All surveys employ, implicitly or explicitly, procedures for linking observational units (the individual elements of a population under study) to selection units (collectively, the elements of a sampling frame or universe used to acquire a sample of observational units). These procedures are called counting rules. For the development of estimators, it will be convenient to define a network to b...

‎We first give bounds for domains where the unitarizabile subquotients can show up in the parabolically induced representations of classical $p$-adic groups‎. ‎Roughly‎, ‎they can show up only if the‎ ‎central character of the inducing irreducible cuspidal representation is dominated by the‎ ‎square root of the modular character of the minimal parabolic subgroup‎. ‎For unitarizable subquotients...

‎In this paper‎, ‎we characterize the class of orthogonality preserving operators on an infinite-dimensional Hilbert space $H$ as scalar multiples of unitary operators between $H$ and some closed subspaces of $H$‎. ‎We show that any circle (centered at the origin) is the spectrum of an orthogonality preserving operator‎. ‎Also‎, ‎we prove that every compact normal operator is a strongly orthogo...

Unitary discharges were extracellularly recorded from cortical cells in the rabbit's visual area. Most of the cortical units were responsive to large-field illumination which was turned on and off at about 0.8/sec. Response characteristics of cortical cells were largely similar to those of retinal ganglion cells . One hundred and twenty-nine units which were analyzed successfully were categoriz...

Governed by locality, we explore a connection between unitary braid group representations associated to a unitary R-matrix and to a simple object in a unitary braided fusion category. Unitary R-matrices, namely unitary solutions to the Yang-Baxter equation, afford explicitly local unitary representations of braid groups. Inspired by topological quantum computation, we study whether or not it is...

If we interpret the Bekenstein–Hawking entropy of Hubble horizon as thermodynamic entropy, then entanglement superhorizon modes curvature perturbation entangled with subhorizon will exceed bound at some point; call this unitary paradox cosmological perturbations by analogy black hole. In order to avoid a fine-tuned problem, must occur during inflationary era critical time [Formula: see text] (i...

The search for fast unitary transforms and the need for data compression in linear systems are complementary issues. Compression requires the definition of a threshold dependent on the condition number, which is invariant over the unitary group. With respect tot this threshold it is shown that the SVD is the optimal tool. Considerations in connection with the Kronecker product and direct sum of...