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Point-of-care tests (POCTs) have become technological solutions for many global health challenges. This meta-ethnography examines what has been learned about the 'social lives' of POCTs from in-depth qualitative research, highlighting key social considerations for policymakers, funders, developers and users in the design, development and deployment of POCTs. We screened qualitative research examining POCTs in low- and middle-income countries and selected 13 papers for synthesis. The findings illuminate five value-based logics—technological autonomy, care, scalability, rapidity and certainty—shaping global health innovation ecosystems and their entanglement with health systems. Our meta-ethnography suggests that POCTs never achieve the technological autonomy often anticipated during design and development processes. Instead, they are both embedded in and constitutive of the dynamic relationships that make up health systems in practice. POCTs are often imagined as caring commodities; however, in use, notions of care inscribed in these devices are constantly negotiated and transformed in relation to multiple understandings of care. POCTs promise to standardize care across scale, yet our analysis indicates nonstandard processes, diagnoses and treatment pathways as essential to 'fluid technologies' rather than dangerous aberrations. The rapidity of POCTs is constructed and negotiated within multiple distinct temporal registers, and POCTs operate as temporal objects that can either speed up or slow down experiences of diagnosis and innovation. Finally, while often valued as epistemic tools that can dispel diagnostic uncertainty, these papers demonstrate that POCTs contribute to new forms of uncertainty. Together, these papers point to knowledge practices as multiple, and POCTs as contributing to, rather than reducing, this multiplicity. The values embedded in POCTs are fluid and contested, with important implications for the kind of care these tools can deliver. These findings can contribute to more reflexive approaches to global health innovation, which take into account limitations of established global health logics, and recognize the socio-technical complexity of health systems. [ABSTRACT FROM AUTHOR]

Flexible systems are linear systems of inclusions in which the elements of the coefficient matrix are external numbers in the sense of nonstandard analysis. External numbers represent real numbers with small, individual error terms. Using Gaussian elimination, a flexible system can be put into a row-echelon form with increasing error terms on the right-hand side. Then parameters are assigned to the error terms and the resulting system is solved by common methods of linear algebra. The solution set may have indeterminacy not only in terms of linear spaces, but also of modules. We determine maximal robustness for flexible systems. [ABSTRACT FROM AUTHOR]

Einsteinian gravity, of which Newtonian gravity is a part, is fraught with the problem of singularity that has been established as a theorem by Hawking and Penrose. The hypothesis that founds the basis of both Einsteinian and Newtonian theories of gravity is that bodies with unequal magnitudes of masses fall with the same acceleration under the gravity of a source object. Since, the Einstein's equations is one of the assumptions that underlies the proof of the singularity theorem, therefore, the above hypothesis is implicitly one of the founding pillars of the same. In this work, I demonstrate how one can possibly write a non-singular theory of gravity which manifests that the above mentioned hypothesis is only valid in an approximate sense in the "large distance" scenario. To mention a specific instance, under the gravity of the earth, a 5 kg and a 500 kg fall with accelerations which differ by approximately 113.148 × 10 - 32 meter/sec 2 and the more massive object falls with less acceleration. Further, I demonstrate why the concept of gravitational field is not definable in the "small distance" regime which automatically justifies why the Einstein's and Newton's theories fail to provide any "small distance" analysis. In course of writing down this theory, I demonstrate why the continuum hypothesis as spelled out by Goedel, is undecidable. The theory has several aspects which provide the following realizations: (i) Descartes' self-skepticism concerning exact representation of numbers by drawing lines (ii) Born's wish of taking into account "natural uncertainty in all observations" while describing "a physical situation" by means of "real numbers" (iii) Klein's vision of having "a fusion of arithmetic and geometry" where "a point is replaced by a small spot" (iv) Goedel's assertion about "non-standard analysis, in some version" being "the analysis of the future". [ABSTRACT FROM AUTHOR]

Despite the fact that several technologies have been developed to assist healthcare workers in reducing errors and improving accuracy in illness diagnosis, there is still substantial ambiguity regarding the accurate disease diagnosis based on symptoms. The goal of this work is to establish a group decision-making problem in an uncertain situation to assist medical practitioners in generating accurate illness predictions based on symptoms. This study proposes a novel distance measure for Pythagorean fuzzy sets that incorporates the inherent uncertainty of complex, uncertain data by incorporating indeterminacy in the computation. First, we establish the proposed Mabala distance measure by describing it's properties. Then, the suggested distance measure is applied to solve group decision-making problems in uncertain situations. A case study of disease analysis based on symptoms is presented to illustrate the decision-making procedure involving four medical professionals, five symptoms, and five probable diseases. Furthermore, We have presented two cases of disease analysis using non-standard and standard Pythagorean fuzzy soft matrices. The results suggest that the proposed Mabala's distance measure has great potential for improving disease analysis. The proposed Mabala distance measure is compared to five existing distance measures using an identical data set of prospective disease symptoms. The comparative analysis indicates that the suggested Mabala distance measure's result almost coincides with the results of the other distance measurements. A set of sensitivity analysis is provided to analyze the durability and consistency of the proposed distance measurements across different input scenarios. [ABSTRACT FROM AUTHOR]

