Continuous Extension Research Articles

Manhattan geodesics and the boundary of the space of metric structures on hyperbolic groups

For any non-elementary hyperbolic group \Gamma , we find an outer automorphism invariant geodesic bicombing for the space of pseudometric structures on \Gamma equipped with a symmetrized version of the Thurston metric on Teichmüller space. We construct and study a boundary for this space and show that it contains many well-known pseudometrics. As corollaries we obtain results regarding continuous extensions of translation length functions to the space of geodesic currents and settle a conjecture of Bonahon in the negative.

Determination of the elemental composition and changes in thermal and electrical conductivity of “Hanford” and low-ash medium-grained graphite’s grade graphites depending on the fast neutrons fluence

Studying the properties of graphite recovered from operating nuclear reactors is vital for predicting the properties and integrity of graphite as part of assessing the continued operation and life extension of nuclear reactors. The purpose of the study is to determine the electrical conductivity and thermal conductivity of low-ash medium-grained graphite’s grade graphite in the thermal column masonry of the VVR-SM research reactor in the measurement temperature range corresponding to the conditions of normal operation of the reactor to determine the service life. In this work, the change in thermal conductivity and electrical conductivity of GMZ graphite was studied, as well as for comparison of Hanford grade graphite depending on the fluence of fast neutrons and the measurement temperature. The dependence of electrical conductivity and thermal conductivity on dose and temperature has been established. It has been shown that the greater the neutron fluence, the more both the thermal conductivity and electrical conductivity of the material decreases. The service life of the thermal column has been determined.

South Tibetan Detachment System (STDS), NW Himalaya: A possible Cambro–Ordovician tectonic terrane boundary, and its Cenozoic remobilization

The South Tibetan Detachment System is an important extensional fault zone, separating the Greater Himalayan Sequence from the overlying Tethyan Himalayan Sequence, and is well exposed in the upper reaches of the Dhauliganga valley, NW Himalaya. This fault system is characterized by the occurrence of an extensive Cambro–Ordovician granite belt between Sutlej and Dhauliganga valleys, although only a few small granitoids intrude the high-grade mylonite gneiss of the Greater Himalayan Sequence in its immediate footwall. These bodies yielded U-Pb zircon crystallization ages between 498.92 ± 5.5 Ma and 486.54 ± 2.3 Ma. This work postulates that the South Tibetan Detachment System evolved as a major proto-tectonic marginal extensional terrane boundary during the Cambro–Ordovician Kurgiakh/Bhimphedian Orogeny, when it was the conduit for emplacement of the Cambro–Ordovician granite belt. Denudation of the Neoproterozoic Greater Himalayan Sequence and the Paleozoic granites on its footwall provided approximately ∼ 10 km thick sediments into the Tethyan Basin due to this fault system as a master growth fault. Reactivation of this fault system controlled further melting and emplacement of the Higher Himalayan Leucogranite belt during the Cenozoic. Zircon growth is observed in two distinct modes: pulsative from the Late Eocene to Early Oligocene, with peaks at 33.99 ± 1.07 Ma, 30.53 ± 0.32 Ma and 25.03 ± 0.54 Ma; and in the continuous mode from 23.68 ± 0.94 Ma to 13.30 ± 0.30 Ma, in the Miocene, for nearly 10.0 myr. These datasets reveal some of the oldest pulsative movements in the Late Eocene–Early Oligocene during crustal thickening, thrusting and associated metamorphism, followed by continuous extension during the Miocene. Data from the South Tibetan Detachment System are distinct in character, and do not support either its eastwards younging or diachronous movements along the Dhauliganga valley.

Continuous extension of the discrete shift translations on one-dimensional quantum lattice systems

We study the continuous extension of discrete shift translations on one-dimensional quantum lattice systems. We explore a specific example provided by a quasi-free C ∗ {C}^{\ast } -flow on the one-dimensional fermion lattice system, comparing it with its original discrete shift-translations. Specifically, we demonstrate its explicit dynamical formula, which reveals violations of causality and locality. Furthermore, we prove that this quasi-free C ∗ {C}^{\ast } -flow on the one-dimensional fermion lattice system cannot be extended to the one-dimensional quantum spin lattice system via the Jordan-Wigner transformation.

Fine boundary regularity for the singular fractional p-Laplacian

We study the boundary weighted regularity of weak solutions u to a s-fractional p-Laplacian equation in a bounded C1,1 domain Ω with bounded reaction and nonlocal Dirichlet type boundary condition, with s∈(0,1). We prove optimal up-to-the-boundary regularity of u, which is Cs(Ω‾) for any p>1 and, in the singular case p∈(1,2), that u/dΩs has a Hölder continuous extension to the closure of Ω, dΩ(x) meaning the distance of x from the complement of Ω. This last result is the singular counterpart of the one in [30], where the degenerate case p⩾2 is considered.

