Affirmative Answer Research Articles

Series expansion, higher-order monotonicity properties and inequalities for the modulus of the GrÖtzsch ring

Abstract For $r\in(0,1)$ , let $\mu \left( r\right) $ be the modulus of the plane Grötzsch ring $\mathbb{B}^2\setminus[0,r]$ , where $\mathbb{B}^2$ is the unit disk. In this paper, we prove that \begin{equation*} \mu \left( r\right) =\ln \frac{4}{r}-\sum_{n=1}^{\infty }\frac{\theta _{n}}{ 2n}r^{2n}, \end{equation*} with $\theta _{n}\in \left( 0,1\right)$ . Employing this series expansion, we obtain several absolutely monotonic and (logarithmically) completely monotonic functions involving $\mu \left( r\right) $ , which yields some new results and extend certain known ones. Moreover, we give an affirmative answer to the conjecture proposed by Alzer and Richards in H. Alzer and K. Richards, On the modulus of the Grötzsch ring, J. Math. Anal. Appl. 432(1): (2015), 134–141, DOI 10.1016/j.jmaa.2015.06.057. As applications, several new sharp bounds and functional inequalities for $\mu \left( r\right) $ are established.

Is ChatGPT Full of Bullshit?

It is undeniable that conversational agents took the world by storm. Chatbots such as ChatGPT (Generative Pre Trained) are used for translations, financial advice, and even as therapists, by millions of users every month. When interacting with technology it’s important to be careful, especially if we do so by using natural language, since our relationship with artificial agents is shaped by the technology’s features and the manufacturer's goal. The paper, organized into three sections, explores the question of whether ChatGPT’s production can be described as ‘bullshit’. In the first section, the focus is on ChatGPT’s architecture and development; in the second a new formulation of the concept of Frankfurt’s ‘bullshit’ is presented, in which its central features of indifference, deception and manipulation are highlighted; in the last section, the title question is tackled, proposing an affirmative answer to it, arguing that ChatGPT can be considered a ‘bullshit’ generator.

$\mathrm{C}^{*}$ -algebras hereditarily containing nonzero, square-zero elements

Abstract We introduce and study the weak Glimm property for $\mathrm{C}^{*}$ -algebras, and also a property we shall call (HS $_0$ ). We show that the properties of being nowhere scattered and residual (HS $_0$ ) are equivalent for any $\mathrm{C}^{*}$ -algebra. Also, for a $\mathrm{C}^{*}$ -algebra with the weak Glimm property, the properties of being purely infinite and weakly purely infinite are equivalent. It follows that for a $\mathrm{C}^{*}$ -algebra with the weak Glimm property such that the absolute value of every nonzero, square-zero, element is properly infinite, the properties of being (weakly, locally) purely infinite, nowhere scattered, residual (HS $_0$ ), residual (HS $_{\text {t}}$ ), and residual (HI) are all equivalent, and are equivalent to the global Glimm property. This gives a partial affirmative answer to the global Glimm problem, as well as certain open questions raised by Kirchberg and Rørdam.

