Search

In this paper, we study the multiplicity of normalized solutions to a class of nonlinear fractional Schrödinger–Poisson systems with Hardy potential. First, by using some ideas of the fountain theorem, we define a sequence of minimax values, and then we prove that these minimax values are critical values of the energy function restricted to a constraint set, which leads to the multiplicity of normalized solutions and extends some related results. [ABSTRACT FROM AUTHOR]

In this paper, we prove that if Cohen–Macaulay local/graded rings A , B and R satisfy certain conditions regarding multiplicity and Cohen–Macaulay type, then almost Gorenstein property of R implies Gorenstein properties for all of A , B and R. We apply our theorem to tensor products of semi-standard graded rings and some classes of affine semigroup rings, i.e., numerical semigroup rings, edge rings and stable set rings. [ABSTRACT FROM AUTHOR]

We investigate the existence and multiplicity of abstract weak solutions of the equation - Δ p u - Δ q u = α | u | p - 2 u + β | u | q - 2 u in a bounded domain under zero Dirichlet boundary conditions, assuming 1 < q < p and α , β ∈ R . We determine three generally different ranges of parameters α and β for which the problem possesses a given number of distinct pairs of solutions with a prescribed sign of energy. As auxiliary results, which are also of independent interest, we provide alternative characterizations of variational eigenvalues of the q-Laplacian using smaller and larger constraint sets than in the standard minimax definition. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence of at least two solutions to some semilinear elliptic equation defined in the whole euclidean space R 2. The nonlinearity consists of two terms: one presents a singularity at the origin and the other has a doubly exponential behavior at infinity. This new exponential behavior is governed by a recently established weighted inequality of Trudinger–Moser type. A combination of perturbation arguments and variational tools is employed to obtain our multiplicity result. [ABSTRACT FROM AUTHOR]

In his monograph on Infinite Abelian Groups, I. Kaplansky raised three "test problems" concerning their structure and multiplicity. As noted by Azoff, these problems make sense for any category admitting a direct sum operation. Here, we are interested in the operator theoretic version of Kaplansky's second problem which asks: if A and B are operators on an infinite-dimensional, separable Hilbert space and A ⊕ A is equivalent to B ⊕ B in some (precise) sense, is A equivalent to B? We examine this problem under a strengthening of the hypothesis, where a "primitive" square root J 2 (A) of A ⊕ A is assumed to be equivalent to the corresponding square root J 2 (B) of B ⊕ B . When "equivalence" refers to similarity of operators and A is a compact operator, we deduce from this stronger hypothesis that A and B are similar. We exhibit a counterexample (due to J. Bell) of this phenomenon in the setting of unital rings. Also, we exhibit an uncountable family { U α } α ∈ Ω of unitary operators, no two of which are unitarily equivalent, such that each U α is unitarily equivalent to J n (U α) , a "primitive" n th root of U α ⊕ U α ⊕ ⋯ ⊕ U α . [ABSTRACT FROM AUTHOR]

Bipartite determinantal ideals are introduced in Illian and Li (Gröbner basis for the double determinantal ideals, http://arxiv.org/abs/2305.01724) as a vast generalization of the classical determinantal ideals intensively studied in commutative algebra, algebraic geometry, representation theory, and combinatorics. We introduce a combinatorial model called concurrent vertex maps to describe the Stanley–Reisner complex of the initial ideal of any bipartite determinantal ideal, and study properties and applications of this model including vertex decomposability, shelling orders, formulas of the Hilbert series, and h-polynomials. [ABSTRACT FROM AUTHOR]

In the present paper, we study the existence and concentration of multiple normalized solutions to the following nonlinear biharmonic Schrödinger equation: ε 4 Δ 2 u + V ( x ) u = λ u + h ( u ) , x ∈ R N , ∫ R N | u | 2 d x = c 2 ε N , x ∈ R N , where ε > 0 is a positive parameter, λ ∈ R is unknown and appears as a Lagrange multiplier, and V is a positive potential such that inf Λ V < inf ∂ Λ V for some open bounded subset Λ ⊂ R N ( N ⩾ 5 ). Applying the penalization techniques and Ljusternik–Schnirelmann theory, we obtain multiple mormalized solutions u ε . When ε → 0, these solutions concentrates around a local minimum of V.This paper extends the results of Alves and Thin (2023), which considered the nonlinear Schrödinger equations with general nonlinearities, to the biharmonic Schrödinger equations. We develop a truncated skill to obtain the minimum via careful analysis. Moreover, we also obtain orbital stability of the solutions. [ABSTRACT FROM AUTHOR]

