Search

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]

Let (A , m A) be a Cohen–Macaulay local ring. Let M be a finitely generated A -module and let M ∗ denote the A -dual of M. Furthermore, if M ∗ is a maximal Cohen–Macaulay A -module, then we prove that μ A (M ∗) ≤ μ A (M) e (A) , where μ A (M) is the cardinality of a minimal generating set of M as an A -module and e (A) is the multiplicity of the local ring A. Furthermore, if M is a reflexive A -module then μ A (M) e (A) ≤ μ A (M ∗). As an application, we study the bound on the minimal number of generators of specific modules over two-dimensional normal local rings. We also mention some relevant examples. [ABSTRACT FROM AUTHOR]

Let (G/\Gamma,R_a) be an ergodic k-step nilsystem for k\geq 2. We adapt an argument of Parry [Topology 9 (1970), pp. 217–224] to show that L^2(G/\Gamma) decomposes as a sum of a subspace with discrete spectrum and a subspace of Lebesgue spectrum with infinite multiplicity. In particular, we generalize a result previously established by Host–Kra–Maass [J. Anal. Math. 124 (2014), pp. 261–295] for 2-step nilsystems and a result by Stepin [Uspehi Mat. Nauk 24 (1969), pp. 241–242] for nilsystems G/\Gamma with connected, simply connected G. [ABSTRACT FROM AUTHOR]

It is proposed that an approach to difference through repetition, inspired by the writing of Gilles Deleuze, provides a conceptual approach to understand the endurance of urban life in medieval England. Perceptions of urban decline in later medieval England are contradicted by the persistence of urban places and communities. A tension, whereby persistence implies repetition yet decline implies discontinuity and difference, is evident. By developing a framework for understanding medieval urbanity as a series of repetitive processes of differentiation, this paper outlines how we might shift our approach to understanding past urban lives, with implications for how we engage with critical issues in urban studies, including the multiplicity, resilience and sustainability of urban lives. [ABSTRACT FROM AUTHOR]

In recent years, psychoanalysis has undergone a very welcomed transformation away from a predominant emphasis on repressive symptomatology and intrapsychic conflict, toward an appreciation of dissociative symptomatology and the unformulated. And yet, much ambiguity surrounds our understanding of dissociation as a process, defense, and structure of the self. In this paper, I outline a self-state continuum model to help formulate the different ways defensive dissociation may be operating from a discrete process into becoming a structure of the self. I elaborate on this continuum model and go on to examine how discontinuous self-system patients may be better identified and treated from within a psychoanalytic perspective. [ABSTRACT FROM AUTHOR]

The notion of powerful knowledge has received much international attention and has significantly influenced curriculum development in many countries, including South Africa, from where this paper is written. The paper’s argument begins with philosophical positions and tensions raised by both proponents and critics of the notion of powerful knowledge in curriculum contexts. In response, it then describes a knowledge model that incorporates, first, the value of specialized and systematic powerful disciplinary knowledge (described in this paper as potentially powerful knowledge). Second, the model describes the notion of kinetically powerful knowledge (its situated nature of contextualization, appraisal and transformation). This model is then translated into a tool for assessing curriculum (acronymised as D-CAT). The tool is illustrated by using it to probe two extracts from the South African curriculum. The implications are that the knowledge model and curriculum assessment tool can be used by designers in the official and pedagogical recontextualising fields either analytically or to inform curriculum development. This is with a view to maximize the power of curriculum texts for enabling epistemological access and developing at once the powers of abstract, positioned and judgemental rationality, each of which has an important role to play in understanding and changing the world. [ABSTRACT FROM AUTHOR]

In this paper, we consider the existence and multiplicity of solutions for the critical Neumann problem 0.1 −▵u−12x·∇u=λ|u|2∗−2u+μ|u|p−2uinR+N,∂u∂n=λ|u|2∗−2uon∂R+N,$$\begin{equation} \hspace*{40pt}\left\{ \def\eqcellsep{&}\begin{array}{rcll} -\triangle u-\displaystyle\frac{1}{2}\left(x\cdot \nabla u\right)& =& \lambda |u{|}^{{2}^{*}-2}u+\mu |u{|}^{p-2}u & \text{in }{\mathbb{R}}_{+}^{N},\\ [12pt] \displaystyle\frac{\partial u}{\partial n}& =& \sqrt{\lambda}|u{|}^{{2}_{*}-2}u & \text{on }\partial {\mathbb{R}}_{+}^{N}, \end{array} \right. \end{equation}$$where R+N={(x′,xN):x′∈RN−1,xN>0}$ \mathbb {R}^{N}_{+}=\lbrace (x{^{\prime }}, x_{N}): x{^{\prime }}\in {\mathbb {R}}^{N-1}, x_{N}>0\rbrace$, N≥3$N\ge 3$, λ>0$\lambda >0$, μ∈R$\mu \in \mathbb {R}$, 20$\lambda >0$ and the different values of the parameters p$p$ and μ>0${\mu }>0$. Particularly, for λ>0$\lambda >0$, N≥4$N\ge 4$, 20$\mu >0$. Moreover, the existence of multiple solutions for (0.1) is also obtained by dual variational principle for all μ>0$\mu >0$ and suitable λ$\lambda$. [ABSTRACT FROM AUTHOR]

