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Gender can be seen not only as a binary category but also as a performance or doing that is shaped by, and shapes organizational processes and structures that are deeply embedded in (sport) organizations in multiple and complex ways. The purpose of this paper is to explore strategies for addressing the undoing of gender in sport organizations with the use of an overarching or meta-approach. Strategies that aim to undo gender require a recognition of the complexity of regimes of inequality and the need to use incremental steps in the form of small wins while acknowledging change is not linear. The complexity and multiplicity of the gendering of sport organizations should, therefore, be considered a wicked problem. The naming of heterotopias can provide directions or goals for small wins and for addressing the wicked problem of the doing of gender in sport organizations. [ABSTRACT FROM AUTHOR]

The rules governing IRA required minimum distributions (RMDs) are complex. Throw the complexity of trusts on top of them and one begins to see the multiplicity of complications that can arise when they interact. This column will help sort it all out. [ABSTRACT FROM AUTHOR]

The rules governing IRA required minimum distributions (RMDs) are complex. Throw the complexity of trusts on top of them and one begins to see the multiplicity of complications that can arise when they interact. This column will help sort it all out. [ABSTRACT FROM AUTHOR]

In this paper, we prove the converse of Rees' mixed multiplicity theorem for modules, which extends the converse of the classical Rees' mixed multiplicity theorem for ideals given by Swanson-Theorem 1.3. Specifically, we demonstrate the following result: Let (R , m) be a d -dimensional formally equidimensional Noetherian local ring and E 1 , ... , E k be finitely generated R -submodules of a free R -module F of positive rank p , with x i ∈ E i for i = 1 , ... , k. Consider S , the symmetric algebra of F , and I E i , the ideal generated by the homogeneous component of degree 1 in the Rees algebra [ R (E i) ] 1. Assuming that (x 1 , ... , x k) S and I E i have the same height k and the same radical, if the Buchsbaum-Rim multiplicity of (x 1 , ... , x k) and the mixed Buchsbaum-Rim multiplicity of the family E 1 , ... , E k are equal, i.e., e BR ((x 1 , ... , x k) p ; R p) = e BR ( E 1 p , ... , E k p , R p) for all prime ideals p minimal over ((x 1 , ... , x k) : R F) , then (x 1 , ... , x k) is a joint reduction of (E 1 , ... , E k). In addition to proving this theorem, we establish some properties that relate joint reduction and mixed Buchsbaum-Rim multiplicities. [ABSTRACT FROM AUTHOR]

For a numerical semigroup S ⊆ N , let m , e , c , g denote its multiplicity, embedding dimension, conductor and genus, respectively. Wilf's conjecture (1978) states that e (c − g) ≥ c. As of 2023, Wilf's conjecture has been verified by computer up to genus g ≤ 66. In this paper, we extend the verification of Wilf's conjecture up to genus g ≤ 100. This is achieved by combining three main ingredients: (1) a theorem in 2020 settling Wilf's conjecture in the case e ≥ m / 3 , (2) an efficient trimming of the tree T of numerical groups identifying and cutting out irrelevant subtrees, and (3) the implementation of a fast parallelized algorithm to construct the tree T up to a given genus. We further push the verification of Wilf's conjecture up to genus 120 in the particular case where m divides c. Finally, we unlock three previously unknown values of the number n g of numerical semigroups of genus g , namely for g = 73 , 74 , 75. [ABSTRACT FROM AUTHOR]

Drawing on experiences from Abya Yala/Latin America, and based on the Andean philosophy and praxes of Allin kawsay, this article proposes and introduces the idea of a 'rhizomatic pluriverse' as a horizontal structure of dialogue(s) between multiple and diverse pluriversal alternatives. The article draws on the experiences of the Global Tapestry of Alternatives and the Crianza Mutua Networks as points of reference to argue for the possibility of bringing territorial alternatives into dialogue with one another, based on a common rejection of the forces of oppression and a shared struggle for the existence of a multiplicity or worlds, knowledges, cultures, and praxes. [ABSTRACT FROM AUTHOR]

Let k and n be natural numbers. Let ω k (n) denote the number of distinct prime factors of n with multiplicity k as studied by Elma and the third author [5]. We obtain asymptotic estimates for the first and the second moments of ω k (n) when restricted to the set of h -free and h -full numbers. We prove that ω 1 (n) has normal order log ⁡ log ⁡ n over h -free numbers, ω h (n) has normal order log ⁡ log ⁡ n over h -full numbers, and both of them satisfy the Erdős-Kac Theorem. Finally, we prove that the functions ω k (n) with 1 < k < h do not have normal order over h -free numbers and ω k (n) with k > h do not have normal order over h -full numbers. [ABSTRACT FROM AUTHOR]