A review of the trajectory planning of Industrial robots

With the continuous extension of the application scenarios of industrial robots, industrial robots have made great contributions to increase productivity and automation in the industrial field. And trajectory planning of industrial robots is the key link for its successful completion of tasks. In order to deeply analyze the mechanism of trajectory planning of industrial robots, this paper firstly introduces the principle of trajectory optimization. And then it reviews the relevant theories and methods of trajectory planning. Finally, it summarizes the development trend of trajectory planning of industrial robots.

Organized sports and recreation activities for persons deprived of liberty (PDL): A comprehensive survey-analysis for continuous extension program provision and reintegration

Organized sports and recreation activities for persons deprived of liberty (PDL): A comprehensive survey-analysis for continuous extension program provision and reintegration

Simulation-based data reduction and data processing for sheet metal forming in the hybrid twin framework

In sheet metal forming, the interaction between virtual models and the real world remains challenging. Process simulations can exhibit significant errors, and reliable measurements are often scarce during early production stages. This study presents a hybrid twin framework that systematically unifies computer-aided design, simulation, and measurement data in an adaptive manner. Central to this framework is a reverse engineering algorithm that reconstructs and transforms the geometry of deep-drawn components from optical scan data into B-spline surfaces. The algorithm demonstrated high precision, indicating its suitability for process control and geometric analysis. The hybrid twin framework integrates virtual data from simulations and real-world data, as evidenced by a sensor concept for inline surface measurement. The framework ensures robust and redundant measurement concepts by estimating complete geometries from a few systematically preselected measuring points. This adaptive approach permits continuous updates and extensions to the database, accommodating both sparse inline signals and offline inspection data. This framework provides a conceptual model for integrating direct feedback interactions between virtual and physical environments, thereby enhancing the precision of analytical and predictive models in sheet metal forming processes.

Faculty of Pharmacy Shares Experience Transitioning from Traditional Lab Practicals to Objective Structured Pharmacy Assessment (OSPA)

The Faculty of Pharmacy revamped its curriculum for the Bachelor of Pharmacy (Honours) 2019 cohort due to the Covid-19 pandemic. The Nutraceutical (PHC560) course transitioned its hands-on tablet formulation practical to a virtual format with recorded demonstrations. The third cohort's reassessment led to redesigning the lab component into an Objective Structured Pharmacy Assessment (OSPA), focusing on Ethics, Regulatory Aspects, Quality Assurance, and Case Study with Role Play. Positive outcomes have sparked optimism for continued OSPA implementation and potential extension to other courses.

On Bivariate Distributions with Singular Part

There are many families of bivariate distributions with given marginals. Most families, such as the Farlie–Gumbel–Morgenstern (FGM) and the Ali–Mikhail–Haq (AMH), are absolutely continuous, with an ordinary probability density. In contrast, there are few families with a singular part or a positive mass on a curve. We define a general condition useful to detect the singular part of a distribution. By continuous extension of the bivariate diagonal expansion, we define and study a wide family containing these singular distributions, obtain the probability density, and find the canonical correlations and functions. The set of canonical correlations is described by a continuous function rather than a countable sequence. An application to statistical inference is given.

On prime end distortion estimates of mappings with the Poletsky condition in domains with the Poincar´e inequality

This article is devoted to the study of mappings with bounded andfinite distortion defined in some domain of the Euclidean space. Weconsider mappings that satisfy some upper estimates for thedistortion of the modulus of families of paths, where the order ofthe modulus equals to $p,$ $n-1<p\leqslant n.$ The main problemstudied in the manuscript is the investigation of the boundarybehavior of such mappings, more precisely, the distortion of thedistance under mappings near boundary points. The publication isprimarily devoted to definition domains with ``bad boundaries'', inwhich the mappings not even have a continuous extension to theboundary in the Euclidean sense. However, we introduce the conceptof a quasiconformal regular domain in which the specified continuousextension is valid and the corresponding distance distortionestimates are satisfied; however, both must be understood in thesense of the so-called prime ends. More precisely, such estimateshold in the case when the mapping acts from a quasiconformal regulardomain to an Ahlfors regular domain with the Poincar\'e inequality.The consideration of domains that are Ahlfors regular and satisfythe Poincar\'e inequality is due to the fact that, lower estimates forthe modulus of families of paths through the diameter of thecorresponding sets hold in these domains. (There are the so-calledLoewner-type estimates). We consider homeomorphisms and mappingswith branching separately. The main analytical condition under whichthe results of the paper were obtained is the finiteness of theintegral averages of some majorant involved in the defining modulusinequality under infinitesimal balls. This condition includes thesituation of quasiconformal and quasiregular mappings, because forthem the specified majorant is itself bounded in a definitiondomain. Also, the results of the article are valid for more generalclasses for which Poletsky-type upper moduli inequalities aresatisfied, for example, for mappings with finite length distortion.

