Complete list of Darboux Integrable Chains of the form t1x=tx+d(t,t1)t_{1x}=t_x+d(t,t_1)

We study differential-difference equation of the form $$\frac{d}{dx}t(n+1,x)=f(t(n,x),t(n+1,x),\frac{d}{dx}t(n,x))$$ with unknown $t(n,x)$ depending on continuous and discrete variables $x$ and $n$. Equation of such kind is called Darboux integrable, if there exist two functions $F$ and $I$ of a finite number of arguments $x$, $\{t(n\pm k,x)\}_{k=-\infty}^\infty$, ${\frac{d^k}{dx^k}t(n,x)}_{k=1}^\infty$, such that $D_xF=0$ and $DI=I$, where $D_x$ is the operator of total differentiation with respect to $x$, and $D$ is the shift operator: $Dp(n)=p(n+1)$. Reformulation of Darboux integrability in terms of finiteness of two characteristic Lie algebras gives an effective tool for classification of integrable equations. The complete list of Darboux integrable equations is given in the case when the function $f$ is of the special form $f(u,v,w)=w+g(u,v)$

Mn local moments prevent superconductivity in iron-pnictides Ba(Fe 1-x Mn x)2As2

75As nuclear magnetic resonance (NMR) experiments were performed on Ba(Fe1-xMnx)2As2 (xMn = 2.5%, 5% and 12%) single crystals. The Fe layer magnetic susceptibility far from Mn atoms is probed by the75As NMR line shift and is found similar to that of BaFe2As2, implying that Mn does not induce charge doping. A satellite line associated with the Mn nearest neighbours (n.n.) of 75As displays a Curie-Weiss shift which demonstrates that Mn carries a local magnetic moment. This is confirmed by the main line broadening typical of a RKKY-like Mn-induced staggered spin polarization. The Mn moment is due to the localization of the additional Mn hole. These findings explain why Mn does not induce superconductivity in the pnictides contrary to other dopants such as Co, Ni, Ru or K.Comment: 6 pages, 7 figure

Scintillator light yield measurements with waveform digitizers

The proton light yield of organic scintillators has been measured extensively in recent years using fast waveform digitizers and large discrepancies exist in the values reported by different authors. In this letter, we address principles of digital signal processing that must be considered when conducting scintillator light yield measurements. Digitized waveform pulse height values are only proportional to the amount of scintillation light if the temporal shape of the scintillation pulse is independent of the amount of energy deposited. This is not the case for scintillation pulses resulting from fast neutron interactions in organic scintillators. Authors measuring proton light yield should therefore report pulse integral values and ensure that the integration length is long enough to capture most of the scintillation light.Comment: 6 pages, 2 figure

Absolute light yield of the EJ-204 plastic scintillator

The absolute light yield of a scintillator, defined as the number of scintillation photons produced per unit energy deposited, is a useful quantity for scintillator development, research, and applications. Yet, literature data on the absolute light yield of organic scintillators are limited. The goal of this work is to assess the suitability of the EJ-204 plastic scintillator from Eljen Technology to serve as a reference standard for measurements of the absolute light yield of organic scintillators. Four EJ-204 samples were examined: two manufactured approximately four months prior and stored in high-purity nitrogen, and two aged approximately eleven years and stored in ambient air. The scintillator response was measured using a large-area avalanche photodiode calibrated using low energy $\gamma$-ray and X-ray sources. The product of the quantum efficiency of the photodetector and light collection efficiency of the housing was characterized using an experimentally-benchmarked optical photon simulation. The average absolute light yield of the fresh samples, 9100 $\pm$ 400 photons per MeV, is lower than the manufacturer-reported value of 10400 photons per MeV. Moreover, the aged samples demonstrated significantly lower light yields, deviating from the manufacturer specification by as much as 26\%. These results are consistent with recent work showcasing environmental aging in plastic scintillators and suggest that experimenters should use caution when deploying plastic scintillators in photon counting applications.Comment: 12 pages, 9 figure

On the Drach superintegrable systems

Cubic invariants for two-dimensional degenerate Hamiltonian systems are considered by using variables of separation of the associated St\"ackel problems with quadratic integrals of motion. For the superintegrable St\"ackel systems the cubic invariant is shown to admit new algebro-geometric representation that is far more elementary than the all the known representations in physical variables. A complete list of all known systems on the plane which admit a cubic invariant is discussed.Comment: 16 pages, Latex2e+Amssym

Statistical properties of 243^{243}Pu, and 242^{242}Pu(n,γ\gamma) cross section calculation

The level density and gamma-ray strength function (gammaSF) of 243Pu have been measured in the quasi-continuum using the Oslo method. Excited states in 243Pu were populated using the 242Pu(d,p) reaction. The level density closely follows the constant-temperature level density formula for excitation energies above the pairing gap. The gammaSF displays a double-humped resonance at low energy as also seen in previous investigations of actinide isotopes. The structure is interpreted as the scissors resonance and has a centroid of omega_{SR}=2.42(5)MeV and a total strength of B_{SR}=10.1(15)mu_N^2, which is in excellent agreement with sum-rule estimates. The measured level density and gammaSF were used to calculate the 242Pu(n,gamma) cross section in a neutron energy range for which there were previously no measured data.Comment: 9 pages, 8 figure

A Physicist's Proof of the Lagrange-Good Multivariable Inversion Formula

We provide yet another proof of the classical Lagrange-Good multivariable inversion formula using techniques of quantum field theory.Comment: 9 pages, 3 diagram

Pressure as a Source of Gravity

The active mass density in Einstein's theory of gravitation in the analog of Poisson's equation in a local inertial system is proportional to $\rho+3p/c^2$. Here $\rho$ is the density of energy and $p$ its pressure for a perfect fluid. By using exact solutions of Einstein's field equations in the static case we study whether the pressure term contributes towards the mass

Future multimodal mobility scenarios within Europe

The European transport system faces multiple pressing challenges, including the need for significant emissions reduction in the sector and the provision of a seamless, multimodal journey to travellers. In order to address these challenges, a thorough understanding and assessment of different development pathways are required. This paper elaborates on four different scenarios developed within the scope of the Modus project. Based on these as well as additional insights from experts of the air and rail sector, initial implications for emissions reduction potential, travel times, or technological options are discussed