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Given $X$ a smooth projective toric variety, we construct a morphism from a closed substack of the moduli space of stable maps to $X$ to the moduli space of quasimaps to $X$. If $X$ is Fano, we show that this morphism is surjective. The construction relies on the notion of degree of a quasimap at a base-point, which we define. We show that a quasimap is determined by its regular extension and the degree of each of its basepoints., Comment: 35 pages, 2 figures. Comments welcome

This work presents the IMPROVE dataset, designed to evaluate the effects of mobile phone usage on learners during online education. The dataset not only assesses academic performance and subjective learner feedback but also captures biometric, behavioral, and physiological signals, providing a comprehensive analysis of the impact of mobile phone use on learning. Multimodal data were collected from 120 learners in three groups with different phone interaction levels. A setup involving 16 sensors was implemented to collect data that have proven to be effective indicators for understanding learner behavior and cognition, including electroencephalography waves, videos, eye tracker, etc. The dataset includes metadata from the processed videos like face bounding boxes, facial landmarks, and Euler angles for head pose estimation. In addition, learner performance data and self-reported forms are included. Phone usage events were labeled, covering both supervisor-triggered and uncontrolled events. A semi-manual re-labeling system, using head pose and eye tracker data, is proposed to improve labeling accuracy. Technical validation confirmed signal quality, with statistical analyses revealing biometric changes during phone use., Comment: Article under review in the journal Scientific Data. GitHub repository of the dataset at: https://github.com/BiDAlab/IMPROVE

Here a minimum power dissipation coil transducer has been designed to allow in-flight noise characterization of a low-frequency magnetic measurement system. The coil was produced using PCB technology to provide mechanical stability and easy integration close to the magnetic sensors. The transducer design strategy relies on an inverse boundary element method, which has been efficiently adapted to produce optimal multilayer PCB coils subjected to different geometrical and performance constraints. The resulting coil transducer was simulated and experimentally validated under realistic conditions where the payload is magnetically shielded from low-frequency fluctuations by using a three-layer cylindrical mu-metal enclosure. The results show that the specific transducer coil proposed efficiently produces stable magnetic conditions for adequate validation of the magnetic diagnostic system while providing reduced power dissipation and optimal mechanical stability.

The internal structure of the lowest-lying pseudo-scalar mesons with heavy-light quark content is thoroughly studied using an algebraic model that has been successfully applied to similar physical observables of pseudoscalar and vector mesons with hidden-flavor quark content, ranging from light to heavy quark sectors. This model is based on constructing simple and evidence-based ans\"atze for the mesons' Bethe-Salpeter amplitude (BSA) and quark propagator, allowing the Bethe-Salpeter wave function (BSWF) to be computed algebraically. Its projection onto the light front yields the corresponding light-front wave function (LFWF), which provides easy access to the valence-quark Parton Distribution Amplitude (PDA) by integrating over the transverse momentum squared. We leverage our current knowledge of the PDAs of the lowest-lying pseudo-scalar heavy-light mesons to compute their Generalized Parton Distributions (GPDs) via the overlap representation of the LFWFs. From this three-dimensional information, various limits and projections allow us to deduce the related Parton Distribution Functions (PDFs), Electromagnetic Form Factors (EFFs), and Impact Parameter Space GPDs (IPS-GPDs). Whenever possible, we make explicit comparisons with available experimental results and previous theoretical predictions., Comment: Submitted to the proceedings of the 10th International Conference on Quarks and Nuclear Physics (QNP2024), PoS format

Excess molar enthalpies, $H_{\text{m}}^{\text{E}}$, have been measured using a Tian-Calvet microcalorimeter for the systems CH$_3$(CH$_2$)$_{u-1}$OH ($u$ = 1,2,3,4,7,10) + cyclohexylamine at 298.15 K and 0.1 MPa. The $H_{\text{m}}^{\text{E}}$ values are large and negative, indicating the existence of strong interactions between unlike molecules, which is consistent with the also large and negative excess molar volumes, $V_{\text{m}}^{\text{E}}$, of these solutions, previously measured by us. The contribution from the equation of state term to $H_{\text{m}}^{\text{E}}$ has been evaluated for the 1-alkanol + cyclohexylamine, or + 1-hexylamine, or + aniline mixtures, and the corresponding excess molar internal energies at constant volume, $U_{\text{m,}V}^{\text{E}}$, have been determined. It is shown that such contribution is particularly important for the methanol + aniline system, in such a way that the excess functions $H_{\text{m}}^{\text{E}}$ and $U_{\text{m,}V}^{\text{E}}$ have different sign at $x_1$ = 0.5. The DISQUAC and ERAS models have been applied to the cyclohexylamine systems, and the interaction parameters have been reported. DISQUAC improves ERAS results on $H_{\text{m}}^{\text{E}}$. The latter model describes correctly the $V_{\text{m}}^{\text{E}}$ curves. The variation of of CH$_3$(CH$_2$)$_{u-1}$OH + cyclohexylamine, or + 1-hexylamine, or + aniline mixtures with $u$ along a homologous series with a given amine, or with the amine in mixtures with a given 1-alkanol is discussed in terms of the different interactional contributions to $H_{\text{m}}^{\text{E}}$.

Excess molar enthalpies, $H_{\text{m}}^{\text{E}}$, at 298.15 K and 0.1 MPa have been measured by means of a Tian-Calvet microcalorimeter for the systems benzylamine (phenylmethanamine) + heptane, or + methanol, or + 1-propanol, or + 1-pentanol, or + 1-heptanol, or + 1-decanol. In addition, excess molar volumes, $V_{\text{m}}^{\text{E}}$, at the same conditions have been also determined using a densimeter Anton Paar model DSA 5000 for the benzylamine + heptane mixture. The $H_{\text{m}}^{\text{E}}$ of this solution is large and positive since at 298.15 K the system temperature is close to its upper critical solution temperature. Thus, systems with n-alkanes show positive deviations from the Raoult's law. The measured $|V_{\text{m}}^{\text{E}}|$ values are low, indicating the existence of large structural effects. $H_{\text{m}}^{\text{E}}$ values of mixtures involving 1-alkanols are large and negative. That is, interactions between unlike molecules are dominant and the systems are characterized by negative deviations from Raoult's law. It is shown that the enthalpy of the hydrogen bonding between molecules of 1-alkanol and benzyalmine are more negative than those between 1-alkanol molecules. The $V_{\text{m}}^{\text{E}}$ values of the systems with 1-alkanols are also large and negative, and are determined mainly by interactional effects since they increase in line with $H_{\text{m}}^{\text{E}}$ and with the alcohol size. The different contributions to $H_{\text{m}}^{\text{E}}$ have been evaluated. The systems have been studied using the DISQUAC and ERAS models. ERAS describes correctly the $V_{\text{m}}^{\text{E}}$ function. DISQUAC largely improves ERAS results on $H_{\text{m}}^{\text{E}}$ or on excess molar heat capacities at constant pressure for the mixtures with 1-alkanols, which underlines that physical interactions are very relevant in such solutions.