For bifurcation analysis, we study the positive solution set for a semilinear elliptic equation of the logistic type, equipped with a sublinear boundary condition modeling coastal fishery harvesting. This work is a continuation of the author's previous studies (Umezu in Nonlinear Anal. Real World Appl. 70:103788, 2023, J. Math. Anal. Appl. 534:128134, 2024), where certain results were obtained in a non-resonant case, including the existence, uniqueness, multiplicity, and strong positivity for positive solutions. In this paper, we consider the delicate resonant case and develop a sort of nonstandard bifurcation technique at zero to evaluate the positive solution set depending on a parameter. The nonlinear boundary condition is not right-differentiable at zero. [ABSTRACT FROM AUTHOR]

This article examines individualising processes in the context of Municipal Adult Education in Swedish for Immigrants (SFI). Demands to adapt education to individual students' needs are increasingly evident in adult education policies, requiring accountable authorities' active engagement in enacting effective organisational frameworks while accommodating the labour market's needs. Such endeavours are often sources of tensions. Conceptual tools from cultural-historical activity theory are employed to address the complexity and multiplicity of individualising processes. An analysis of policy documents and interviews with municipal actors shows that individualising processes are played out through tensions found in three areas of object formation: making of an individual student; making of an effective education; and making of a coherent society. Hence, the study unpacks how individualising processes elicit transformations of SFI education through destabilisation/restabilisation cycles in the involved actors' activities, concluding by highlighting the concept's dynamic and potentiality for development in contemporary adult education settings. [ABSTRACT FROM AUTHOR]

Close encounter between a star and a supermassive black hole (SMBH) results in the tidal disruption of the star, known as a tidal disruption event (TDE). Recently, a few TDEs, e.g., ASASSN-15oi and AT2018hyz, have shown late-time (hundreds of days after their UV/optical peaks) radio flares with radio luminosities of 1038∼39 erg s−1. The super-Eddington fallback or accretion in a TDE may generate a mass outflow. Here, we investigate a scenario that the late-time radio flares come from the interaction of the outflow with the circumnuclear gaseous clouds, in addition to the slow-evolving emission component due to the outflow–diffuse medium interaction. We calculate the associated radio temporal and spectral signatures and find that they reproduce well the observations. The outflows have the inferred velocity of 0.2 c ∼ 0.6 c, the total mass of 10−3 ∼ 10−1 M ⊙ and the ejection duration of a month to a year. The distances of the clouds to the SMBH are 0.1 ∼ 1 pc. This scenario has advantages in explaining the long delay, sharpness of the rise, and the multiplicity of the late radio flares. Future observations may build up a much larger sample of late-time radio flares and enable their use as a probe of the TDE physics and the host circumnuclear environment. [ABSTRACT FROM AUTHOR]

We address a maximally structured case of the question, "Can you hear your location on a manifold," posed by Wyman and Xi [ Can you hear your location on a manifold? , https://arxiv.org/abs/2304.04659, 2023] for dimension 2. In short, we show that if a compact surface without a boundary sounds the same at every point, then the surface has a transitive action by the isometry group. In the process, we show that you can hear your location on Klein bottles and that you can hear the lengths and multiplicities of looping geodesics on compact hyperbolic quotients. [ABSTRACT FROM AUTHOR]

Although the spatiality of sounding and listening practices has been broadly and deeply discussed within humanities in general and sound studies in particular, the implications of such "place-taking" and "place-making" characteristics remain highly relevant nowadays. Starting from Peter Sloterdijk's concept of the phonotope, through which sound and space are closely related in the production of social, it will be argued, following philosopher and ethologist Vinciane Despret, that the importance of sound for "making place" matters far beyond human-centered thought. In what she calls the Phonocene, Despret invites us not only to listen to others, humans and nonhumans, but also to compose with multiple modes of existence, through the sonic. In short, the Phonocene addresses the importance of sonic thinking, which, for instance in sociology, challenges hegemonic and anthropocentric practices of knowledge production. Experimenting with "thinking-with sounds" within social sciences and philosophy thus implies not only to understand the spatiality inherent to the practices of sounding and listening, but to engage with those practices critically, as they are also always "situated," in the sense of Donna Haraway, and therefore, in the midst of multiple "interests," as understood in Actor-Network Theory, including a multiplicity of human, nonhuman, and more-than-human actors. [ABSTRACT FROM AUTHOR]

In this article, we investigate a class of fractional p-Kirchhoff equations with Trudinger–Moser nonlinearities: ε N (a + b [ v ] s , p p) (- Δ) p s v + Z (x) | v | p - 2 v = g (v) , x ∈ R N , where a > 0 , b > 0 , N = p s , p ⩾ 2 , s ∈ (0 , 1) and ε is a positive parameter, the nonlinear function g has critical exponential growth in the sense of Trudinger–Moser inequality, the continuous potential function Z satisfies appropriate conditions. By using some delicate variational techniques, we first prove the existence of the ground state solutions for above problem, and which are concentrated at a global minimum of Z under some suitable conditions. Then, we prove that these solutions satisfy a decay property. Finally, we get the multiplicity of solutions by the Ljusternik–Schnirelmann theory and the Morse theory, respectively. [ABSTRACT FROM AUTHOR]