AbstractThis paper is devoted to studying the coupled system of multiparameter k-Hessian equationswhere B = {x ∈ ℝn : |x| < 1}, λ1, λ2 are positive parameters, ρi(i = 1, 2) is singular near the boundary ∂B, fi(i = 1, 2) satisfies a combined superlinear condition at ∞. Employing the fixed point theorem of Krasnosel’skii type in Banach space, the existence and multiplicity of nontrivial radial solutions are established. In particular, the dependence of the solutions on the parameters λ1, λ2 is also discussed. Finally, we study the nonexistence results of nontrivial radial solutions for the case λ1, λ2 ≫ 1. [ABSTRACT FROM AUTHOR]

Conformal inference is a popular tool for constructing prediction intervals. We consider here the scenario of post-selection/selective conformal inference, that is, prediction intervals are reported only for individuals selected from unlabelled test data. To account for multiplicity, we develop a general split conformal framework to construct selective prediction intervals with the false coverage-statement rate control. We first investigate the false coverage rate–adjusted method of Benjamini & Yekutieli (2005) in the present setting, and show that it is able to achieve false coverage-statement rate control, but yields uniformly inflated prediction intervals. We then propose a novel solution to the problem called selective conditional conformal prediction. Our method performs selection procedures on both the calibration set and test set, and then constructs conformal prediction intervals for the selected test candidates with the aid of the conditional empirical distribution obtained by the post-selection calibration set. When the selection rule is exchangeable, we show that our proposed method can exactly control the false coverage-statement rate in a model-free and distribution-free guarantee. For nonexchangeable selection procedures involving the calibration set, we provide non-asymptotic bounds for the false coverage-statement rate under mild distributional assumptions. Numerical results confirm the effectiveness and robustness of our method under false coverage-statement rate control and show that it achieves more narrowed prediction intervals over existing methods across various settings. [ABSTRACT FROM AUTHOR]

We consider the stabilization of a class of linear evolution systems z ′ = A z + B v under the observation y = C z by means of a finite dimensional control v. The control is based on the design of a Luenberger observer which can be infinite or finite dimensional (of dimension large enough). In the infinite dimensional case, the operator A is supposed to generate an analytical semigroup with compact resolvent and the operators B and C are unbounded operators whereas in the finite dimensional case, A is assumed to be a self-adjoint operator with compact resolvent, B and C are supposed to be bounded operators. In both cases, we show that if (A, B) and (A, C) verify the Fattorini-Hautus Criterion, then we can construct an observer-based control v of finite dimension (greater or equal than largest geometric multiplicity of the unstable eigenvalues of A) such that the evolution problem is exponentially stable. As an application, we study the stabilization of the diffusion system. [ABSTRACT FROM AUTHOR]

Developing a Land Administration Domain Model (LADM) profile for a country is an important process. This enables sound management of land and facilitates complete Land Administration covering cadaster, registry, valuation, taxation and land use. By considering the current processes in that country, their legal or customary framework, an ideal model can be developed. Kenya has four requirements that were identified and addressed as key considerations. The ISO LADM packages and sub package were considered necessary, while most classes were adopted with additional attributes, code lists and multiplicities. Expert opinion on the model was solicited to inform and validate the model. The model presents a starting point for modernizing and completing the land administration process in Kenya. The modernization includes data exchange and interoperability, data and system integration, deployment model, workflows, capacity development and change management. [ABSTRACT FROM AUTHOR]

In this article, we prove the existence and multiplicity of nontrivial solutions for the stationary quantum Zakharov system with a sign-changing potential and a general nonlinearity involving a combination of a superlinear $ f(x,u) $ f (x , u) source term and a sublinear term $ (K(x)\vert u\vert ^{q-2}u, K\in L^{\frac {2}{2-q}}(\mathbb {R}^3) $ (K (x) | u | q − 2 u , K ∈ L 2 2 − q (R 3) , where $ 1 1 < q < 2). [ABSTRACT FROM AUTHOR]

