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The heterogeneous distribution of water-repellent materials at the soil surface causes a phenomenon known as fractional wettability. This condition frequently triggers destabilization of the wetting front during water infiltration, resulting in the formation of fingered bypass flow. However, few analytical tools exist to understand and model this behavior. Moreover, existing infiltration models fail to fit certain infiltration curves that exist in experimental data. For these reasons, we introduce a novel infiltration model to simulate water infiltration under fractional wettable conditions. We conceptualize the soil surface as a composite of two distinct portions: a water-repellent fraction, where hydrophobic effects impede water infiltration, and a wettable fraction, where capillarity and gravity are the dominant forces controlling the process. The new model was validated using a dataset comprising infiltration data from 60 field measurements. Additionally, validation was performed using 660 analytically generated infiltration curves from six synthetic soils with varying textures. This innovative approach enabled us to account for the combined influence of these two fractions and to enhance the interpretation of infiltration curves with mixed shapes, which other common methods are unable to reproduce.

We prove a rigidity result for maps between \v{C}ech-Stone remainders under fairly mild forcing axioms., Comment: 8 pages

We extend the notion of a p-permutation equivalence to an equivalence between direct products of block algebras. We prove that a p-permutation equivalence between direct products of blocks gives a bijection between the factors and induces a p-permutation equivalence between corresponding blocks.

Let $k$ be an algebraically closed field of characteristic $p>0$ and let $\mathbb{F}$ be an algebraically closed field of characteristic $0$. Recently, together with Bouc, we introduced the notion of functorial equivalences between blocks of finite groups and proved that given a $p$-group $D$, there is only a finite number of pairs $(G,b)$ of a finite group $G$ and a block $b$ of $kG$ with defect groups isomorphic to $D$, up to functorial equivalence over $\mathbb{F}$. In this paper, we classify the functorial equivalence classes over $\mathbb{F}$ of blocks with cyclic defect groups and $2$-blocks of defects $2$ and $3$. In particular, we prove that for all these blocks, the functorial equivalence classes depend only on the fusion system of the block., Comment: arXiv admin note: text overlap with arXiv:2212.02054

Let $k$ be an algebraically closed field of characteristic $2$, let $G$ be a finite group and let $B$ be the principal $2$-block of $kG$ with a dihedral or a generalised quaternion defect group $P$. Let also $\mathcal{T}(B)$ denote the group of splendid Morita auto-equivalences of $B$. We show that \begin{align*} \mathcal{T}(B)\cong \mathrm{Out}_P(A)\rtimes \mathrm{Out}(P,\mathcal{F})\,, \end{align*} where $\mathrm{Out}(P,\mathcal{F})$ is the group of outer automorphisms of $P$ which stabilize the fusion system $\mathcal{F}$ of $G$ on $P$ and $\mathrm{Out}_P(A)$ is the group of algebra automorphisms of a source algebra $A$ of $B$ fixing $P$ modulo inner automorphisms induced by $(A^P)^\times$.

Let $k$ be an algebraically closed field of characteristic $p>0$, let $R$ be a commutative ring and let $\mathcal{F}$ be an algebraically closed field of characteristic $0$. We introduce the category $\overline{\mathcal{F}_{Rpp_k}}$ of stable diagonal $p$-permutation functors over $R$. We prove that the category $\overline{\mathcal{F}_{\mathbb{F}pp_k}}$ is semisimple and give a parametrization of its simple objects in terms of the simple diagonal $p$-permutation functors. We also introduce the notion of a stable functorial equivalence over $R$ between blocks of finite groups. We prove that if $G$ is a finite group and if $b$ is a block idempotent of $kG$ with an abelian defect group $D$ and Frobenius inertial quotient $E$, then there exists a stable functorial equivalence over $\mathbb{F}$ between the pairs $(G,b)$ and $(D\rtimes E,1)$., Comment: arXiv admin note: text overlap with arXiv:2212.02054

In this study, Higgs production processes, Higgsstrahlung and vector boson (W and Z) fusion processes, were investigated for four different future lepton colliders (CEPC, ILC, CLIC, and FCC-ee). The cross sections for each production process and corresponding backgrounds were calculated considering the ISR and beamstrahlung effects. Various cuts and the b-tagging method were used to reduce the background. Finally, the number of events for each collider was determined, and significance calculations were performed. In our calculations, high event numbers were obtained for all four colliders for the Higgsstrahlung, W, and Z fusion process. This shows that electron-positron colliders will play an important role in future Higgs physics research., Comment: 10 pages, 8 figures

Let $\mathbb{F}$ be an algebraically closed field of characteristic zero. In this article we show that isotypic blocks of finite groups are functorially equivalent over $\mathbb{F}$., Comment: There is a gap in the proof of Lemma 3.2

Let $k$ be an algebraically closed field of characteristic $p>0$, let $R$ be a commutative ring, and let $\mathbb{F}$ be an algebraically closed field of characteristic 0. We consider the $R$-linear category $\mathcal{F}^\Delta_{Rpp_k}$ of diagonal $p$-permutation functors over $R$. We first show that the category $\mathcal{F}^\Delta_{\mathbb{F}pp_k}$ is semisimple, and we give a parametrization of its simple objects, together with a description of their evaluations. Next, to any pair $(G,b)$ of a finite group $G$ and a block idempotent $b$ of $kG$, we associate a diagonal $p$-permutation functor $RT^{\Delta}_{G,b}$ in $\mathcal{F}^\Delta_{Rpp_k}$. We find the decomposition of the functor $\mathbb{F}T^{\Delta}_{G,b}$ as a direct sum of simple functors in $\mathcal{F}^\Delta_{\mathbb{F}pp_k}$. This leads to a characterization of nilpotent blocks in terms of their associated functors in $\mathcal{F}^\Delta_{\mathbb{F}pp_k}$. Finally, for such pairs $(G,b)$ of a finite group and a block idempotent, we introduce the notion of functorial equivalence over $R$, which (in the case $R=\mathbb{Z}$) is slightly weaker than $p$-permutation equivalence, and we prove a corresponding finiteness theorem: for a given finite $p$-group $D$, there is only a finite number of pairs $(G,b)$, where $G$ is a finite group and $b$ a block idempotent of $kG$ with defect isomorphic to $D$, up to functorial equivalence over $\mathbb{F}$.