RELEVANCE OF COMPETENCE DEVELOPMENTAND ADVANCED TRAINING PROGRAMMES FOR PHYSICAL THERAPISTS WORKING IN PAEDIATRICS

Physical therapists in Ukraine complete six years of study (4 years of first (bachelor's) degree and 2 years of second (master's) degree) to obtain a speciality and diploma of physical therapist, which involves the acquisition of a number of professional competencies described in the relevant educational standards and curricula. These educational standards and the vast majority of educational programmes contain a minimum amount of paediatric physical therapy component. Therefore, additional training based on the competency-based approach in paediatrics is needed to enable physical therapists to provide effective, qualified services to children. The aim of the study is to substantiate the need to develop a list of competencies to improve the training of physical therapists in Ukraine who will specialise in paediatrics. Materials and methods. The study was conducted by questionnaire survey of physical therapists working in paediatrics from 1 to 14 September 2023. The questionnaire was developed to assess the need for advanced training programmes for physical therapists working in paediatrics, as well as to assess the areas of clinical activity and the level of competencies of specialists. Results. The survey involved 82 physical therapists working in paediatrics. Of the 82 physical therapists, 59 (71.9%) were representatives of public institutions, 13 - private, and 10 respondents did not indicate the type of institution. In 80.4% of physical therapists, the total length of service is equal to the length of service in paediatrics. Only 10.97% of the surveyed physical therapists agree with the statement that university education in Ukraine is sufficient to start an effective practice in paediatrics. 6.10% believe that there are sufficient opportunities for advanced training in paediatric physical therapy in Ukraine, while 21.95% disagree with this statement. The majority of respondents provide services on an outpatient basis, only 25.60% - in acute rehabilitation. Among the proposed areas of physical therapy in paediatrics, most physical therapists work with patients with musculoskeletal disorders (79.26%). The next area in terms of the number of physical therapists working in it is physical therapy in neurology (70.73%). Almost not covered areas in physical therapy for children were assistance in neonatal intensive care (only 8.53% of respondents work in this area) and assistance in intensive care units (only 12.19% gave an affirmative answer to the question about this area). Only 4.87% of respondents work with burns, 7.32% - with amputations, 24.4% - with cardiovascular and respiratory disorders. Few specialists are engaged in physical therapy for such complex conditions as Spina bifida (24.4%), spinal cord injury (21.95%) and traumatic brain injury (24.9%). In addition, 14.63% of the surveyed physical therapists indicated other areas of clinical activity. The total number of educational components in paediatric physical therapy is very low compared to the total number of all disciplines in educational and professional programmes. Conclusions. Practicing physical therapists believe that university education in Ukraine does not sufficiently develop professional competencies for work in paediatrics. It is advisable to form the competencies of a physical therapist in paediatrics, which would be the basis for improving university curricula, educational components and the development of postgraduate training programmes.

Haagerup and Størmer's conjecture on pointwise inner automorphisms

In 1988, Haagerup and Størmer conjectured that every pointwise inner automorphism of a type ${\rm III_1}$ factor is a composition of an inner and a modular automorphism. We study this conjecture and prove that every type ${\rm III_1}$ factor with trivial bicentralizer indeed satisfies this condition. In particular, this shows that Haagerup and Størmer's conjecture holds in full generality if Connes’ bicentralizer problem has an affirmative answer. Our proof is based on Popa's intertwining theory and Marrakchi's recent work on relative bicentralizers.

Time-periodic traveling waves and propagating terraces for multistable equations with a fractional Laplacian: An abstract dynamical systems approach

This paper is devoted to studying the existence of traveling wave solutions for reaction-diffusion equations with fractional Laplacians in time-periodic environments. By developing a dynamical systems approach, we establish the existence of propagating terraces for equations with multistable nonlinearities, which consequently implies the existence of bistable traveling waves. Furthermore, we investigate whether traveling waves exist in the multistable case. We provide an affirmative answer to this question for a special type of nonlinearity in high-frequency oscillating environments, and determine the homogenized limit of the traveling waves as the period approaches 0.

Better stopping through cross validation in an iterative ensemble smoother: A perspective from supervised machine learning

Iterative ensemble smoothers (IES) are among the popular reservoir data assimilation (RDA) algorithms for reservoir characterization. The actual deployment of an IES algorithm requires implementing certain stopping criteria, normally adopted for runtime control (e.g., by stopping the IES when it reaches the maximum number of iterations) and/or safeguarding the RDA performance (e.g., by preventing the simulated data from overfitting the actual observations). In practice, for various reasons, it is often challenging for existing stopping criteria to simultaneously achieve both purposes. One noticeable issue, as illustrated in this work, is that in many situations, the qualities of the estimated reservoir models may already start to deteriorate before a conventional stopping criterion activates to terminate the iteration process. Following this observation, one practically important question arises: Is it possible to further improve the efficacy of the IES algorithm by designing a different stopping criterion so that the IES can stop earlier, saving computational costs while achieving better RDA performance?As one of the rare attempts in the community, this work aims to investigate the use of a new IES stopping criterion that has the potential to provide an affirmative answer to the above question. In this regard, our main idea is based on the concept of cross validation (CV), routinely adopted in supervised machine learning (SML) problems for early stopping to prevent SML models from overfitting the training data. Despite the noticed similarities between RDA and SML problems, some fundamental differences exist, making it fail to work well if one directly extends a vanilla CV procedure from SML to RDA. To tackle this identified challenge, we design an efficient CV procedure tailored for RDA problems, and inspect the performance of an IES algorithm equipped with this CV procedure (IES-CV) in both synthetic and real field case studies. Our numerical investigation indicates that the IES-CV algorithm achieves promising RDA performance in all case studies, confirming the possibility that with the aid of a proper stopping criterion, an IES algorithm can terminate at an appropriate iteration step with near-optimal RDA performance. Beyond these numerical findings, it is also our hope that the current work may help improve the best practices of applying IES to RDA problems, taking advantage of the effective, CV-based stopping criterion.

