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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]

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 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]

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]

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 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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

The p‐Laplacian fractional differential equations have been studied extensively because of their numerous applications in science and engineering. In this study, a class of p‐Laplacian fractional differential equations with instantaneous and noninstantaneous impulses is considered. The existence and multiplicity results of solutions are obtained by using variational methods and critical point theory. In addition, some examples are given to prove the feasibility of the proposed results. [ABSTRACT FROM AUTHOR]

The bond distance is the simplest and most obvious indicator of the nature of a given chemical bond. However, for rare chemistry, it may happen that it is not yet firmly established. In this communication, we will show that the formally-triple protactinium(V) mono-oxo bond is predicted to be longer than what was previously reported in the solid state and in solution, based on robust quantum mechanical calculations, supported by an extensive methodological study. Furthermore, additional calculations are used to demonstrate that the Pa–Ooxo bond of interest is more sensitive to complexation than the supposedly analogous U–Oyl ones, not only in terms of bond distance but also of finer bond descriptors associated with the effective bond multiplicity. [ABSTRACT FROM AUTHOR]

We introduce and study a notion of Serre liftable modules; these are modules that are liftable to modules of the maximal possible dimension over a regular local ring. We establish new cases of Serre's positivity conjecture over ramified regular local rings by proving it for Serre liftable modules. Furthermore, we show that the length of a nonzero Serre liftable module is bounded below by the Hilbert–Samuel multiplicity of the local ring. This establishes special cases of the Length Conjecture of Iyengar–Ma–Walker. [ABSTRACT FROM AUTHOR]

Let m (G , λ) , c (G) and p (G) be the multiplicity of an eigenvalue λ , the cyclomatic number and the number of pendant vertices of a connected graph G , respectively. Yang et al. (2023) [10] proved that m (L (T) , λ) ≤ p (T) − 1 for any tree T , and characterized all trees T with m (L (T) , λ) = p (T) − 1 , where L (T) is the line graph of T. In this paper, we extend their result from a tree T to any graph G ≠ C n , and prove that m (L (G) , λ) ≤ 2 c (G) + p (G) − 1 for any graph G ≠ C n. Moreover, all graphs G with m (L (G) , − 1) = 2 c (G) + p (G) − 1 are completely characterized. [ABSTRACT FROM AUTHOR]

In a recent article Projective geometries, Q-polynomial structures, and quantum groups Terwilliger (arXiv:2407.14964) defined a certain weighted adjacency matrix, depending on a free (positive real) parameter, associated with the projective geometry, and showed (among many other results) that it is diagonalizable, with the eigenvalues and their multiplicities explicitly written down, and that it satisfies the Q -polynomial property (with respect to the zero subspace). In this note we • Write down an explicit eigenbasis for this matrix. • Evaluate the adjacency matrix-eigenvector products, yielding a new proof for the eigenvalues and their multiplicities. • Evaluate the dual adjacency matrix-eigenvector products and directly show that the action of the dual adjacency matrix on the eigenspaces of the adjacency matrix is block-tridiagonal, yielding a new proof of the Q -polynomial property. [ABSTRACT FROM AUTHOR]

We study asymptotic behaviour of positive ground state solutions of the nonlinear Choquard equation (P ε) − Δ u + ε u = (I α ⁎ | u | p) | u | p − 2 u + | u | q − 2 u , in R N , where N ≥ 3 is an integer, p ∈ [ N + α N , N + α N − 2 ] , q ∈ (2 , 2 N N − 2) , I α is the Riesz potential of order α ∈ (0 , N) and ε > 0 is a parameter. We show that as ε → 0 (resp. ε → ∞), the ground state solutions of (P ε) , after appropriate rescalings dependent on parameter regimes, converge in H 1 (R N) to particular solutions of five different limit equations. We also establish a sharp asymptotic characterisation of such rescalings, and the precise asymptotic behaviour of u ε (0) , ‖ ∇ u ε ‖ 2 2 , ‖ u ε ‖ 2 2 , ∫ R N (I α ⁎ | u ε | p) | u ε | p and ‖ u ε ‖ q q , which depend in a non-trivial way on the exponents p , q and the space dimension N. Further, we discuss a connection of our results with a mass constrained problem, associated to (P ε) with normalization constraint ∫ R N | u | 2 = c 2. As a consequence of the main results, we obtain the existence, multiplicity and precise asymptotic behaviour of positive normalized solutions of such a problem as c → 0 and c → ∞. [ABSTRACT FROM AUTHOR]

We study commutative Schur rings over the symplectic groups Sp (n , 2) that contain the class C of symplectic transvections. We find the possible partitions of C determined by the Schur ring. We show how this restricts the possibilities for multiplicity one subgroups of Sp (n , 2). [ABSTRACT FROM AUTHOR]

