced | Streptozocin | Glycated Hemoglobin A - metabolism | Homeostasis | Male | Diabetes Complications - diagnosis | Diabetic Nephropathies - blood | Inflammation - blood | Diabetes Mellitus, Experimental - blood | Time Factors | Interleukin-6 - blood | Diabetes Mellitus, Type 1 - chemically induced | Inhalation Exposure - adverse effects | Diabetes Mellitus, Experimental - chemically induced | Diabetic Cardiomyopathies - blood | Inflammation - diagnosis | Diabetic Angiopathies - chemically induced | Diabetes Mellitus, Experimental - diagnosis | Risk Factors | Diabetic Nephropathies - chemically induced | Inflammation Mediators - blood | Toxicity Tests, Subchronic | Biomarkers - blood | Diabetic Angiopathies - blood | Myocarditis - blood | Diabetes Complications - blood | Rats, Sprague-Dawley | Blood Glucose - drug effects | Particle Size | Diabetes Complications - chemically induced | Animals | Diabetes Mellitus, Type 1 - blood | Fibrinogen - metabolism | Blood Glucose - metabolism | Diabetic Cardiomyopathies - chemically induced | Glucose metabolism | Type 1 diabetes | Fibrinogen | Hemoglobin | Glucose | Health aspects | Dextrose | HOMEOSTASIS | INJURIES | RATS | AIR | COMPARATIVE EVALUATIONS | 60 APPLIED LIFE SCIENCES | AIR POLLUTION | DAMAGE | KIDNEYS | STREPTOZOCIN | GLOBAL ASPECTS | HYPERGLYCEMIA | BLOOD VESSELS | GLUCOSE | INFLAMMATION | DIABETES MELLITUS | FIBRINOGEN
Journal Article
Chaos, Solitons and Fractals, ISSN 0960-0779, 2004, Volume 19, Issue 1, pp. 47 - 53
Integrable systems satisfied by the curvatures of curves under inextensible motions in similarity geometries are identified. It is shown that motions of curves... 
DYNAMICS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | SOLITON
Journal Article
Nonlinear Differential Equations and Applications NoDEA, ISSN 1021-9722, 4/2012, Volume 19, Issue 2, pp. 177 - 194
... DOI 10.1007/s00030-011-0123-4 and Applications NoDEA The curve shortening problem under Robin boundary condition Kai-Seng Chou and Xiao-Liu Wang Abstract... 
Robin boundary condition | Long-time behavior of solution | Primary 53C44 | Analysis | Mathematics | 35B30 | 35B50 | Secondary 35B05 | Curve shortening problem | MATHEMATICS, APPLIED | CONTACT | PARABOLIC EQUATIONS | CONVERGENCE | MEAN-CURVATURE FLOW | ANGLE | PLANE-CURVES | SURFACES
Journal Article
Journal of the Physical Society of Japan, ISSN 0031-9015, 2001, Volume 70, Issue 7, pp. 1912 - 1916
It is shown that the KdV, Harry Dym, Sawada-Kotera hierarchies and the Kaup-Kupershmidt equation naturally arise from the motions of plane curves in special... 
traveling wave | KdV equation | motion of plane curve | special linear geometry | integrable equation | Traveling wave | Integrable equation | Motion of plane curve | Special linear geometry | SYMMETRIES | SOLITONS | LINEAR EVOLUTION-EQUATIONS | PHYSICS, MULTIDISCIPLINARY | TRANSFORM | SPACE CURVES
Journal Article
Advances in Mathematics, ISSN 0001-8708, 09/2006, Volume 205, Issue 1, pp. 33 - 83
The L -Minkowski problem introduced by Lutwak is solved for p ≥ n + 1 in the smooth category. The relevant Monge-Ampère equation (0.1) is solved for all p > 1.... 
Blaschke-Santalo inequality | Minkowski problem | Monge-Ampère equation | Centroaffine Minkowski problem
Journal Article
Nonlinearity, ISSN 0951-7715, 12/2010, Volume 23, Issue 12, pp. 3003 - 3028
... and multiple droplets for equations of thin film type Ka-Luen Cheung 1 and Kai-Seng Chou 2 1 Department of Mathematics and Information Technology, The Hong Kong Institute... 