A graph G = (V G , E G) is said to be a cograph if the path P 4 does not appear among its induced subgraphs. The vicinal preorder ≺ on the vertex set V G is defined in terms of inclusions between neighborhoods. The minimum number ∇ (G) of ≺-chains required to cover G is called the Dilworth number of G. In this paper it is proved that for a cograph G , the multiplicity of every Seidel eigenvalue λ ≠ ± 1 does not exceed ∇ (G). This bound turns out to be tight and can be further improved for threshold graphs. Moreover, it is shown that cographs with at least two vertices have no Seidel eigenvalues in the interval (− 1 , 1). [ABSTRACT FROM AUTHOR]

In this paper we study the existence of multiple normalized solutions to the following class of elliptic problems - ϵ 2 Δ u + V (x) u = λ u + f (u) , in R N , ∫ R N | u | 2 d x = a 2 ϵ N , where a , ϵ > 0 , λ ∈ R is an unknown parameter that appears as a Lagrange multiplier, V : R N → [ 0 , ∞) is a continuous function, and f is a continuous function with L 2 -subcritical growth. It is proved that the number of normalized solutions is related to the topological richness of the set where the potential V attains its minimum value. In the proof of our main result, we apply minimization techniques, Lusternik-Schnirelmann category and the penalization method due to del Pino and Felmer (Calc. Var. Partial Differential Equations 4, 121–137 1996). [ABSTRACT FROM AUTHOR]

The aim of this study was to explore molecular measures of P. falciparum malaria burden (FOI and MOI) in the context of seasonal malaria chemoprevention. We analyzed malaria cases collected as part of a longitudinal cohort study. The cohort included P. falciparum-negative children aged 1.5 to 12, as confirmed by PCR 21 days after a radical cure using DHA-PQ or AS. Children were followed up for six months using active and passive case detection methods. At each visit, dried blood spots and blood smears were collected by finger prick, along with clinical data. Parasite DNA was extracted and analyzed by nested PCR for detection and genotyping of P. falciparum parasites. A total of 458 P. falciparum isolates collected during follow-up from October 2020 to March 2021 were genotyped. During the follow-up, children contracted 1.05 (95% IC [0.81–1.30]) new P. falciparum infections/child/time of exposure, and the MOI value was 3.00 (SD 1.60). Age is a protective factor (IRR: 0.74; 95% CI: 0.61, 0.90) against the occurrence of an episode of malaria, unlike an increase in MOI (IRR: 1.63; 95% CI: 1.04, 1.99), which is a favorable factor (p < 0.05). This study confirms the reduction in malaria transmission in our study area, probably due to the massive deployment of control tools. [ABSTRACT FROM AUTHOR]

This paper deals with global compactness and the multiplicity of positive solutions to problems of the type −Δ픹Nu − λu = a(x)|u|2∗−2u + f(x)in 픹N, u ∈ H1(픹N), where 픹N denotes the ball model of the hyperbolic space of dimension N ≥ 4, 2∗ = 2N N−2, N(N−2) 4 < λ < (N−1)2 4 and f ∈ H−1(픹N) (f≢0) is a nonnegative functional in the dual space of H1(픹N). The potential a ∈ L∞(픹N) is assumed to be strictly positive, such that limd(x,0)→∞a(x) = 1, where d(x, 0) denotes the geodesic distance. We establish profile decomposition of the functional associated with the above equation. We show that concentration occurs along two different profiles, namely, hyperbolic bubbles and localized Aubin–Talenti bubbles. For f = 0 and a ≡ 1, profile decomposition was studied in Bhakta and Sandeep [Poincaré–Sobolev equations in the hyperbolic space, Calc. Var. Partial Differential Equations 44 (2012) 247–269]. However, due to the presence of the potential a(.), an extension of profile decomposition to the present set-up is highly nontrivial and requires several delicate estimates and geometric arguments concerning the isometry group (Möbius group) of the hyperbolic space. Further, using the decomposition result, we derive various energy estimates involving the interacting hyperbolic bubbles and hyperbolic bubbles with localized Aubin–Talenti bubbles. Finally, combining these estimates with topological and variational arguments, we establish a multiplicity of positive solutions in the cases: a ≥ 1 and a < 1 separately. The equation studied in this paper can be thought of as a variant of a scalar-field equation with a critical exponent in the hyperbolic space, although such a critical exponent problem in the Euclidean space ℝN has only a trivial solution when f ≡ 0, a(x) ≡ 1 and λ < 0. [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]