Let $ R_i $, $ i = 1,2 $, be a root system in $ {\mathbb{R}}^{N_i}\backslash\{0\} $, $ N_i\geq 1 $, $ W_i = W(R_i) $ be the associated finite reflection group, and $ k_i: R_i\to [0,\infty) $ be a multiplicity function, i.e. $ k_i $ is $ W_i $-invariant. For $ \ell\geq 0 $, we introduce the operator $ L_{\ell,k_1,k_2} $ defined by$ L_{\ell,k_1,k_2}u(x,y) = \Delta_{k_1}u(x,y)+|x|^{2\ell}\Delta_{k_2}u(x,y),\,\,(x,y)\in {\mathbb{R}}^{N_1}\times {\mathbb{R}}^{N_2}, $where $ \Delta_{k_i} $ is the Dunkl Laplacian operator associated with $ R_i $ and $ k_i $. Our goal in this paper is to establish a Liouville-type result for the semilinear inequality$ -L_{\ell,k_1,k_2}u\geq |u|^p,\,\, (x,y)\in {\mathbb{R}}^{N_1}\times {\mathbb{R}}^{N_2}, $where $ u = u(x,y) $ and $ p>1 $. [ABSTRACT FROM AUTHOR]

In this paper, we first investigate the Palais-Smale compactness condition of the energy functional associated to a m (ξ) -Kirchhoff-type operator in the appropriate fractional space setting. In this sense, using the Mountain Pass Theorem and the Fountain Theorem, we investigate the existence and multiplicity of weak solutions for a new class of fractional differential equations with m (ξ) -Kirchhoff-type equation. [ABSTRACT FROM AUTHOR]

This article is about the following Kirchhoff–Schrödinger–Poisson system with steep potential well 1.1−(a+b∫ℝ3|∇u|2dx)△u+λV(x)u+μϕ(x)u=f(x,u)+h(x)|u|αinℝ3,−△ϕ=u2,inℝ3,$$ \left\{\begin{array}{ll}-\left(a&#x0002B;b{\int}_{{\mathrm{\mathbb{R}}}&#x0005E;3}{\left&#x0007C;\nabla u\right&#x0007C;}&#x0005E;2 dx\right)\triangle u&#x0002B;\lambda V(x)u&#x0002B;\mu \phi (x)u&#x0003D;f\left(x,u\right)&#x0002B;h(x){\left&#x0007C;u\right&#x0007C;}&#x0005E;{\alpha }& \mathrm{in}\kern0.4em {\mathrm{\mathbb{R}}}&#x0005E;3,\\ {}-\triangle \phi &#x0003D;{u}&#x0005E;2,& \mathrm{in}\kern0.4em {\mathrm{\mathbb{R}}}&#x0005E;3,\end{array}\right. $$where a,b,λ>0$$ a,b,\lambda >0 $$ are constants, μ>0$$ \mu >0 $$, and 0<α<1,f∈C(ℝN×ℝ,ℝ)$$ 0<\alpha <1,f\in C\left({\mathrm{\mathbb{R}}}&#x0005E;N\times \mathrm{\mathbb{R}},\mathrm{\mathbb{R}}\right) $$. By using the variational principle, we overcome the difficulties caused by Poisson's term and obtain system (1.1) that has two nontrivial solutions under certain assumptions. Moreover, we study the concentration of solutions and obtain new conclusions of system (1.1). Finally, we present the case where the solution to system (1.1) does not exist. [ABSTRACT FROM AUTHOR]