Green supply chain management and sustainable performance: exploring the role of circular economy capability and green ambidexterity innovation

PurposeThe present research aims to analyze the influence of Green Supply Chain Management (GSCM) on the Sustainable Performance (SP) of Spanish wineries, examining the intermediary roles of Circular Economy Capability (CEC) and Green Ambidexterity Innovation (GAI) within this primary relationship. In particular, the study seeks to answer the following Research Questions (RQs): (RQ1), does GSCM exert a positive impact on wineries’ SP? (RQ2), does CEC play a mediating role in the interconnection between GSCM and wineries’ SP? And (RQ3), does GAI function as a mediator in the interplay between GSCM and wineries’ SP?Design/methodology/approachThe research utilizes Partial Least Squares Structural Equation Modeling (PLS-SEM) to evaluate the hypothesized theoretical model using primary data collected from 196 Spanish wineries from September 2022 to January 2023.FindingsThe results reveal a positive relationship between GSCM and SP in Spanish wineries, as well as the existence of positive partial mediations of CEC and GAI in this main linkage, which allows an affirmative answer to the three RQs formulated.Originality/valueDistinguished by its innovative exploration, this research marks a pioneering effort in the uncharted field of scrutinizing CEC and GAI as mediating factors in the GSCM-SP nexus, thereby enriching the existing body of knowledge and opening new avenues for future academic research on sustainability in the wine industry.

C-symmetric Toeplitz operators on Hardy spaces

We characterize all the Toeplitz operators that are complex symmetric with respect to a class of conjugations induced by a permutation. Our results provide an affirmative answer to a conjecture from a paper of Chattopadhyay et al. (2023) [1].

Classification of Solutions to the Anisotropic N-Liouville Equation in ℝN

Abstract Given $N\geq 2$, we completely classify solutions to the anisotropic $N$-Liouville equation $$ \begin{align*} &-\Delta_N^H\,u=e^u \quad\textrm{in}\ \mathbb{R}^N,\end{align*} $$ under the finite mass condition $\int _{\mathbb{R}^{N}} e^{u}\,dx<+\infty $. Here $\Delta _{N}^{H}$ is the so-called Finsler $N$-Laplacian induced by a positively homogeneous function $H$. As a consequence in the planar case $N=2$, we give an affirmative answer to a conjecture made in [ 53].

Dynamics and bifurcations in a model of chronic myeloid leukemia with optimal immune response windows.

Chronic Myeloid Leukemia is a blood cancer for which standard therapy with Tyrosine-Kinase Inhibitors is successful in the majority of patients. After discontinuation of treatment half of the well-responding patients either present undetectable levels of tumor cells for a long time or exhibit sustained fluctuations of tumor load oscillating at very low levels. Motivated by the consequent question of whether the observed kinetics reflect periodic oscillations emerging from tumor-immune interactions, in this work, we analyze a system of ordinary differential equations describing the immune response to CML where both the functional response against leukemia and the immune recruitment exhibit optimal activation windows. Besides investigating the stability of the equilibrium points, we provide rigorous proofs that the model exhibits at least two types of bifurcations: a transcritical bifurcation around the tumor-free equilibrium point and a Hopf bifurcation around a biologically plausible equilibrium point, providing an affirmative answer to our initial question. Focusing our attention on the Hopf bifurcation, we examine the emergence of limit cycles and analyze their stability through the calculation of Lyapunov coefficients. Then we illustrate our theoretical results with numerical simulations based on clinically relevant parameters. Besides the mathematical interest, our results suggest that the fluctuating levels of low tumor load observed in CML patients may be a consequence of periodic orbits arising from predator-prey-like interactions.