A differential scanning calorimetric technique has been used to obtain solid-liquid equilibrium temperatures for the mixtures naphthalene or biphenyl + 1-tetradecanol, or + 1-hexadecanol. All the systems show a simple eutectic point, whose final composition was determined by means of the Tamman's plots using the needed values of the eutectic heat and of the heat of melting, which are also reported. DISQUAC interaction parameters for the OH/aromatic contacts in the selected systems are given. The present experimental SLE phase diagrams are similarly described by DISQUAC and UNIFAC (Dortmund) models. However, the comparison of DISQUAC and UNIFAC results for systems involving naphthalene and shorter 1-alkanols (methanol-1-octanol) reveals that the temperature dependence of the interaction parameters is more suitable in DISQUAC. The systems are also investigated in terms of the concentration-concentration structure factor. It is shown that the positive deviations from the Raoult's law of the studied solutions become weaker when the homocoordination decreases.

Densities ($\rho$), speeds of sound ($c$), relative permittivities at 1 MHz ($\varepsilon_{\text{r}}$) and refractive indices at the sodium D-line ($n_{\text{D}}$) at $T$ = (293.15 K to 303.15 K) and $p$ = 0.1 MPa are reported for binary liquid mixtures alkan-1-ol + benzylamine. Methanol, propan-1-ol and pentan-1-ol are the alkan-1-ols studied in this work. The values of the excess molar volume ($V_{\text{m}}^{\text{E}}$), excess isentropic compressibility ($\kappa_S^{\text{E}}$), excess speed of sound ($c^{\text{E}}$), excess refractive index ($n_{\text{D}}^{\text{E}}$), excess relative permittivity ($\varepsilon_{\text{r}}^{\text{E}}$) and its temperature derivative ${(\partial{\varepsilon_{\text{r}}}/\partial T)}_p$ are calculated, and they are adjusted to Redlich-Kister polynomials. The $V_{\text{m}}^{\text{E}}$ values are negative, indicating a predominance of the solvation between unlike molecules and structural effects. $\varepsilon_{\text{r}}^{\text{E}}$ values indicate a positive contribution from the creation of (alkan-1-ol)-benzylamine interactions, and the positive value for the methanol mixture emphasises the importance of solvation. Calculations on excess molar refractions point out to weaker dispersive interactions than in the ideal mixture, which may be explained by the mentioned solvation effects. The Kirkwood-Fr\"ohlich model has been applied to the mixtures, and the Kirkwood correlation factors suggest an important relative weight, especially in the methanol system, of linear-like molecules in the solutions, which is in accordance with the positive contribution of the formed multimers to $\varepsilon_{\text{r}}^{\text{E}}$ due to their good effective response to the electric field., Comment: arXiv admin note: substantial text overlap with arXiv:2409.17926

Relative permittivities at 1 MHz, $\varepsilon_{\text{r}}$, at 0.1 MPa and (293.15-303.15) K and refractive indices, $n_{\text{D}}$, at similar conditions have been measured for the alkan-1-ol (methanol, propan-1-ol, butan-1-ol, pentan-1-ol or heptan-1-ol) + N,N-diethylethanamine (TEA) systems. Positive values of the excess permittivities, $\varepsilon_{\text{r}}^{\text{E}}$ , are encountered for the methanol system at high alcohol concentrations. The remaining mixtures are characterized by negative $\varepsilon_{\text{r}}^{\text{E}}$ values over the whole composition range. At ${\phi}_1$ (volume fraction) = 0.5, $\varepsilon_{\text{r}}^{\text{E}}$ changes in the order: methanol > propan-1-ol > butan-1-ol < pentan-1-ol < heptan-1-ol. Mixtures formed by alkan-1-ol and an isomeric amine, hexan-1-amine (HxA) or N-propylpropan-1-amine (DPA) or cyclohexylamine, behave similarly. This has been explained in terms of the lower and weaker self-association of longer alkan-1-ols. From the permittivity data, it is shown that: (i) (alkan-1-ol)-TEA interactions contribute positively to $\varepsilon_{\text{r}}^{\text{E}}$; (ii) TEA is an effective breaker of the network of the alkan-1-ols; (iii) structural effects, which are very important for the volumetric and calorimetric data of alkan-1-ol + TEA systems, are also relevant when evaluating dielectric data. This is confirmed by the comparison of $\varepsilon_{\text{r}}^{\text{E}}$ measurements for alkan-1-ol + aliphatic amine mixtures; (iv) the aromaticity effect (i.e., the replacement of TEA by pyridine in systems with a given alkan-1-ol) leads to an increase of the mixture polarization. Calculations conducted in the framework of the Kirkwood-Fr\"ohlich model are consistent with the previous statements., Comment: arXiv admin note: text overlap with arXiv:2409.11801, arXiv:2409.17926

Systems of the type linear primary or secondary amine + cyclohexane, or + polar compound (namely, linear or cyclic monoether, + 1,4-dioxane, + N,N-dialkylamide, or + ethanitrile) have been investigated using literature data, and by means of DISQUAC. Interaction parameters for the contacts amine/ether, amine/amide and amine/nitrile are provided. For a given contact, the QUAC interchange coefficients remain practically constant along each homologous series. A similar trend has been encountered in other many previous studies. DISQUAC correctly describes excess molar enthalpies, $H_{\text{m}}^{\text{E}}$, and vapour-liquid and solid-liquid equilibria of the studied mixtures and improves calculations on $H_{\text{m}}^{\text{E}}$ from the UNIFAC (Dortmund) model. The experimental data have been used to determine the enthalpy of the interactions between unlike molecules, which are stronger in systems with N,N-dialkylamides or ethanenitrile than in mixtures with ethers. On the other hand, it is shown that $H_{\text{m}}^{\text{E}}$ values of amine + C$_6$H$_{12}$ mixtures are closely related to the amine self-association, and that interactions between molecules of the polar compounds are determinant on $H_{\text{m}}^{\text{E}}$ results of the mixtures amine + fixed polar compound or of the systems fixed amine + polar compound (no linear monoether). Structural effects are relevant in the di-n-butylamine + linear ether systems. The application of the Flory model reveals that orientational effects are rather weak in the investigated solutions. This is in agreement with previous studies on this type of mixtures using the ERAS model.

The Electron-Ion Collider, a next generation electron-hadron and electron-nuclei scattering facility, will be built at Brookhaven National Laboratory. The wealth of new data will shape research in hadron physics, from nonperturbative QCD techniques to perturbative QCD improvements and global QCD analyses, for the decades to come. With the present proposal, Latin America based physicists, whose expertise lies on the theory and phenomenology side, make the case for the past and future efforts of a growing community, working hand-in-hand towards developing theoretical tools and predictions to analyze, interpret and optimize the results that will be obtained at the EIC, unveiling the role of the glue that binds us all. This effort is along the lines of various initiatives taken in the U.S., and supported by colleagues worldwide, such as the ones by the EIC User Group which were highlighted during the Snowmass Process and the Particle Physics Project Prioritization Panel (P5)., Comment: White Paper contribution to the Latin American Strategy Forum for Research Infrastructure (III LASF4RI