In 1950, Erdős posed a question known as the minimum modulus problem on covering systems for \mathbb {Z}, which asked whether the minimum modulus of a covering system with distinct moduli is bounded. This long-standing problem was finally resolved by Hough [Ann. of Math. (2) 181 (2015), no. 1, pp. 361–382] in 2015, as he proved that the minimum modulus of any covering system with distinct moduli does not exceed 10^{16}. Recently, Balister, Bollobás, Morris, Sahasrabudhe, and Tiba [Invent. Math. 228 (2022), pp. 377–414] developed a versatile method called the distortion method and significantly reduced Hough's bound to 616,000. In this paper, we apply this method to present a proof that the smallest degree of the moduli in any covering system for \mathbb {F}_q[x] of multiplicity s is bounded by a constant depending only on s and q. Consequently, we successfully resolve the minimum modulus problem for \mathbb {F}_q[x] and disprove a conjecture by Azlin [ Covering Systems of Polynomial Rings Over Finite Fields , University of Mississippi, Electronic Theses and Dissertations. 39, 2011]. [ABSTRACT FROM AUTHOR]

In the existing literatures, there exist at least four limit cycles for 3D Lotka-Volterra competitive systems in Zeeman's classes 26 and 27 with no explicit critical parameter values, and three limit cycles in Zeeman's classes 27 and 29 with explicit critical parameter values. Giving explicit critical parameter values in Zeeman's classes 26 - 31 and accurate focus values at them except class 30, we rigorously prove that Zeeman's classes 27 - 30 have at least three limit cycles, and Zeeman's classes 26 and 31 have at least two small amplitude limit cycles. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and multiplicity of nontrivial solutions for an anisotropic discrete nonlinear problem with variable exponent. The analysis makes use of variational methods and critical point theory. [ABSTRACT FROM AUTHOR]

In this article, we are first concerned with the existence of multiple normalized solutions to the following fractional p-Laplace problem: { (- Δ) p s ⁢ v + 풱 ⁢ (ξ ⁢ x) ⁢ | v | p - 2 ⁢ v = λ ⁢ | v | p - 2 ⁢ v + f ⁢ (v) in ⁢ ℝ N , ∫ ℝ N | v | p ⁢ 푑 x = a p , where a , ξ > 0 , p ≥ 2 , λ ∈ ℝ is an unknown parameter that appears as a Lagrange multiplier, 풱 : ℝ N → [ 0 , ∞) is a continuous function, and f is a continuous function with L p -subcritical growth. We prove that there exists the multiplicity of solutions by using the Lusternik–Schnirelmann category. Next, we show that the number of normalized solutions is at least the number of global minimum points of 풱 , as ξ is small enough via Ekeland's variational principle. [ABSTRACT FROM AUTHOR]

Copyright of Arts for Linguistic & Literary Studies is the property of Thamar University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We prove a theorem which unifies some formulas, for example the counting function, of some sets of numbers including all positive integers, h-free numbers, h-full numbers, etc. We also establish a conjecture and give some examples where the conjecture holds. [ABSTRACT FROM AUTHOR]

We prove new multiplicity results for some critical growth p$p$‐biharmonic problems in bounded domains. More specifically, we show that each of the problems considered here has 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 will be in terms of an unbounded sequence of eigenvalues of a related eigenvalue problem. Our multiplicity results are new even in the semilinear case p=2$p = 2$. The proofs are based on an abstract critical point theorem. [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]