Carbon Taxes and CO2 Emissions: A Replication of Andersson (American Economic Journal: Economic Policy, 2019)

Abstract Do carbon taxes reduce CO2 emissions in the countries that adopt it? Andersson (2019. Carbon taxes and CO2 emissions: Sweden as a case study. American Economic Journal: Economic Policy, 11(4), 1–30) provides a clear, affirmative answer. His article has been widely cited as evidence that carbon taxes “work.” To check whether the estimates from Andersson (2019) are reliable, I replicate his article using its publicly available data and codes. I modify his synthetic control method (SCM) by using a more restricted set of control units (excluding one potentially treated unit). I also use a more efficient methodology, the Prais-Winsten estimator, to estimate price effects on gasoline consumption. In addition, I compute prediction intervals (PIs) and add these to the SCM estimates, using the newly developed scpi R package. My best estimate is that carbon taxes reduced per-capita CO2 emissions in Sweden’s transport sector by 7.7%, confirming Andersson’s main finding. I then extend Andersson’s approach to the Norwegian transport sector, estimating a smaller reduction of 2.4%. However, this effect falls within the PIs of the estimates assuming no carbon taxes. When I extend the analysis to the national level in Sweden, I estimate wide PIs and obtain inconclusive results.

Well-posedness of nonautonomous abstract Cauchy problems under dissipativity conditions expressed by metric-like functionals

Under a dissipativity condition expressed by a metric-like functional, the well-posedness of a nonautonomous abstract Cauchy problem is established. The main result not only extends Martin's result on the generation of an evolution operator in a class of uniformly convex Banach spaces but also can be applied to mixed problems for nonautonomous evolution equations of Kirchhoff type with which Kato's quasilinear theory or the theory of quasi-contractive semigroups cannot directly deal. The main result also gives an affirmative answer to Kōmura's conjecture that an evolution operator of linear operators with moving domains can be generated even under a weak stability condition rather than Kato's stability condition, and the result provides an effective means for solving degenerate wave equations.

Survival Probability, Particle Imbalance, and Their Relationship in Quadratic Models.

We argue that the dynamics of particle imbalance in quadratic fermionic models is, for the majority of initial many-body product states in the site occupation basis, virtually indistinguishable from the dynamics of survival probabilities of single-particle states. We then generalize our statement to a similar relationship between the non-equal time and space density correlation functions in many-body states, and the transition probabilities of single-particle states at nonzero distances. Finally, we study the equal-time connected density-density correlation functions in many-body states, which exhibit certain qualitative analogies with the survival and transition probabilities of single-particle states. Our results are numerically tested for two paradigmatic models of single-particle localization: the 3D Anderson model and the 1D Aubry-André model. This work gives an affirmative answer to the question of whether it is possible to measure features of single-particle survival and transition probabilities by the dynamics of observables in many-body states.

The effect of PV generation's hourly variations on Israel's solar investment

Limited by sunniness and conversion efficiency, one installed MW of photovoltaic (PV) capacity can only produce ωt MWh of electricity in daytime hour t, where ωt = positive fraction that we call PV's hourly effective capacity (HEC). Based on a sample of commercially operating PV plants in Israel, HEC rises throughout the 08:00–11:00 period, peaks in the 11:00–14:00 period and then declines in the 14:00–18:00 period. Further, HEC values in spring and summer exceed those in autumn and winter, thus motivating our research question: do HEC variations by hour and season adversely affect the plans for and assessment of PV investment in Israel? An affirmative answer would cause concerns regarding Israel's announced policy of relying on increasing market penetration of PV generation transitionally supported by merchant natural-gas-fired generation (NG) to achieve a low-carbon electricity future. Hence, we propose a two-stage model of Israel's forthcoming Cournot wholesale electricity market with independent power producers (IPPs) operating PV and NG power plants. By comparing the model's solutions under alternative HEC scenarios, we find that the level of detail in modelling the HEC variations by hour and season does not materially affect the optimal PV and NG investments, thus lending support to the use of relatively simple models with only two daily non-seasonal HEC values to assess Israel's announced policy of deep decarbonization. Our methodology is general and real-world relevant because it can be readily adapted for applications in other regions with ample sunshine and wholesale electricity market competition (e.g., California, Texas and Australia).

Full Souslin trees at small cardinals

AbstractA ‐tree is full if each of its limit levels omits no more than one potential branch. Kunen asked whether a full ‐Souslin tree may consistently exist. Shelah gave an affirmative answer of height a strong limit Mahlo cardinal . Here, it is shown that these trees may consistently exist at small cardinals. Indeed, there can be many full ‐trees such that the product of any countably many of them is an ‐Souslin tree.