Densities and speeds of sound at a temperature $T$ = 298.15 K, relative permittivities at 1 MHz and refractive indices at the sodium D-line at $T$ = (293.15 K to 303.15 K), all at a pressure p = 0.1 MPa, are reported for liquid mixtures methanol, propan-1-ol or pentan-1-ol + aniline. Excess molar volume ($V_{\text{m}}^{\text{E}}$), excess isentropic compressibility, excess speed of sound, excess refractive index, excess relative permittivity ($\varepsilon_{\text{r}}^{\text{E}}$) and its temperature derivative are calculated and fitted to Redlich-Kister polynomials. The agreement among the reported data and other literature sources is analysed by comparing $V_{\text{m}}^{\text{E}}$, $n_{\text{D}}^{\text{E}}$, $\varepsilon_{\text{r}}^{\text{E}}$ and the deviation of the speed of sound from mole-fraction linearity. The positive excess molar internal energies at constant volume ($U_{\text{m,}V}^{\text{E}}$) show the dominance of the breaking of interactions between like molecules in the energy balance on mixing, particularly the breaking of strong dipolar interactions between aniline molecules. This contribution is also dominant for the $\varepsilon_{\text{r}}^{\text{E}}$ values, as they are negative and decrease with the length of the alkan-1-ol chain. Calculations on the concentration-concentration structure factor are consistent with these statements, revealing homocoordination in the studied systems. The $V_{\text{m}}^{\text{E}}$ are negative, which together with the positive $U_{\text{m,}V}^{\text{E}}$ indicate the existence of important structural effects in the studied mixtures. The application of the Kirkwood-Fr\"ohlich model shows that the average relative orientation of neighbouring dipoles is similar in the mixtures methanol + aniline or + pyridine, in spite of the different character of the predominant interactions in the latter mixture (heterocoordination).

Excess molar enthalpies, $H_{\text{m}}^{\text{E}}$, over the whole composition range have been determined for the liquid mixtures N,N-dimethylformamide (DMF) or N,N-dimethylacetamide (DMA) + butan-1-amine (BA), or + hexan-1-amine (HxA), or + N-propylpropan-1-amine (DPA), or N-butylbutan-1-amine (DBA) at 298.15 K and at 0.1 MPa using a BT2.15 calorimeter from Setaram adapted to work in dynamic mode at constant temperature and pressure. All the $H_{\text{m}}^{\text{E}}$ values are positive, indicating that interactions between like molecules are predominant. The replacement of DMF by DMA in systems with a given amine leads to lower $H_{\text{m}}^{\text{E}}$ results, which have been ascribed to stronger amide-amide interactions in DMF mixtures. The replacement of HxA by DPA in systems with a given amide leads to slightly higher $H_{\text{m}}^{\text{E}}$ values, as interactions between unlike molecules are weaker for the latter. Structural effects in the investigated solutions are also present, since the corresponding excess molar volumes ($V_{\text{m}}^{\text{E}}$), previously determined, are negative or slightly positive. The systems have been characterized in terms of the ERAS model reporting the interaction parameters. The model correctly describes both $H_{\text{m}}^{\text{E}}$ and $V_{\text{m}}^{\text{E}}$. The application of the model suggests that, in the systems under study, solvation effects are of minor importance and that physical interactions are dominant.

Relative permittivities at 1 MHz, $\varepsilon_{\text{r}}$, and refractive indices at the sodium D-line, $n_{\text{D}}$, are reported at 0.1 MPa and at (293.15-303.15) K for the binary systems 1-alkanol + di-n-propylamine (DPA). Their corresponding excess functions are calculated and correlated. For the methanol mixture, positive values of the excess permittivities, $\varepsilon_{\text{r}}^{\text{E}}$, are found. Except at high concentrations of the alcohol in the 1-propanol mixture, the remaining systems show negative values of this property. This fact reveals that the creation of (1-alkanol)-DPA interactions contributes positively to $\varepsilon_{\text{r}}^{\text{E}}$, being this contribution dominant in the methanol mixture. At ${\phi}_1$ (volume fraction) = 0.5, $\varepsilon_{\text{r}}^{\text{E}}$ changes in the sequence: methanol > 1-propanol > 1-butanol > 1-pentanol < 1-heptanol. An analogous variation with the chain length of the 1-alkanol is observed in mixtures such as 1-alkanol + heptane, + cyclohexylamine or + n-hexylamine (HxA). Moreover, for a given 1-alkanol, $\varepsilon_{\text{r}}^{\text{E}}$ is larger for DPA than for HxA mixtures, suggesting that in DPA solutions multimers with parallel alignment of the molecular dipoles are favoured and cyclic multimers are disfavoured when compared to HxA mixtures. The ${(\partial{\varepsilon_{\text{r}}}/\partial T)}_p$ values are higher for the mixtures than for pure 1-alkanols, because (1-alkanol)-DPA interactions are stronger than those between 1-alkanol molecules. Molar refractions indicate that dispersive interactions in DPA systems increase with the chain length of the 1-alkanol and are practically identical to those in HxA solutions. The considered mixtures are treated by means of the Kirkwood-Fr\"ohlich model, reporting the Kirkwood correlation factors and their excess values., Comment: arXiv admin note: substantial text overlap with arXiv:2409.11801

Densities, $\rho$, and kinematic viscosities, $\nu$, have been determined at atmospheric pressure and at (293.15-303.15) K for binary mixtures formed by methanol and one linear polyether of the type CH$_3$-O-(CH$_2$CH$_2$O)$_n$-CH$_3$ ($n$ = 2,3,4). The $\rho$ values are used to compute excess molar volumes, $V_{\text{m}}^{\text{E}}$, and, together with $\nu$ results, dynamic viscosities ($\eta$). Deviations from linear dependence on mole fraction for viscosity, $\Delta \eta$, are also provided. Different semi-empirical equations have been employed to correlate viscosity data. Particularly, the equations used are: Grunberg-Nissan, Hind, Frenkel, Katti-Chaudhri, McAllister and Heric. Calculations show that better results are obtained from the Hind equation. The $V_{\text{m}}^{\text{E}}$ values are large and negative and contrast with the positive excess molar enthalpies, $H_{\text{m}}^{\text{E}}$, available in the literature, for these systems. This indicates that structural effects are dominant. The $\Delta \eta$ results are positive and correlate well with the difference in volume of the mixture compounds confirming the importance of structural effects. The temperature dependences of $\eta$ and of the molar volume have been used to calculate enthalpies, entropies and Gibbs energies, $\Delta G^*$, of viscous flow. It is demonstrated that $\Delta G^*$ is essentially determined by enthalpic effects. Methanol + CH$_3$-O-(CH$_2$CH$_2$O)$_n$-CH$_3$ mixtures have been treated in the framework of the ERAS model. Results on $H_{\text{m}}^{\text{E}}$ are acceptable, while the composition dependence of the $V_{\text{m}}^{\text{E}}$ curves is poorly represented. This has been ascribed to the existence of strong dipolar and structural effects in the present solutions.