Knowledge integration based on the relationship between structure and function of the neural substrate is one of the main targets of neuroinformatics and data-driven computational modeling. However, the multiplicity of data sources, the diversity of benchmarks, the mixing of observables of different natures, and the necessity of a long-term, systematic approach make such a task challenging. Here we present a first snapshot of a long-term integrative modeling program designed to address this issue in the domain of the visual system: a comprehensive spiking model of cat primary visual cortex. The presented model satisfies an extensive range of anatomical, statistical and functional constraints under a wide range of visual input statistics. In the presence of physiological levels of tonic stochastic bombardment by spontaneous thalamic activity, the modeled cortical reverberations self-generate a sparse asynchronous ongoing activity that quantitatively matches a range of experimentally measured statistics. When integrating feed-forward drive elicited by a high diversity of visual contexts, the simulated network produces a realistic, quantitatively accurate interplay between visually evoked excitatory and inhibitory conductances; contrast-invariant orientation-tuning width; center surround interactions; and stimulus-dependent changes in the precision of the neural code. This integrative model offers insights into how the studied properties interact, contributing to a better understanding of visual cortical dynamics. It provides a basis for future development towards a comprehensive model of low-level perception. Author summary: Computational modeling can integrate fragments of understanding generated by experimental neuroscience. However, most models considered only a few features of neural computation at a time, leading to either poorly constrained models with many parameters, or lack of expressiveness in over-simplified models. A solution is to develop detailed models, but constrain them with a broad range of anatomical and functional data to prevent overfitting. This requires a long-term systematic approach. Here we present a first snapshot of such an integrative program: a large-scale spiking model of cat primary visual cortex, that is constrained by an extensive range of anatomical and functional features. Together with the associated modeling infrastructure, this study lays the groundwork for a broad integrative modeling program seeking an in-depth understanding of vision. [ABSTRACT FROM AUTHOR]

The existence of multiple pairs of smooth positive solutions for a Carrier problem, driven by a p (x) -Laplacian operator, is studied. The approach adopted combines sub-super solutions, truncation, and variational techniques. In particular, after an explicit computation of a sub-solution, obtained combining a monotonicity type hypothesis on the reaction term and the Giacomoni–Takáč's version of the celebrated Díaz–Saá's inequality, we derive a multiplicity of solution by investigating an associated one-dimensional fixed point problem. The nonlocal term involved may be a sign-changing function and permit us to obtain the existence of multiple pairs of positive solutions, one for each "positive bump" of the nonlocal term. A new result, also for a constant exponent, is established and an illustrative example is proposed. [ABSTRACT FROM AUTHOR]

We show that there exists only one solution (the trivial identically zero solution) for some nonlinear elliptic Dirichlet problems, involving the p-Laplacian operator and nonlinear terms with supercritical growth, in bounded contractible ramified domains, that is domains of ℝn with n ≥ 2, close to a prescribed subset of ℝn, which is contractible in itself and consists of a finite number of smooth curves. In dimension n = 2 we expect that this result might be extended to cover all the bounded contractible domains of ℝ2. On the contrary, this extension is not possible in dimension n ≥ 3 because of some counterexamples concerning existence and multiplicity of nontrivial solutions in some contractible domains that may be even arbitrarily close to starshaped domains (where the well-known Pohozaev nonexistence result holds). However, also for n ≥ 3 our result allows us to prove nonexistence of nontrivial solutions in bounded contractible domains that may be very different from the starshaped ones and even arbitrarily close to some noncontractible domains where there exist many positive and nodal solutions. [ABSTRACT FROM AUTHOR]

Polysemy is a phenomenon involving single lexical items with multiple related senses. Much theorizing about it has focused on developing linguistic accounts that are responsive to various compositional and representational challenges in semantics and psychology. We focus on an underexplored question: Why does systematic polysemy cluster in the ways it does? That is, why do we see certain regular patterns of sense multiplicity, but not others? Drawing on an independently motivated view of kind cognition – i.e. the formal structures for different classes of kind representations – we argue for an answer centered on conceptual individuation. Specifically, we argue that classes of kind concepts vary in what they individuate (i.e. counting as one and specifying what makes it the same or different from others). By elucidating these differences, we can explain why a range of patterns of systematic polysemy are found cross-linguistically and why other patterns are not attested. Overall, our account provides an explanatory framework addressing an important question at the interface between language and mind and opens new avenues for future theoretical and empirical research. [ABSTRACT FROM AUTHOR]

Over the past decades, literature in dementia ethics has extensively looked at moral questions revolving around the care of older people living with dementia. Particularly prevalent are autonomy-related concerns regarding topics such as advance directives. In this paper, we argue that these discussions are crucially premised on how dementia is understood and represented. Despite the multiplicity of dementia presentations in people, the dominant discourse predominantly frames dementia as 'monstrous,' an 'enemy,' a destructive experience in need of eradication. We contend that such a monolithic approach, from a moral standpoint, is problematic in several respects. Indeed, framing heavily influences the way dementia is understood and experienced, leading to stigmatization, bias, and distress. Not only does it influence decisions and discussions on advance directives, but we argue that this flawed understanding of dementia is rooted in and contributes to epistemic harm. In the first section, we introduce the ethics of advance directives. More specifically, we introduce the view developed by Dworkin who has largely influenced the debate by making the case for advance directives by grounding them in the principles of autonomy and beneficence. In the second section, we show how dementia is still mostly framed monolithically as a 'destructive experience.' We then show that this framing is problematic because it oversteps the different pathologies dementia implies, which leads to an inaccurate representation of the condition. In the third section, we present possible alternative framings: dementia as normal aging, a person-centered care framework, and an embodied view. In the fourth section, drawing on recent developments in the epistemic injustice literature, we explore how maintaining and utilizing flawed understandings of dementia may lead to distinct moral-epistemic harms for those living with dementia and inform ongoing discussions on advance directives. Finally, in the concluding section, we return to the case of advance directives and what the implications of rethinking dementia are. [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]

