This note supplies the proof of a theorem stated in the forthcoming book by Longley and Normann: namely, that Spector’s bar recursion functional is not representable by a left-well-founded sequential procedure, and hence is not definable in the language T + min (that is, Gödel’s System T augmented with the minimization operator), for instance within the Kleene–Kreisel model of total continuous ...

We consider bounded occurrence (degree) instances of a minimum constraint satisfaction problem MIN-LIN2 and a MIN-BISECTION problem for graphs. MIN-LIN2 is an optimization problem for a given system of linear equations mod 2 to construct a solution that sat-isses the minimum number of them. E3-OCC-MIN-E3-LIN2 is the bounded occurrence (degree) problem restricted as follows: each equation has ex...

We analyze two and three-dimensional variants of Hotelling’s model of differentiated products. In our setup, consumers can place different importance on each product attribute; this is measured by a weight in the disutility of distance in each dimension. Two firms play a two-stage game; they choose locations in stage 1 and prices in stage 2. We seek subgame-perfect equilibria. We find that all ...

in this paper, using a generalized translation operator, we prove theestimates for the generalized fourier-bessel transform in the space l2 on certainclasses of functions.

We provide a simple and efficient algorithm for the projection operator for weighted l1-norm regularization subject to a sum constraint, together with an elementary proof. The implementation of the proposed algorithm can be downloaded from the author’s homepage. 1 The problem In this report, we consider the following optimization problem: min x 1 2 ‖x − y‖ 2 + n

This paper is devoted to a general min-max characterization of the eigenvalues in a gap of the essential spectrum of a self-adjoint unbounded operator. We prove an abstract theorem, then we apply it to the case of Dirac operators with a Coulomb-like potential. The result is optimal for the Coulomb potential.

We provide a simple and efficient algorithm for the projection operator for weighted l1-norm regularization subject to a sum constraint, together with an elementary proof. The implementation of the proposed algorithm can be downloaded from the author’s homepage. 1 The problem In this report, we consider the following optimization problem: min x 1 2 ‖x− y‖ 2 + n

It is now well-known that many classes of deterministic control problems may be solved by max-plus or minplus (more generally, idempotent) numerical methods. These methods include max-plus basis-expansion approaches [1], [2], [6], [9], as well as the more recently developed curseof-dimensionality-free methods [9], [14]. It has recently been discovered that idempotent methods are applicable to s...

In this paper, based on the induced ordered weighted distance(IOWD) measure, we present a wide range of 2-tuple linguistic induced generalized weighted distance operators. Firstly, we introduce the 2-tuple linguistic induced generalized ordered weighted distance(2TLIGOWD) operator, which is a generalization of the classical induced ordered weighted averaging(IOWA) operator that uses 2-tuple lin...

High-level fluoroscopic boost options that exceed conventional exposure limits are available as a means of reducing quantum mottle during angiography. Federal law does not specify exposure limits for such high-level controls but requires specific means of activation to safeguard against inadvertent use. The American Association of Physicists in Medicine recently recommended that high-level expo...