Mixtures formed by 1-alkanol and one strongly polar compound (nitromethane (NM), ethanenitrile (EtN), dimethyl sulfoxide (DMSO), sulfolane (SULF), nitrobenzene (NTBz) or benzonitrile (BzCN)) have been investigated on the basis of a set of thermophysical data, which includes: excess molar functions (enthalpies, $H_{\text{m}}^{\text{E}}$, Gibbs energies, $G_{\text{m}}^{\text{E}}$, entropies, $T S_{\text{m}}^{\text{E}}$, isobaric heat capacities, $C_{p \text{m}}^{\text{E}}$, volumes, $V_{\text{m}}^{\text{E}}$); liquid-liquid equilibria (LLE), excess permittivities and deviations from the linearity of dynamic viscosities. In addition, calculations have been conducted to determine the Kirkwood-Buff integrals and the Kirkwood correlations factors, $g_{\text{K}}$, of the investigated mixtures. In the former case, DISQUAC has been employed for modeling the needed vapour-liquid equilibria data. Many systems under consideration are characterized by dipolar interactions between like molecules and have positive values of $H_{\text{m}}^{\text{E}}$, $C_{p \text{m}}^{\text{E}}$ and $T S_{\text{m}}^{\text{E}}$. On the other hand, alkanol-solvent interactions, for mixtures with a fixed 1-alkanol, become weakened in the sequence: DMSO $\approx$ SULF > EtN > NM > BzCN > NTBz. In systems with a given solvent, such interactions become also weaker when the chain length of the 1-alkanol is increased. Interestingly, the considered mixtures also show strong structural effects. Results on Kirkwood-Buff integrals reveal that nitriles are more preferred than nitroalkanes around a central alcohol molecule. Calculations on $g_{\text{K}}$ show that, in terms of the mixture polarization, the systems are rather unstructured, and that this trend becomes more important when the 1-alkanol size increases in solutions with a given solvent.

Relative permittivities at 1 MHz, $\varepsilon_{\text{r}}$, and at (293.15-303.15) K are reported for the binary systems N,N-dimethylacetamide (DMA) + N-propylpropan-1-amine (DPA), + N-butylbutan-1-amine (DBA), + butan-1-amine (BA) or + hexan-1-amine (HxA) and for N,N-dimethylformamide (DMF) + aniline. The excess permittivities, $\varepsilon_{\text{r}}^{\text{E}}$, are large and negative for systems with DMA, whereas they are large and positive for the aniline mixture. From the analysis of these $\varepsilon_{\text{r}}^{\text{E}}$ data and of measurements previously reported, it is concluded: (i) the main contribution to $\varepsilon_{\text{r}}^{\text{E}}$ in systems with linear amines arises from the breaking of interactions between like molecules; (ii) in the DMF + aniline mixture, interactions between unlike molecules contribute positively to $\varepsilon_{\text{r}}^{\text{E}}$, and such a contribution is dominant; (iii) longer linear amines are better breakers of the amide-amide interactions; (iv) interactions between unlike molecules are more easily formed when shorter linear amines, or DMF, participate. These findings are confirmed by a general study conducted in terms of excess values of molar orientational and induced polarizabilities and of the relative Kirkwood correlation factors for systems and components. The ERAS model is also applied to amide + amine mixtures. ERAS represents rather accurately the excess enthalpies and volumes of the mentioned systems. The variation of the cross-association equilibrium constants, determined using ERAS, with the molecular structure is in agreement with that observed for $\varepsilon_{\text{r}}^{\text{E}}$., Comment: arXiv admin note: text overlap with arXiv:2409.15208

Interactions and structure of organic carbonate + alkane, and 1-alkanol + organic carbonate mixtures have been investigated by means of a set of molar excess functions: enthalpies, volumes, isobaric heat capacities, or entropies; and considering internal pressure, liquid-liquid equilibria or permittivity data. In addition, the mentioned systems have been studied using the Flory model and the concentration-concentration structure factor formalism. The mixtures under consideration are characterized by dipolar interactions and by homocoordination (that is, by interactions between like molecules). In systems with a given solvent, dipolar interactions are weakened in the order: propylene carbonate (PC) > dimethyl carbonate (DMC) > diethyl carbonate (DEC). Comparison of mixtures containing DMC or DEC with those involving 2-propanone or 3-pentanone shows that dipolar interactions are not determined merely by values of the dipole moment, but they also depend on the group size. The enthalpies of the alkanol-carbonate interactions have been evaluated from calorimetric data. They are stronger in DMC solutions and become weaker when the alcohol size increases in mixtures with a given carbonate. Application of the Flory model to 43 systems of the type 1-alkanol + carbonate provides a mean relative standard deviation for excess molar enthalpy equal to 0.107. Results reveal that orientational effects decrease in the order DEC > PC > DMC. Orientational effects are particularly relevant in methanol or ethanol + DEC mixtures. Interestingly, the mentioned effects are weaker in 1-alkanol + DMC mixtures than in DMC + alkane systems. A similar trend is observed in DEC solutions when the considered alcohol is longer than ethanol.

Relative permittivities at 1 MHz, $\varepsilon_{\text{r}}$, and at (293.15-303.15) K, are reported for the binary systems N,N-dimethylformamide (DMF) + N-propylpropan-1-amine (DPA), + N-butylbutan-1-amine (DBA), + butan-1-amine (BA) or + hexan-1-amine (HxA). The values of the excess relative permittivities, $\varepsilon_{\text{r}}^{\text{E}}$, have also been determined for these solutions. The measurements were realized by means of a precision impedance analyser 4294A, to which a 16452A cell connected using a 16048G test lead, all of them from Agilent. The $\varepsilon_{\text{r}}^{\text{E}}$ values are large and negative, and diminish when the size of the amine increases along a homologous series, which has been ascribed mainly to the rupture of interactions between like molecules along mixing. Calculations on excess molar orientational polarizabilities support this conclusion, indicating a dominant contribution to $\varepsilon_{\text{r}}^{\text{E}}$ from the orientational polarizability of the molecules in the mixture. The analysis of excess relative Kirkwood correlation factors shows that the correlation between dipoles is effectively decreased along the mixing process.

The solid-liquid equilibria and excess enthalpies of the binary systems of propiophenone and {N-methylformamide, or N,N-dimethylformamide, or N,N-dimethylacetamide, or N-methyl-2-pyrrolidone} were measured. The SLE datawere determined by the cloud-point method, partly supplemented by the DSC technique. The excess enthalpieswere measured by the titration calorimetry at 298.15 K and 308.15 K for all the systems and additionally at 293.15 K and 318.15 K for the system with N-methylformamide, and at 293.15 K for the system with N,N-dimethylformamide. The activity coefficients of both components as a function of concentration and temperature were calculated by the correlation which included both types of data. The results of the prediction by the modified UNIFAC model were comparedwith the experimental data. The observed trends and differences between the systems were discussed., Comment: 8 tables, 9 figures

The systems C$_6$H$_5$Cl, or C$_6$H$_5$Br, or 1-chloronaphthalene, or 1,2,4-trichlorobenzene, or 1-methylnaphthalene, or 1,2,4-trimethylbenzene + alkane have been investigated by means of the their excess molar properties, including, when the needed data are available, those at constant volume, internal energies ($U_{V\text{m}}^{\text{E}}$) and heat capacities ($C_{V\text{m}}^{\text{E}}$), and using the DISQUAC, and Flory models, and the concentration-concentration structure factor formalism. The position of the mixtures within the $G_{\text{m}}^{\text{E}}$ (excess molar Gibbs energy) vs. $H_{\text{m}}^{\text{E}}$ (excess molar enthalpy) diagram has been also determined. Interactions between C$_6$H$_5$X molecules become stronger in the sequence X = H $\approx$ F $\approx$ Cl < Br. These interactions are weaker than those between 1-chloronaphtahlene or 1,2,4-trichlorobenzene molecules. It is shown that the considered systems have some common features: dispersive interactions are dominant, structural effects for solutions with shorter n-alkanes are large and $U_{V\text{m}}^{\text{E}}$ decreases when the number ($n$) of C atoms of the alkane increases. This variation is held when an n-alkane is replaced by a branched alkane with the same $n$ in systems with C$_6$H$_5$Cl or 1-chloronaphthalene. This suggests that larger alkanes are poorer breakers of the interactions between aromatic halogenated compounds. Viscosity and $C_{V\text{m}}^{\text{E}}$ data support this conclusion. The parabolic dependence of $C_{V\text{m}}^{\text{E}}$ with $n$ indicates that the short orientational order of long n-alkanes is destroyed. Aromaticity and proximity effects are discussed.

