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We review properties of confluent functions and the closely related Laguerre polynomials, and determine their bilinear integrals. As is well-known, these integrals are convergent only for a limited range of parameters. However, when one uses the generalized integral they can be computed essentially without restricting the parameters. This gives the (generalized) Gram matrix of Laguerre polynomials. If the parameters are not negative integers, then Laguerre polynomials are orthogonal, or at least pseudo-orthogonal in the case of generalized integrals. For negative integer parameters, the orthogonality relations are more complicated., Comment: 21 pages

A one-dimensional, dynamic, two-phase, isothermal and finite-difference model of proton exchange membrane fuel cell (PEMFC) systems has been developed. It is distinct from most existing models which are either fast but imprecise, such as lumped-parameter models, or detailed but computationally intensive, such as computational fluid dynamics models. This model, partially validated using experimental polarisation curves, provides a comprehensive description of cell internal states while maintaining a low computational burden. Additionally, a new physical quantity, named the limit liquid water saturation coefficient ($s_{lim}$), is introduced in the overvoltage calculation equation. This quantity replaces the limit current density coefficient ($i_{lim}$) and establishes a connection between the voltage drop at high current densities, the amount of liquid water present in the catalyst layers of the cell, and the operating conditions. At high current densities, a significant amount of liquid water is generated, which limits the accessibility of reactants to certain triple point zones within the catalyst layers by covering them. This, in turn, increases overpotential. It has also been observed that $s_{lim}$ is influenced, at minimum, by the gas pressure imposed by the operator.

In dimensions d= 1, 2, 3 the Laplacian can be perturbed by a point potential. In higher dimensions the Laplacian with a point potential cannot be defined as a self-adjoint operator. However, for any dimension there exists a natural family of functions that can be interpreted as Green's functions of the Laplacian with a spherically symmetric point potential. In dimensions 1, 2, 3 they are the integral kernels of the resolvent of well-defined self-adjoint operators. In higher dimensions they are not even integral kernels of bounded operators. Their construction uses the so-called generalized integral, a concept going back to Riesz and Hadamard. We consider the Laplace(-Beltrami) operator on the Euclidean space, the hyperbolic space and the sphere in any dimension. We describe the corresponding Green's functions, also perturbed by a point potential. We describe their limit as the scaled hyperbolic space and the scaled sphere approach the Euclidean space. Especially interesting is the behavior of positive eigenvalues of the spherical Laplacian, which undergo a shift proportional to a negative power of the radius of the sphere. We expect that in any dimension our constructions yield possible behaviors of the integral kernel of the resolvent of a perturbed Laplacian far from the support of the perturbation. Besides, they can be viewed as toy models illustrating various aspects of renormalization in Quantum Field Theory, especially the point-splitting method and dimensional regularization., Comment: 51 pages

We investigate the dynamics of a multifield dark energy model, which arises from certain rapid-turning and inspiraling trajectories in field space. We find the speed of sound $c_s$ of the dark energy perturbations around the background and show that $c_s$ is monotonically decreasing with time. Furthermore, it has a positive-definite lower bound that implies a certain clustering scale. We also extend the previously known background solution for dark energy to an exact solution that includes matter. This allows us to address the implications of our model for two cosmological tensions. More precisely, we argue that the $\sigma_8$ tension can be alleviated generically, while reducing the Hubble tension requires certain constraints on the parameter space of the model. Notably, a necessary condition for alleviating the Hubble tension is that the transition from matter domination to the dark energy epoch begins earlier than in $\Lambda$CDM., Comment: 36 pages; minor improvements, references added

First we recall a method of computing scalar products of eigenfunctions of a Sturm-Liouville operator. This method is then applied to Macdonald and Gegenbauer functions, which are eigenfunctions of the Bessel, resp. Gegenbauer operators. The computed scalar products are well defined only for a limited range of parameters. To extend the obtained formulas to a much larger range of parameters, we introduce the concept of a generalized integral. The (standard as well as generalized) integrals of Macdonald and Gegenbauer functions have important applications to operator theory. Macdonald functions can be used to express the integral kernels of the resolvent (Green functions) of the Laplacian on the Euclidean space in any dimension. Similarly, Gegenbauer functions appear in Green functions of the Laplacian on the sphere and the hyperbolic space. In dimensions 1,2,3 one can perturb these Laplacians with a point potential, obtaining a well defined self-adjoint operator. Standard integrals of Macdonald and Gegenbauer functions appear in the formulas for the corresponding Green functions. In higher dimensions the Laplacian perturbed by point potentials does not exist. However, the corresponding Green function can be generalized to any dimension by using generalized integrals., Comment: 9 pages

The recent report of a half-quantized thermal Hall effect in the Kitaev material $\alpha$-RuCl$_3$ has sparked a strong debate on whether it is generated by Majorana fermion edge currents or whether other more conventional mechanisms involving magnons or phonons are at its origin. A more direct evidence for Majorana fermions which could be expected to arise from a contribution to the longitudinal heat conductivity $\kappa_{xx}$ at $T\rightarrow0$ is elusive due to a very complex magnetic field dependence of $\kappa_{xx}$. Here, we report very low temperature (below 1~K) thermal conductivity ($\kappa$) of another candidate Kitaev material, Na$_2$Co$_2$TeO$_6$. The application of a magnetic field along different principal axes of the crystal reveals a strong directional-dependent magnetic-field ($\bf B$) impact on $\kappa$. We show that no evidence for mobile quasiparticles except phonons can be concluded at any field from 0~T to the field polarized state. In particular, severely scattered phonon transport is observed across the $B-T$ phase diagram, which is attributed to prominent magnetic fluctuations. Cascades of phase transitions are uncovered for all $\bf B$ directions by probing the strength of magnetic fluctuations via a precise record of $\kappa$($B$). Our results thus rule out recent proposals for itinerant magnetic excitations in Na$_2$Co$_2$TeO$_6$, and emphasise the importance of discriminating true spin liquid transport properties from scattered phonons in candidate materials.