In this paper, we investigate various types of symmetries and their mutual relationships in Hamiltonian systems defined on manifolds with different geometric structures: symplectic, cosymplectic, contact and cocontact. In each case, we pay special attention to non-standard (non-canonical) symmetries, in particular scaling symmetries and canonoid transformations, as they provide new interesting tools for the qualitative study of these systems. Our main results are the characterizations of these non-standard symmetries and the analysis of their relation with conserved (or dissipated) quantities. [ABSTRACT FROM AUTHOR]

The Huxley equation, which is a nonlinear partial differential equation, is used to describe the ionic mechanisms underlying the initiation and propagation of action potentials in the squid giant axon. This equation, just like many other nonlinear equations, is often very difficult to analyze because of the presence of the nonlinearity term, which is always very difficult to approximate. This paper aims to design a reliable scheme that consists of a combination of the nonstandard finite difference in time method, the Galerkin method and the compactness methods in space variables. This method is used to show that the solution of the problem exists uniquely. The a priori estimate from the existence process is applied to the scheme to show that the numerical solution from the scheme converges optimally in the L 2 as well as the H 1 norms. We proceed to show that the scheme preserves the decaying properties of the exact solution. Numerical experiments are introduced with a chosen example to validate the proposed theory. [ABSTRACT FROM AUTHOR]

This research endeavor seeks to investigate the presence and viability of canard solutions within the context of the generalized Hindmarsh-Rose model, specifically when extended to four dimensions. To achieve this, nonstandard analysis is employed as a powerful tool for identifying and characterizing canard solutions within the four-dimensional singularly perturbed system, wherein two fast variables are considered in the folded saddle case. By undertaking this rigorous approach, we aim to contribute valuable insights to the understanding of canard phenomena in complex dynamical systems. [ABSTRACT FROM AUTHOR]

Existing testing methods for Automatic Emergency Braking (AEB) systems mostly rely on standard-based qualitative analysis of specific scenarios, with a focus on whether collisions occur. To explore scenarios beyond the standard conduct, a comprehensive testing model construction and analysis, and provide a more quantitative evaluation of AEB performance, this study extracted three typical hazardous driving scenarios from the KITTI (The Automated Driving dataset was created by the Karlsruhe Institute of Technology in Germany and the Toyota Institute of Technology in the United States) naturalistic driving dataset using kinematic data. A DME (Data Missing Estimation) scene construction method was proposed, and these scenarios were simulated and reconstructed in PRESCAN (PRESCAN is an automotive simulation software owned by Siemens, Munich, Germany). A C-AEB (Curve-Automatic Emergency Braking) testing model was developed and tested based on simulations. Finally, a BCEM (Boundary collision evaluation model) was proposed to quantitatively evaluate AEB performance. The focus of the analysis was on the identified cornering scenario A (severely failed AEB scenario). A C-AEB testing model was constructed based on the DME scene construction method for this cornering AEB failure scenario, and it was evaluated using the BCEM. The study found that the average performance degradation rate (performance degradation rate refers to the ratio of AEB performance in the current scenario compared to the standard straightaway test) of the AEB system in this cornering scenario reached 75.44%, with a maximum performance degradation rate of 89.47%. It was also discovered that the severe failure of AEB in this cornering scenario was mainly caused by sensor system perception defects and limitations of traditional AEB algorithms. This fully demonstrates the effectiveness of our testing and evaluation methodology. [ABSTRACT FROM AUTHOR]

In this article, we consider the numerical approximation of dynamics of calcium ion concentrations in liver cells by a non‐linear first‐order system of ordinary differential equations. At first, we summarize some analytical results of the time‐continuous problem formulation which are of importance to numerically solving this system. We continue with the presentation of our numerical framework which contains two ingredients—an optimization approach for determining the unique equilibrium state and, as our main contribution, a non‐standard finite‐difference scheme for numerical approximation of the time‐discretized dynamical system. We prove that our proposed scheme conserves non‐negativity, and we show convergence towards the time‐continuous unique solution. Conclusively, we stress our theoretical findings by numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we show that the spectral problem associated to stretching modes in a thin folded plate can be derived from the three-dimensional eigenvalue problem of linear elasticity through a rigourous convergence analysis as the thickness of the plate goes to zero. We show, using a nonstandard asymptotic analysis technique, that each stretching frequency of an elastic thin folded plate is the limit of a family of high frequencies of the three-dimensional linearized elasticity system in the folded plate, as the thickness approaches zero. [ABSTRACT FROM AUTHOR]