Solid-liquid equilibria for the binary systems of acetophenone and {N-methylformamide, or N,Ndimethylformamide, or N,N-dimethylacetamide, or N-methyl-2-pyrrolidone} were determined by the cloudpoint and DSC techniques. For the same systems, excess enthalpies were measured at 293.15 K and 308.15 K by the titration calorimetry. Both types of data were correlated by the Redlich-Kister equation. The description of the solid-liquid equilibria incorporated measured excess enthalpies. The results of the prediction performed by the modified UNIFAC modelwere compared with the experimental data. The observed trends and differences between systems were discussed., Comment: 8 tables, 8 figures

Fluorobenzene, or 1,4-difluorobenzene or hexafluorobenzene + alkane mixtures and hexafluorobenzene + benzene, or + toluene, or + 1,4-dimethylbenzene systems have been studied using thermodynamic properties from the literature and through the application of the DISQUAC and UNIFAC (Dortmund) models and the concentration-concentration structure factor ($S_{\text{CC}}(0)$). Interaction parameters for the contacts F/alkane and F/aromatic have been determined for DISQUAC, and they have been taken from the literature for UNIFAC. Both models predict double azeotropy for the C$_6$F$_6$ + C$_6$H$_6$ system, although in different temperature ranges. Excess molar enthalpies ($H_{\text{m}}^{\text{E}}$) of the fluorobenzene, or 1,4-difluorobenzene + n-alkane systems are positive and are accurately described by the models using interaction parameters independent of the n-alkane, discarding Patterson's effect in such mixtures. DISQUAC calculations confirm that conclusion for C$_6$F$_6$ + n-alkane mixtures. DISQUAC provides better results than UNIFAC on excess molar isobaric heat capacities ($C_{p\text{m}}^{\text{E}}$) of solutions involving n-alkanes, or on $H_{\text{m}}^{\text{E}}$ of C$_6$F$_6$ + aromatic hydrocarbon systems. For mixtures with a given n-alkane, the relative variation of excess molar internal energies at constant volume ($U_{V\text{m}}^{\text{E}}$) and $H_{\text{m}}^{\text{E}}$ and with the fluorohydrocarbons is different, due to structural effects. C$_6$F$_6$ + aromatic hydrocarbon mixtures are characterized by interactions between unlike molecules, as seen from their negative $H_{\text{m}}^{\text{E}}$ values. The $S_{\text{CC}}(0)$ formalism reveals that homocoordination is more important in C$_6$F$_6$ + n-alkane mixtures than in the corresponding systems with C$_6$H$_5$F, and that heterocoordination is dominant in the solutions of C$_6$F$_6$ with an aromatic hydrocarbon.

Relative permittivities at 1 MHz, $\varepsilon_{\text{r}}$, and refractive indices at the sodium D-line, $n_{\text{D}}$, are reported at 0.1 MPa and at (293.15-303.15) K for the binary systems 1-alkanol + n-hexylamine (HxA). Also, their corresponding excess functions are calculated and correlated. Positive values of the excess permittivities, $\varepsilon_{\text{r}}^{\text{E}}$, are encountered for the methanol system, whereas the remaining mixtures show negative values. This reveals that interactions between unlike molecules contribute positively to $\varepsilon_{\text{r}}^{\text{E}}$. This contribution is dominant for the methanol mixture, while those arising from the breaking of interactions between like molecules are prevalent for the remaining mixtures. At ${\phi}_1$ (volume fraction) = 0.5, $\varepsilon_{\text{r}}^{\text{E}}$ changes in the order: methanol > 1-propanol > 1-butanol > 1-pentanol < 1-heptanol. Similar variation with the chain length of the 1-alkanol is observed for mixtures such as 1-alkanol + heptane, or + cyclohexylamine, and can be explained in terms of the lower and weaker self-association of longer 1-alkanols. The effect of the replacement of HxA by cyclohexylamine, or by aniline, is also shown. Calculations on molar refractions indicate that dispersive interactions in the systems under study increase with the length of the 1-alkanol. The mixtures are studied by means of the application of the Kirkwood-Fr\"ohlich model, and the Kirkwood correlation factors, including the corresponding excess values, are reported.

We study existence, uniqueness, norm estimates and asymptotic time behaviour (in some cases can be claimed to be sharp) for the solution of a general evolutionary integral (differential) equation of scalar type on a locally compact separable unimodular group $G$ governed by any positive left invariant operator (unbounded and either with discrete or continuous spectrum) on $G$. We complement our studies by proving some time-space (Strichartz type) estimates for the classical heat equation, and its time-fractional counterpart, as well as for the time-fractional wave equation. The latter estimates allow us to give some results about the well-posedness of nonlinear partial integro-differential equations. We provide many examples of the results by considering particular equations, operators and groups through the whole paper.

Data on density, $\rho$, speed of sound, $c$, and refractive index, $n_{\text{D}}$, have been reported at (293-303.15) K for the N,N-dimethylacetamide (DMA) + CH$_3$CO(CH$_2$)$_{u-1}$CH$_3$ ($u$ = 1, 2, 3) systems, and at 298.15 K for the mixture with $u$ = 5. These data have been used to compute excess molar volumes, $V_{\text{m}}^{\text{E}}$, excess adiabatic compressibilities, $\kappa_S^{\text{E}}$, and excess speeds of sound $c^{\text{E}}$. Negative $V_{\text{m}}^{\text{E}}$ values indicate the existence of structural effects and interactions between unlike molecules. From excess molar enthalpies, $H_{\text{m}}^{\text{E}}$, available in the literature for N,N-dimethylformamide (DMF), or N-methylpyrrolidone (NMP) + n-alkanone systems, it is shown: (i) amide-ketone interactions are stronger in DMF systems than in those with NMP; (ii) they become weaker when $u$ increases in mixtures with a given amide. Structural effects largely contribute to $H_{\text{m}}^{\text{E}}$ and are more relevant in mixtures containing NMP. The application of the Flory's model reveals that the random mixing hypothesis is valid to a large extent for DMF solutions, while NMP systems are characterized by rather strong orientational effects. From values of molar refraction and of the product $P_{\text{int}} V_{\text{m}}$ (where $P_{\text{int}}$ is the internal pressure and $V_{\text{m}}$ the molar volume), it is concluded that dispersive interactions increase with $u$, or when DMF is replaced by DMA in mixtures with a fixed ketone.

