Splitting fields and general differential Galois theory

An algebraic technique is presented that does not use results of model theory and makes it possible to construct a general Galois theory of arbitrary nonlinear systems of partial differential equations. The algebraic technique is based on the search for prime differential ideals of special form in tensor products of differential rings. The main results demonstrating the work of the technique obtained are the theorem on the constructedness of the differential closure and the general theorem on the Galois correspondence for normal extensions..Comment: 33 pages, this version coincides with the published on

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

Cinematic and aesthetic cartographies of subjective mutation

This article exmaines the use of cinema as a mapping of subjective mutation in the work of Deleuze, Gauttari and Berardi. Drawing on Deleuze's distinciton between the reduction of the art-work to the symptom and the idea of art as symptomatology, the article focuses on Berardi's use of cinematic examples, posing the quesiton in each case of to what extent they function as symptomatologies or mere symptoms of cultural and subjective mutations in examples ranging from Bergman's Persona to Van Sant's Elephant to finish on speculations about Fincher's The Social Network as a cirtical engagement with subjective mutation in the 21st Century

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

Constructible motivic functions and motivic integration

We introduce a direct image formalism for constructible motivic functions. One deduces a very general version of motivic integration for which a change of variables theorem is proved. These constructions are generalized to the relative framework, in which we develop a relative version of motivic integration. These results have been announced in math.AG/0403349 and math.AG/0403350. Main results and statements unchanged. Many minor slips corrected and some details added.Comment: Final versio

BioLPG for Clean Cooking in Sub-Saharan Africa: Present and Future Feasibility of Technologies, Feedstocks, Enabling Conditions and Financing

Energy supply for clean cooking is a priority for Sub-Saharan Africa (SSA). Liquefied petroleum gas (LPG, i.e., propane or butane or a mixture of both) is an economically efficient, cooking energy solution used by over 2.5 billion people worldwide and scaled up in numerous low- and middle-income countries (LMICs). Investigation of the technical, policy, economic and physical requirements of producing LPG from renewable feedstocks (bioLPG) finds feasibility at scale in Africa. Biogas and syngas from the circular economic repurposing of municipal solid waste and agricultural waste can be used in two groundbreaking new chemical processes (Cool LPG or Integrated Hydropyrolysis and Hydroconversion (IH2)) to selectively produce bioLPG. Evidence about the nature and scale potential of bioLPG presented in this study justifies further investment in the development of bioLPG as a fuel that can make a major contribution toward enabling an SSA green economy and universal energy access. Techno-economic assessments of five potential projects from Ghana, Kenya and Rwanda illustrate what might be possible. BioLPG technology is in the early days of development, so normal technology piloting and de-risking need to be undertaken. However, fully developed bioLPG production could greatly reduce the public and private sector investment required to significantly increase SSA clean cooking capacity

The SCRIPT trial: study protocol for a randomised controlled trial of a polygenic risk score to tailor colorectal cancer screening in primary care

BACKGROUND: Polygenic risk scores (PRSs) can predict the risk of colorectal cancer (CRC) and target screening more precisely than current guidelines using age and family history alone. Primary care, as a far-reaching point of healthcare and routine provider of cancer screening and risk information, may be an ideal location for their widespread implementation. METHODS: This trial aims to determine whether the SCRIPT intervention results in more risk-appropriate CRC screening after 12 months in individuals attending general practice, compared with standard cancer risk reduction information. The SCRIPT intervention consists of a CRC PRS, tailored risk-specific screening recommendations and a risk report for participants and their GP, delivered in general practice. Patients aged between 45 and 70 inclusive, attending their GP, will be approached for participation. For those over 50, only those overdue for CRC screening will be eligible to participate. Two hundred and seventy-four participants will be randomised to the intervention or control arms, stratified by general practice, using a computer-generated allocation sequence. The primary outcome is risk-appropriate CRC screening after 12 months. For those in the intervention arm, risk-appropriate screening is defined using PRS-derived risk; for those in the control arm, it is defined using family history and national screening guidelines. Timing, type and results of the previous screening are considered in both arms. Objective health service data will capture screening behaviour. Secondary outcomes include cancer-specific worry, risk perception, predictors of CRC screening behaviour, screening intentions and health service use at 1, 6 and 12 months post-intervention delivery. DISCUSSION: This trial aims to determine whether a PRS-derived personalised CRC risk estimate delivered in primary care increases risk-appropriate CRC screening. A future population risk-stratified CRC screening programme could incorporate risk assessment within primary care while encouraging adherence to targeted screening recommendations. TRIAL REGISTRATION: Australian and New Zealand Clinical Trial Registry ACTRN12621000092897p. Registered on 1 February 2021. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s13063-022-06734-7

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