We establish an operator-theoretic uncertainty principle over arbitrary compact groups, generalizing several previous results. As a consequence, we show that every nonzero square-integrable function f on a compact group G satisfies μ(supp f) · P ρ∈Ĝ dρ rk f̂(ρ) ≥ 1. For finite groups, our principle implies the following: if P and R are projection operators on the group algebra CG such that P com...

A nonlinear electrical transmission line with an intersite circuit element acting as a nonlinear resistance is introduced and investigated. In the continuum limit, the dynamics of localized signals is described by a nonlinear evolution equation belonging to the family of nonlinear diffusive Burgers’ equations. This equation admits compact pulse solutions and shares some symmetry properties with...

This paper proposes a chosen-ciphertext secure variant of the ElGamal public-key encryption scheme which generates very compact ciphertexts for messages of arbitrary length. The ciphertext overhead (i.e., the difference between ciphertext and plaintext) is one group element only. Such a property is particularly useful when encrypting short messages such as a PIN or a credit card number in bandw...

We study homoclinic points of non-expansive automorphisms of compact abelian groups. Connections between the existence of non-trivial homoclinic points, expansiveness, entropy and adjoint automorphisms (in the sense of Einsiedler and Schmidt) are explored. Some implications for countable abelian group actions by automorphisms of compact abelian groups are also considered and it is shown that if...

We demonstrate a compact system, incorporating a 32-element linear array of ultraviolet (290 nm and 340 nm) light-emitting diodes (LEDs) and a multi-anode photomultiplier tube, to the in-flight fluorescence detection of aerosolized particles, here containing the biological molecules tryptophan and NADH. This system illustrates substantial advances in the growth and fabrication of new semiconduc...

Let X be a proper CAT(0)-space and let G be a closed subgroup of the isometry group Iso(X) of X. We show that if G is non-elementary and contains a rank-one element then its second bounded cohomology group with coefficients in the regular representation is non-trivial. As a consequence, up to passing to an open subgroup of finite index, either G is a compact extension of a totally disconnected ...

Miniaturization of optical spectrometers has a significant practical value as it can enable compact, affordable spectroscopic systems for chemical and biological sensing applications. For many applications, the spectrometer must gather light from sources that span a wide range of emission angles and wavelengths. Here, we report a lens-free spectrometer that is simultaneously compact (<0.6  cm<s...

Measurements of CMB anisotropy are ideal experiments for discovering the non-trivial global topology of the universe. To evaluate the CMB anisotropy in multiply-connected(MC) compact cosmological models, one needs to compute the eigenmodes of the Laplace-Beltrami operator. We numerically obtain the low-lying eigenmodes on a compact 3-hyperbolic space called m003(−2, 3) in the SnapPea using the ...

We report the results of our study on the role of microfluidic infiltration technique in improving the coupling characteristics of dual-core photonic crystal fiber (PCF) couplers. Using the finite element method (FEM), we evaluate the effective mode area, dispersion and coupling parameters of an infiltrated dual-core PCF. We use these parameters to design a compact and reconfigurable coupler by...

In this case, a set C ∈ C may be called a cell in X. A compact Hausdorff space with a cellular structure is a cellular space. For example, the usual construction of the Cantor set leads to a natural cellular structure, where the cells are the parts of the Cantor set in the closed intervals generated in the construction. Of course, a Hausdorff topological space with a base for its topology consi...