We consider the following Neumann boundary problem with a nonlocal Kirchhoff term −a+b∫Ω|∇u|2Δu=λm(x)u+h(x)up+d(x)uq,x∈Ω,∂u∂ν=0,x∈∂Ω,$$ \left\{\begin{array}{ll}-\left(a&#x0002B;b{\int}_{\Omega}{\left&#x0007C;\nabla u\right&#x0007C;}&#x0005E;2\right)\Delta u&#x0003D;\lambda \left(m(x)u&#x0002B;h(x){u}&#x0005E;p&#x0002B;d(x){u}&#x0005E;q\right),& x\in \Omega, \\ {}\frac{\partial u}{\partial \nu }&#x0003D;0,& x\in \mathrm{\partial \Omega },\end{array}\right. $$where Ω⊂ℝN$$ \Omega \subset {\mathrm{\mathbb{R}}}&#x0005E;N $$ is a bounded smooth domain and m$$ m $$ and d$$ d $$ are sign‐changing coefficients which play important impact on the study. By using variational method and dividing corresponding Nehari manifold into two disjoint subsets, we study the existence of two positive solutions. To show the multiplicity of positive solutions, we find a set whose elements can be mapped to two subsets of Nehari manifold, which is also the key to proving strong convergence for minimizing sequences. Finally, the asymptotic behavior of solutions is studied as parameter λ$$ \lambda $$ tends to 0. Different from Dirichlet boundary problem, we show that the two solutions of Neumann problem tend to two different positive constants, respectively. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the existence of multiplicity of positive solutions to a new generalized Riemann–Liouville type fractional Fisher‐like equation on a semi‐infinite interval equipped with nonlocal multipoint boundary conditions involving Riemann–Liouville fractional derivative and integral operators. The existence of at least two positive solutions for the given problem is established by using the concept of complete continuity and iterative positive solutions. We show the existence of at least three positive solutions to the problem at hand by applying the generalized Leggett–Williams fixed‐point theorem due to Bai and Ge [Z. Bai, B. Ge, Existence of three positive solutions for some second‐order boundary value problems, Comput. Math. Appl. 48 (2014) 699‐70]. Illustrative examples are constructed to demonstrate the effectiveness of the main results. It has also been indicated in Section 5 that some new results appear as special cases by choosing the parameters involved in the given problem appropriately. [ABSTRACT FROM AUTHOR]

The signless Laplacian matrix of a graph G is defined as Q (G) = D (G) + A (G) , where D (G) is the degree-diagonal matrix of G and A (G) is the adjacency matrix of G. The multiplicity of an eigenvalue μ of Q (G) is denoted by m Q (G , μ). Let G = C (T 1 , ... , T g) be a unicyclic graph with a perfect matching, where T i is a rooted tree attached at the vertex v i of the cycle C g. It is proved that Q (G) has 2 as an eigenvalue if and only if g + t is divisible by 4, where t is the number of T i of even orders. Another main result of this article gives a characterization for a connected graph G with a perfect matching such that m Q (G , 2) = θ (G) + 1 , where θ (G) = | E (G) | − | V (G) | + 1 is the cyclomatic number of G. [ABSTRACT FROM AUTHOR]

In this paper, we study the shapes of bifurcation curves of positive solutions for the one-dimensional perturbed Gelfand problem with the Minkowski-curvature operator { − ( u ′ (x) 1 − (u ′ (x)) 2 ) ′ = λ exp ⁡ (a u a + u) , − L < x < L , u (− L) = u (L) = 0 , where λ > 0 is a bifurcation parameter and a , L > 0 are evolution parameters. We determine the shapes of the bifurcation curves for different positive values a and L. [ABSTRACT FROM AUTHOR]

We establish global multiplicity of positive solutions (existence and nonexistence theory) for the following problem { Δ u + λ h (x) f (u) = 0 in R N , u > 0 in R N , u ∈ D 1 , 2 (R N) , where N ≥ 3 , λ > 0 is a parameter, 0 ≤ h ∈ L ∞ (R N) and f is a sublinear nonlinearity at ∞. In order to obtain our results we use a combination of the sub- super solution method and variational techniques. For instance, we need to implement a relevant result of type D 1 , 2 (R N) versus X local minimizer for some appropriate space X. [ABSTRACT FROM AUTHOR]

In this paper, we study a Kirchhoff-type problem driven by a multi-phase operator with three variable exponents. Such problem has a right-hand side consisting of a Carathéodory perturbation which is defined only locally as well as the Kirchhoff term. Using a generalized version of the symmetric mountain pass theorem along with recent a priori upper bounds for multi-phase problems, we get whole a sequence of nontrivial solutions for our problem converging to zero in the appropriate Musielak-Orlicz Sobolev space and in L ∞ (Ω) . [ABSTRACT FROM AUTHOR]

In this work, optimal rigidity results for eigenvalues on Kähler manifolds with positive Ricci lower bound are established. More precisely, for those Kähler manifolds whose first eigenvalue agrees with the Ricci lower bound, we show that the complex projective space is the only one with the largest multiplicity of the first eigenvalue. Moreover, there is a specific gap between the largest and the second largest multiplicity. In the Kähler–Einstein case, almost rigidity results for eigenvalues are also obtained. [ABSTRACT FROM AUTHOR]

