The Point Of Singularity

Singularity | Complex Functions | Britannica

singularity, also called singular point, of a function of the complex variable z is a point at which it is not analytic (that is, the function cannot be expressed as an infinite series in powers of z) although, at points arbitrarily close to the singularity, the function may be analytic, in which case it is called an isolated singularity. In general, because a function behaves in an anomalous manner at singular points, singularities must be treated separately when analyzing the function, or mathematical model, in which they appear. For example, the function f (z) = ez/z is analytic throughout the singularity, also called singular point, of a function of the complex variable z is a point at which it is not analytic (that is, the function cannot be ... [ReadMore..]

What Is The Singularity And Will You Live To See It?

If you read any science fiction or futurism, you've probably heard people using the term "singularity" to describe the world of tomorrow. But what exactly does it mean, and where does the idea come from? We answer in today's backgrounder. May 10, 2010 ... If you read any science fiction or futurism, you've probably heard people using the term "singularity" to describe the world of tomorrow. [ReadMore..]

The Omega Point And Beyond: The Singularity Event | American ...

Mar 1, 2012 ... “Omega Point” is a term coined by Pierre Teilhard de Chardin to describe the evolution of our universe. A Jesuit who later abandoned the ... [ReadMore..]

Curie Point Singularity In The Temperature Derivative Of Resistivity In ...

We observe a singularity in the temperature derivative $d\ensuremath{\rho}/dT$ of resistivity at the Curie point of high-quality (Ga,Mn)As ferromagnetic semiconductors with ${T}_{c}$'s ranging from approximately 80 to 185 K. The character of the anomaly is sharply distinct from the critical contribution to transport in conventional dense-moment magnetic semiconductors and is reminiscent of the $d\ensuremath{\rho}/dT$ singularity in transition metal ferromagnets. Within the critical region accessible in our experiments, the temperature dependence on the ferromagnetic side can be explained by dominant scattering from uncorrelated spin fluctuations. The singular behavior of $d\ensuremath{\rho}/dT$ on the paramagnetic side points to the important role of short-range correlated spin fluctuations. Aug 12, 2008 ... We observe a singularity in the temperature derivative $d\ensuremath{\rho}/dT$ of resistivity at the Curie point of high-quality (Ga,Mn)As ... [ReadMore..]

Singularity: Explain It To Me Like I'm 5-Years-Old

The Singularity will mark the moment when artificial intelligence becomes smarter than humans. There are a variety of theories of what that may mean. These kinds of dramatic shifts in thinking are called Singularity – a phrase that is originally derived from mathematics and describes a point which we are ... [ReadMore..]

Supersymmetric Quantum Mechanics With A Point Singularity

We study the possibility of supersymmetry (SUSY) in quantum mechanics in one dimension under the presence of a point singularity. The system considered is the free particle on a line R or on the interval [-l, l] where the point singularity lies at x = 0. In one dimension, the singularity is known to admit a U(2) family of different connection conditions which include as a special case the familiar one that arises under the Dirac delta-potential. Similarly, each of the walls at x = l and x = -l admits a U(1) family of boundary conditions including the Dirichlet and the Neumann boundary conditions. Under these general connection/boundary conditions, the system is shown to possess an N = 1 or N = 2 SUSY for various choices of the singularity and the walls, and the SUSY is found to be `good' or `broken' depending on the choices made. We use the supercharge which allows for a constant shift in the energy, and argue that if the system is supersymmetric then the supercharge is self-adjoint on states that respect the Oct 11, 2002 ... The system considered is the free particle on a line R or on the interval [-l, l] where the point singularity lies at x = 0. In one dimension, ... [ReadMore..]

Conformal Basis, Optical Theorem, And The Bulk Point Singularity

We study general properties of the conformal basis, the space of wavefunctions in $(d+2)$-dimensional Minkowski space that are primaries of the Lorentz group $SO(1,d+1)$. Scattering amplitudes written in this basis have the same symmetry as $d$-dimensional conformal correlators. We translate the optical theorem, which is a direct consequence of unitarity, into the conformal basis. In the particular case of a tree-level exchange diagram, the optical theorem takes the form of a conformal block decomposition on the principal continuous series, with OPE coefficients being the three-point coupling written in the same basis. We further discuss the relation between the massless conformal basis and the bulk point singularity in AdS/CFT. Some three- and four-point amplitudes in (2+1) dimensions are explicitly computed in this basis to demonstrate these results. Nov 16, 2017 ... ... the massless conformal basis and the bulk point singularity in AdS/CFT. Some three- and four-point amplitudes in (2+1) dimensions are ... [ReadMore..]

What Is The Singularity?

Learn about the singularity, a hypothetical future where technology growth leads to intelligent technologies that will radically transform our reality. In physics, there is gravitational singularity or space-time singularity that describes a location in space-time. According to Albert Einstein's Theory of ... [ReadMore..]

What Is A Singularity? - Universe Today

The concept of a space-time singularity - where time and space itself become infinite and undifferentiated - is one of the most fascinated and confounding problems of modern physics. Feb 16, 2011 ... In scientific terms, a gravitational singularity (or space-time singularity) is a location where the quantities that are used to measure the ... [ReadMore..]

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