LIQUID-FILMS | DROPS | MATHEMATICS, APPLIED | STEADY-STATES | LONG-TIME BEHAVIOR | SINGULARITIES | RUPTURE | BREAKUP | FLOWS | PHYSICS, MATHEMATICAL | INSTABILITIES
Journal Article
Oral diseases, ISSN 1601-0825, 2019, Volume 26, Issue 1, pp. 62 - 71
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 2/2019, Volume 58, Issue 1, pp. 1 - 22
... equation Kai-Seng Chou 1 · Ying-Chuen Kwong 2 Received: 1 May 2018 / Accepted: 7 December 2018 / Published online: 2 January 2019 © Springer-Verlag GmbH Germany, part... 
93D20 | 37B30 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | 35B35 | Analysis | Theoretical, Mathematical and Computational Physics | Secondary 76A20 | Mathematics | Primary 35Q35 | MATHEMATICS | MATHEMATICS, APPLIED | CONTINUITY | WEAK SOLUTIONS
Journal Article
Zeitschrift für angewandte Mathematik und Physik, ISSN 0044-2275, 10/2017, Volume 68, Issue 5, pp. 1 - 21
... and Kai-Seng Chou Abstract. The 2-D thin film equation describing the evolution of hang drops is studied. All radially symmetric steady states are classified... 
Droplets with zero contact angle | Engineering | Mathematical Methods in Physics | Secondary 35B35 | Primary 76A20 | The thin film equation | Energy stable solution | Radial symmetry | Theoretical and Applied Mechanics | 35K55 | MATHEMATICS, APPLIED | VISCOUS FILMS | STEADY-STATES | RAYLEIGH-TAYLOR INSTABILITY | BEHAVIOR | EQUATIONS | Thin films | Dielectric films
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 02/2017, Volume 145, Issue 2, pp. 853 - 860
It is shown that every positive, stable H^2_0-solution to \Delta u+f(u)=c in \mathbb{R}^2 is radially symmetric. This problem arises from the study of the... 
MATHEMATICS | MATHEMATICS, APPLIED | STEADY-STATES | STABILITY | BEHAVIOR
Journal Article
Nonlinearity, ISSN 0951-7715, 02/2007, Volume 20, Issue 2, pp. 299 - 317
... der Waals forces Kai-Seng Chou 1 and Ying-Chuen Kwong 2 1 Department of Mathematics, The Chinese University of Hong Kong, Hong Kong 2 Department of Mathematics... 
LIQUID-FILMS | MATHEMATICS, APPLIED | STEADY-STATES | STABILITY | EQUATIONS | DYNAMICS | PHYSICS, MATHEMATICAL | INSTABILITIES
Journal Article
Journal of the Physical Society of Japan, ISSN 0031-9015, 2002, Volume 71, Issue 4, pp. 1039 - 1043
It is shown that the determining system for motions of surfaces can be reduced to seven equations with nine unknown quantities. By choosing the velocities... 
Euler equation | KP and NVN equations | motions of surfaces | integrable equations | Integrable equations | Motions of surfaces | SPACE | PHYSICS, MULTIDISCIPLINARY | PLANE | DYNAMICS | NONLINEAR EVOLUTION-EQUATIONS | CURVES
Journal Article
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, ISSN 1078-0947, 05/2020, Volume 40, Issue 5, pp. 2963 - 2986
The Cauchy problem for a class of non-uniformly parabolic equations including (4) is studied for initial data with less regularity. When m is an element of... 
MATHEMATICS | LEVEL SETS | MATHEMATICS, APPLIED | MOTION | Widder's theorem | Initial trace | curve shortening problem | BLOW-UP | porous medium equations | Cauchy problem | SURFACES
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2001, Volume 261, Issue 2, pp. 741 - 751
A rigorous proof of the optimality of one-to-five-parameter systems for the symmetry group of the one-dimensional heat equation is given. 
optimal system | Lie group of symmetry | heat equation | adjoint representation | invariant | Invariant | Optimal system | Heat equation | Adjoint representation | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Advances in Mathematics, ISSN 0001-8708, 2006, Volume 205, Issue 1, pp. 33 - 83
The L p -Minkowski problem introduced by Lutwak is solved for p ⩾ n + 1 in the smooth category. The relevant Monge–Ampère equation (0.1) is solved for all p >... 
Blaschke–Santalo inequality | [formula omitted]-Minkowski problem | Centroaffine Minkowski problem | Monge–Ampère equation | Blaschke-Santalo inequality | MATHEMATICS | Monge-Ampere equation | GAUSS CURVATURE FLOW | REGULARITY | L-p-Minkowski problem | centroaffine Minkowski problem | AFFINE | SELF-SIMILAR SOLUTIONS
Journal Article
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