International large-scale assessments (ILSA) are an important source of information for education policymakers across the globe. Despite sponsors' warnings, when results are published, media attention focuses on country rankings and changes in scores. Score changes are evaluated using a two-sided z-statistic, with statistical significance declared if the statistic exceeds 1.96 in absolute value. Findings of significance occasion much commentary and may also have policy implications. Particularly problematic, however, are cases in which a significant trend in one direction is followed in the next cycle by a significant trend in the opposite direction. Such reporting reversals are often difficult to explain on substantive grounds and, consequently, can undermine the credibility of the ILSA. This article proposes and evaluates a new approach to determining the significance of observed score changes. It employs a two one-sided test (TOST) procedure. A key feature is establishing an equivalence zone around zero. A change is declared only if the test statistic does not fall in the equivalence zone. Thus, the procedure combines consideration of statistical significance and substantive importance. We augment the TOST procedure with the Benjamini–Hochberg procedure (BH-TOST) to control the False Discovery Rate , to address the problem of multiplicity. Using data from TIMSS (2011, 2015, 2019), we explore different parameter choices for BH-TOST and evaluate the operating characteristics of the selected version with respect to three different criteria. Our results indicate that BH-TOST is generally superior to the current procedure, concluding that it merits serious consideration as a basis for reporting TIMSS results. [ABSTRACT FROM AUTHOR]

We explore the spectra of transverse momenta of hadrons with strange quark content ( K S 0 , ϕ , Λ + Λ ̄ , Ξ ̄ + Ξ ̄ + , and Ω − + Ω ̄ + ) produced in proton–proton collisions at s N N = 7 TeV. We applied Tsallis statistics in a blast wave model (T B W) to the ALICE Collaboration's experimental data and extracted the freezeout parameters (Tsallis temperature, transverse flow velocity, and the parameter q , which is the non-extensive parameter). The changing trend of these parameters is studied with changing multiplicity. The parameter q decreases while the parameter T and β T increases toward higher multiplicities. β T is noted to drop to zero in the system with the lowest multiplicities. In addition, the interrelationships between the parameters T with β T and T with q are presented where the former correlation is positive and the latter one is negative. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the local convergence of Schröder's method for finding zeros of analytic functions with unknown multiplicity. Thus, we obtain a convergence theorem that provides exact domains of initial points together with error estimates to ensure the Q-quadratic convergence of Schröder's method right from the first step. A comparison with the famous Newton's method, based on the convergence and dynamics when it is applied to some polynomial and non-polynomial equations, is also provided. [ABSTRACT FROM AUTHOR]

This paper introduces a novel iteration inequality for the Maslov-type (L , P) -index of iterated symplectic paths. Here, P is a fixed 2 n -dimensional symplectic and orthogonal matrix satisfying P m = I. These advancements in index theory are then applied to investigate the multiplicity of subharmonic solutions in Hamiltonian systems exhibiting dihedral equivariance with period mτ. Notably, a criterion of geometric distinction is established for two subharmonic P -symmetric brake orbits with periods kmτ and lmτ within the set { k m τ | k ≡ 1 (mod m) }. This criterion is based on a lower bound estimate for the ratio l / k. Specifically, for odd k , the lower bound must be not less than (1 2 dim ⁡ ker ⁡ (P − I) + 2) m + 1 , while for even k , it must be not less than (1 2 dim ⁡ ker ⁡ (P − I) + n + 2) m + 1. [ABSTRACT FROM AUTHOR]

This paper deals with the existence and multiplicity results for a bi‐nonlocal problem without the Ambrosetti–Rabinwitz condition, in the context of variable exponents of Sobolev spaces on compact Riemannian manifolds. Using the mountain pass theorem, we obtain that our problem admits at least nontrivial weak solutions. Also, using the fountain and dual fountain theorems, we obtain the existence of infinitely many nontrivial high or small energy solutions. [ABSTRACT FROM AUTHOR]

This manuscript aims to investigate the existence of weak solutions for a system of partial differential equations (PDEs) described by Equation (1.2). The system consists of a set of PDEs with Leray–Lions operators and nonlinear terms. The goal is to establish the existence of at least one nontrivial weak solution and at least three weak solutions for the system. The PDEs are defined on a bounded domain in ℝN$$ {\mathrm{\mathbb{R}}}^N $$, with N≥3$$ N\ge 3 $$, and subject to appropriate boundary conditions. The system involves various parameters, functions, and growth conditions that are carefully defined throughout the paper. The study focuses on understanding the behavior and existence of solutions for this system of PDEs, which has applications in physics, engineering, and other scientific fields. [ABSTRACT FROM AUTHOR]

We decompose the tensor product of two irreducible representations of GL2(픽q) for odd q and classify the pairs such that their tensor product is multiplicity free. We also classify the pairs such that their tensor product has unique decomposition property. We additionally characterize the self-dual irreducible representations of GL2(픽q). [ABSTRACT FROM AUTHOR]