We explore the existence, uniqueness, and multiplicity of positive solutions to a system of Hadamard fractional differential equations that contain fractional integral terms. Defined on a finite interval, this system is subject to general coupled nonlocal boundary conditions encompassing Riemann–Stieltjes integrals and Hadamard fractional derivatives. To establish the main results, we employ several fixed-point theorems, namely the Banach contraction mapping principle, the Schauder fixed-point theorem, the Leggett–Williams fixed-point theorem, and the Guo–Krasnosel'skii fixed-point theorem. [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]

Copyright of Journal of Latin American & Caribbean Anthropology is the property of Wiley-Blackwell 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.)

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.)

Copyright of Beytulhikme: An International Journal of Philosophy is the property of Beytulhikme: An International Journal of Philosophy 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.)

Tumor‐informed mutation‐based approaches are frequently used for detection of circulating tumor DNA (ctDNA). Not all mutations make equally effective ctDNA markers. The objective was to explore if prioritizing mutations using mutational features—such as cancer cell fraction (CCF), multiplicity, and error rate—would improve the success rate of tumor‐informed ctDNA analysis. Additionally, we aimed to develop a practical and easily implementable analysis pipeline for identifying and prioritizing candidate mutations from whole‐exome sequencing (WES) data. We analyzed WES and ctDNA data from three tumor‐informed ctDNA studies, one on bladder cancer (Cohort A) and two on colorectal cancer (Cohorts I and N). The studies included 390 patients. For each patient, a unique set of mutations (median mutations/patient: 6, interquartile 13, range: 1–46, total n = 4023) were used as markers of ctDNA. The tool PureCN was used to assess the CCF and multiplicity of each mutation. High‐CCF mutations were detected more frequently than low‐CCF mutations (Cohort A: odds ratio [OR] 20.6, 95% confidence interval [CI] 5.72–173, p = 1.73e−12; Cohort I: OR 2.24, 95% CI 1.44–3.52, p = 1.66e−04; and Cohort N: OR 1.78, 95% CI 1.14–2.79, p = 7.86e−03). The detection‐likelihood was additionally improved by selecting mutations with multiplicity of two or above (Cohort A: OR 1.55, 95% CI 1. 14–2.11, p = 3.85e−03; Cohort I: OR 1.78, 95% CI 1.23–2.56, p = 1.34e−03; and Cohort N: OR 1.94, 95% CI 1.63–2.31, p = 2.83e−14). Furthermore, selecting the mutations for which the ctDNA detection method had the lowest error rates, additionally improved the detection‐likelihood, particularly evident when plasma cell‐free DNA tumor fractions were below 0.1% (p = 2.1e−07). Selecting mutational markers with high CCF, high multiplicity, and low error rate significantly improve ctDNA detection likelihood. We provide free access to the analysis pipeline enabling others to perform qualified prioritization of mutations for tumor‐informed ctDNA analysis. [ABSTRACT FROM AUTHOR]

Denote by m (S) the multiplicity of a numerical semigroup S. A covariety is a nonempty family C of numerical semigroups that fulfils the following conditions: there is the minimum of C , the intersection of two elements of C is again an element of C and S \ { m (S) } ∈ C for all S ∈ C such that S ≠ min (C). In this work we describe an algorithmic procedure to compute all the elements of C. We prove that there exists the smallest element of C containing a set of positive integers. We show that A (F) = { S ∣ S is a numerical semigroup with Frobenius number F } is a covariety, and we particularize the previous results in this covariety. Finally, we will see that there is the smallest covariety containing a finite set of numerical semigroups. [ABSTRACT FROM AUTHOR]

Let $\Delta$ be a numerical semigroup. In this work we show that $\mathcal{J}(\Delta) =\{I\cup\nobreak\{0\} I is an ideal of \Delta\}$ is a distributive lattice, which in addition is a Frobenius restricted variety. We give an algorithm which allows us to compute the set $\mathcal{J}_a(\Delta)=\{S\in\mathcal{J}(\Delta) \max(\Delta\backslash S)=a\}$ for a given $a\in\Delta.$ As a consequence, we obtain another algorithm that computes all the elements of $\mathcal{J}(\Delta)$ with a fixed genus.