A matching prior at level |$1-\alpha$| is a prior such that an associated |$1-\alpha$| credible region is also a |$1-\alpha$| confidence set. We study the existence of matching priors for general families of credible regions. Our main result gives topological conditions under which matching priors for specific families of credible regions exist. Informally, we prove that, on compact parameter spaces, a matching prior exists if the so-called rejection-probability function is jointly continuous when we adopt the Wasserstein metric on priors. In light of this general result, we observe that typical families of credible regions, such as credible balls, highest-posterior density regions, quantiles, etc. fail to meet this topological condition. We show how to design approximate posterior credible balls and highest-posterior density regions that meet these topological conditions, yielding matching priors. Finally, we evaluate a numerical scheme for computing approximately matching priors based on discretization and iteration. The proof of our main theorem uses tools from nonstandard analysis and establishes new results about the nonstandard extension of the Wasserstein metric that may be of independent interest. [ABSTRACT FROM AUTHOR]

he United Nation's Sustainable Development Goals encourage countries to solve many social problems. One of these problems is homelessness. We consider those goals which are most pertinent to homelessness according to [13]. We rank countries with respect to the achievement of these goals. We use fuzzy similarity measures to determine the degree of similarity between these rankings. We use three methods to rank the counties, namely, the Analytic Hierarchy Process, the Guiasu method, and the Yen method. Overall scores of categories in some basic research papers pertaining to Sustainable Development Goals were obtained by using multiplication of the scores of the category's targets. Multiplication was used to agree with the philosophy that in order for a high score to be obtained, all targets must have a high score. To support this philosophy in the decision process, we use the t-norms bounded difference, algebraic product, and standard intersection as experts. We also suggest a way the techniques used here can be extended to nonstandard analysis. [ABSTRACT FROM AUTHOR]

We introduce a categorical approach to nonstandard methods, loosely inspired on Internal Set Theory (IST) and reliant on the rich notions of hyperdoctrine and tripos from categorical logic. A different point of view is adopted: the axioms of IST should be expressed in terms of interactions between doctrines, which can be thought of as saying that instead of adding a new predicate we only add new quantifiers. Moreover, it differs from the typical approaches in that the foremost axiom is Standardisation rather than Transfer, all of which can be expressed in a point-free way. This opens the way to the usage of nonstandard proofs methods in the internal language of a doctrine. [ABSTRACT FROM AUTHOR]

Based on the authors' article [5] and the work of Hrbácek [11], we prove that every unlimited natural number ω is of the form ω = ω1 · ω2 + ω3 · ω4 in at least k different ways (k ≥ 1 is limited), where ωi ∈ N is unlimited and ωi/ωj is appreciable for 1 ≤ i, j ≤4. Other similar representations of unlimited natural numbers are also presented. [ABSTRACT FROM AUTHOR]

Using an alternative to Tarskian semantics for first-order logic known as possibility semantics, I introduce an approach to nonstandard analysis that remains within the bounds of semiconstructive mathematics, i.e., does not assume any fragment of the Axiom of Choice beyond the Axiom of Dependent Choices. I define the Fr'echet hyperreal line †R as a possibility structure and show that it shares many fundamental properties of the classical hyperreal line, such as a Transfer Principle and a Saturation Principle. I discuss the technical advantages of †R over some other alternative approaches to nonstandard analysis and argue that it is well-suited to address some of the philosophical and methodological concerns that have been raised against the application of nonstandard methods to ordinary mathematics. [ABSTRACT FROM AUTHOR]

One-sided heavy tailed distributions have been used in many engineering applications, ranging from teletraffic modelling to financial engineering. In practice, the most interesting heavy tailed distributions are those having a finite mean and a diverging variance. The LogNormal distribution is sometimes discarded from modelling heavy tailed phenomena because it has a finite variance, even when it seems the most appropriate one to fit the data. In this work we provide for the first time a LogNormal distribution having a finite mean and a variance which converges to a well-defined infinite value. This is possible thanks to the use of Non-Standard Analysis. In particular, we have been able to obtain a Non-Standard LogNormal distribution, for which it is possible to numerically and experimentally verify whether the expected mean and variance of a set of generated pseudo-random numbers agree with the theoretical ones. Moreover, such a check would be much more cumbersome (and sometimes even impossible) when considering heavy tailed distributions in the traditional framework of standard analysis. [ABSTRACT FROM AUTHOR]