This paper considers the selection and optimization of drive nodes based on the controllability of multilayer networks. The intra-layer network topologies are arbitrary, and the node dynamics are linear time-invariant dynamical systems. The study focuses on the number and selection of drive nodes in a special class of drive-response networks. Several conclusions are drawn through the investigation: (1) All the drive nodes cannot be placed in the response layer but can be contained in the drive layer; (2) The minimum number of drive nodes placed in the drive layer is equal to the maximum geometric multiplicity of the system matrix of the drive layer; (3) The configuration of interlayer coupling weight significantly affects the number and distribution of drive nodes. Moreover, an optimization scheme is proposed based on the Gershgorin circle theorem, which aims to minimize the number of drive nodes in the entire network. This scheme ensures that regardless of the drive nodes originally needed, they can be reduced to the maximum geometric multiplicity of the system matrix of the drive layer. Numerical simulations on a general two-layer network as well as various synthetic networks are provided to validate the results. [ABSTRACT FROM AUTHOR]

In this paper, we consider the semilinear Dirichlet problem (P ε) : − Δ u + V (x) u = u n + 2 n − 2 − ε , u > 0 in Ω , u = 0 on ∂ Ω , where Ω is a bounded regular domain in R n , n ≥ 4 , ε is a small positive parameter, and V is a non-constant positive C 2 -function on Ω ¯ . We construct interior peak solutions with isolated bubbles. This leads to a multiplicity result for (P ε) . The proof of our results relies on precise expansions of the gradient of the Euler–Lagrange functional associated with (P ε) , along with a suitable projection of the bubbles. This projection and its associated estimates are new and play a crucial role in tackling such types of problems. [ABSTRACT FROM AUTHOR]

This paper is concerned with a class of fractional p-Laplacian systems with critical homogeneous nonlinearities. Under proper conditions, the existence and multiplicity results of nontrivial solutions are obtained by variational methods. To some extent, our results improve and supplement some existing relevant results. [ABSTRACT FROM AUTHOR]

We develop a min-max theory for the construction of capillary surfaces in 3-manifolds with smooth boundary. In particular, for a generic set of ambient metrics, we prove the existence of nontrivial, smooth, almost properly embedded surfaces with any given constant mean curvature 푐, and with smooth boundary contacting at any given constant angle 휃. Moreover, if 푐 is nonzero and 휃 is not π 2 , then our min-max solution always has multiplicity one. We also establish a stable Bernstein theorem for minimal hypersurfaces with certain contact angles in higher dimensions. [ABSTRACT FROM AUTHOR]

Recent research reveals that EU agencies have initiated a whole set of voluntary accountability practices. Reputational considerations have been put forward as an important mechanism driving such organisational behaviour. This paper tests this theoretical explanation in a quantitative manner based on a survey among EU agency leaders. We find that the factors explaining voluntary accountability differ depending on the audience to whom account is rendered. Nonetheless, a consistent finding is that media salience is associated with voluntary account-giving, which supports the argument that voluntary account-giving helps agencies to mitigate the risks of reputational threats. The analysis also suggests that voluntary accountability is useful for highlighting the agency's competence when principals are not paying close attention to the agency's performance. These results show that a reputational, multi-audience perspective helps us understand which EU agencies are likely to become accountability entrepreneurs and to whom they will expand their accountability. [ABSTRACT FROM AUTHOR]

In the present work we establish the existence and multiplicity of positive solutions for a critical elliptic problem in the whole space R N . The main feature here is to treat a Kirchhoff-type elliptic problem where the nonlinearity is critical and defines a sign-changing function. Our approach relies on the minimization method applied to the Nehari manifold together with the nonlinear Rayleigh quotient method. Here, we use the fibering maps associated with the energy functional which exhibits degenerate points under suitable values on the two parameters within the nonlinearity. This difficulty does not allow us to apply the Lagrange Multipliers Theorem in general. Furthermore, our nonlinearity does not satisfy the famous Ambrosetti-Rabinowitz condition. Our main contribution relies on restoring the strong convergence and compactness results from the Sobolev spaces into the Lebesgue spaces. Here, we establish also some nonexistence results under specific assumptions on the nonlinearity by using a Pohozaev identity. [ABSTRACT FROM AUTHOR]

Felt understanding in intergroup context is the belief that members of an outgroup understand and accept ingroup members' perspectives. A series of studies in Europe recently conducted by Andrew Livingstone and colleagues showed the unique effect of felt understanding in intergroup relations. The effects were apparent even when controlling for outgroup beliefs and metabeliefs. The present article reports a cross‐cultural replication of those findings for Japanese and Chinese relations in Japan. Consistent with the results of Livingstone and colleagues, felt understanding uniquely predicted intergroup outcomes (e.g., action intentions, outgroup trust, and intergroup orientation). The effects remained significant after adjusting for multiplicity with multiple variables. However, there were two differences. Felt understanding did not predict (a) negative approach intentions or (b) institutional trust. [ABSTRACT FROM AUTHOR]