In this paper, we studied the existence of multiple normalized solutions to the following Kirchhoff type equation:$ \begin{equation*} \begin{cases} -\left(a\varepsilon^2+b\varepsilon\int_{\mathbb{R}^3}|\nabla u|^2dx\right)\Delta u+V(x)u = \mu u+f(u) & {\rm{in}}\;\mathbb{R}^3, \\ \int_{\mathbb{R}^3}|u|^2dx = m\varepsilon^3 , u\in H^1(\mathbb{R}^3) , \end{cases} \end{equation*} $where $ a $, $ b $, $ m > 0 $, $ \varepsilon $ is a small positive parameter, $ V $ is a nonnegative continuous function, $ f $ is a continuous function with $ L^2 $-subcritical growth and $ \mu\in\mathbb{R} $ will arise as a Lagrange multiplier. Under the suitable assumptions on $ V $ and $ f $, the existence of multiple normalized solutions was obtained by using minimization techniques and the Lusternik-Schnirelmann theory. We pointed out that the number of normalized solutions was related to the topological richness of the set where the potential $ V $ attained its minimum value.

In this paper, we consider the multiplicity of solutions to the following Choquard equation - ε 2 Δ u + V (x) u = λ u + ε - α (I α ∗ [ h (x) | u | p ]) h (x) | u | p - 2 u in R N , with a prescribed mass ∫ R N | u | 2 d x = a ε N , where N ≥ 1 , a , ε > 0 , α ∈ (0 , N) , N + α N < p < N + α + 2 N , I α is the Riesz potential, λ ∈ R appears as an unknown Lagrange multiplier, h : R N → [ 0 , ∞) is a bounded and continuous function and the potential V is a continuous function. Under some assumptions on V, we show that when ε is small enough the numbers of normalized ground states are at least the numbers of global maximum points of h. [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 this paper, we study the multiplicity of normalized solutions to the following Gross-Pitaevskii equation arising in trapped dipolar quantum gases: - 1 2 Δ u + λ 1 | u | 2 u + λ 2 (K ∗ | u | 2 ) u - h (ε x) | u | p - 2 u + μ u = 0 in R 3 under the mass constraint ∫ R 3 | u | 2 d x = c 2 , where (λ 1 , λ 2) ∈ R 2 , c , ε > 0 , 2 < p < 10 3 , h : R 3 → [ 0 , ∞) is a continuous function and K is the classical dipole-dipole interaction kernel. In the unstable regime, that is, (λ 1 , λ 2) ∈ D = { (λ 1 , λ 2) ∈ R 2 : λ 1 < 4 π 3 λ 2 ≤ 0 or λ 1 < - 8 π 3 λ 2 ≤ 0 } , we establish the existence of a normalized solution that corresponds to an interior local minimizer of the constraint functional provided that inf x ∈ R 3 h (x) = lim | x | → ∞ h (x) = h ∞ > 0. Moreover, if the origin is a maximum point of function h, we obtain that the number of normalized solutions is not less than the number of global maximum points of h when ε > 0 is sufficiently small. [ABSTRACT FROM AUTHOR]

This paper considers the existence of multiple normalized solutions of the following $(2,q)$-Laplacian equation: \begin{equation*} \begin{cases} -\Delta u-\Delta_q u=\lambda u+h(\epsilon x)f(u), &\mathrm{in}\ \mathbb{R}^{N},\\ \int_{\mathbb{R}^{N}}|u|^2\mathrm{d}x=a^2, \end{cases} \end{equation*} where $20, a>0$ and $\lambda \in \mathbb{R}$ is a Lagrange multiplier which is unknown, $h$ is a continuous positive function and $f$ is also continuous satisfying $L^2$-subcritical growth. When $\epsilon$ is small enough, we show that the number of normalized solutions is at least the number of global maximum points of $h$ by Ekeland's variational principle.