The CH$_3$(CH$_2$)$_u$COO(CH$_3$)$_v$CH$_3$ + n-alkane mixtures have been investigated on the basis of an experimental database containing effective dipole moments of esters, and excess molar functions of the systems: enthalpies ($H_{\text{m}}^{\text{E}}$), volumes ($V_{\text{m}}^{\text{E}}$), isobaric heat capacities ($C_{p\text{m}}^{\text{E}}$) and isochoric internal energies ($U_{V\text{m}}^{\text{E}}$) and by means of the application of the Flory model and the Kirkwood-Buff formalism. The situation of the mixtures within the $G_{\text{m}}^{\text{E}}$ (excess molar Gibbs energy) vs. $H_{\text{m}}^{\text{E}}$ diagram has also been briefly considered. Results indicate that dispersive interactions are dominant and that steric effects can explain some differences between solutions containing heptane and isomeric esters. Proximity and orientational effects are also discussed in diester + hexane mixtures. In the case of systems with a given alkane and different isomeric polar compounds, orientational effects become weaker in the order: n-alkanone > dialkyl carbonate > n-alkanoate. Results from the Kirkwood-Buff formalism indicate that the number of ester-ester interactions decreases in systems with alkyl ethanoates when the alkyl size increases and that preferential solvation between polar molecules decreases as follows: dialkyl carbonate > n-alkanone > n-alkanoate.

Kinematic viscosities were measured for iodobenzene + n-alkane mixtures at (288.15-308.15) K and atmospheric pressure. Using our previous density data, dynamic viscosities ($\eta$), deviations in absolute viscosity ($\Delta \eta$) and quantities of viscous flow were determined. The McAllister, Grunberg-Nissan and Fang-He correlation equations and Bloomfield-Dewan's model (with residual Gibbs energies calculated using DISQUAC with interaction parameters available in the literature) were applied to iodobenzene, or 1-chloronaphthalene, or 1,2,4-trichlorobenzene, or methyl benzoate or benzene or cyclohexane + n-alkane systems. The dependence of $U_{\text{m,}V}^{\text{E}}$ (isochoric molar excess internal energy) and $\Delta \eta$ with $n$ (the number of C atoms of the n-alkane) shows that the fluidization loss of mixtures containing iodobenzene, 1,2,4-trichlorobenzene, or 1-chloronaphthalene when $n$ increases is due to a decrease upon mixing of the number of broken interactions between like molecules. The breaking of correlations of molecular orientations characteristic of longer n-alkanes may explain the decreased negative $\Delta \eta$ values of benzene mixtures with $n$ =14,16. The replacement, in this type of systems of benzene by cyclohexane leads to increased positive $\Delta \eta$ values, probably due to the different shape of cyclohexane. On the other hand, binary mixtures formed by one of the aromatic polar compounds mentioned above and a short n-alkane show large structural effects and large negative $\Delta \eta$ values. From the application of the models, it seems that dispersive interactions are dominant and that size effects are not relevant on $\eta$ values. The free volume model provides good results for most of the systems considered. Results improve when, within Bloomfield-Dewan's theory, the contribution to $\eta$ of the absolute reaction rate model is also considered.

(Iodobenzene + n-alkane) liquid mixtures have been studied experimentally, in terms of densities and speeds of sound at a pressure $p$ = 0.1 MPa and in the temperature range $T$ = (288.15 to 308.15) K, and theoretically, by the application of the Prigogine-Flory-Patterson (PFP) model. The n-alkanes considered are n-heptane, n-decane, n-dodecane, and n-tetradecane. Excess molar volumes ($V_{\text{m}}^{\text{E}}$) and excess isentropic compressibilities ($\kappa_S^{\text{E}}$) have been calculated and correlated by Redlich-Kister polynomials. ${(\partial{V_{\text{m}}^{\text{E}}}/\partial T)}_p$ curves at the same (p,T) conditions have been obtained from correlated $V_{\text{m}}^{\text{E}}$ values. From these experimental results and the knowledge of the excess molar enthalpies and volumes of mixtures containing fluorobenzene, chlorobenzene or bromobenzene with n-alkanes, we have inferred: (i) the presence of structural effects, especially important for the n-heptane mixture and less relevant for volumetric properties as the length of the n-alkane increases; and (ii) that the interactional effects on $V_{\text{m}}^{\text{E}}$ do not vary appreciably with the length of the n-alkane, so the observed $V_{\text{m}}^{\text{E}}$ variation is fundamentally determined by the corresponding variation of the contribution from structural effects. The application of the PFP model supports this interpretation, providing free volume contributions to $V_{\text{m}}^{\text{E}}$ that vary parallelly to $V_{\text{m}}^{\text{E}}$ with the length of the n-alkane, and interactional contributions that rest approximately constant independently of the n-alkane size.

Liquid-liquid equilibrium (LLE) phase diagrams have been determined, by means of the critical opalescence method with a laser scattering technique, for the mixtures 4-phenylbutan-2-one + CH$_3$(CH$_2$)$_n$CH$_3$ ($n = 10,12,14$) and for benzyl ethanoate + CH$_3$(CH$_2$)$_n$CH$_3$ ($n = 12,14$). The systems are characterized by having an upper critical solution temperature (UCST), which increases with n. The corresponding LLE curves show a rather horizontal top and become skewed toward higher mole fractions of the polar compound when n is increased. Calorimetric and LLE measurements show that, for mixtures with molecules with a given functional group, interactions between aromatic molecules are stronger than those between homomorphic linear molecules (aromaticity effect). This has been ascribed to proximity effects arising from the presence of the polar group and the aromatic ring within the same molecule. Proximity effects become weaker in the sequence 1-phenylpropan-2-one > 4-phenylbutan-2-one > 1-phenylethanone and are more important in benzyl ethanoate than in ethyl benzoate molecules. Values of the critical compositions and temperatures calculated with the DISQUAC group contribution model are in good agreement with the experimental results. Accordingly, the shape of the LLE curves is also correctly described by DISQUAC.

Data on density, $\rho$, speed of sound, $c$, and refractive index, $n_{\text{D}}$, of binary systems containing N,N-dimethylacetamide (DMA) + N-propylpropan-1-amine (DPA) or + butan-1-amine (BA) at 293.15 K, 298.15 K and 303.15 K, and + N-butylbutan-1-amine (DBA) or + hexan-1-amine (HxA) at 298.15 K are reported. A densimeter and sound analyzer Anton Paar DSA 5000 has been used for the measurement of $\rho$ and $c$, whereas $n_{\text{D}}$ values have been obtained by means of a refractometer RFM970 from Bellingham+Stanley. Also, values of excess molar volumes, $V_{\text{m}}^{\text{E}}$, excess isentropic compressibilities, $\kappa_S^{\text{E}}$, excess speeds of sound, $c^{\text{E}}$, excess isobaric thermal expansion coefficients, $\alpha_p^{\text{E}}$, and of excess refractive indices, $n_{\text{D}}^{\text{E}}$, have been determined from these data. The investigated systems are characterized by amide-amine interactions and structural effects, as it is shown by their negative or low positive $V_{\text{m}}^{\text{E}}$ values and by the results from the application of the Prigogine-Flory-Patterson (PFP) model. The breaking of amine-amine interactions is more relevant in systems containing linear primary amines than in those with linear secondary amines, and the $V_{\text{m}}^{\text{E}}$ values are lower for the latter systems. Molar refraction has been used to evaluate the dispersive interactions in the mixtures under study, yielding the result that DPA and HxA systems present similar dispersive interactions and mainly differ in their dipolar character. Steric hindrance of the amide group in DMA leads to weaker amide-amine interactions than in the corresponding N,N-dimethylformamide (DMF) + amine systems.