We study the bifurcation curve and exact multiplicity of positive solutions in the space C 2 ((− L , L)) ∩ C ([ − L , L ]) for the Minkowski-curvature equation { − ( u ′ (x) 1 − (u ′ (x)) 2 ) ′ = λ f (u) , − L < x < L , u (− L) = u (L) = 0. where λ > 0 is a bifurcation parameter, f ∈ C [ 0 , ∞) ∩ C 2 (0 , ∞) satisfies f (u) > 0 for u > 0 and f is either concave or geometrically concave on (0 , ∞) . If f is a concave function, we prove that the bifurcation curve is monotone increasing on the (λ , ∥ u ∥ ∞) -plane. If f is a geometrically concave function, we prove that the bifurcation curve is either ⊂-shaped or monotone increasing on the (λ , ∥ u ∥ ∞) -plane under a mild condition. Some interesting applications are given. [ABSTRACT FROM AUTHOR]

In this work, we prove existence and multiplicity of solutions to a Kirchhoff elliptic problem in the whole space ℝN. More specifically, we consider the following nonlocal elliptic problem: − m(∥∇u∥22)Δu + V (x)u = λa(x)|u|q−2u − 휃b(x)|u|p−2uin ℝN,u ∈ H1(ℝN), where N ≥ 3, the parameters λ,휃 > 0, 2 < 2(σ + 1) < q < p < 2∗ := 2N/(N − 2), σ ∈ (0, 2/(N − 2)) and a,b ∈ L∞(ℝN) with a(x),b(x) > 0 almost everywhere in ℝN. This type of problem contains the function m : ℝ+ → ℝ+ known as the Kirchhoff function given by m(t) = α1 + α2tσ with α1,α2 > 0 and t ∈ ℝ+. Under our assumptions the potential V : ℝN → ℝ and the nonlinearities can be sign changing functions. Hence, our main objective is to prove that the above problem has at least two distinct nontrivial solutions, one of them being a ground state, whenever λ ∈ (λ∗, +∞) for some suitable λ∗ > 0. The main idea is to use the minimization method in the Nehari manifold together with the nonlinear Rayleigh quotient. In our setting, the main difficulty is ensuring the existence of nontrivial solutions by using the Nehari method considering the Lagrange Multipliers Theorem. In other words, we study the case where the fibering map admits inflections points with λ,휃 > 0. Furthermore, for each λ ∈ (−∞,λ∗], we show a nonexistence result for our main problem. It is important to emphasize that λ∗ > 0 is sharp in order to find the existence and multiplicity of nontrivial solutions for our main problem. [ABSTRACT FROM AUTHOR]

Competition in the German audiovisual and media system is analyzed, based on the Political Economy of Communication (EPC) and its update based on the analysis of the dynamics of digital platforms. The article aims to be a starting point for comparative analyzes of countries in the rearrangement of the global media market, which face multiplicity of supply, digitalization and competition between local audiovisual industry leaders, private and public, with audiovisual streaming services. It is concluded that the EPC’s theoretical proposal allows a Latin American theoretical and critical look at empirical research in different contexts that, despite the differences, are influenced by common categories, such as Capital, the State and the Public in their interrelations and challenges that accompany digital platforms. [ABSTRACT FROM AUTHOR]

We consider the adjacency spectrum of cycle-spliced signed graphs (CSSG), i.e., signed graphs whose blocks are (independent) signed cycles. For a signed graph S, the nullity η(S) is the multiplicity of the 0-eigenvalue. The adjancency spectrum of cycle-spliced (signed) graphs is studied in the literature for the relation between the nullity η and the cyclomatic number c, in particular, it is known that 0 = η(S) = c(S) + 1. In this paper, nonsingular cycle-spliced bipartite signed graphs are characterized. For cycle-spliced signed graphs S having only odd cycles, we show that η(S) is 0 or 1. Finally, we compute the nullity of CSSGs consisting of at most three cycles. [ABSTRACT FROM AUTHOR]

