An axiomatic approach to the non-linear theory of generalized functions and consistency of Laplace transforms

We offer an axiomatic definition of a differential algebra of generalized functions over an algebraically closed non-Archimedean field. This algebra is of Colombeau type in the sense that it contains a copy of the space of Schwartz distributions. We study the uniqueness of the objects we define and the consistency of our axioms. Next, we identify an inconsistency in the conventional Laplace transform theory. As an application we offer a free of contradictions alternative in the framework of our algebra of generalized functions. The article is aimed at mathematicians, physicists and engineers who are interested in the non-linear theory of generalized functions, but who are not necessarily familiar with the original Colombeau theory. We assume, however, some basic familiarity with the Schwartz theory of distributions.Comment: 23 page

A p-adic analogue of Siegel's Theorem on sums of squares

Siegel proved that every totally positive element of a number field K is the sum of four squares, so in particular the Pythagoras number is uniformly bounded across number fields. The p ‐adic Kochen operator provides a p ‐adic analogue of squaring, and a certain localisation of the ring generated by this operator consists of precisely the totally p ‐integral elements of K . We use this to formulate and prove a p ‐adic analogue of Siegel's theorem, by introducing the p ‐Pythagoras number of a general field, and showing that this number is uniformly bounded across number fields. We also generally study fields with finite p ‐Pythagoras number and show that the growth of the p ‐Pythagoras number in finite extensions is bounded

A Study of Time-Dependent CP-Violating Asymmetries and Flavor Oscillations in Neutral B Decays at the Upsilon(4S)

We present a measurement of time-dependent CP-violating asymmetries in neutral B meson decays collected with the BABAR detector at the PEP-II asymmetric-energy B Factory at the Stanford Linear Accelerator Center. The data sample consists of 29.7 ${\rm fb}^{-1}$ recorded at the $\Upsilon(4S)$ resonance and 3.9 ${\rm fb}^{-1}$ off-resonance. One of the neutral B mesons, which are produced in pairs at the $\Upsilon(4S)$, is fully reconstructed in the CP decay modes $J/\psi K^0_S$, $\psi(2S) K^0_S$, $\chi_{c1} K^0_S$, $J/\psi K^{*0}$ ($K^{*0}\to K^0_S\pi^0$) and $J/\psi K^0_L$, or in flavor-eigenstate modes involving $D^{(*)}\pi/\rho/a_1$ and $J/\psi K^{*0}$ ($K^{*0}\to K^+\pi^-$). The flavor of the other neutral B meson is tagged at the time of its decay, mainly with the charge of identified leptons and kaons. The proper time elapsed between the decays is determined by measuring the distance between the decay vertices. A maximum-likelihood fit to this flavor eigenstate sample finds $\Delta m_d = 0.516\pm 0.016 {\rm (stat)} \pm 0.010 {\rm (syst)} {\rm ps}^{-1}$. The value of the asymmetry amplitude $\sin2\beta$ is determined from a simultaneous maximum-likelihood fit to the time-difference distribution of the flavor-eigenstate sample and about 642 tagged $B^0$ decays in the CP-eigenstate modes. We find $\sin2\beta=0.59\pm 0.14 {\rm (stat)} \pm 0.05 {\rm (syst)}$, demonstrating that CP violation exists in the neutral B meson system. (abridged)Comment: 58 pages, 35 figures, submitted to Physical Review

Measurement of the Branching Fraction for B- --> D0 K*-

We present a measurement of the branching fraction for the decay B- --> D0 K*- using a sample of approximately 86 million BBbar pairs collected by the BaBar detector from e+e- collisions near the Y(4S) resonance. The D0 is detected through its decays to K- pi+, K- pi+ pi0 and K- pi+ pi- pi+, and the K*- through its decay to K0S pi-. We measure the branching fraction to be B.F.(B- --> D0 K*-)= (6.3 +/- 0.7(stat.) +/- 0.5(syst.)) x 10^{-4}.Comment: 7 pages, 1 postscript figure, submitted to Phys. Rev. D (Rapid Communications

Evidence for the Rare Decay B -> K*ll and Measurement of the B -> Kll Branching Fraction

We present evidence for the flavor-changing neutral current decay $B\to K^*\ell^+\ell^-$ and a measurement of the branching fraction for the related process $B\to K\ell^+\ell^-$, where $\ell^+\ell^-$ is either an $e^+e^-$ or $\mu^+\mu^-$ pair. These decays are highly suppressed in the Standard Model, and they are sensitive to contributions from new particles in the intermediate state. The data sample comprises $123\times 10^6$ $\Upsilon(4S)\to B\bar{B}$ decays collected with the Babar detector at the PEP-II $e^+e^-$ storage ring. Averaging over $K^{(*)}$ isospin and lepton flavor, we obtain the branching fractions ${\mathcal B}(B\to K\ell^+\ell^-)=(0.65^{+0.14}_{-0.13}\pm 0.04)\times 10^{-6}$ and ${\mathcal B}(B\to K^*\ell^+\ell^-)=(0.88^{+0.33}_{-0.29}\pm 0.10)\times 10^{-6}$, where the uncertainties are statistical and systematic, respectively. The significance of the $B\to K\ell^+\ell^-$ signal is over $8\sigma$, while for $B\to K^*\ell^+\ell^-$ it is $3.3\sigma$.Comment: 7 pages, 2 postscript figues, submitted to Phys. Rev. Let