The unstable time fractional Schrödinger model (UTFSM) is studied through the development of disturbances in marginally stable or unstable media. A modified Sardar-sub equation technique (MSSE) for a conformable fractional-order nonlinear evolution model is presented in this paper. The objective here is to construct new wave solutions for UTFSM. These solutions have particular relevance in quantum physics and assume several forms such as rational, exponential, trigonometric and hyperbolic functions, as well as combo solutions. This technique produces various shapes of dark, kink-type solitons and periodic solitary waves by setting proper parametric values. These discrete physical frameworks contribute to an understanding from analysis of unstable dynamical models. Additionally, we investigate modulation instability and stability analysis to ensure that obtained solutions are highly stable. The multiplicity of waves and solutions emphasizes how this technique can be used for different nonlinear fractional models in quantum physics and other areas. [ABSTRACT FROM AUTHOR]

We initiate the axiomatic study of affine oriented matroids (AOMs) on arbitrary ground sets, obtaining fundamental notions such as minors, reorientations and a natural embedding into the frame work of Complexes of Oriented Matroids. The restriction to the finitary case (FAOMs) allows us to study tope graphs and covector posets, as well as to view FAOMs as oriented finitary semimatroids. We show shellability of FAOMs and single out the FAOMs that are affinely homeomorphic to R n . Finally, we study group actions on AOMs, whose quotients in the case of FAOMs are a stepping stone towards a general theory of affine and toric pseudoarrangements. Our results include applications of the multiplicity Tutte polynomial of group actions of semimatroids, generalizing enumerative properties of toric arrangements to a combinatorially defined class of arrangements of submanifolds. This answers partially a question by Ehrenborg and Readdy. [ABSTRACT FROM AUTHOR]

Let C be field of complex numbers and X be a connected quandle of prime order. We study the regular representation of X by describing the quandle ring C [ X ] as direct sum of right simple ideals. We provide description of tensor product of connected quandles of prime order. We further discuss multiplicity freeness of quandle ring decomposition for connected quandles of order ≤ 47 and prove that C [ X ] decomposes multiplicity free for affine connected quandle X. [ABSTRACT FROM AUTHOR]

The poor conductivity of β‐Ga2O3 limits its application in optoelectronic devices. Currently, there have been advancements in investigating the impact of Mo doping on the photoelectric characteristics of β‐Ga2O3. However, there are few studies on the impact of different valence states of Mo doping and the coexistence of O vacancy and interstitial H on the electrical properties of β‐Ga2O3. In the process of preparing β‐Ga2O3, O vacancy and interstitial H inevitably exist. In response to these problems, the first‐principles GGA + U method is used to study the impact of different valence states of Mo doping and the coexistence of interstitial H and O vacancy on the electrical properties of β‐Ga2O3. The electronic structure, mobility, conductivity, and carrier lifetime of the system are calculated and analyzed. The results show that all doping systems are more stable under Ga‐rich conditions. The band gap of the Mo‐doped β‐Ga2O3 system gradually narrows, which is mainly attributed to the Burstein–Moss effect and the multiplicity reintegration effect. Mo doping effectively improves the electrical conductivity of the system. Ga47O72Mo16+H11+ system has the longest carrier lifetime; Ga47O72Mo16+H10 has the largest mobility; Ga47O72Mo15+H10 system has the highest conductivity. Therefore, Mo‐doped β‐Ga2O3 materials help to prepare new electrical performance devices. [ABSTRACT FROM AUTHOR]

In music educators' endeavoring to integrate equity into our curriculum, adopting a rhizomatic approach could provide a valuable perspective for reassessing the Western classical tradition as the norm. From a philosophical perspective, the rhizome is perceived as an interconnected multiplicity, where various elements are intricately connected without a central or hierarchical control system. In essence, a rhizomatic approach is more expansive than top-down alternatives and inherently places greater emphasis on equity. Given a rhizome's noncentered and nonhierarchical nature, the concept of a rhizome encourages engagement with music comparatively or relationally, fostering a broad perspective that recognizes the interconnectedness between musics. More importantly, lessons using a rhizomatic approach may promote teachers and students to view all forms of musics as equally significant, honoring diverse musical traditions rather than exclusively prioritizing Western classical heritage. [ABSTRACT FROM AUTHOR]

In this article, we study a class of elliptic problems involving both local and nonlocal operators with different orders and a singular nonlinearity in combination with critical Hartree type nonlinearity (see problem $ (P_\lambda) $ (P λ) below). Using variational methods together with the critical point theory of nonsmooth analysis, we show the existence, the regularity and the multiplicity of weak solutions with respect to the parameter λ. [ABSTRACT FROM AUTHOR]