It is generally desirable to construct a higher order iterative method for locating roots of multiplicity m that preserves its theoretical convergence in applications, but in reality, this is not the case in general. With this aim, a three-step Traub-Steffensen-type (derivative-free) iterative family is proposed and investigated for obtaining roots of multiplicity m of nonlinear equations. The iterative scheme uses four function evaluations per iteration and possesses eighth order of convergence, hence it is optimal. Special cases of the family are thoroughly investigated for their dynamical properties and numerical performance. Estimation of the convergence domain in the complex plane and comparison of the results with existing methods provide a substantial idea about the convergence of new methods. The findings of analysis are remarkable in the sense that the developed scheme exhibits superiority over the existing counterparts by displaying the wider convergence regions along with the rapid convergence rates. In addition, numerical accuracy is analyzed by locating the multiple zeros of selected nonlinear problems including some of the applied nature like Van der Waals equation and Eigen value problem. The performance analysis also shows additional properties of the family by demonstrating high precision in numerical computations while preserving the theoretical order of convergence. [ABSTRACT FROM AUTHOR]

Platform trials offer a framework to study multiple interventions in one trial with the opportunity of opening and closing arms. The use of common controls can increase efficiency as compared to individual controls. The need for multiplicity adjustment because of common controls is currently a debate among researchers, pharmaceutical companies, and regulators. The impact of common controls on the type one error in a fixed platform trial, i.e. when all treatments start and end recruitment at the same time, has been discussed in the literature before. We complement these findings by investigating the impact of a common control on the type one error and power in a flexible platform trial, i.e. when one arm joins the platform later. We derived the correlation of test statistics to assess the impact of the overlap and compared the results to a trial with individual controls. Furthermore, we evaluate the power, and the impact of multiplicity adjustment on the power in fixed and flexible platform trials. These methodological considerations are complemented by a regulatory guideline review. With multiple arms, the FWER is inflated when no multiplicity adjustment is applied. However, the FWER inflation is smaller with common controls than with individual controls. Even after multiplicity adjustment, a trial with common controls is often beneficial in terms of sample size and power. However, in some cases, the trial with common controls loses the efficiency gain and it might be advisable to run a separate trial rather than joining a platform trial. [ABSTRACT FROM AUTHOR]

In this paper, we aim to show the process of simulating survival data when the distribution of the overall population and one subgroup (called "positive subgroup") as well as the proportion of the subgroup is known, while the distribution of the other subgroup (called "negative subgroup") is unknown. We propose a combination method which generates survival data of the positive subgroup and negative subgroup, respectively, and survival data of the overall population are the combination of the two subgroups. The parameters of the overall population and the positive subgroup need to satisfy certain constraints, otherwise the parameters may lead to contradictions. From simulation, we show that our proposed combination method can reflect the correlation between the test statistics of overall population and positive subgroup, which makes the simulated data more realistic and the results of simulation more reliable. Moreover, for a multiplicity control in trial design, the combination method can help to determine the ${\rm{\alpha }}$ α splitting strategy between primary endpoints, and is helpful in designs of clinical trials as shown in three applications. [ABSTRACT FROM AUTHOR]

Starting from the observation that the notion of "multiple geographies" has gained considerable traction in geographical research in the past years while its theoretical foundations have often remained abstract, in this paper we contribute toward elaboration of multiple geographies as a research perspective, recognizing its potential as a valuable framework for analyzing divergent spatial relations. Initially, we provide an overview of the diverse applications of multiple geographies through a review of relevant literature, focusing on papers within the realms of political geographies that mention the term in their title or abstract. Subsequently, we categorize these papers thematically, identifying three main theoretical strains: post‐colonial geographies, uneven geographical development, and feminist geographies. We then propose a theoretical scaffold for navigating the complexities of multiple geographies by engaging with broader discussions on plurality and multiplicity in relation to the aforementioned strains. Finally, we synthesize the insights garnered from this analysis, exploring the potential of a multiple geographies research perspective to contribute to a nuanced understanding of the diverse ways in which space is produced and experienced. Our contribution aims to enrich ongoing debates within human geography on how space can be redefined in more relational, decolonial, socially just, feminist, and diverse ways, opening pathways for pluralistic geographical imaginations. [ABSTRACT FROM AUTHOR]