In this paper we propose a new approach to realizability interpretations for nonstandard arithmetic. We deal with nonstandard analysis in the context of (semi) intuitionistic realizability, focusing on the Lightstone-Robinson construction of a model for nonstandard analysis through an ultrapower. In particular, we consider an extension of the λ-calculus with a memory cell, that contains an integer (the state), in order to indicate in which slice of the ultrapower MN the computation is being done. We pay attention to the nonstandard principles (and their computational content) obtainable in this setting. In particular, we give non-trivial realizers to Idealization and a non-standard version of the LLPO principle. We then discuss how to quotient this product to mimic the Lightstone-Robinson construction. [ABSTRACT FROM AUTHOR]

In the context of nonstandard analysis, the somewhat vague equality relation of near-equality allows us to relate objects that are indistinguishable but not necessarily equal. This relation appears to enable us to better understand certain paradoxes, such as the paradox of Theseus's ship, by identifying identity at a time with identity over a short period of time. With this view in mind, I propose and discuss two mathematical models for this paradox. [ABSTRACT FROM AUTHOR]

Consider two branching random walks SnX and SnX on a supercritical random Galton--Watson tree. We compute, almost surely and simultaneously, the Hausdorff and packing dimensions of the level set EX, X, X (a, b) of infinite branches in the boundary of the tree along which the averages SnX/SnX have a given set of limit points [a, b]. [ABSTRACT FROM AUTHOR]

In this paper, we first establish well-posedness results for one-dimensional McKean–Vlasov stochastic differential equations (SDEs) and related particle systems with a measure-dependent drift coefficient that is discontinuous in the spatial component, and a diffusion coefficient which is a Lipschitz function of the state only. We only require a fairly mild condition on the diffusion coefficient, namely to be non-zero in a point of discontinuity of the drift, while we need to impose certain structural assumptions on the measure-dependence of the drift. Second, we study Euler–Maruyama type schemes for the particle system to approximate the solution of the one-dimensional McKean–Vlasov SDE. Here, we will prove strong convergence results in terms of the number of time-steps and number of particles. Due to the discontinuity of the drift, the convergence analysis is non-standard and the usual strong convergence order 1/2 known for the Lipschitz case cannot be recovered for all presented schemes. [ABSTRACT FROM AUTHOR]

This work presents a generalized implementation of the infeasible primal-dual interior point method (IPM) achieved by the use of non-Archimedean values, i.e., infinite and infinitesimal numbers. The extended version, called here the non-Archimedean IPM (NA-IPM), is proved to converge in polynomial time to a global optimum and to be able to manage infeasibility and unboundedness transparently, i.e., without considering them as corner cases: by means of a mild embedding (addition of two variables and one constraint), the NA-IPM implicitly and transparently manages their possible presence. Moreover, the new algorithm is able to solve a wider variety of linear and quadratic optimization problems than its standard counterpart. Among them, the lexicographic multi-objective one deserves particular attention, since the NA-IPM overcomes the issues that standard techniques (such as scalarization or preemptive approach) have. To support the theoretical properties of the NA-IPM, the manuscript also shows four linear and quadratic non-Archimedean programming test cases where the effectiveness of the algorithm is verified. This also stresses that the NA-IPM is not just a mere symbolic or theoretical algorithm but actually a concrete numerical tool, paving the way for its use in real-world problems in the near future. [ABSTRACT FROM AUTHOR]

Alexander Pruss has given a quick argument against the claim that consistency is possibility using Gödel's second incompleteness theorem. The argument does not distinguish metalanguage claims of consistency from object-language ones, rendering it unsound. [ABSTRACT FROM AUTHOR]

Equipment installed in a power system network has to tolerate impulse overvoltage throughout its life span. Lightning impulses are one of the primary reasons of this overvoltage. Hence, insulation of the power equipment is designed and tested with standard lightning impulse. However, in reality, various complex, oscillatory non-standard lightning impulse waveforms exist in natural lightning impulses. Therefore, for the better design of insulation of the power equipment, identification of the non-standard lightning impulse waveform is essential. This article presents a comprehensive review of the effects of non-standard lightning impulse voltage on the insulation of power equipment. This article will help to classify the non-standard lightning impulse waveforms and identify the parameters, generation circuit, and analysis of non-standard lightning impulse waveforms till the present day. Hence, the information presented in the article can be helpful for the insulation design of the power equipment. [ABSTRACT FROM AUTHOR]

