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Louis Nirenberg
Louis Nirenberg (born 28 February 1925) is a Canadian American mathematician, considered one of the outstanding analysts of the 20th century. He has made fundamental contributions to linear and nonlinear partial differential equations (PDEs) and their application to complex analysis and geometry [...More Info...] [...Related Items...] 

Hamilton, Ontario
Hamilton (/ˈhæmɪltʌn/; is a port city in the Canadian province of Ontario. An industrialized city in the Golden Horseshoe at the west end of Lake Ontario, Hamilton has a population of 536,917, and a metropolitan population of 747,545. On January 1, 2001, the new City of Hamilton was formed through the amalgamation of the former city and the other constituent lowertier municipalities of the Regional Municipality of HamiltonWentworth with the uppertier regional government. Residents of the old city are known as Hamiltonians. Since 1981, the metropolitan area has been listed as the ninth largest in Canada and the third largest in Ontario. Hamilton is home to the Royal Botanical Gardens, the Canadian Warplane Heritage Museum, the Bruce Trail, McMaster University, Redeemer University College and Mohawk College [...More Info...] [...Related Items...] 

Navier–Stokes Existence And Smoothness
The Navier–Stokes existence and smoothness problem concerns the mathematical properties of solutions to the Navier–Stokes equations, one of the pillars of fluid mechanics (such as with turbulence). These equations describe the motion of a fluid in space. Solutions to the Navier–Stokes equations are used in many practical applications. However, theoretical understanding of the solutions to these equations is incomplete. In particular, solutions of the Navier–Stokes equations often include turbulence, which remains one of the greatest unsolved problems in physics, despite its immense importance in science and engineering. Even more basic properties of the solutions to Navier–Stokes have never been proven. For the threedimensional system of equations, and given some initial conditions, mathematicians have not yet proved that smooth solutions always exist, or that if they do exist, they have bounded energy [...More Info...] [...Related Items...] 

Partial Differential Equation
In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. PDEs are used to formulate problems involving functions of several variables, and are either solved by hand, or used to create a relevant computer model. A special case is ordinary differential equations (ODEs), which deal with functions of a single variable and their derivatives. PDEs can be used to describe a wide variety of phenomena such as sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, or quantum mechanics. These seemingly distinct physical phenomena can be formalised similarly in terms of PDEs. Just as ordinary differential equations often model onedimensional dynamical systems, partial differential equations often model multidimensional systems [...More Info...] [...Related Items...] 

Complex Analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, applied mathematics; as well as in physics, including the branches of hydrodynamics, thermodynamics, and particularly quantum mechanics [...More Info...] [...Related Items...] 

Geometry
Geometry (from the Ancient Greek: γεωμετρία; geo "earth", metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer. Geometry arose independently in a number of early cultures as a practical way for dealing with lengths, areas, and volumes [...More Info...] [...Related Items...] 

Elliptic Partial Differential Equation
Second order linear partial differential equations (PDEs) are classified as either elliptic, hyperbolic, or parabolic [...More Info...] [...Related Items...] 

Elasticity (physics)
In physics, elasticity (from Greek ἐλαστός "ductible") is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed. Solid objects will deform when adequate forces are applied on them. If the material is elastic, the object will return to its initial shape and size when these forces are removed. The physical reasons for elastic behavior can be quite different for different materials. In metals, the atomic lattice changes size and shape when forces are applied (energy is added to the system). When forces are removed, the lattice goes back to the original lower energy state. For rubbers and other polymers, elasticity is caused by the stretching of polymer chains when forces are applied. Perfect elasticity is an approximation of the real world. The most elastic body in modern science found is quartz fibre which is not even a perfect elastic body [...More Info...] [...Related Items...] 

Martingale (probability Theory) In probability theory, a martingale is a sequence of random variables (i.e., a stochastic process) for which, at a particular time in the realized sequence, the expectation of the next value in the sequence is equal to the present observed value even given knowledge of all prior observed values. 

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs. The society is one of the four parts of the Joint Policy Board for Mathematics and a member of the Conference Board of the Mathematical Sciences. 

Fluid Mechanics
Fluid mechanics is a branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them. Fluid mechanics has a wide range of applications, including mechanical engineering, civil engineering, chemical engineering, biomedical engineering, geophysics, astrophysics, and biology. Fluid mechanics can be divided into fluid statics, the study of fluids at rest; and fluid dynamics, the study of the effect of forces on fluid motion. It is a branch of continuum mechanics, a subject which models matter without using the information that it is made out of atoms; that is, it models matter from a macroscopic viewpoint rather than from microscopic. Fluid mechanics, especially fluid dynamics, is an active field of research with many problems that are partly or wholly unsolved. Fluid mechanics can be mathematically complex, and can best be solved by numerical methods, typically using computers [...More Info...] [...Related Items...] 

Mathematician A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems. Mathematics is concerned with numbers, data, quantity, structure, space, models, and change. 

Turbulence
Turbulence or turbulent flow is a flow regime in fluid dynamics characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow regime, which occurs when a fluid flows in parallel layers, with no disruption between those layers. Turbulence is commonly observed in everyday phenomena such as surf, fast flowing rivers, billowing storm clouds, or smoke from a chimney, and most fluid flows occurring in nature and created in engineering applications are turbulent. Turbulence is caused by excessive kinetic energy in parts of a fluid flow, which overcomes the damping effect of the fluid's viscosity. For this reason turbulence is easier to create in low viscosity fluids, but more difficult in highly viscous fluids. In general terms, in turbulent flow, unsteady vortices appear of many sizes which interact with each other, consequently drag due to friction effects increases [...More Info...] [...Related Items...] 

Millennium Prize Problems
The Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute in 2000. The problems are the Birch and SwinnertonDyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Poincaré conjecture, Riemann hypothesis, and Yang–Mills existence and mass gap [...More Info...] [...Related Items...] 

Unsolved Problems In Physics
Some of the major unsolved problems in physics are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result [...More Info...] [...Related Items...] 