Weighted maximal regularity estimates of higher order elliptic systems on Lipschitz domains

For the homogeneous biharmonic equation Δ2u=0 in Ω with boundary data in WAk(∂Ω,ωσdS), the Banach space of the kth order Whitney Arrays on ∂Ω, we investigate values for σ in the power weightωσ=|z|σforσ>1−d such that the weighted L2 Dirichlet or regularity problem is solvable. Specifically, we show that there exists α>0 such that the Dirichlet and regularity problems are uniquely solvable for−min⁡(2+α,d−1)<σ<α, and−α<σ<2+α respectively. This gives a partially affirmative answer to a question posed by Shen (2005) [15].

The State of Nationalism (SoN): Nationalism and International Conflict

Does nationalism increase the probability of international conflict? An affirmative answer has intuitive appeal: Nationalists promote force to protect their land and people from foreign threats. Research on nationalism in international conflict implicates elites, masses, and political interactions between these actors when asserting its status as a powerful force that raises the risk for interstate wars. Yet both micro- and macro-level evidence cautions against drawing broad conclusions about how nationalism affects conflict. Nationalism sometimes prompts aggression. In other contexts, nationalism produces restraint. Systematic knowledge about how nationalism relates to international conflict therefore requires answers to questions about which nationalisms promote conflict and whose nationalism matters. This article first reviews theory and evidence about nationalism’s conflict-causing potential. We discuss the microfoundations that link nationalism to foreign policy attitudes before describing research that implicates nationalism as a cause of militarized conflict. Next, we argue that understanding the complex relationships between nationalism and conflict requires theorizing the causal processes that connect various stakeholders’ nationalism to foreign policy outcomes. Moreover, research on identity content suggests that nationalism is compatible with a variety of foreign policy preferences. Throughout, we centre research that features nationalism as a principal independent variable or causal mechanism precipitating conflict. Any review about nationalism must contend with the delicate matter of conceptualization — the field contains nearly as many definitions for nationalism as articles about nationalism and war. The research we discuss variously describes nationalism as an identity, ideology, or belief, for example. For our purposes, nationalism captures a set of sentiments related to a national group and its superiority. This broad perspective centers the phenomenon implicated in international conflict research.

Non-fungible tokens, tokenization, and ownership

The emergence of non-fungible tokens (NFTs) in the blockchain environment has prompted many intriguing questions for private law scholars around the world. A question as basic as whether NFTs can be owned has proven difficult in many countries. This is the first research question of our article, which focuses on NFTs created in the Ethereum system by utilizing standard ERC-721. Because these NFTs are identifiable and distinguishable from all other tokens, the notion of owning an NFT is not unthinkable. Yet no universal answer can be offered. Whether NFTs qualify as objects of ownership must be studied at the level of individual legal systems. We argue that NFTs can be owned under Finnish law, with the same probably applying to many other legal systems. Starting with this notion, we pose two further research questions. As the second research question, we ask what problems of a patrimonial law nature may arise in attempts to connect different kinds of rights, even irrevocably, to owning or holding an NFT. Creditor rights seem relatively easy in this respect because most legal systems allow prospective debtors to obligate themselves as they wish. We also study whether a limited liability company could issue an NFT as a share certificate with legal effects corresponding to those of a physical (paper) share certificate. While an affirmative answer could be justified in some legal systems, Finnish law makes it difficult to tokenize a company's shares other than in the framework of a settlement system within the meaning of the European Union's DLT Pilot Regulation. Even greater difficulties arise in attempts to connect the ownership of a (material) thing and of an NFT so that a person who owns a token also owns the thing. Our third and final research question addresses tokenization of digital art, which gives rise to some special questions. We ask what rights the transferee of an NFT can receive in connection with tokenization of digital art. Here, our main finding is that digital art can be meaningfully tokenized even though digital copies are not regarded as possible objects of ownership.

On the maximum local mean order of sub‐k $k$‐trees of a k $k$‐tree

AbstractFor a ‐tree , a generalization of a tree, the local mean order of sub‐‐trees of is the average order of sub‐‐trees of containing a given ‐clique. The problem whether the maximum local mean order of a tree (i.e., a 1‐tree) at a vertex is always taken on at a leaf was asked by Jamison in 1984 and was answered by Wagner and Wang in 2016. Actually, they proved that the maximum local mean order of a tree at a vertex occurs either at a leaf or at a vertex of degree 2. In 2018, Stephens and Oellermann asked a similar problem: for any ‐tree , does the maximum local mean order of sub‐‐trees containing a given ‐clique occur at a ‐clique that is not a major ‐clique of ? In this paper, we give it an affirmative answer.