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كثير من الجهود حول 248
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في هذه المذكرة، نقدم ثلاثة تمثيلات للجبر الخطي الذي يتكون من 248 بعد، وهي الجبر الخطي الذي يسمح بنظام من خمسة معادلات تفاضل عادية بسيطة كل منها بترتيب 44، والذي يسمح بنظام من سبعة معادلات تفاضل عادية بسيطة كل منها بترتيب 28، والذي يسمح بمعادلة تفاضل عادية بسيطة واحدة بترتيب 244.
In this note we present three representations of a 248-dimensional Lie algebra, namely the algebra of Lie point symmetries admitted by a system of five trivial ordinary differential equations each of order forty-four, that admitted by a system of seven trivial ordinary differential equations each of order twenty-eight and that admitted by one trivial ordinary differential equation of order two hundred and forty-four.
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We prove an analog of the Ado theorem - the existence of a finite-dimensional faithful representation - for a certain kind of finite-dimensional nilpotent Hom-Lie algebras.
We consider the production of charmed baryons and mesons in the proton-antiproton binary reactions at the energies of the future $bar{P}$ANDA experiment. To describe these processes in terms of hadronic interaction models, one needs strong couplings of the initial nucleons with the intermediate and final charmed hadrons. Similar couplings enter the models of binary reactions with strange hadrons. For both charmed and strange hadrons we employ the strong couplings and their ratios calculated from QCD light-cone sum rules. In this method finite masses of $c$ and $s$ quarks are taken into account. Employing the Kaidalovs quark-gluon string model with Regge poles and adjusting the normalization of the amplitudes in this model to the calculated strong couplings, we estimate the production cross section of charmed hadrons. For $pbar{p}to Lambda_cbar{Lambda}_c$ it can reach several tens of $nb$ at $p_{lab}= 15 {GeV}$, whereas the cross sections of $Sigma_c$ and $D$ pair production are predicted to be smaller.
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In astronomical and cosmological studies one often wishes to infer some properties of an infinite-dimensional field indexed within a finite-dimensional metric space given only a finite collection of noisy observational data. Bayesian inference offers an increasingly-popular strategy to overcome the inherent ill-posedness of this signal reconstruction challenge. However, there remains a great deal of confusion within the astronomical community regarding the appropriate mathematical devices for framing such analyses and the diversity of available computational procedures for recovering posterior functionals. In this brief research note I will attempt to clarify both these issues from an applied statistics perpective, with insights garnered from my post-astronomy experiences as a computational Bayesian / epidemiological geostatistician.
We prove an explicit upper bound on the amount of entanglement required by any strategy in a two-player cooperative game with classical questions and quantum answers. Specifically, we show that every strategy for a game with n-bit questions and n-qubit answers can be implemented exactly by players who share an entangled state of no more than 5n qubits--a bound which is optimal to within a factor of 5/2. Previously, no upper bound at all was known on the amount of entanglement required even to approximate such a strategy. It follows that the problem of computing the value of these games is in NP, whereas previously this problem was not known to be computable.
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