Advancing estimation techniques and their applications in engineering and medical data analysis through novel continuous and discrete linear failure rate distribution extension

In this paper, we present a new heavy-tailed distribution called the heavy-tailed linear failure rate (HTLFR) distribution. Various statistical properties of the proposed distribution are derived, including the quantile function, the median, the ordinary moments, the moment generating function, the incomplete moments and the conditional moments. Some actuarial measures such as value at risk, expected shortfall, tail value at risk, tail variance and tail variance premium are calculated. Three different methods of estimation such as the maximum likelihood method, the maximum product spacing method and the Bayesian method as well as some simulation results for the model parameters of the HTLFR distribution under complete samples are examined. The results of the real data set show that the proposed distribution has greater flexibility and has been empirically evaluated under complete data. Discrimination analysis was employed to ensure fairness, equity, and accuracy in decision-making processes for selecting the best model, comparing the proposed distribution with known distributions. A discrete analog of the HTLFR distribution is proposed.

Improvements to the Blade Element Momentum Formulation of OpenFAST for Skewed Inflows

In this work, we modify the blade element momentum algorithm of OpenFAST to improve its predictions under large skewed inflow conditions. We use the well-known Glauert’s skew correction and introduce continuous extension of the model for high-thrust conditions. We present the rationale behind Glauert’s empirical model and discuss the different conventions possible for the axial induction factor. We verify the model against the higher-fidelity lifting-line vortex method and blade-resolved computational fluid dynamics, and we observe that the new implementation enhances the accuracy and reliability of OpenFAST’s aerodynamic modeling capabilities in conditions involving large skew angles. For the parametric studies run using the different codes, we find that the power changes with the skew angle as cos1.7(θ skew) and the thrust as cos0.65(θ skew). An analysis of the azimuthal variation of the induced velocities in the rotor plane reveals that current redistribution models used in blade element momentum codes may need to be refined.

The factors contributing to better workplaces for farmers on pasture-based dairy farms

Herd size expansion, combined with the reduced availability of people to work on farms, has led to an increased focus on techniques that can improve dairy farm social sustainability. Effective work organization is one such entity, which could influence farm social sustainability; focusing on having a productive, flexible and standardized farm workload. The objective of this study was to examine the factors that contribute to better workplaces for the farmer using a survey of representative pasture-based dairy farms in Ireland. Potential contributing factors to better workplaces for farmers were identified, namely; farm and farmer characteristics, working day structure, farmer attitudes, farm facilities, labor efficient practices and human resource management practices. A survey was completed by 313 Irish dairy farmers between 20 November and 3 January 2019 to capture relevant information. One proxy indicator was selected to represent each of productivity, flexibility and standardization within the workplace, and each of the 313 farms were categorized into quartiles based on their ranking for these 3 indicators (1 = most effective quartile to 4 = least effective quartile). The average farmer that completed the survey was 51 years old, milked 125 cows, reported to work 69.6 h/ week, take 10.3 d of holidays/ year and had a finish time of 19:52 in spring. The quartile of farms with the most effective farmer workplace reported reduced hours worked per week (58.6 v 82.6 h per week), more holiday days (16.6 v 5.1 d) and weekends off (8.3 v 2.4) per year, and earlier finish times (18:41 v 21:14 in spring) compared with the least effective quartile. Similarly, the most effective farms reported better facilities, and greater implementation of labor efficient and human resource management practices compared with the least effective farms. The most effective quartile for farmer workplace effectiveness were more positive about the industry's potential to offer an effective work-life balance, would be more likely to encourage young people to pursue careers in dairy, and had more positive attitudes toward attracting and retaining workers compared with the least effective quartile. The study highlighted the range of factors contributing to more effective workplaces for farmers, indicating scope for improvement on many farms, and challenges across all farms when compared with other industries in the case of some indicators (e.g., time-off). The results can support the continued extension of concepts regarding work organization to assist farms in alleviating social sustainability challenges; highlighting the differentiating factors between the most and least effective farmer workplaces.