An Advanced Method to Assess the Diet of Free-Ranging Large Carnivores Based on Scats

<div><h3>Background</h3><p>The diet of free-ranging carnivores is an important part of their ecology. It is often determined from prey remains in scats. In many cases, scat analyses are the most efficient method but they require correction for potential biases. When the diet is expressed as proportions of consumed mass of each prey species, the consumed prey mass to excrete one scat needs to be determined and corrected for prey body mass because the proportion of digestible to indigestible matter increases with prey body mass. Prey body mass can be corrected for by conducting feeding experiments using prey of various body masses and fitting a regression between consumed prey mass to excrete one scat and prey body mass (correction factor 1). When the diet is expressed as proportions of consumed individuals of each prey species and includes prey animals not completely consumed, the actual mass of each prey consumed by the carnivore needs to be controlled for (correction factor 2). No previous study controlled for this second bias.</p> <h3>Methodology/Principal Findings</h3><p>Here we use an extended series of feeding experiments on a large carnivore, the cheetah (<em>Acinonyx jubatus</em>), to establish both correction factors. In contrast to previous studies which fitted a linear regression for correction factor 1, we fitted a biologically more meaningful exponential regression model where the consumed prey mass to excrete one scat reaches an asymptote at large prey sizes. Using our protocol, we also derive correction factor 1 and 2 for other carnivore species and apply them to published studies. We show that the new method increases the number and proportion of consumed individuals in the diet for large prey animals compared to the conventional method.</p> <h3>Conclusion/Significance</h3><p>Our results have important implications for the interpretation of scat-based studies in feeding ecology and the resolution of human-wildlife conflicts for the conservation of large carnivores.</p> </div

Why Has Human–Carnivore Conflict Not Been Resolved in Namibia?

Human–wildlife conflict has historically been portrayed as a management problem where solutions lie in technical changes or financial incentives. However, recent research shows many conflicts stem from social, economic, and political drivers. We undertook qualitative data collection on livestock farms to determine whether relationships between farmers and their workers affected frequency of reported livestock depredation in Namibia. We found that the conflict was affected by social and economic inequalities embedded in the previous apartheid regime. Macro- and microlevel socioeconomic problems created an environment where livestock depredation was exacerbated by unmotivated farm workers. Poor treatment of workers by farmers resulted in vengeful behaviors, such as livestock theft and wildlife poaching. Successfully addressing this situation therefore requires recognition and understanding of its complexity, rather than reducing it to its most simplistic part

Measurement of the B0-anti-B0-Oscillation Frequency with Inclusive Dilepton Events

The $B^0$-$\bar B^0$ oscillation frequency has been measured with a sample of 23 million \B\bar B pairs collected with the BABAR detector at the PEP-II asymmetric B Factory at SLAC. In this sample, we select events in which both B mesons decay semileptonically and use the charge of the leptons to identify the flavor of each B meson. A simultaneous fit to the decay time difference distributions for opposite- and same-sign dilepton events gives $\Delta m_d = 0.493 \pm 0.012{(stat)}\pm 0.009{(syst)}$ ps$^{-1}$.Comment: 7 pages, 1 figure, submitted to Physical Review Letter

Measurement of the branching fraction and CP content for the decay B(0) -> D(*+)D(*-)

This is the pre-print version of the Article. The official published version can be accessed from the links below. Copyright @ 2002 APS.We report a measurement of the branching fraction of the decay B0→D*+D*- and of the CP-odd component of its final state using the BABAR detector. With data corresponding to an integrated luminosity of 20.4  fb-1 collected at the Υ(4S) resonance during 1999–2000, we have reconstructed 38 candidate signal events in the mode B0→D*+D*- with an estimated background of 6.2±0.5 events. From these events, we determine the branching fraction to be B(B0→D*+D*-)=[8.3±1.6(stat)±1.2(syst)]×10-4. The measured CP-odd fraction of the final state is 0.22±0.18(stat)±0.03(syst).This work is supported by DOE and NSF (USA), NSERC (Canada), IHEP (China), CEA and CNRS-IN2P3 (France), BMBF (Germany), INFN (Italy), NFR (Norway), MIST (Russia), and PPARC (United Kingdom). Individuals have received support from the A.P. Sloan Foundation, Research Corporation, and Alexander von Humboldt Foundation