In [11], Hausel introduced a commutative algebra — the multiplicity algebra — associated to a fixed point of the C ∗ -action on the Higgs bundle moduli space. Here we describe this algebra for a fixed point consisting of a very stable rank 2 vector bundle and zero Higgs field for a curve of low genus. Geometrically, the relations in the algebra are described by a family of quadrics and we focus on the discriminant of this family, providing a new viewpoint on the moduli space of stable bundles. The discriminant in our examples demonstrates that as the bundle varies, we obtain a continuous variation in the isomorphism class of the algebra. [ABSTRACT FROM AUTHOR]

We consider the one-parametric family of self-adjoint realizations of the two-dimensional massive Dirac operator with a Lorentz scalar δ-shell interaction of strength τ ∈ R \ { − 2 , 0 , 2 } supported on a broken line of opening angle 2ω with ω ∈ (0 , π 2 ). The essential spectrum of any such self-adjoint realization is symmetric with respect to the origin with a gap around zero whose size depends on the mass and, for τ < 0, also on the strength of the interaction, but does not depend on ω. As the main result, we prove that for any N ∈ N and strength τ ∈ (−∞, 0)\{−2} the discrete spectrum of any such self-adjoint realization has at least N discrete eigenvalues, with multiplicities taken into account, in the gap of the essential spectrum provided that ω is sufficiently small. Moreover, we obtain an explicit estimate on ω sufficient for this property to hold. For τ ∈ (0, ∞)\{2}, the discrete spectrum consists of at most one simple eigenvalue. [ABSTRACT FROM AUTHOR]

The present paper is devoted to the study of the following double-phase equation - div (| ∇ u | p - 2 ∇ u + μ ε (x) | ∇ u | q - 2 ∇ u) + V ε (x) (| u | p - 2 u + μ ε (x) | u | q - 2 u) = f (u) in R N , where N ≥ 2 , 1 < p < q < N , q < p ∗ with p ∗ = Np N - p , μ : R N → R is a continuous non-negative function, μ ε (x) = μ (ε x) , V : R N → R is a positive potential satisfying a local minimum condition, V ε (x) = V (ε x) , and the nonlinearity f : R → R is a continuous function with subcritical growth. Under natural assumptions on μ , V and f, by using penalization methods and Lusternik–Schnirelmann theory we first establish the multiplicity of solutions, and then, we obtain concentration properties of solutions. [ABSTRACT FROM AUTHOR]

This paper explores the operationalization of policy directionality in terms of goal consistency as well as the spatial dimensions of problems and solutions. The study focuses on cross-border regions (CBRs), since they are engaged in cooperation to tackle common challenges. This study employs a comparative analysis across two EU CBRs, drawing on a theoretical framework that integrates the trinity of agency scholarships and the literature on the multiplicity of border functions. By combining these perspectives, we aim to illustrate how agents navigate the opportunity spaces generated within CBRs. This paper aims to shed light on the interplay between agents to navigate the conditions that the presence of international border generates in the EU cross-border regions (CBR)s to tackle Societal Challenges (SC)s. Through this integrated framework, we explore how agents perceive, interpret, and respond to the complex dynamics and possibilities that emerge in CBRs, shedding light on the interplay between structure and agency in these unique spatial settings. The findings show how SC can be framed at different scales with ambivalent results in terms of consistency of policy goals. Framed through the trinity agency framework, actors interacted collectively to generate and transfer knowledge in the CBRs. [ABSTRACT FROM AUTHOR]

A semidualizing module is a generalization of Grothendieck's dualizing module. For a local Cohen–Macaulay ring R, the ring itself and its canonical module are always realized as (trivial) semidualizing modules. Reasonably, one might ponder the question; when do nontrivial examples exist? In this paper, we study this question in the realm of numerical semigroup rings and, up to multiplicity 9, completely classify which of these rings possess a nontrivial semidualizing module. Using this classification, for each integer n > 8 , we construct a numerical semigroup ring of multiplicity n which admits a nontrivial semidualizing module. [ABSTRACT FROM AUTHOR]

AbstractOur most significant aim is to guarantee multiplicity results for a Kirchhoff-type problem involving two parameters and p(x)-triharmonic operator subject to the Navier boundary condition. More precisely, two critical point theorems are exploited to attain main theorems. [ABSTRACT FROM AUTHOR]