Abstract When different researchers study the same research question using the same dataset they may obtain different and potentially even conflicting results. This is because there is often substantial flexibility in researchers’ analytical choices, an issue also referred to as “researcher degrees of freedom”. Combined with selective reporting of the smallest p-value or largest effect, researcher degrees of freedom may lead to an increased rate of false positive and overoptimistic results. In this paper, we address this issue by formalizing the multiplicity of analysis strategies as a multiple testing problem. As the test statistics of different analysis strategies are usually highly dependent, a naive approach such as the Bonferroni correction is inappropriate because it leads to an unacceptable loss of power. Instead, we propose using the “minP” adjustment method, which takes potential test dependencies into account and approximates the underlying null distribution of the minimal p-value through a permutation-based procedure. This procedure is known to achieve more power than simpler approaches while ensuring a weak control of the family-wise error rate. We illustrate our approach for addressing researcher degrees of freedom by applying it to a study on the impact of perioperative $$paO_2$$ p a O 2 on post-operative complications after neurosurgery. A total of 48 analysis strategies are considered and adjusted using the minP procedure. This approach allows to selectively report the result of the analysis strategy yielding the most convincing evidence, while controlling the type 1 error—and thus the risk of publishing false positive results that may not be replicable.

The technique for investigating isomeric states of nuclei with a large values of energy and total momentum created in the neutron capture reaction has been developed. The technique is based on the spectrometry of multiplicity, energy, and time of registration of instantaneous and delayed gamma cascades of isomer occupancy and decay, respectively. The technique was tested in measurements of the isomeric ratio of the 183W level with energy Eiz = 1.285 MeV with total moment Jπiz = 4-, 5- and lifetime Tiz = 8.2 μs in the neutron absorption reaction, which is equal to αiz = (4.7 ± 0.9)⋅10-3. At large values of the efficiency of registration of acts of settlement and decay of the isomer (0.6 - 0.8), the level of the corresponding background of the spectrometer is only 3.5⋅10-4 s-1. At the countable load at the spectrometer input ∼1.5⋅103 s-1, the expected sensitivity of determining the isomeric ratio in measurements with the mono isotope of the sample is αiz ∼(0.3 ± 1.0)⋅10-4.

Let a = (a i) i ≥ 1 be a sequence in a field F , and f : F × F → F be a function such that f (a i , a i) ≠ 0 for all i ≥ 1. For any tournament T over [ n ] , consider the n × n symmetric matrix M T with zero diagonal whose (i , j) th entry (for i < j) is f (a i , a j) if i → j in T , and f (a j , a i) if j → i in T. It is known [3] that if T is a uniformly random tournament over [ n ] , then rank (M T) ≥ (1 2 − o (1)) n with high probability when char (F) ≠ 2 and f is a linear function. In this paper, we investigate the other extremal question: how low can the ranks of such matrices be? We work with sequences a that take only two distinct values, so the rank of any such n × n matrix is at least n / 2. First, we show that the rank of any such matrix depends on whether an associated bipartite graph has certain eigenvalues of high multiplicity. Using this, we show that if f is linear, then there are real matrices M T (f ; a) of rank at most n 2 + O (1). For rational matrices, we show that for each ε > 0 we can find a sequence a (ε) for which there are matrices M T (f ; a) of rank at most (1 2 + ε) n + O (1). These matrices are constructed from symmetric designs, and we also use them to produce bisection-closed families of size greater than ⌊ 3 n / 2 ⌋ − 2 for n ≤ 15 , which improves the previously best known bound given in [5]. [ABSTRACT FROM AUTHOR]

We consider the problem of complex root classification, i.e., finding the conditions on the coefficients of a univariate polynomial for all possible multiplicity structures on its complex roots. It is well known that such conditions can be written as conjunctions of several polynomial equalities and one inequality in the coefficients. Those polynomials in the coefficients are called discriminants for multiplicities. It is also known that discriminants can be obtained by using repeated parametric gcd's. The resulting discriminants are usually nested determinants, i.e., determinants of matrices whose entries are determinants, and so on. In this paper, we give a new type of discriminants which are not based on repeated gcd's. The new discriminants are simpler in the sense that they are non-nested determinants and have smaller maximum degrees. [ABSTRACT FROM AUTHOR]