ABSTRACT Consider the nonlinear difference equations of the form ℒu=fm(u),m∈ℤ$$ \mathit{\mathcal{L}u}={f}_m(u),\kern0.3em m\in \mathbb{Z} $$, where ℒ$$ \mathcal{L} $$ is a Jacobi operator given by ℒum=amum+1+am−1um−1+bmum$$ \mathcal{L}{u}_m={a}_m{u}_{m+1}+{a}_{m-1}{u}_{m-1}+{b}_m{u}_m $$ for m∈ℤ,am$$ m\in \mathbb{Z},\kern0.3em \left\{{a}_m\right\} $$ and bm$$ \left\{{b}_m\right\} $$ are real valued T$$ T $$‐periodic sequences, and f:ℤ×ℝ→ℝ$$ f:\mathbb{Z}\times \mathbb{R}\to \mathbb{R} $$. Applying critical point theory and a new analytical method, we obtain that the above problem has ground state solutions and infinitely many geometrically distinct solutions under the local superlinear condition limx→∞∫0xfm(t)dt|x|2=∞$$ {\lim}_{verbarxverbar\to \infty}\frac{\int_0^x{f}_m(t) dt}{{\left|x\right|}^2}=\infty $$ uniformly in m∈D$$ m\in D $$ for some set D⊂ℤ$$ D\subset \mathbb{Z} $$ instead of the global superlinear condition limx→∞∫0xfm(t)dt|x|2=∞$$ {\lim}_{verbarxverbar\to \infty}\frac{\int_0^x{f}_m(t) dt}{{\left|x\right|}^2}=\infty $$ uniformly in m∈ℤ$$ m\in \mathbb{Z} $$. [ABSTRACT FROM AUTHOR]

This study explores the interactive effect of individual and institutional factors of public support for populist parties. Focussing on European countries, it investigates how multiplicity and variability of mainstream political parties moderate the effect of citizens’ grievances related to immigration on their populist support. We hypothesise that while a more inclusive party system may decrease the effect of citizens’ economic anxiety on populist support, it cannot mitigate the effect of cultural concern about immigrants. Instead, it may amplify that effect. A comparative multilevel analysis of 20 European countries for a period of 15 years yields supportive findings for our hypothesis. [ABSTRACT FROM AUTHOR]

In this article we develop an information-theoretic framework of multiple sequence alignments (MSAs), based on sub-sampling. The key component of this framework is an information-theoretical potential defined on pairs of sites (links) within the MSA. This potential quantifies the expected drop in variation of information between the two constituent sites. The expectation is taken with respect to all possible sub-alignments, obtained by removing a finite, fixed number of rows. We show that the potential is zero for linked sites representing columns, for which symbols are in bijective correspondence and that it is strictly positive, otherwise. It is furthermore shown that the potential assumes its unique minimum for links at which each symbol pair appears with the same multiplicity. We then show that the established drop of the variation of information exceeds finite-size effects inherent to the construction of the potential. Finally, we provide as a proof of concept an application of our results to a specific MSA composed of the inverse fold solutions of three distinguished secondary structures. [ABSTRACT FROM AUTHOR]

Recently, with the upgradation of LHC, it is realized that study of heavy-flavored hadrons, namely Λc+ and D0 in hadronic collisions, could reveal the possibility of thermalization of charm quarks. With this motivation, we study the production dynamics of these hadrons using a pQCD-inspired Monte Carlo event generator called PYTHIA8 in proton+proton collisions at s=13TeV. The production dynamics of these hadrons are analyzed through charged-particle multiplicity, transverse momentum and pseudorapidity. With the help of the established PYTHIA8 tunes to mimic the behavior of flow-like features, we investigated the variation of effective temperature and degree of nonextensivity using thermodynamically consistent nonextensive Tsallis statistics. We further attempted to establish a connection between the initial state and final state by estimating the correlation between the number of multi-partonic interactions (nMPI) with the Knudsen number. [ABSTRACT FROM AUTHOR]

We consider an elliptic problem with nonlinear boundary condition involving nonlinearity with superlinear and subcritical growth at infinity and a bifurcation parameter as a factor. We use re-scaling method, degree theory and continuation theorem to prove that there exists a connected branch of positive solutions bifurcating from infinity when the parameter goes to zero. Moreover, if the nonlinearity satisfies additional conditions near zero, we establish a global bifurcation result, and discuss the number of positive solution(s) with respect to the parameter using bifurcation theory and degree theory. [ABSTRACT FROM AUTHOR]

We show that a Sergeev–Veselov difference operator of rational Macdonald–Ruijsenaars (MR) type for the deformed root system B C (l , 1) preserves a ring of quasi-invariants in the case of non-negative integer values of the multiplicity parameters. We prove that in this case the operator admits a (multidimensional) Baker–Akhiezer eigenfunction, which depends on spectral parameters and which is, moreover, as a function of the spectral variables an eigenfunction for the (trigonometric) generalised Calogero–Moser–Sutherland (CMS) Hamiltonian for B C (l , 1) . By an analytic continuation argument, we generalise this eigenfunction also to the case of more general complex values of the multiplicities. This leads to a bispectral duality statement for the corresponding MR and CMS systems of type B C (l , 1) . [ABSTRACT FROM AUTHOR]

