In this paper I am careful to distinguish between the space of signals and the space of their Fourier transforms. Folland and Sitaram [4] give a survey of uncertainty principles in analysis. First we will go through the talk by Emmanuel Candès and Terence Tao, “The uniform uncertainty principle and compressed sensing”, Harmonic Analysis and Related Topics, Seville, December 5, 2008. Let G = Z/n...

The Brill-Lindquist time-symmetric initial-value solution for two uncharged black holes is rederived using the Hamiltonian constraint equation with Dirac delta distributions as a source for the binary black-hole field. The bare masses of the Brill-Lindquist black holes are introduced in a way which is applied, after straightforward modification, to the Misner-Linquist binary black-hole solution.

We study Wilson-’t Hooft loop operators in a class of N = 2 superconformal field theories recently introduced by Gaiotto. In the case that the gauge group is a product of SU(2) groups, we classify all possible loop operators in terms of their electric and magnetic charges subject to the Dirac quantization condition. We then show that this precisely matches Dehn’s classification of homotopy clas...

It has been proposed recently [3] that excitations in Spin Ice can be of the form of magnetic monopoles that does not obey the Dirac Quantization Condition. It is also well known [5] that the above scenario leads to non-associativity among translation generators. It will be interesting to see how the monopole picture in Spin Ice survives in the light of the latter observation.

Let f and g be distributions and let gn = (g ∗ δn)(x), where δn(x) is a certain sequence converging to the Dirac-delta function δ(x). The noncommutative neutrix product f ◦ g of f and g is defined to be the neutrix limit of the sequence { f gn}, provided the limit h exists in the sense that N-limn→∞〈 f (x)gn(x),φ(x)〉 = 〈h(x),φ(x)〉, for all test functions in . In this paper, using the concept of...

Let F be a distribution inD′ and let f be a locally summable function. The composition F f x of F and f is said to exist and be equal to the distribution h x if the limit of the sequence {Fn f x } is equal to h x , where Fn x F x ∗ δn x for n 1, 2, . . . and {δn x } is a certain regular sequence converging to the Dirac delta function. In the ordinary sense, the composition δ s sinh−1x r does no...

We establish the existence and uniqueness of the Dipole Solution of the porous medium equation (PME), i.e. the solution of u t = (juj m?1 u) ; in Q = f(x; t) : x = (x i) 2 R N ; t > 0g ; with m > 1 and initial value u(x; 0) = M @ @x 1 (x) ; where is Dirac delta function in R N and M 6 = 0. It has the self-similar form u(x; t) = t ? U(xt ?) ; with exponents and determined from dimensional consid...

The weak coupling asymptotics, to order r c 2 ( ) , of the ground state energy of the delta-function Bose gas is derived. Here  c 2 0 is the delta-function potential amplitude and ρ the density of the gas in the thermodynamic limit. The analysis uses the electrostatic interpretation of the Lieb–Liniger integral equation.

A classical result in differential geometry due to Lichnerowicz [8] is concerned with the decomposition of the square of Dirac operators defined by Clifford connections on a Clifford module E over a Riemannian manifold M . Recently, this formula has been generalized to arbitrary Dirac operators [2]. In this paper we prove a supersymmetric version of the generalized Lichnerowicz formula, motivat...