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

Outsourcing of health-commodity supplies to third-party logistics providers is one of the ways of reducing costs and/or improving service levels in the public sector. This paper evaluates three forms of outsourcing: full outsourcing of inventory management, partial outsourcing of specific activities, and contingent partial outsourcing of specific logistics activities. It notes that, in Africa, contracting-out supply logistics has mostly taken the form of partial outsourcing of transportation only or storage and transportation of specific health commodities to all or selected geographical regions. Partial outsourcing offers limited benefits since it cannot provide adequate pressures on public-sector logistics to be efficient or maintain uninterrupted supplies in times of catastrophes. Improvements in logistics performance achieved through partial outsourcing should not mask the need for more expansive arrangements that support not only partial outsourcing but also full outsourcing in situations of inefficiency and in times of supply-disruption catastrophe. [ABSTRACT FROM AUTHOR]

Fluidity and ubiquity are two fundamental principles of our contemporary world, representing new ways of perceiving, thinking, experiencing, organising, and creating various aspects of our present world. These principles have radically transformed models of economic exchanges, industrial production, social relations, cultural representations, and aesthetic expressions. Fluidity serves as a philosophical antithesis to the modern rigid, stratified, and binary worldview, celebrating a fluid, non-stratified, and non-binary perspective driven by dynamic flow, flux, and connectivity. On the other hand, ubiquity defines our present world of objects, which are created through augmented and mixed reality, giving them the property of being present anywhere and everywhere. Both fluidity and ubiquity serve as contemporary models for generating disruptive ideas, forms, styles, products, organisations, and systems. Fluidity represents the fluid-creative organisation of physical, social, cultural, and aesthetic elements, independent of binary structures, while ubiquity represents the transformation of objects from the virtual to the trans-material. [ABSTRACT FROM AUTHOR]

When different researchers study the same research question using the same dataset they may obtain different and potentially even conflicting results. This is because there is often substantial flexibility in researchers' analytical choices, an issue also referred to as "researcher degrees of freedom". Combined with selective reporting of the smallest p-value or largest effect, researcher degrees of freedom may lead to an increased rate of false positive and overoptimistic results. In this paper, we address this issue by formalizing the multiplicity of analysis strategies as a multiple testing problem. As the test statistics of different analysis strategies are usually highly dependent, a naive approach such as the Bonferroni correction is inappropriate because it leads to an unacceptable loss of power. Instead, we propose using the "minP" adjustment method, which takes potential test dependencies into account and approximates the underlying null distribution of the minimal p-value through a permutation-based procedure. This procedure is known to achieve more power than simpler approaches while ensuring a weak control of the family-wise error rate. We illustrate our approach for addressing researcher degrees of freedom by applying it to a study on the impact of perioperative p a O 2 on post-operative complications after neurosurgery. A total of 48 analysis strategies are considered and adjusted using the minP procedure. This approach allows to selectively report the result of the analysis strategy yielding the most convincing evidence, while controlling the type 1 error—and thus the risk of publishing false positive results that may not be replicable. [ABSTRACT FROM AUTHOR]

In clinical trials, multiple comparisons arising from various treatments/doses, subgroups, or endpoints are common. Typically, trial teams focus on the comparison showing the largest observed treatment effect, often involving a specific treatment pair and endpoint within a subgroup. These findings frequently lead to follow‐up pivotal studies, many of which do not confirm the initial positive results. Selection bias occurs when the most promising treatment, subgroup, or endpoint is chosen for further development, potentially skewing subsequent investigations. Such bias can be defined as the deviation in the observed treatment effects from the underlying truth. In this article, we propose a general and unified Bayesian framework to address selection bias in clinical trials with multiple comparisons. Our approach does not require a priori specification of a parametric distribution for the prior, offering a more flexible and generalized solution. The proposed method facilitates a more accurate interpretation of clinical trial results by adjusting for such selection bias. Through simulation studies, we compared several methods and demonstrated their superior performance over the normal shrinkage estimator. We recommended the use of Bayesian Model Averaging estimator averaging over Gaussian Mixture Models as the prior distribution based on its performance and flexibility. We applied the method to a multicenter, randomized, double‐blind, placebo‐controlled study investigating the cardiovascular effects of dulaglutide. [ABSTRACT FROM AUTHOR]