The multiplicity of an eigenvalue λ of a graph G is denoted by m (G , λ). In a connected graph G with at least two vertices, a vertex is called external if it is not a cut vertex. In a tree, an external vertex is exactly a pendant vertex. Let ϵ (G) be the number of external vertices in G. In this paper, we prove that m (G , λ) ≤ ϵ (G) − 1 for any λ and characterize the extremal graphs with m (G , − 1) = ϵ (G) − 1 , which generalizes the main result of Wang et al. [Linear Multi. Alg., 2020] from a tree to an arbitrary connected graph. [ABSTRACT FROM AUTHOR]

Motivated by applications in matrix constructions used in the inverse eigenvalue problem for graphs, we study a concept of genericity for eigenvectors associated with a given spectrum and a connected graph. This concept generalizes the established notion of a nowhere-zero eigenbasis. Given any simple graph G on n vertices and any spectrum with no multiple eigenvalues, we show that the family of eigenbases for symmetric matrices with this graph and spectrum is generic, strengthening a result of Monfared and Shader. We illustrate applications of this result by constructing new achievable ordered multiplicity lists for partial joins of graphs and providing several families of joins of graphs that are realizable by a matrix with only two distinct eigenvalues. [ABSTRACT FROM AUTHOR]

Egyptian temples are profusely decorated with scenes showing the pharaoh performing animal sacrifices, offering food, or presenting various objects with symbolic value. In this last case, the image of what is offered is usually easy to identify, but the image alone is not sufficient to explain the purpose of the offering. Texts accompanying the offering scene explain the role of the pharaoh and gods involved, the nature of the offering, and its role based on mythological events and their theological interpretation. Some lists of materia sacra, unfortunately, almost all from the Hellenistic or Roman period, give information of this kind but in a very laconic form. In some cases, the offered object is not immediately recognisable. Discovering its identity as a real object, then as a symbolic one, leads to revealing its apparent multiplicity of roles and even materialities. The example of the object called mnpḥ is particularly illustrative in this respect. It is an oryx skin, but it was also regarded as a cloth and as a part of boats belonging to different gods. This article aims at explaining the logic that links these different roles. [ABSTRACT FROM AUTHOR]

Territory and population, migration, division of territories and their globalised populations... Re-presenting in this paper Wars and Capital (written with Maurizio Lazzarato, first published 2016), we'll argue that Deleuze and Guattari's view on this complex of relations must be reconstructed from their understanding of war's constitutive relationship with capitalism by taking up the confrontation with Clausewitz to reverse the famous formula that war is/is only the continuation of politics by other means. Except that, as with Foucault, albeit differently, it is not so much a question of reversal but an interweaving of war in politics and politics in war that adopts the movements of capitalism in the twentieth century's world economy. Politics is not, as in Clausewitz, the politics of the state but the war machine of the financialised economy interwoven in the multiplicity of wars that move and hold together the war of destruction in action with wars of class, race and sex under the auspices of a 'war amongst the people' that provide the fractal environment of all the others when war and peace become indistinguishable in a neoliberalism of combat. A transversal and global civil war that is also a war of subjectivity fractures all territories in the North(s) and South(s) since internal and external colonisations are no longer distributed only geographically. As proof, if needed, more than forty years after the publication of A Thousand Plateaus – it is not enough to state that micropolitics has to pass into macropolitics to transform it: both micro- and macropolitics have to be part of the multiplicity of wars that take place, without which both micro- and macropolitics collapse in the 'becoming-minor' of the 'missing people'. [ABSTRACT FROM AUTHOR]

We draw upon the metaphor of navigation to rethink how we think about place. We highlight three extensions that dominate current place-sensitive organizational research. We draw upon a set of six important papers published in Organization Studies that showcase the diversity, multiplicity and multidimensionality of place. The studies we select highlight three important movements in the study of place – from stable to dynamic, from physical to polymorphic, and from neutral to political. In doing so, they serve as a compass to guide our thinking and research on how place is created, negotiated and experienced. [ABSTRACT FROM AUTHOR]

Existence and multiplicity of three weak solutions for a Leray-Lions p(x)-biharmonic problem involving Hardy potential and indefinite weight were proved. Our main tools combined variational methods and some critical theorems. [ABSTRACT FROM AUTHOR]

Copyright of Journal of the American Institute for Conservation is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We consider the multiplicity of solutions for the following class of non-autonomous $ p $-Laplace equations:$ \begin{equation*} \begin{cases} -\Delta_p u = \lambda |u|^{p-2}u + h(\epsilon x)f(u), \quad x\in\mathbb{R}^N, \\ \int_{\mathbb{R}^N} |u|^pdx = a^p, \end{cases} \end{equation*} $where $ \epsilon, a>0 $, $ 1