Values of density ($\rho$), speed of sound ($c$) and refractive index ($n_{\text{D}}$) for N,N-dimethylformamide (DMF) + N-propylpropan-1-amine (DPA) or + butan-1-amine (BA) mixtures at (293.15-303.15) K, and for DMF + N-butylbutan-1-amine (DBA) or hexan-1-amine (HxA) mixtures at 298.15 K are reported. $\rho$ and $c$ measurements were conducted using a vibrating-tube densimeter and sound analyzer, Anton Paar model DSA5000; $n_{\text{D}}$ values were obtained by means of a RFM970 refractometer from Bellingham+Stanley. The experimental $\rho$, $c$ and $n_{\text{D}}$ values have been used to determine excess molar volumes, $V_{\text{m}}^{\text{E}}$, excess adiabatic compressibilities, $\kappa_S^{\text{E}}$, excess speeds of sound, $c^{\text{E}}$, excess thermal expansion coefficients, $\alpha_p^{\text{E}}$, and excess refractive indices, $n_{\text{D}}^{\text{E}}$. This set of data shows the existence of interactions between unlike molecules and of structural effects in the mixtures under study. $V_{\text{m}}^{\text{E}}$ values of solutions including linear secondary amines are lower than those of mixtures with linear primary amines. In fact, the contribution to $V_{\text{m}}^{\text{E}}$ from the breaking of amine-amine interactions is larger for the latter systems. Calculations on Rao's constant point out that there is no complex formation between the mixture components. Dispersive interactions have been analyzed by means of the molar refraction. It is shown that solutions with DPA or HxA are characterized by similar dispersive interactions and that they mainly differ in dipolar interactions.

Densities, $\rho$, speeds of sound, $c$, and refractive indices, $n_{\text{D}}$, have been measured for the systems N,N-dimethylformamide (DMF) + propanone, + 2-butanone, or + 2-pentanone in the temperature ($T$) range from 293.15 to 303.15 K and at 298.15 K for the DMF + 2-heptanone mixture. Due to the high volatility of acetone, the corresponding $n_{\text{D}}$ measurements were developed at 293.15 K and 298.15 K. The direct experimental data were used to determine the excess molar volumes, $V_{\text{m}}^{\text{E}}$, and the excess refractive indices, $n_{\text{D}}^{\text{E}}$, at the working $T$. Values of the excess functions at 298.15 K, for the speed of sound, $c^{\text{E}}$, the isentropic compressibility, $\kappa_S^{\text{E}}$ and for the excess thermal expansion coefficient, $\alpha_p^{\text{E}}$, were also calculated. The investigated systems are characterized by strong amide-ketone interactions, which become weaker when the alkanone size is increased. This is supported by negative $V_{\text{m}}^{\text{E}}$ values; by the dependence on $T$ and pressure of $V_{\text{m}}^{\text{E}}$, and by positive $P_{\text{int}}^{\text{E}}$ (excess internal pressure) values. Analysis of the systems in terms of the Rao's constant indicates that there is no complex formation. In addition, negative $V_{\text{m}}^{\text{E}}$ values also reveal the existence of structural effects, which largely contribute to the excess molar enthalpy, $H_{\text{m}}^{\text{E}}$. $V_{\text{m}}^{\text{E}}$ and $H_{\text{m}}^{\text{E}}$ values increase with the chain length of the 2-alkanone. It allows to conclude that the relative $V_{\text{m}}^{\text{E}}$ variation with the ketone size is closely related to that of the interactional contribution to this excess function. Molar refraction values, $R_{\text{m}}$, show that dispersive interactions become more relevant for the systems including longer 2-alkanones.

1-Alkanol + alkanenitrile systems have been studied by means of the DISQUAC, ERAS and UNIFAC (Dortmund) models. DISQUAC and ERAS parameters for the alkanol/nitrile interactions are reported. DISQUAC describes a whole set of thermodynamic properties: phase equilibria, vapour-liquid (VLE), liquid-liquid (LLE) and solid-liquid (SLE) equilibria, molar excess functions, Gibbs energies, $G_{\text{m}}^{\text{E}}$, and enthalpies, $H_{\text{m}}^{\text{E}}$, and partial excess molar enthalpies at infinite dilution, $H_{\text{mi}}^{\text{E,}\infty }$ using the same set of interaction parameters for each solution. The dependence on the molecular structure of the interaction parameters is similar to that observed in other previous applications to mixtures formed by 1-alkanols and a strongly polar compound, in such way that the quasichemical interchange coefficients can be kept constant from 1-propanol. However, methanol and ethanol solutions behave differently. From the analysis of experimental data for $H_{\text{m}}^{\text{E}}$, $TS_{\text{m}}^{\text{E}}(=H_{\text{m}}^{\text{E}}-G_{\text{m}}^{\text{E}})$, and molar excess volumes, $V_{\text{m}}^{\text{E}}$, it is concluded that the studied systems are characterized by dipolar interactions and strong structural effects. The former are more relevant in acetonitrile solutions. Association effects are more important in butanenitrile mixtures. DISQUAC improves $H_{\text{m}}^{\text{E}}$ results from the ERAS model. ERAS results on $H_{\text{m}}^{\text{E}}$ for systems containing acetonitrile are also improved by UNIFAC. This remarks the importance of dipolar interactions in the investigated mixtures. ERAS describes the variation of $V_{\text{m}}^{\text{E}}$(${{x}_{1}}$=0.5) with the 1-alkanol size for mixtures with a given nitrile, but the concentration dependence of this excess function is poorly represented.

Results are presented for the measurement of large-scale anisotropies in the arrival directions of ultra-high-energy cosmic rays detected at the Pierre Auger Observatory during 19 years of operation, prior to AugerPrime, the upgrade of the Observatory. The 3D dipole amplitude and direction are reconstructed above $4\,$EeV in four energy bins. Besides the established dipolar anisotropy in right ascension above $8\,$EeV, the Fourier amplitude of the $8$ to $16\,$EeV energy bin is now also above the $5\sigma$ discovery level. No time variation of the dipole moment above $8\,$EeV is found, setting an upper limit to the rate of change of such variations of $0.3\%$ per year at the $95\%$ confidence level. Additionally, the results for the angular power spectrum are shown, demonstrating no other statistically significant multipoles. The results for the equatorial dipole component down to $0.03\,$EeV are presented, using for the first time a data set obtained with a trigger that has been optimized for lower energies. Finally, model predictions are discussed and compared with observations, based on two source emission scenarios obtained in the combined fit of spectrum and composition above $0.6\,$EeV., Comment: Minor typo in table 4 corrected

Ultra-high-energy cosmic rays are known to be mainly of extragalactic origin, and their propagation is limited by energy losses, so their arrival directions are expected to correlate with the large-scale structure of the local Universe. In this work, we investigate the possible presence of intermediate-scale excesses in the flux of the most energetic cosmic rays from the direction of the supergalactic plane region using events with energies above 20 EeV recorded with the surface detector array of the Pierre Auger Observatory up to 31 December 2022, with a total exposure of 135,000 km^2 sr yr. The strongest indication for an excess that we find, with a post-trial significance of 3.1{\sigma}, is in the Centaurus region, as in our previous reports, and it extends down to lower energies than previously studied. We do not find any strong hints of excesses from any other region of the supergalactic plane at the same angular scale. In particular, our results do not confirm the reports by the Telescope Array collaboration of excesses from two regions in the Northern Hemisphere at the edge of the field of view of the Pierre Auger Observatory. With a comparable exposure, our results in those regions are in good agreement with the expectations from an isotropic distribution., Comment: submitted to ApJ

