Unary Primitive Recursive Functions

In this article, we study some new characterizations of primitive recursive functions based on restricted forms of primitive recursion, improving the pioneering work of R. M. Robinson and M. D. Gladstone in this area. We reduce certain recursion schemes (mixed/pure iteration without parameters) and we characterize one-argument primitive recursive functions as the closure under substitution and iteration of certain optimal sets

Stress correlations of dislocations in a double-pileup configuration: a continuum dislocation density approach – complas XII

Dislocation motion in the crystal lattice of materials is the basis for macroscopic plasticity. While continuum models for describing the role of dislocations in plasticity have existed for decades, only recently have the mathematical tools become available to describe ensembles of moving, oriented lines. These tools have allowed for the creation of a Continuum Dislocation Dynamics (CDD) theory describing a second-order dislocation density tensor, a higher order analog of the classical dislocation density tensor, and its evolution in time. In order to reduce the computational complexity of the theory, a simplified theory has also been developed, which more readily allows for a numerical implementation, useful for describing larger systems of dislocations. In order to construct a self-consistent implementation, several issues have to be resolved including calculation of the stress field of a system of dislocations, coarse graining, and boundary values. The present work deals with the implementation including treatment of the near- and far-field stresses caused by the dislocation density tensor as well as boundary value considerations. The implementation is then applied to a few simple benchmark problems, notably the double pileup of dislocations in 1D. Applications to more general problems are considered, as well as comparisons with analytical solutions to classical dislocation problems. Focus is placed on problems where analytical solutions as well as simulations of discrete dislocations are known which act, along with experimental results, as the basis of comparison to determine the validity of the results

On the Finite Dimensional Laws of Threshold GARCH Processes

In this chapter we establish bounds for the finite dimensional laws of a threshold GARCH process, X, with generating process Z. In this class of models the conditional standard deviation has different reactions according to the sign of past values of the process. So, we firstly find lower and upper bounds for the law of \left ({X}_{1}^{+},-{X}_{1}^{+},\ldots,{X}_{n}^{+},-{X}_{n}^{+}\right), in certain regions of R^{2n}, and use them to find bounds of the law of \left ({X}_{1},\ldots,{X}_{n}\right). Some of these bounds only depend on the parameters of the model and on the distribution function of the independent generating process, Z. An application of these bounds to control charts for time series is presented

Measurement of the Branching Ratio for the Beta Decay of 14^{14}O

We present a new measurement of the branching ratio for the decay of $^{14}$O to the ground state of $^{14}$N. The experimental result, $\lambda _0/\lambda _{\rm total} = (4.934 \pm 0.040\kern 1pt{\rm (stat.)} \pm 0.061\kern 1pt{\rm (syst.)}) \times 10^{-3}$, is significantly smaller than previous determinations of this quantity. The new measurement allows an improved determination of the partial halflife for the superallowed $0^+ \rightarrow 0^+$ Fermi decay to the $^{14}$N first excited state, which impacts the determination of the $V_{ud}$ element of the CKM matrix. With the new measurement in place, the corrected $^{14}$O ${\cal F} t$ value is in good agreement with the average ${\cal F} t$ for other superallowed $0^+ \rightarrow 0^+$ Fermi decays.Comment: 8 pages, 4 figure

The Half-lives of 132^{132}La and 135^{135}La

The half-lives of $^{135}$La and $^{132}$La were determined via gamma spectroscopy and high-precision ionization chamber measurements. The results are 18.930(6) h for $^{135}$La and 4.59(4) h for $^{132}$La compared to the previously compiled values of 19.5(2) h and 4.8(2) h, respectively. The new results represent an improvement in the precision and accuracy of both values. These lanthanum isotopes comprise a medically interesting system with positron emitter $^{132}$La and Auger electron emitter $^{135}$La forming a matched pair for internal diagnostics and therapeutics. The precise half-lives are necessary for proper evaluation of their value in medicine and for a more representative tabulation of nuclear data.Comment: 11 pages, 3 figure

In Vivo Radionuclide Generators for Diagnostics and Therapy

In vivo radionuclide generators make complex combinations of physical and chemical properties available for medical diagnostics and therapy. Perhaps the best-known in vivo generator is 212Pb/212Bi, which takes advantage of the extended half-life of 212Pb to execute a targeted delivery of the therapeutic short-lived α-emitter 212Bi. Often, as in the case of 81Rb/81Kr, chemical changes resulting from the transmutation of the parent are relied upon for diagnostic value. In other instances such as with extended alpha decay chains, chemical changes may lead to unwanted consequences. This article reviews some common and not-so-common in vivo generators with the purpose of understanding their value in medicine and medical research. This is currently relevant in light of a recent push for alpha emitters in targeted therapies, which often come with extended decay chains

Which One? Grounding the Referent Based on Efficient Human-Robot Interaction

In human-robot interaction, a robot must be prepared to handle possible ambiguities generated by a human partner. In this work we propose a set of strategies that allow a robot to identify the referent when the human partner refers to an object giving incomplete information, i.e. an ambiguous description. Moreover, we propose the use of an ontology to store and reason on the robot's knowledge to ease clarification, and therefore, improve interaction. We validate our work through both simulation and two real robotic platforms performing two tasks: a daily-life situation and a game.Psycholog