Inspired by the modeling of grain growth in polycrystalline materials, we consider a nonlinear Fokker–Plank model, with inhomogeneous diffusion and with variable mobility parameters. We develop large time asymptotic analysis of such nonstandard models by reformulating and extending the classical entropy method, under the assumption of periodic boundary condition. In addition, illustrative numerical tests are presented to highlight the essential points of the current analytical results and to motivate future analysis. [ABSTRACT FROM AUTHOR]

The SOC change index, defined as the normalized difference between the actual Soil Organic Carbon and the value assumed at an initial reference year, is here tailored to the RothC carbon model dynamics. It assumes as a baseline the value of the SOC equilibrium under constant environmental conditions. A sensitivity analysis is performed to evaluate the response of the model to changes in temperature, Net Primary Production (NPP), and land use soil class (forest, grassland, arable). A non-standard monthly time-stepping procedure has been proposed to approximate the SOC change index in the Alta Murgia National Park, a protected area in the Italian Apulia region, selected as a test site. The SOC change index exhibits negative trends for all the land use considered without fertilizers. The negative trend in the arable class can be inverted by a suitable organic fertilization program here proposed. [ABSTRACT FROM AUTHOR]

Integration logic is a logical (model theoretic) framework for studying measure and probability structures by logical means. The Daniell–Stone theorem for Daniell integrals and Riesz representation theorem are two important classical results in analysis concerning existence of measures with certain properties. Many proofs of the Riesz representation theorem can be found in the literature from elementary ones which use ordinary techniques from measure theory and analysis, to more sophisticated ones that highly employ techniques from other fields of mathematics such as nonstandard analysis. There are also a few proofs for the Daniell–Stone theorem. This paper pursues two main goals. One is to give novel and uniform proofs for both these theorems using some ideas from logic. The second and maybe even more important one is to try to reveal more the power of the logical methods in mathematics in particular measure theory, and make stronger connections between analysis and logic. Our proofs are uniform in the sense that they are based on the same general idea and rely on the application of the same technical tool from logic to measure theory, namely the logical compactness theorem. We use the setting of "integration logic" mentioned above, elaborate it and use its expressive power and a version of the compactness theorem holding in it to prove our results. The paper is mostly written for general mathematicians, in particular the people active in logic or analysis as the main audience. It is self-contained and the reader does not need to have any advanced prerequisite knowledge from logic or measure theory. [ABSTRACT FROM AUTHOR]

Accurate measurement and inference of phase difference between two time series are critical across several fields, including signal processing, economic dynamics, and air pollution research. Wavelet methods offer advantages over traditional approaches by allowing time–frequency localization and adaptability to non-stationary signals, which makes them widely used for phase difference estimation. However, existing methods do not provide a statistical test to determine whether a measured phase difference reflects a true underlying relationship between the signals or is merely an artifact of measurement errors or randomness. In this paper, we propose a bootstrap method to fill this gap. Our method is particularly suited to the analysis of non-standard data distributions and complex temporal dependencies. Extensive simulations demonstrate its desirable power and control of type-I error. Furthermore, we apply the method to study air pollution dispersion in China and elucidate the factors influencing phase differences. [ABSTRACT FROM AUTHOR]

In the fifth version of our response-paper [26] to Imamura's criticism, we recall that NonStandard Neutrosophic Logic was never used by neutrosophic community in no application, that the quarter of century old neutrosophic operators (1995-1998) criticized by Imamura were never utilized since they were improved shortly after but he omits to tell their development, and that in real world applications we need to convert/approximate the NonStandard Analysis hyperreals, monads and binads to tiny intervals with the desired accuracy - otherwise they would be inapplicable. We point out several errors and false statements by Imamura [21] with respect to the inf/sup of nonstandard subsets, also Imamura's "rigorous definition of neutrosophic logic" is wrong and the same for his definition of nonstandard unit interval, and we prove that there is not a total order on the set of hyperreals (because of the newly introduced Neutrosophic Hyperreals that are indeterminate), whence the Transfer Principle from R to R* is questionable. After his criticism, several response publications on theoretical nonstandard neutrosophics followed in the period 2018-2022. As such, I extended the NonStandard Analysis by adding the left monad closed to the right, right monad closed to the left, pierced binad (we introduced in 1998), and unpierced binad - all these in order to close the newly extended nonstandard space (R*) under nonstandard addition, nonstandard subtraction, nonstandard multiplication, nonstandard division, and nonstandard power operations [23, 24]. Improved definitions of NonStandard Unit Interval and NonStandard Neutrosophic Logic, together with NonStandard Neutrosophic Operators are presented. [ABSTRACT FROM AUTHOR]