In this manuscript, we undertake an examination of a classical plasma deployed on two finite co-planar surfaces: a circular region $\Omega_{in}$ into an annular region $\Omega_{out}$ with a gap in between. It is studied both from the point of view of statistical mechanics and the electrostatics of continua media. We employ a dual perspective: the first one is by using Molecular Dynamics (MD) simulations to find the system's positional correlation functions and velocity distributions. That by modeling the system as a classical two-dimensional Coulomb plasma of point-like charged particles $q_1$ and $q_2$ on the layers $\Omega_{in}$ and $\Omega_{out}$ respectively with no background density. The second one corresponds to a finite surface electrode composed of planar metallic layers displayed on the regions $\Omega_{in}$, $\Omega_{out}$ at constant voltages $V_{in}$, $V_{out}$ considering axial symmetry. The surface charge density is calculated by the Method of Moments (MoM) under the electrostatic approximation. Point-like and differential charges elements interact via a $1/r$ - electric potential in both cases. The thermodynamic averages of the number density, and electric potential due to the plasma depend on the coupling and the charge ratio $\xi=q_1/q_2$ once the geometry of the layers is fixed. On the other hand, the fields due to the SE depend on the layer's geometry and their voltage. In the document, is defined a protocol to properly compare the systems. We show that there are values of the coupling parameter, where the thermodynamic averages computed via MD agree with the results of MoM for attractive $\xi=-1$ and repulsive layers $\xi=1$. Keywords: molecular dynamics, method of moments, Coulomb systems, long-range interaction., Comment: 32 pages, 16 Figures

We perform a detailed study of the $\Upsilon$-, $\eta_b$- and $B_c$-nucleus systems in momentum space to calculate the bound-state energies and the corresponding coordinate space radial wave functions. A comparison is made among different methods to obtain the partial wave decomposition of meson-nucleus potentials in momentum space, namely, (i) the spherical Bessel transform of the numerically obtained original potential in coordinate space, (ii) the partial wave decomposition of the Fourier transform of the Woods-Saxon approximated form for the original potential, and (iii) the spherical Bessel transform of the Woods-Saxon approximation of the numerically obtained original potential. The strong nuclear bound-state energies for the $\Upsilon$-$^{4}$He, $\Upsilon$-$^{12}$C, $\eta_b$-$^{4}$He, $\eta_b$-$^{12}$C, $B_c$-$^{4}$He (no Coulomb), and $B_c$-$^{12}$C (no Coulomb) systems and the corresponding wave functions in coordinate space are compared for the three methods. Furthermore, as an initial and realistic study, the $B_c^{\pm}$-$^{12}$C bound states are studied for the first time, with the effects of self-consistently calculated Coulomb potentials in $^{12}$C (when the $B_c^{\pm}$ mesons are absent)., Comment: 19 pages, 23 figures (69 .eps files for figures)

The Pierre Auger Observatory is the most sensitive instrument to detect photons with energies above $10^{17}$ eV. It measures extensive air showers generated by ultra high energy cosmic rays using a hybrid technique that exploits the combination of a fluorescence detector with a ground array of particle detectors. The signatures of a photon-induced air shower are a larger atmospheric depth of the shower maximum ($X_{max}$) and a steeper lateral distribution function, along with a lower number of muons with respect to the bulk of hadron-induced cascades. In this work, a new analysis technique in the energy interval between 1 and 30 EeV (1 EeV = $10^{18}$ eV) has been developed by combining the fluorescence detector-based measurement of $X_{max}$ with the specific features of the surface detector signal through a parameter related to the air shower muon content, derived from the universality of the air shower development. No evidence of a statistically significant signal due to photon primaries was found using data collected in about 12 years of operation. Thus, upper bounds to the integral photon flux have been set using a detailed calculation of the detector exposure, in combination with a data-driven background estimation. The derived 95% confidence level upper limits are 0.0403, 0.01113, 0.0035, 0.0023, and 0.0021 km$^{-2}$ sr$^{-1}$ yr$^{-1}$ above 1, 2, 3, 5, and 10 EeV, respectively, leading to the most stringent upper limits on the photon flux in the EeV range. Compared with past results, the upper limits were improved by about 40% for the lowest energy threshold and by a factor 3 above 3 EeV, where no candidates were found and the expected background is negligible. The presented limits can be used to probe the assumptions on chemical composition of ultra-high energy cosmic rays and allow for the constraint of the mass and lifetime phase space of super-heavy dark matter particles., Comment: 19 pages, 22 figures

We report an investigation of the mass composition of cosmic rays with energies from 3 to 100 EeV (1 EeV=$10^{18}$ eV) using the distributions of the depth of shower maximum $X_\mathrm{max}$. The analysis relies on ${\sim}50,000$ events recorded by the Surface Detector of the Pierre Auger Observatory and a deep-learning-based reconstruction algorithm. Above energies of 5 EeV, the data set offers a 10-fold increase in statistics with respect to fluorescence measurements at the Observatory. After cross-calibration using the Fluorescence Detector, this enables the first measurement of the evolution of the mean and the standard deviation of the $X_\mathrm{max}$ distributions up to 100 EeV. Our findings are threefold: (1.) The evolution of the mean logarithmic mass towards a heavier composition with increasing energy can be confirmed and is extended to 100 EeV. (2.) The evolution of the fluctuations of $X_\mathrm{max}$ towards a heavier and purer composition with increasing energy can be confirmed with high statistics. We report a rather heavy composition and small fluctuations in $X_\mathrm{max}$ at the highest energies. (3.) We find indications for a characteristic structure beyond a constant change in the mean logarithmic mass, featuring three breaks that are observed in proximity to the ankle, instep, and suppression features in the energy spectrum., Comment: Version accepted for publication in Phys. Rev. D, 29 pages, 19 figures, 5 tables

We present measurements of the atmospheric depth of the shower maximum $X_\mathrm{max}$, inferred for the first time on an event-by-event level using the Surface Detector of the Pierre Auger Observatory. Using deep learning, we were able to extend measurements of the $X_\mathrm{max}$ distributions up to energies of 100 EeV ($10^{20}$ eV), not yet revealed by current measurements, providing new insights into the mass composition of cosmic rays at extreme energies. Gaining a 10-fold increase in statistics compared to the Fluorescence Detector data, we find evidence that the rate of change of the average $X_\mathrm{max}$ with the logarithm of energy features three breaks at $6.5\pm0.6~(\mathrm{stat})\pm1~(\mathrm{sys})$ EeV, $11\pm 2~(\mathrm{stat})\pm1~(\mathrm{sys})$ EeV, and $31\pm5~(\mathrm{stat})\pm3~(\mathrm{sys})$ EeV, in the vicinity to the three prominent features (ankle, instep, suppression) of the cosmic-ray flux. The energy evolution of the mean and standard deviation of the measured $X_\mathrm{max}$ distributions indicates that the mass composition becomes increasingly heavier and purer, thus being incompatible with a large fraction of light nuclei between 50 EeV and 100 EeV., Comment: Version accepted for publication in Phys. Rev. Lett., 9 pages, 3 figures, 1 table