A relationship between the diameter and the intersection number c 2 for a distance-regular graph

In this paper we will look at the relationship between the intersection number c ₂ and the diameter of a distance-regular graph. We also give some tools to show that a distance-regular graph with large c ₂ is bipartite, and a tool to show that if k _D is too small then the distance-regular graph has to be antipodal.     

Updating incomplete factorization preconditioners for model order reduction

When solving a sequence of related linear systems by iterative methods, it is common to reuse the preconditioner for several systems, and then to recompute the preconditioner when the matrix has changed significantly. Rather than recomputing the preconditioner from scratch, it is potentially more efficient to update the previous preconditioner. Unfortunately, it is not always known how to update a preconditioner, for example, when the preconditioner is an incomplete factorization. A recently proposed iterative algorithm for computing incomplete factorizations, however, is able to exploit an initial guess, unlike existing algorithms for incomplete factorizations. By treating a previous factorization as an initial guess to this algorithm, an incomplete factorization may thus be updated. We use a sequence of problems from model order reduction. Experimental results using an optimized GPU implementation show that updating a previous factorization can be inexpensive and effective, making solving sequences of linear systems a potential niche problem for the iterative incomplete factorization algorithm.     

Holistic electron theory

A relativistic, non-quantum theory of electrons is constructed in which the electron is not considered to be composed of any type of distribution of charge. The electron's structurelessness is defined by several assumptions which, together with Maxwell's equations outside the electron, yield the general fields produced by such an arbitrarily movingholistic electron. Several equations of motion for the holistic electron are found to result from the formulation, the Lorentz-Dirac equation being among them. The formulation, by its very nature, avoids the problems of the electron self-energy and the need for normalization.     

A Proposal for a Low-Frequency Axion Search in the 1–2 μ eV Range and Below with the BabyIAXO Magnet

In the near future BabyIAXO will be the most powerful axion helioscope, relying on a custom-made magnet of two bores of 70 cm diameter and 10 m long, with a total available magnetic volume of more than 7 m³. In this document, it proposes and describe the implementation of low-frequency axion haloscope setups suitable for operation inside the BabyIAXO magnet. The RADES proposal has a potential sensitivity to the axion-photon coupling $g_{a\gamma }$ down to values corresponding to the KSVZ model, in the (currently unexplored) mass range between 1 and 2 $\mu$ eV, after a total effective exposure of 440 days. This mass range is covered by the use of four differently dimensioned 5-meter-long cavities, equipped with a tuning mechanism based on inner turning plates. A setup like the one proposed will also allow an exploration of the same mass range for hidden photons coupled to photons. An additional complementary apparatus is proposed using LC circuits and exploring the low energy range ( $\approx {10}^{-4}-{10}^{-1}\mu$ eV). The setup includes a cryostat and cooling system to cool down the BabyIAXO bore down to about 5 K, as well as an appropriate low-noise signal amplification and detection chain.     

Analytically Continued Hypergeometric Expression of the Incomplete Beta Function

The Incomplete Beta Function is rewritten as a Hypergeometric Function that is the analytic continuation of the conventional form, a generalization of the finite series, which simpifies the Stieltjes transform of powers of a monomial divided by powers of a binomial.     

Modelling thermal front dynamics in microwave heating

The formation and propagation of thermal fronts in a cylindricalmedium that is undergoing microwave heating is studied in detail.The model consists of Maxwell's wave equation coupled to a temperaturediffusion equation containing a bistable nonlinear term. When the thermal diffusivity is sufficiently small the leading-ordertemperature solution of a singular perturbation analysis isused to reduce the system to a free boundary problem. This approximationis then used to derive predictions for the steady-state penetrationand profiles of the temperature and electric fields. These solutionsare valid for arbitrary values of the electric conductivity,and thus extend the previous (small conductivity) results foundin the literature. A quasi-static approximation for the electric field is thenused to obtain an ordinary differential equation for the relaxationdynamics to the steady state. This equation appears to accuratelydescribe the time scale of the electric field's evolution bothwith and without the presence of a strongly coupled temperaturefront, and may be of wider interest than the model for microwaveheating studied here.