Acute ischemic stroke is a critical health condition that requires timely intervention. Following admission, clinicians typically use perfusion imaging to facilitate treatment decision-making. While deep learning models leveraging perfusion data have demonstrated the ability to predict post-treatment tissue infarction for individual patients, predictions are often represented as binary or probabilistic masks that are not straightforward to interpret or easy to obtain. Moreover, these models typically rely on large amounts of subjectively segmented data and non-standard perfusion analysis techniques. To address these challenges, we propose a novel deep learning approach that directly predicts follow-up computed tomography images from full spatio-temporal 4D perfusion scans through a temporal compression. The results show that this method leads to realistic follow-up image predictions containing the infarcted tissue outcomes. The proposed compression method achieves comparable prediction results to using perfusion maps as inputs but without the need for perfusion analysis or arterial input function selection. Additionally, separate models trained on 45 patients treated with thrombolysis and 102 treated with thrombectomy showed that each model correctly captured the different patient-specific treatment effects as shown by image difference maps. The findings of this work clearly highlight the potential of our method to provide interpretable stroke treatment decision support without requiring manual annotations. • Novel acute ischemic stroke tissue outcome prediction approach is annotation-free. • Proposed deep learning model predicts follow-up CT images from perfusion scans. • Proposed temporal compression method avoids complex perfusion analysis processing. • Predictions capture patient-specific thrombolysis and thrombectomy treatment effects. • Predictions show comparable accuracy to state-of-the-art annotation-dependent method. [ABSTRACT FROM AUTHOR]

We determine sufficient structure for an elementary topos to emulate Nelson's Internal Set Theory in its internal language, and show that any topos satisfying the internal axiom of choice occurs as a universe of standard objects and maps. This development allows one to employ the proof methods of nonstandard analysis (transfer, standardisation, and idealisation) in new environments such as toposes of G -sets and Boolean étendues. [ABSTRACT FROM AUTHOR]

Underwater oil and gas pipelines are prone to alignment differences and angle offsets during docking, and the spherical flange connector can address this problem. Its main function is to enable compensation of the different angles of the pipeline during docking and to apply a non-standard spherical sealing structure using O-rings to the connection. In this paper, the study of a spherical sealing structure using O-rings was based on a spherical structural model of the connector. The Mooney–Rivlin constitutive equation and material parameters of the O-ring were determined according to nonlinear theory. The structure of the non-standard spherical sealing groove was designed and analysed with reference to the standard sealing groove, the calculation expression of the spherical groove specific size was deduced, and the width and depth of the groove were determined. A finite element analysis of the non-standard O-ring sealing structure was carried out using ANSYS Workbench software; the effects of different pressures and compression ratios on the O-ring sealing performance were analysed and studied in terms of von Mises stress, contact pressure and contact width of different contact surfaces so as to determine a more reasonable compression ratio in the sealing structure. Finally, the theoretical analysis of the non-standard spherical sealing structure using O-rings was validated by testing, and it was proven that it could maintain a good seal under high pressure. [ABSTRACT FROM AUTHOR]

The article presents an analysis of a non-standard approach to the segmentation of textural areas in aerospace images. The question of the applicability of sets of textural features for the analysis of experimental data is being investigated to identify characteristic areas on aerospace images that in the future it will be possible to identify types of crops, weeds, diseases, and pests. The selection of suitable algorithms was carried out and appropriate software tools were created on Matlab 2021a and in the software package for statistical analysis Statistica 12. The main way to extract information is to decrypt images, which are the main carrier of information about the underlying surface. The main tasks of texture area analysis include selection and formation of features describing textural differences; selection and segmentation of textural areas; classification of textural areas; identification of an object by texture. ure. To solve the tasks, spectral brightness coefficient (SBC), Normalized Difference Vegetation Index (NDVI), textural features of various crops and weeds. Much attention will be paid to the development of software tools that allow the selection of features describing textural differences for the segmentation of textural areas into subdomains. That is the question of the applicability of sets of textural features and other parameters for the analysis of experimental data to identify types of soils and soils, vegetation types, humidity, crop damage in aerospace images will be resolved. This approach is universal and has great potential for identifying objects using image clustering. To identify the boundaries of areas with different properties of the image under study, images of the same surface area taken at different times are considered. [ABSTRACT FROM AUTHOR]