Current WHO guidelines set prevalence thresholds below which a Neglected Tropical Disease can be considered to have been eliminated as a public health problem, and specify how surveys to assess whether elimination has been achieved should be designed and analysed, based on classical survey sampling methods. In this paper we describe an alternative approach based on geospatial statistical modelling. We first show the gains in efficiency that can be obtained by exploiting any spatial correlation in the underlying prevalence surface. We then suggest that the current guidelines implicit use of a significance testing argument is not appropriate; instead, we argue for a predictive inferential framework, leading to design criteria based on controlling the rates at which areas whose true prevalence lies above and below the elimination threshold are incorrectly classified. We describe how this approach naturally accommodates context-specific information in the form of georeferenced covariates that have been shown to be predictive of disease prevalence. Finally, we give a progress report of an ongoing collaboration with the Guyana Ministry of Health Neglected Tropical Disease program on the design of an IDA (Ivermectin, Diethylcarbamazine and Albendazole) Impact Survey (IIS) of lymphatic filariasis to be conducted in Guyana in early 2023, Comment: 11 pages, 3 figures

Let $f$ be a Gaussian random field on $\mathbb{R}^d$ and let $X$ be the number of critical points of $f$ contained in a compact subset. A long-standing conjecture is that, under mild regularity and non-degeneracy conditions on $f$, the random variable $X$ has finite moments. So far, this has been established only for moments of order lower than three. In this paper, we prove the conjecture. Precisely, we show that $X$ has finite moment of order $p$, as soon as, at any given point, the Taylor polynomial of order $p$ of $f$ is non-degenerate. We present a simple and general approach that is not specific to critical points and we provide various applications. In particular, we show the finiteness of moments of the nodal volumes and the number of critical points of a large class of smooth, or holomorphic, Gaussian fields, including the Bargmann-Fock ensemble., Comment: 24 pages. In this second version, we have weakened the assumption of our main theorem: we require nondegeneracy of the Taylor polynomial of order p, instead of p+1. Furthermore, we have included Corollary 1.4, concerning a central limit theorem for the number of connected components of the nodal and excursion sets

Observations from the NASA Solar Dynamic Observatory Atmospheric Imaging Assembly were employed to investigate targeted physical properties of coronal active region structures across the entirety of Solar Cycle 24 (dates). This is the largest consistent study to date which analyses emergent trends in structural width, location, and occurrence rate by performing an automatic and long-term examination of observable coronal limb features within equatorial active region belts across four extreme ultraviolet wavelengths (171, 193, 211, and 304 angstroms). This has resulted in over thirty thousand observed coronal structures and hence allows for the production of spatial and temporal distributions focused upon the rise, peak and decay activity phases of Solar Cycle 24. Employing a self-organized-criticality approach as a descriptor of coronal structure formation, power law slopes of structural widths versus frequency are determined, ranging from -1.6 to -3.3 with variations of up to 0.7 found between differing periods of the solar cycle, compared to a predicted Fractal Diffusive Self Organized Criticality (FD-SOC) value of -1.5. The North-South hemispheric asymmetry of these structures was also examined with the northern hemisphere exhibiting activity that is peaking earlier and decaying slower than the southern hemisphere, with a characteristic "butterfly" pattern of coronal structures detected. This represents the first survey of coronal structures performed across an entire solar cycle, demonstrating new techniques available to examine the composition of the corona by latitude in varying wavelengths at selected altitudes., Comment: 16 pages, 10 figures. Preprint copy

The structure of quantum interactions with fields of helicity two ("gravitons") is strongly constrained by three principles: positivity (Hilbert space), covariance, and locality of observables. To fulfil them simultaneously, some (non-observable) fields need to be non-local. We work with string-localized fields. The results then follow from the condition that entities closely related to observables, like the S-matrix, be local and string-independent. They in particular reproduce the interactions dictated by general covariance in classical field theory. Graviton-matter couplings are consistent only when the graviton self-interaction is taken into account as well., Comment: 36 pages. v2: 38 pages, Dirac coupling case included, otherwise as to appear in Class. Qu. Grav

We compute bilinear integrals involving Macdonald and Gegenbauer functions. These integrals are convergent only for a limited range of parameters. However, when one uses generalized integrals they can be computed essentially without restricting the parameters. The generalized integral is a linear functional extending the standard integral to a certain class of functions involving finitely many homogeneous non-integrable terms at the edpoints of the interval. For generic values of parameters, generalized bilinear integrals of Macdonald and Gegenbauer functions can be obtained by analytic continuation from the region in which the integrals are convergent. In the case of integer parameters we obtain expressions with explicit additional terms related to an anomaly, namely the failure of the generalized integral to be scaling invariant., Comment: 39 pages