The azimuthal correlation angle, Δ ϕ , between the scattered lepton and the leading jet in deep inelastic e ± p scattering at HERA has been studied using data collected with the ZEUS detector at a centre-of-mass energy of s = 318 Ge V , corresponding to an integrated luminosity of 326 pb - 1 . A measurement of jet cross sections in the laboratory frame was made in a fiducial region corresponding to photon virtuality 10 Ge V 2 < Q 2 < 350 Ge V 2 , inelasticity 0.04 < y < 0.7 , outgoing lepton energy E e > 10 Ge V , lepton polar angle 140 ∘ < θ e < 180 ∘ , jet transverse momentum 2.5 Ge V < p T,jet < 30 Ge V , and jet pseudorapidity - 1.5 < η jet < 1.8 . Jets were reconstructed using the k T algorithm with the radius parameter R = 1 . The leading jet in an event is defined as the jet that carries the highest p T,jet . Differential cross sections, d σ / d Δ ϕ , were measured as a function of the azimuthal correlation angle in various ranges of leading-jet transverse momentum, photon virtuality and jet multiplicity. Perturbative calculations at O (α s 2) accuracy successfully describe the data within the fiducial region, although a lower level of agreement is observed near Δ ϕ → π for events with high jet multiplicity, due to limitations of the perturbative approach in describing soft phenomena in QCD. The data are equally well described by Monte Carlo predictions that supplement leading-order matrix elements with parton showering. [ABSTRACT FROM AUTHOR]

To a complex reflection arrangement with an invariant multiplicity function one can relate the space of logarithmic vector fields and the space of quasi-invariants, which are both modules over invariant polynomials. We establish a close relation between these modules. Berest–Chalykh freeness results for the module of quasi-invariants lead to new free complex reflection multiarrangements. Saito's primitive derivative gives a linear map between certain spaces of quasi-invariants. We also establish a close relation between non-homogeneous quasi-invariants for root systems and logarithmic vector fields for the extended Catalan arrangements. As an application, we prove the freeness of Catalan arrangements corresponding to the non-reduced root system |$BC_{N}$|⁠. [ABSTRACT FROM AUTHOR]

We prove new multiplicity results for some nonlocal critical growth elliptic problems in bounded domains. More specifically, we show that the problems considered here have arbitrarily many solutions for all sufficiently large values of a certain parameter λ>0$\lambda > 0$. In particular, the number of solutions goes to infinity as λ→∞$\lambda \rightarrow \infty$. We also give an explicit lower bound on λ$\lambda$ in order to have a given number of solutions. This lower bound is in terms of a sequence of eigenvalues of the associated nonlocal elliptic operator. The proofs are based on an abstract critical point theorem. [ABSTRACT FROM AUTHOR]

We investigate the homogeneous Dirichlet boundary value problem for generalized Laplacian equations with a singular, potentially non-integrable weight. By examining asymptotic behaviors of the nonlinear term near 0 and ∞, we establish the existence, nonexistence, and multiplicity of positive solutions for all positive values of the parameter λ. Our proofs rely on the fixed point theorem concerning cone expansion and compression of norm type and the Leray–Schauder's fixed point theorem. [ABSTRACT FROM AUTHOR]

The goal of this paper is to investigate the minimisation of the first eigenvalue of the (vectorial) incompressible Dirichlet–Stokes operator. After providing an existence result, we investigate optimality conditions and we prove the following surprising result: while the ball satisfies first and second-order optimality conditions in dimension 2, it does not in dimension 3, so that the Faber–Krahn inequality for the Stokes operator is probably true in R 2 , but does not hold in R 3 . The multiplicity of the first eigenvalue of the Dirichlet–Stokes operator in the ball in R 3 plays a crucial role in the proof of that claim. [ABSTRACT FROM AUTHOR]

We prove the existence of at least two positive weak solutions for mixed local-nonlocal singular and critical semilinear elliptic problems in the spirit of Hirano et al. (J Differ Equ 189(2):487–512, 2003), extending the recent results in Garain (J Geom Anal 33:212, 2023) concerning singular problems and, at the same time, the results in Biagi et al. (A Brezis–Nirenberg type result for mixed local and nonlocal operators, https://arxiv.org/abs/2209.07502, 2023) regarding critical problems. [ABSTRACT FROM AUTHOR]

Let X be a very general degree d\geq 5 hypersurface in \mathbb {P}^3. We compute the ample cone of the Hilbert scheme X^{[n]} of n points on X for various small values of n (the answer is already known for large n). We obtain complete answers in some cases and find lower bounds in certain others. We also observe that in the case of X^{[2]} for quintic hypersurfaces X, the existence (or absence) of hyperplane sections with points of high multiplicity also plays a role in the answer to the question at hand, in contrast with cases known earlier. Finally, in the case that a degree d\geq 3 smooth hypersurface X contains a line, we compute the nef cone of X^{[n]} in a slice of the Néron-Severi space. [ABSTRACT FROM AUTHOR]