As part of the EUREC 4 A field campaign, the research vessel Maria S. Merian probed an oceanic region between 6 to 13.8 ∘ N and 51 to 60 ∘ W for approximately 32 d. Trade wind cumulus clouds were sampled in the trade wind alley region east of Barbados as well as in the transition region between the trades and the intertropical convergence zone, where the ship crossed some mesoscale oceanic eddies. We collected continuous observations of cloud and precipitation profiles at unprecedented vertical resolution (7–10 m in the first 3000 m) and high temporal resolution (1–3 s) using a W-band radar and micro rain radar (MRR), installed on an active stabilization platform to reduce the impact of ship motions on the observations. The paper describes the ship motion correction algorithm applied to the Doppler observations to extract corrected hydrometeor vertical velocities and the algorithm created to filter interference patterns in the MRR observations. Radar reflectivity, mean Doppler velocity, spectral width and skewness for W-band and reflectivity, mean Doppler velocity, and rain rate for MRR are shown for a case study to demonstrate the potential of the high resolution adopted. As non-standard analysis, we also retrieved and provided liquid water path (LWP) from the 89 GHz passive channel available on the W-band radar system. All datasets and hourly and daily quicklooks are publically available, and DOIs can be found in the data availability section of this publication. Data can be accessed and basic variables can be plotted online via the intake catalog of the online book "How to EUREC 4 A". [ABSTRACT FROM AUTHOR]

Manevitz and Weinberger (1996) proved that the existence of effective K- Lipschitz Z/nZ-actions implies the existence of effective K-Lipschitz Q/Z-actions for all compact connected manifolds with metrics, where K is a fixed Lipschitz constant. The Q=Z-actions were constructed from suitable actions of a suffciently large hyper-finite cyclic group Z/Z in the sense of nonstandard analysis. By modifying their construction, we prove that for every direct system of torsion groups with monomorphisms, the existence of effective K-Lipschitz actions implies the existence of effective K-Lipschitz lim G-actions. This generalises Manevitz and Weinberger's result. [ABSTRACT FROM AUTHOR]

The present study is conducted to analyse the computational dynamical analysis of the stochastic susceptible-infected-recovered pandemic model of the novel coronavirus. We adopted two ways for stochastic modelling like as transition probabilities and parametric perturbation techniques. We applied different and well-known computational methods like Euler Maruyama, stochastic Euler, and stochastic Runge Kutta to study the dynamics of the model mentioned above. Unfortunately, these computational methods do not restore the dynamical properties of the model like positivity, boundedness, consistency, and stability in the sense of biological reasoning, as desired. Then, for the given stochastic model, we developed a stochastic non-standard finite difference method. Following that, several theorems are presented to support the proposed method, which is shown to satisfy all of the model's dynamical properties. To that end, several simulations are presented to compare the proposed method's efficiency to that of existing stochastic methods. [ABSTRACT FROM AUTHOR]

Alpha-Theory was introduced in 1995 to provide a simplified version of Robinson's non-standard analysis which overcomes the technicalities of symbolic logic. The theory has been improved over the years, and recently it has been used also to solve practical problems in a pure numerical way, thanks to the introduction of algorithmic numbers. In this paper, we introduce Alpha-Theory using a novel axiomatic approach oriented towards real-world applications, to avoid the need to master mathematical logic and model theory. To corroborate the strong link of this Alpha-Theory axiomatization and scientific computations, we report numerical illustrative applications never carried out by means of non-standard numbers within a computer, i.e., the computation of the eigenvalues of a non-Archimedean matrix, some computations related to non-Archimedean Markov chains, and the Cholesky factorization of a non-Archimedean matrix. We also highlight the differences between our numerical routines and pure symbolic approaches: as expected, the former scales better when the dimension of the problem increases. [ABSTRACT FROM AUTHOR]

Mathematical methods based on the variational approach are successfully used in a broad range of applications, especially those fields that are oriented on partial differential equations. Our problem area addresses a wide class of nonlinear variational problems described by all kinds of static and evolution equations, inverse and ill-posed problems, non-smooth and non-convex optimization, and optimal control including shape and topology optimization. Within these directions, we focus but are not limited to singular and unilaterally constrained problems arising in mechanics and physics, which are governed by complex systems of generalized variational equations and inequalities. Whereas classical mathematical tools are not applicable here, we aim at a non-standard well-posedness analysis, numerical methods, asymptotic and approximation techniques including homogenization, which are successful within the primal as well as the dual variational formalism. In a broad scope, the theme issue objectives are directed toward advances that are attained in the mathematical theory of non-smooth variational problems, its physical consistency, numerical simulation and application to engineering sciences. This article is part of the theme issue 'Non-smooth variational problems and applications'. [ABSTRACT FROM AUTHOR]