In this paper, we studied the existence of multiple normalized solutions to the following Kirchhoff type equation: { − (a ε 2 + b ε ∫ R 3 | ∇ u | 2 d x) Δ u + V (x) u = μ u + f (u) i n R 3 , ∫ R 3 | u | 2 d x = m ε 3 , u ∈ H 1 (R 3) , where a , b , m > 0 , ε is a small positive parameter, V is a nonnegative continuous function, f is a continuous function with L 2 -subcritical growth and μ ∈ R will arise as a Lagrange multiplier. Under the suitable assumptions on V and f , the existence of multiple normalized solutions was obtained by using minimization techniques and the Lusternik-Schnirelmann theory. We pointed out that the number of normalized solutions was related to the topological richness of the set where the potential V attained its minimum value. [ABSTRACT FROM AUTHOR]

In an effort to estimate the number of true nulls in large scale multiplicity problems (the normal means problem), we generalize the current Fourier transform based oracle estimator with a Laplace transform based estimator. Our interest in this problem stems from the application of r-power which requires knowledge of the number of nulls (Dasgupta et al. in Sankhya B 78(1):96–118, 2016). We analytically show that our method is consistent and theoretically has lower mean squared error than the existing competitor (Jin in J R Stat Soc Ser B (Stat Methodol) 70(3):461–493, 2008). We follow up by a numerical example and a simulation study that ratifies our theoretical results. [ABSTRACT FROM AUTHOR]

Let P (x) be a system of polynomials in s variables, where x ∈ C s . If z 0 is an isolated zero of P, then the multiplicity and its structure at z 0 can be revealed by the normal set of the quotient ring R (< P >) or its dual space R * or by certain numerical methods. In his book titled "Numerical Polynomial Algebra", Stetter described the so-called distinguished points, which are embedded in a zero manifold of P, and the author defined their multiplicities. In this note, we will generalize the definition of distinguished points and give a more appropriate definition for their multiplicity, as well as show how to calculate the multiplicity of these points. [ABSTRACT FROM AUTHOR]

A subset S of non-negative integers N o is called a numerical semigroup if it is a submonoid of N o and has a finite complement in N o . An undirected graph G (S) associated with S is a graph having V (G (S)) = { v i : i ∈ N o ∖ S } and E (G (S)) = { v i v j ⇔ i + j ∈ S } . In this article, we propose a conjecture for the clique number of graphs associated with a symmetric family of numerical semigroups of arbitrary multiplicity and embedding dimension. Furthermore, we prove this conjecture for the case of arbitrary multiplicity and embedding dimension 7. [ABSTRACT FROM AUTHOR]

Different stimuli can potentially activate overlapping populations of neurons in the brain. How does the brain maintain information about multiple items? Here, we describe a new theory: neurons might switch back and forth between encoding each item across time. Recent statistical advances have allowed neurophysiology studies to probe for such activity fluctuations, generating support for this theory and opening intriguing new research directions. Many open questions remain, such as the time scale of activity fluctuations, the manner in which they are coordinated across (and read out from) neural ensembles, and the implications for perceptual binding, neural oscillations, and cognitive processes like attention, memory, and thought. Our ability to perceive multiple objects is mysterious. Sensory neurons are broadly tuned, producing potential overlap in the populations of neurons activated by each object in a scene. This overlap raises questions about how distinct information is retained about each item. We present a novel signal switching theory of neural representation, which posits that neural signals may interleave representations of individual items across time. Evidence for this theory comes from new statistical tools that overcome the limitations inherent to standard time-and-trial-pooled assessments of neural signals. Our theory has implications for diverse domains of neuroscience, including attention, figure binding/scene segregation, oscillations, and divisive normalization. The general concept of switching between functions could also lend explanatory power to theories of grounded cognition. [ABSTRACT FROM AUTHOR]