We give sufficient conditions on $p$-blocks of $p$-nilpotent groups over $\mathbb{F}_p$ to be splendidly Rickard equivalent and $p$-permutation equivalent to their Brauer correspondents. The paper also contains Galois descent results on $p$-permutation modules and $p$-permutation equivalences that hold for arbitrary groups., Comment: 15 pages, some rearrangement of content of Section 5. Clarification of some arguments

Let $A$ be an abelian group such that $\mathrm{Hom}(G,A)$ is finite for all finite groups $G$, and let $\mathbb{K}$ be a field of characteristic zero containing roots of unity of all orders equal to finite element orders in $A$. In this paper we prove foundational properties of the $A$-fibered Burnside ring functor $B_{\mathbb{K}}^A$ as an $A$-fibered biset functor over $\mathbb{K}$. This includes the determination of the lattice of subfunctors of $B_{\mathbb{K}}^A$ and the determination of the composition factors of $B_{\mathbb{K}}^A$. The results of the paper extend results of Co\c{s}kun and Y\i lmaz for the $A$-fibered Burnside ring functor restricted to $p$-groups and results of Bouc in the case that $A$ is trivial, i.e., the case of the Burnside ring functor over fields of characteristic zero., Comment: 26 pages, referee comments incorporated, consolidated prerequisites from previous Sections 2--4 to Section 2, changed abstract slightly, accepted by Algebras and Representation Theory

To any block idempotent $b$ of a group algebra $kG$ of a finite group $G$ over a field $k$ of characteristic $p>0$, Puig associated a fusion system and proved that it is saturated if the $k$-algebra $kC_G(P)e$ is split, where $(P,e)$ is a maximal $kGb$-Brauer pair. We investigate in the non-split case how far the fusion system is from being saturated by describing it in an explicit way as being generated by the fusion system of a related block idempotent over a larger field together with a single automorphism of the defect group., Comment: 11 pages

Let $k$ be an algebraically closed field of positive characteristic $p$, and $\mathbb{F}$ be an algebraically closed field of characteristic 0. We consider the $\mathbb{F}$-linear category $\mathbb{F} pp_k^\Delta$ of finite groups, in which the set of morphisms from $G$ to $H$ is the $\mathbb{F}$-linear extension $\mathbb{F} T^\Delta(H,G)$ of the Grothendieck group $T^\Delta(H,G)$ of $p$-permutation $(kH,kG)$-bimodules with (twisted) diagonal vertices. The $\mathbb{F}$-linear functors from $\mathbb{F} pp_k^\Delta$ to $\mathbb{F}\hbox{-Mod}$ are called {\em diagonal $p$-permutation functors}. They form an abelian category $\mathcal{F}_{pp_k}^\Delta$. We study in particular the functor $\mathbb{F}T^{\Delta}$ sending a finite group $G$ to the Grothendieck group $\mathbb{F}T(G)$ of $p$-permutation $kG$-modules, and show that $\mathbb{F}T^\Delta$ is a semisimple object of $\mathcal{F}_{pp_k}^\Delta$, equal to the direct sum of specific simple functors parametrized by isomorphism classes of pairs $(P,s)$ of a finite $p$-group $P$ and a generator $s$ of a $p'$-subgroup acting faithfully on $P$. This leads to a precise description of the evaluations of these simple functors. In particular, we show that the simple functor indexed by the trivial pair $(1,1)$ is isomorphic to the functor sending a finite group $G$ to $\mathbb{F} K_0(kG)$, where $K_0(kG)$ is the group of projective $kG$-modules.

We determine the composition factors of the $A$-fibered Burnside functor $kB^A$ for $p$-groups over a field $k$ of characteristic $q$ with $q\neq p$ and cyclic fiber group $A$. We also show that, in this case, $kB^A$ is uniserial., Comment: 24 pages

The spin flavor precession (SFP) is investigated in the three neutrino generation case assuming that the neutrinos are Majorana type. Approximate analytical formulas including all transition magnetic moments are provided for the electron neutrino survival probability and electron neutrino -> electron anti-neutrino transition probability in the SFP framework. The accuracy of the formulas is checked out for two different magnetic field profiles in the Sun., Comment: 19 pages, 6 figures

The combined effect of SFP and the non standard neutrino interaction (NSI) on the survival probability of solar electron neutrinos (assumed to be Dirac particles) is examined for various values of $\epsilon_{11}$, $\epsilon_{12}$ and $\mu B$. It is found that the neutrino survival probability curves affected by SFP and NSI effects individually for some values of the parameters ($\epsilon_{11}$, $\epsilon_{12}$ and $\mu B$) get close to the standard MSW curve when both effects are combined. Therefore, the combined effect of SFP and NSI needs to be taken into account when the solar electron neutrino data obtained by low energy solar neutrino experiments is investigated., Comment: 11 pages, 3 figures, published version