We present a method for assigning probabilities to the solutions of initial value problems that have a Lipschitz singularity. To illustrate the method, we focus on the following toy example: d 2 r (t) d t 2 = r a , r (t = 0) = 0 , and d r (t) d t ∣ r (t = 0) = 0 , with a ∈ ] 0 , 1 [. This example has a physical interpretation as a mass in a uniform gravitational field on a frictionless, rigid dome of a particular shape; the case with a = 1 / 2 is known as Norton's dome. Our approach is based on (1) finite difference equations, which are deterministic; (2) elementary techniques from alpha-theory, a simplified framework for non-standard analysis that allows us to study infinitesimal perturbations; and (3) a uniform prior on the canonical phase space. Our deterministic, hyperfinite grid model allows us to assign probabilities to the solutions of the initial value problem in the original, indeterministic model. [ABSTRACT FROM AUTHOR]

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As part of the EUREC4A field campaign, the research vessel Maria S. Merian probed an oceanic region between 6° N and 13.8° N and 51° W to 60° W for approximately 32 days. Trade wind cumulus clouds were sampled in the trade-wind alley region east of Barbados as well as in the transition region between the trades and the intertropical convergence zone, where the ship crossed some mesoscale oceanic eddies. We collected continuous observations of cloud and precipitation profiles at unprecedented vertical resolution (7-10 m in the first 3000 m) and high temporal resolution (1-3 s) using a W-band radar and micro-rain radar (MRR-PRO), installed on an active stabilization platform to reduce the impact of ship motions on the observations. The paper describes the ship motion correction algorithm applied to the Doppler observations to extract corrected hydrometeors vertical velocities and the algorithm created to filter interference patterns in the MRR-PRO observations. Radar reflectivity, mean Doppler velocity, spectral width and skewness for W-band and attenuated reflectivity, mean Doppler velocity and rain rate for MRR-PRO are shown for a case study to demonstrate the potential of the high resolution adopted. As non-standard analysis, we also retrieved and provided liquid water path (LWP) from the 89 GHz passive channel available on the W-band radar system. All datasets and hourly and daily quicklooks are publically available. Data can be accessed and basic variables can be plotted online via the intake catalog of the online book "How to EUREC4A". [ABSTRACT FROM AUTHOR]

The Advanced Topographic Laser Altimeter System (ATLAS) was launched aboard the Ice Cloud and land‐Elevation Satellite‐2 (ICESat‐2) satellite in September 2018. ATLAS is a single wavelength (532 nm) lidar system designed to acquire high resolution measurements of the earth's surface while also obtaining atmospheric backscatter from molecules, clouds, and aerosols. Because ATLAS is optimized for altimetry, the atmospheric data acquired is unique in many respects and requires non‐standard analysis techniques. For example, the high repetition rate laser limits the vertical extent of the profiles to just 14 km and causes atmospheric scattering from above 15 km to be added to the scattering in the lower 0–14 km profile. In addition, the limited vertical range of the acquired profiles renders it difficult to compute the magnitude of the solar background and hinders the application of standard calibration techniques. Despite these limitations, methods have been developed to successfully produce data products that have value to the atmospheric community for cloud and aerosol research and are currently available at the National Snow and Ice Data Center (NSIDC). In this paper we describe the ICESat‐2 atmospheric channel and the methods used to process the ATLAS raw photon count data to obtain calibrated backscatter and higher level products such as layer heights and type, blowing snow, column optical depth and apparent surface reflectance. Plain Language Summary: ICESat‐2 is a polar orbiting satellite equipped with a high repetition rate laser that fires green pulses of light to earth 10,000 times per second. The main objective of ICESat‐2 is the high‐resolution measurement of the height of the earth's surface, with emphasis on the change in elevation of ice sheets that cover most of Greenland and Antarctica. In addition to surface elevation, ICESat‐2 also obtains information on the vertical structure of the atmosphere including the height and thickness of clouds and aerosols. The atmospheric measurements are important for climate studies and because they extend the data record begun by other earth‐orbiting satellite lidars like Cloud‐Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) which has been acquiring atmospheric data since 2006 and is nearing the end of its life. The creation of a long record of cloud and aerosol observations is very important for detecting changes that may be occurring due to humanity's influence on the climate system. Key Points: ICESat‐2 is a satellite lidar that acquires atmospheric backscatter profiles from 0 to 14 km every 280 m along the satellite trackThe high repetition rate laser creates unusual problems for processing the raw data to higher level data productsProducts such as calibrated backscatter, cloud and aerosol layer heights, column optical depth and blowing snow are described and shown [ABSTRACT FROM AUTHOR]