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Felt understanding in intergroup context is the belief that members of an outgroup understand and accept ingroup members' perspectives. A series of studies in Europe recently conducted by Andrew Livingstone and colleagues showed the unique effect of felt understanding in intergroup relations. The effects were apparent even when controlling for outgroup beliefs and metabeliefs. The present article reports a cross‐cultural replication of those findings for Japanese and Chinese relations in Japan. Consistent with the results of Livingstone and colleagues, felt understanding uniquely predicted intergroup outcomes (e.g., action intentions, outgroup trust, and intergroup orientation). The effects remained significant after adjusting for multiplicity with multiple variables. However, there were two differences. Felt understanding did not predict (a) negative approach intentions or (b) institutional trust. [ABSTRACT FROM AUTHOR]

We generalize the Max Share approach to allow for simultaneous identification of a multiplicity of shocks in a Structural Vector Autoregression. Our machinery therefore overcomes the well-known drawbacks that individually identified shocks (i) tend to be correlated to each other or (ii) can be separated under orthogonalizations with weak economic ground. We show that identification corresponds to solving a nontrivial optimization problem. We provide conditions for non-emptiness of solutions and point-identification, and Bayesian algorithms for estimation and inference. We use the approach to study the effects of uncertainty and financial shocks, allowing for the possibility that the former responds contemporaneously to other shocks, distinguishing macroeconomic from financial uncertainty and credit supply shocks. Using U.S. data we find that financial uncertainty mimics a demand shock, while the interpretation of macro uncertainty is more mixed. Furthermore, variation in uncertainty partially represents the endogenous response of uncertainty to other shocks. [ABSTRACT FROM AUTHOR]

Jiang and Niu [7] extended Zeeman's classification [15] to 3D strongly competitive systems with linearly determined nullclines and proved that a 3D Leslie-Gower competitive system has Hopf bifurcation within each of classes 26–31. This paper proves that there exist at least two, three, and three limit cycles in Jiang-Niu classes 26, 27, and 28 of the 3D Leslie-Gower competitive system, respectively. We compare the commonalities and differences of Hopf bifurcation in 3D competitive LV, Ricker, and LG systems with the same interaction coefficient matrix. [ABSTRACT FROM AUTHOR]

The poor conductivity of β‐Ga2O3 limits its application in optoelectronic devices. Currently, there have been advancements in investigating the impact of Mo doping on the photoelectric characteristics of β‐Ga2O3. However, there are few studies on the impact of different valence states of Mo doping and the coexistence of O vacancy and interstitial H on the electrical properties of β‐Ga2O3. In the process of preparing β‐Ga2O3, O vacancy and interstitial H inevitably exist. In response to these problems, the first‐principles GGA + U method is used to study the impact of different valence states of Mo doping and the coexistence of interstitial H and O vacancy on the electrical properties of β‐Ga2O3. The electronic structure, mobility, conductivity, and carrier lifetime of the system are calculated and analyzed. The results show that all doping systems are more stable under Ga‐rich conditions. The band gap of the Mo‐doped β‐Ga2O3 system gradually narrows, which is mainly attributed to the Burstein–Moss effect and the multiplicity reintegration effect. Mo doping effectively improves the electrical conductivity of the system. Ga47O72Mo16+H11+ system has the longest carrier lifetime; Ga47O72Mo16+H10 has the largest mobility; Ga47O72Mo15+H10 system has the highest conductivity. Therefore, Mo‐doped β‐Ga2O3 materials help to prepare new electrical performance devices. [ABSTRACT FROM AUTHOR]

The total graph T (G) of a graph G has vertex set V (T (G)) = V (G) ∪ E (G) , and two vertices in T (G) are adjacent if and only if their corresponding elements are either adjacent or incident in G. The total graph operation can be used to generate large dense graphs (networks). In this paper, some spectral properties of total graphs are studied. We give expressions for the number of eigenvalues of T (G) belong to the interval (− 2 , ∞) and (− ∞ , − 2) , and use the expressions to derive a lower bound on the clique partition number of T (G). Expressions for the multiplicity and the eigenspace of eigenvalue − 2 of T (G) are obtained. We also give a formula for the characteristic polynomial of T (G) in terms of the adjacency matrix and signless Laplacian matrix of G , and derive some properties for the Perron vector of T (G). [ABSTRACT FROM AUTHOR]

Let F be a non-Archimedean local field. Consider Gn := GLn(F) and let M := Gl ×Gn−l be a maximal Levi subgroup of Gn. In this paper, we compute the semi simplified Jacquet module of representations of Gn with respect to the maximal Levi subgroup M, belonging to a particular category of representations. Utilizing our results, we prove that the Jacquet module is multiplicity-free for a specific subcategory of representations. Our findings are based on the Zelevinsky classification. [ABSTRACT FROM AUTHOR]