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A singularity is originally a mathematical term for a point at which an equation has no solution. In physics, it was proven that a large enough collapsing star would eventually become a black hole, so dense that its own gravity would cause a 'singularity' in the fabric of space-time, a point where many of the physics equations suddenly have no solution.
Singularity has become, in physics, another name for a black hole, a compression of matter so dense, not even light can escape it.
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What is Proof of circle theorem in fluid?
Since z = a^2/z on the circle, we see that w as given by (1) is purely real on the circle C and therefore if* = 0. Thus C is a streamline. If the point z is outside 0, the point az /z is inside 0, and vice-versa. Since all the singularities off(z) are by hypothesis exterior to C, all the singularities off(a?/z) are interior to C ; in particular f(a z /z) has no singularity at infinity, since f(z) has none at z = 0. Thus w has exactly the same singularities as/(z) and so all the conditions are satisfied.
How do you find points that make a complex function non analytic?
To find points that make a complex function non-analytic, you need to identify where the function is not differentiable. This typically occurs at points where the function is not defined, where it has discontinuities, or where the Cauchy-Riemann equations are not satisfied. Additionally, check for singularities, such as poles or essential singularities, which also indicate non-analytic behavior. Analyzing these aspects will help you locate non-analytic points in the function's domain.
What did Karen smith the mathematician do for math?
Karen Smith works in algebra and algebraic geometry. Some of her main contributions involve finding purely algebraic ways to understand geometric objects, such as singularities in algebraic geometry. This is significant because, for example, even a computer can manipulate algebraic equations but it can not understand a drawing as well. I can answer more if you describe how much mathematics you have taken.
What are the drawbacks of numerical integration?
Numerical integration can introduce errors due to approximation methods, especially when the function is complex or not well-behaved. It may require a significant number of function evaluations, leading to increased computational cost and time. Additionally, the accuracy of the results can be highly dependent on the choice of the integration method and the step size, which may necessitate careful tuning. Lastly, it may struggle with singularities or discontinuities in the integrand, leading to unreliable outcomes.
How do you find limit in a line integral in the complex plane?
To find a limit in a line integral in the complex plane, you typically evaluate the integral along a specified contour. This involves parameterizing the contour with a complex variable, substituting this parameterization into the integral, and then computing the limit as the parameter approaches a particular value. If you're evaluating a limit involving singularities, you may need to consider residue theory or deformation of the contour to avoid poles. Finally, apply the appropriate limit process, such as the squeeze theorem or L'Hôpital's rule, if necessary.
What has the author Alexandru Dimca written?
Alexandru Dimca has written: 'Topics on real and complex singularities' -- subject(s): Singularities (Mathematics)
What has the author J W Bruce written?
J. W. Bruce has written: 'Curves and singularities' -- subject(s): Curves, Singularities (Mathematics)
What is singularities?
anything which is single in number are singular.
What has the author J Seade written?
J. Seade has written: 'On the topology of isolated singularities in analytic spaces' -- subject(s): Algebraic Geometry, Analytic spaces, Singularities (Mathematics), Topology
What has the author Zohar Yosibash written?
Zohar Yosibash has written: 'Singularities in elliptic boundary value problems and elasticity and their connection with failure initiation' -- subject(s): Boundary value problems, Singularities (Mathematics)
What has the author Stephen Shing-Toung Yau written?
Stephen Shing-Toung Yau has written: 'Classification of Jacobian ideals invariant by sl(2, C) actions' -- subject(s): Ideals (Algebra), Lie algebras, Polynomials, Singularities (Mathematics) 'Gorenstein quotient singularities in dimension three' -- subject(s): Finite groups, Invariants, Singularities (Mathematics)
When were naked singularities discovered?
they havent been discovered yet its a theor y
What is singularities of big bang theory?
A singularity is a situation in which a certain mass (usually a large mass) is concentrated in ZERO volume, resulting in an infinite density. This can happen, in certain theories, for black holes, and as the initial conditions of the Big Bang. Physicists generally believe that such singularities don't really exist, and that, if singularities to appear in some formula, they represent a failure of the corresponding theory at extreme conditions.
What has the author Pericles S Theocaris written?
Pericles S. Theocaris has written: 'Singularities at the vertices of bi-wedges' -- subject(s): Singularities (Mathematics), Strains and stresses, Wedges 'Matrix theory of photoelasticity' -- subject(s): Photoelasticity
What are similaritiesa between black hole and big bang singularities?
Both black hole and Big Bang singularities are points of infinite density and mass where known physical laws break down. They are both areas where gravity is extremely strong, leading to intense curvature of spacetime. Additionally, our current understanding of physics is unable to fully describe or predict the behavior of matter and energy within these singularities.
What is something we found by looking to see what would make the denominator 0?
You find the singularities of the expression.
What has the author Hampton N Shirer written?
Hampton N. Shirer has written: 'Mathematical structure of the singularities at the transitions between steady states in hydrodynamic systems' -- subject(s): Hydrodynamics, Stability, Bifurcation theory, Catastrophes (Mathematics), Turbulence, Singularities (Mathematics)