Extension of unbounded uniformly continuous functions and pseudometrics

In this paper we aim to characterize uniformly continuous real functions and pseudometrics on metric spaces, having uniformly continuous extension. For functions we use a very similar approach as McShane in [7] using moduli of continuity. By doing that we obtain an explicit formula for the extension. We also show that our characterization for functions is equivalent to one proposed in [8] for uniform spaces. We then show that a similar approach can be done for uniformly continuous pseudometrics.To do so we use the notion of chainable metric spaces and intrinsic metrics defined in [9]. A somewhat similar approach has been studied in [6] for normed linear spaces.

Principle of Information Increase: An Operational Perspective on Information Gain in the Foundations of Quantum Theory

A measurement performed on a quantum system is an act of gaining information about its state. However, in the foundations of quantum theory, the concept of information is multiply defined, particularly in the area of quantum reconstruction, and its conceptual foundations remain surprisingly under-explored. In this paper, we investigate the gain of information in quantum measurements from an operational viewpoint in the special case of a two-outcome probabilistic source. We show that the continuous extension of the Shannon entropy naturally admits two distinct measures of information gain, differential information gain and relative information gain, and that these have radically different characteristics. In particular, while differential information gain can increase or decrease as additional data are acquired, relative information gain consistently grows and, moreover, exhibits asymptotic indifference to the data or choice of Bayesian prior. In order to make a principled choice between these measures, we articulate a Principle of Information Increase, which incorporates a proposal due to Summhammer that more data from measurements leads to more knowledge about the system, and also takes into consideration black swan events. This principle favours differential information gain as the more relevant metric and guides the selection of priors for these information measures. Finally, we show that, of the symmetric beta distribution priors, the Jeffreys binomial prior is the prior that ensures maximal robustness of information gain for the particular data sequence obtained in a run of experiments.

On the Equicontinuity of Generalized Quasiconformal Mappings by Prime Ends

We study mappings satisfying the inverse Poletsky type inequality with respect to a non-conformal modulus. It was prove that such mappings, with some additional conditions, have a continuous extension to the boundary in terms of prime ends and form equicontinuous families of mappings.

Local continuous extension of proper holomorphic maps: Low-regularity and infinite-type boundaries

We prove a couple of results on local continuous extension of proper holomorphic maps F:D→Ω, D,Ω⊊Cn, making local assumptions on ∂D and ∂Ω. The first result allows us to have much lower regularity, for the patches of ∂D,∂Ω that are relevant, than in earlier results. The second result (and a result closely related to it) is in the spirit of a result by Forstnerič–Rosay. However, our assumptions allow ∂Ω to contain boundary points of infinite type.

Assessing hydrothermal changes in the upper Yellow River Basin amidst permafrost degradation

Since the 20th century, the temperature on the Qinghai–Tibetan Plateau (QTP) has increased at a rate of 2–3 times that of global warming. Consequently, the soil temperature and active layer thickness have also increased, which have directly caused severe degradation of the frozen ground on the QTP. Using a hydrological model driven by climate and vegetation forcing, the spatial and temporal changes in the hydrothermal characteristics of the Upper Yellow River Basin (UYRB) from 1960 to 2019 were modeled and the mechanism of the changes was analyzed. During the past six decades, the soil temperature in the UYRB exhibited an increasing trend. The degradation of permafrost in the UYRB was accompanied by thickening of the active layer, a reduction of the maximum depth of the seasonal frost penetration, and continuous extension of the basin thawing time. This degradation was also associated with the increase in the soil moisture content and decrease in the soil ice content, resulting in degradation of the permafrost area by one-tenth of the total area in the UYRB. The reduction of the permafrost area and the thickening of the active layer can profoundly impact hydrological processes and ecosystems. These findings play a critical role in designing efficient strategies to manage and protect frozen ground and serve as a valuable reference for understanding the consequences of frozen ground degradation globally.

Dissipative scaling of development and aging in multicellular organisms

Evolution, self-replication and ontogenesis are highly dynamic, irreversible and self-organizing processes dissipating energy. While progress has been made to decipher the role of thermodynamics in cellular fission, it is not yet clear how entropic balances shape organism growth and aging. This paper derives a general dissipation theory for the life history of organisms. It implies a self-regulated energy dissipation facilitating exponential growth within a hierarchical and entropy lowering self-organization. The theory predicts ceilings in energy expenditures imposed by geometric constrains, which promote thermal optimality during development, and a dissipative scaling across organisms consistent with ecological scaling laws combining isometric and allometric terms. The theory also illustrates how growing organisms can tolerate damage through continuous extension and production of new dissipative structures low in entropy. However, when organisms reduce their rate of cell division and reach a steady adult state, they become thermodynamically unstable, increase internal entropy by accumulating damage, and age.