In this paper, we consider the following nonlinear Schrödinger equation with an L 2 -constraint: - Δ u = λ u + μ | u | q - 2 u + | u | p - 2 u in R N , ∫ R N | u | 2 d x = a 2 , u ∈ H 1 (R N) , where N ≥ 3 , a , μ > 0 , 2 < q < 2 + 4 N < p < 2 ∗ , 2 q + 2 N - p N < 0 and λ ∈ R arises as a Lagrange multiplier. We deal with the concave and convex cases of energy functional constraints on the L 2 sphere, and prove the existence of infinitely solutions with positive energy levels. [ABSTRACT FROM AUTHOR]

Let Let Δ be a numerical semigroup. In this work we show that J(Δ) = {I ∪ {0}: I is an ideal of Δ} is a distributive lattice, which in addition is a Frobenius restricted variety. We give an algorithm which allows us to compute the set Ja(Δ) = {S ∈ J(Δ): max(Δ\S) = a} for a given a ∈ Δ. As a consequence, we obtain another algorithm that computes all the elements of J(Δ) with a fixed genus. be a numerical semigroup. In this work we show that J(Δ) = {I ∪ {0}: I is an ideal of Δ} is a distributive lattice, which in addition is a Frobenius restricted variety. We give an algorithm which allows us to compute the set Ja(Δ) = {S ∈ J(Δ): max(Δ\S) = a} for a given a ∈ Δ. As a consequence, we obtain another algorithm that computes all the elements of J(Δ) with a fixed genus. [ABSTRACT FROM AUTHOR]

In this paper we will investigate the existence of multiple normalized solutions to the logarithmic Schrödinger equation given by - ϵ 2 Δ u + V (x) u = λ u + u log u 2 , in R N , ∫ R N | u | 2 d x = a 2 ϵ N , where N ≥ 1 , a , ϵ > 0 , λ ∈ R is an unknown parameter that appears as a Lagrange multiplier and V : R N → (- 1 , + ∞) is a continuous function. Our analysis demonstrates that the number of normalized solutions of the equation is associated with the topology of the set where the potential function V attains its minimum value. To prove the main result, we employ minimization techniques and use the Lusternik-Schnirelmann category. Additionally, we introduce a new function space where the energy functional associated with the problem is of class C 1 . [ABSTRACT FROM AUTHOR]

Copyright of Revista de Filosofía (0185-3481) is the property of Universidad Iberoamericana Cuidad de Mexico 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.)

Copyright of Revista Conatus: Filosofia de Spinoza is the property of Revista Conatus: Filosofia de Spinoza 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.)

Copyright of Annals of Philosophy / Roczniki Filozoficzne is the property of John Paul II Catholic University of Lublin, Faculty of Philosophy 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 assess the quantitative relevance of expectations-driven sovereign debt crises, focusing on the southern European crisis of the early 2010s and the Argentine default of 2001. The source of multiplicity is the one in Calvo (1988). Crucial for multiplicity is an output process characterized by long periods of either high growth or stagnation, which we estimate using data for these countries. We find that expectations-driven debt crises are quantitatively relevant but state dependent, as they occur only during periods of stagnation. Expectations, and how they respond to policy, are the major factors explaining default rates and credit spread differences between Spain and Argentina. [ABSTRACT FROM AUTHOR]

We characterise the numerical semigroups with a monotone Apéry set (MANS-semigroups for short). Moreover, we describe the families of MANS-semigroups when we fix the multiplicity and the ratio. [ABSTRACT FROM AUTHOR]

This paper aims to take a closer critical look at the multiple and multi-layered nature of urban centrality. Centrality is conceptualized here as a kind of prominence, perceived, planned and represented quality within the urban timespace. We employ three distinct ontological categories of the urban centre (centre-as-event, centre-as-thing and centre-as-structure) to take a deeper insight into the symbolism, ideological narratives and planning practices behind the genesis of the prominent urban places and times. With this approach, we expose even the seemingly subtle phenomena that (co-)shape multiple urban centralities. We are empirically focusing on the case of the city of Brno (Czech Republic). Attention is paid in particular to the period of socialism, more specifically to the influence of socialist ideology on the reorganization of urban central places and times. We are trying to overcome the traditional view of centralized and all-encompassing socialist transformation. Instead, the socialist Brno provides the case study to demonstrate a subtle fabric of overlapping, competing or simply coexisting socialist and pre-socialist centralities. We argue that the physical re-centralization of the city was in the end less significant than the efforts to symbolically recode the urban environment. [ABSTRACT FROM AUTHOR]