Dwork's congruences for the constant terms of powers of a Laurent polynomial

In this paper, we prove that the constant terms of powers of a Laurent polynomial satisfy certain congruences modulo prime powers. As a corollary, the generating series of these numbers considered as a function of a [Formula: see text]-adic variable admits an analytic continuation in a non-trivial way, as it was shown previously by Dwork for a class of hypergeometric series. </jats:p

Spin dependent recombination based magnetic resonance spectroscopy of bismuth donor spins in silicon at low magnetic fields

Low-field (6-110 mT) magnetic resonance of bismuth (Bi) donors in silicon has been observed by monitoring the change in photoconductivity induced by spin dependent recombination. The spectra at various resonance frequencies show signal intensity distributions drastically different from that observed in conventional electron paramagnetic resonance, attributed to different recombination rates for the forty possible combinations of spin states of a pair of a Bi donor and a paramagnetic recombination center. An excellent tunability of Bi excitation energy for the future coupling with superconducting flux qubits at low fields has been demonstrated.Comment: 5 pages, 4 figure

Neutrino energy transport in weak decoupling and big bang nucleosynthesis

We calculate the evolution of the early universe through the epochs of weak decoupling, weak freeze-out and big bang nucleosynthesis (BBN) by simultaneously coupling a full strong, electromagnetic, and weak nuclear reaction network with a multi-energy group Boltzmann neutrino energy transport scheme. The modular structure of our code provides the ability to dissect the relative contributions of each process responsible for evolving the dynamics of the early universe in the absence of neutrino flavor oscillations. Such an approach allows a detailed accounting of the evolution of the $\nu_e$, $\bar\nu_e$, $\nu_\mu$, $\bar\nu_\mu$, $\nu_\tau$, $\bar\nu_\tau$ energy distribution functions alongside and self-consistently with the nuclear reactions and entropy/heat generation and flow between the neutrino and photon/electron/positron/baryon plasma components. This calculation reveals nonlinear feedback in the time evolution of neutrino distribution functions and plasma thermodynamic conditions (e.g., electron-positron pair densities), with implications for: the phasing between scale factor and plasma temperature; the neutron-to-proton ratio; light-element abundance histories; and the cosmological parameter \neff. We find that our approach of following the time development of neutrino spectral distortions and concomitant entropy production and extraction from the plasma results in changes in the computed value of the BBN deuterium yield. For example, for particular implementations of quantum corrections in plasma thermodynamics, our calculations show a $0.4\%$ increase in deuterium. These changes are potentially significant in the context of anticipated improvements in observational and nuclear physics uncertainties.Comment: 37 pages, 12 Figures, 6 Table

Halo Modification of a Supernova Neutronization Neutrino Burst

We give the first self-consistent calculation of the effect of the scattered neutrino halo on flavor evolution in supernovae. Our example case is an O-Ne-Mg core collapse supernova neutronization neutrino burst. We find that the addition of the halo neutrinos produces qualitative and quantitative changes in the final flavor states of neutrinos. We also find that the halo neutrinos produce a novel distortion of the neutrino flavor swap. Our results provide strong motivation for tackling the full multidimensional and composition-dependent aspects of this problem in the future.Comment: 14 pages, 13 figures, 1 tabl

Neutrino scattering and flavor transformation in supernovae

We argue that the small fraction of neutrinos that undergo direction-changing scattering outside of the neutrinosphere could have significant influence on neutrino flavor transformation in core-collapse supernova environments. We show that the standard treatment for collective neutrino flavor transformation is adequate at late times, but could be inadequate in the crucial shock revival/explosion epoch of core-collapse supernovae, where the potentials that govern neutrino flavor evolution are affected by the scattered neutrinos. Taking account of this effect, and the way it couples to entropy and composition, will require a new paradigm in supernova modeling.Comment: 5 pages, 3 figure

Divergences in maximal supersymmetric Yang-Mills theories in diverse dimensions

The main aim of this paper is to study the scattering amplitudes in gauge field theories with maximal supersymmetry in dimensions D=6,8 and 10. We perform a systematic study of the leading ultraviolet divergences using the spinor helicity and on-shell momentum superspace framework. In D=6 the first divergences start at 3 loops and we calculate them up to 5 loops, in D=8,10 the first divergences start at 1 loop and we calculate them up to 4 loops. The leading divergences in a given order are the polynomials of Mandelstam variables. To be on the safe side, we check our analytical calculations by numerical ones applying the alpha-representation and the dedicated routines. Then we derive an analog of the RG equations for the leading pole that allows us to get the recursive relations and construct the generating procedure to obtain the polynomials at any order of (perturbation theory) PT. At last, we make an attempt to sum the PT series and derive the differential equation for the infinite sum. This equation possesses a fixed point which might be stable or unstable depending on the kinematics. Some consequences of these fixed points are discussed.Comment: 43 pages, 13 figures, pdf LaTex, v2 minor changes and references adde

Multimedia technology in teaching mathematics pupils 1 – 4 classes

We describe the use of multimedia technology in teaching mathematics in elementary school. The synthesis, systematization, synthesis of existing theoretical positions that make it possible to organize teaching mathematics elementary school students using multimedia technology. Used systematic and comparative analysis of scientific-methodological and psycho-pedagogical literature. The concept multimedia support teaching mathematics in elementary school. Developed requirements and proposed guidelines for creating and using multimedia learning support during lessons in mathematics 1 – 4 classes: presentations, simulators, dynamic models, educational expert systems. Proved that the use of the investigated technologies grounded in multimedia teaching mathematics accompanied by elementary school students during development is important to ensure the selection of appropriate methods of components that should create new opportunities prepare students while changing living conditions, encourage self-education.Keywords: teaching mathematics, primary school, multimedia technology, multimedia support training requirements.Описано використання мультимедійних технологій у навчанні математики в початковій школі. Здійснено синтез, систематизацію, узагальнення наявних теоретичних положень, що вможливлюють організацію навчання математики учнів початкової школи з використанням мультимедійних технологій.  Використано системний і порівняльний аналіз науково-методичної та психолого-педагогічної літератури. Уточнено поняття мультимедійного супроводу навчання математики в початковій школі. Розроблено вимоги та запропоновано методичні рекомендації щодо створення та використання мультимедійного супроводу навчання під час уроків математики у 1 – 4 класах. Показано, що використання досліджуваних технологій ґрунтоване на мультимедійному супроводі навчання математики учнів початкової школи, під час розроблення якого важливо забезпечувати вибір відповідних компонентів методики, що має створювати можливості нової підготовки учнів під час зміни умов життєдіяльності, стимулювати самоосвіту.Ключові слова: навчання математики, початкова школа, мультимедійні технології, мультимедійний супровід навчання, вимоги

The Structure of UV Divergences in Maximally Supersymmetric Gauge Theories

We consider the UV divergences up to sub-sub leading order for the four-point on-shell scattering amplitudes in D=8 supersymmetric Yang-Mills theory in the planar limit. We trace how the leading, subleading, etc divergences appear in all orders of perturbation theory. The structure of these divergences is typical for any local quantum field theory independently on renormalizability. We show how the generalized RG equations allow one to evaluate the leading, subleading, etc. contributions in all orders of PT starting from one-, two-, etc. loop diagrams respectively. We focus then on subtraction scheme dependence of the results and show that in full analogy with renormalizable theories the scheme dependence can be absorbed into the redefinition of the couplings. The only difference is that the role of the couplings play dimensionless combinations like g^2s^2 or g^2t^2, where s and t are the Mandelstam variables.Comment: Latex, 15 pg, 5 figs. arXiv admin note: text overlap with arXiv:1610.0554