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One apparent feature of mental time travel is the ability to recursively embed temporal perspectives across different times: humans can remember how we anticipated the future and anticipate how we will remember the past. This recursive structure of mental time travel might be formalized in terms of a 'grammar' that is reflective of but more general than linguistic notions of absolute and relative tense. Here, I provide a foundation for this grammatical framework, emphasizing a bounded (rather than unbounded) recursive function that supports mental time travel to a limited temporal depth and to actual and possible scenarios. Anticipated counterfactual thinking, for instance, entails three levels of mental time travel to a possible scenario ('in the future, I will reflect on how my past self could have taken a different future action') and is centrally implicated in complex human decision-making. This perspective calls for further research into the mechanisms, ontogeny, functions and phylogeny of recursive mental time travel, and revives the question of links with other recursive forms of thinking such as theory of mind. This article is part of the theme issue 'Elements of episodic memory: lessons from 40 years of research'. [ABSTRACT FROM AUTHOR]

This paper presents an iterative stress wave log beam imaging algorithm based on external shape to predict the size, shape, and position of internal features in logs. The algorithm's accuracy is analyzed to establish a theoretical and scientific basis for the prediction and evaluation of internal knots in standing trees. Six sample logs with natural knots were selected for study, and cross-sectional stress wave propagation tests were conducted using FAKOPP to collect data. Using the shortest propagation path method, the algorithm iteratively produced fault images of the log cross-sections. While the algorithm can roughly predict the location of internal features, discrepancies between predicted and actual shapes and sizes result in relative errors ranging from 15.66% to 52.08%. Except for sample log 6, the relative error for other logs is mostly within 31%, with logs 1, 2, and 5 showing errors under 20%. However, the imaging accuracy and effectiveness need improvement. Further experimental studies and algorithm enhancements are necessary to improve fault imaging and prediction accuracy, particularly in terms of shape and size precision. [ABSTRACT FROM AUTHOR]

AbstractThe quasidiffusion (QD) method is an established and efficient iterative technique for solving particle transport problems. Each QD iteration consists of a high-order SN sweep, followed by a low-order QD calculation. QD has two defining characteristics: (1) its iterations converge rapidly for any spatial grid and (2) the converged scalar fluxes from the high-order SN sweep and the low-order QD calculation differ, by spatial truncation errors, from each other and from the scalar flux solution of the SN equations. In this paper, we show that by including a transport consistency factor in the low-order equation, the converged high-order and low-order scalar fluxes become equal to each other and to the converged SN scalar flux. However, the inclusion of the transport consistency factor has a negative impact on the convergence rate. We present numerical results that demonstrate the effect of the transport consistency factor on stability. [ABSTRACT FROM AUTHOR]

In this paper, we studied the AA-iterative algorithm for finding fixed points of the class of nonlinear generalized (α, β)-nonexpansive mappings. First, we proved weak convergence and then proved several strong convergence results of the scheme in a ground setting of uniformly convex Banach spaces. We gave a few numerical examples of generalized (α, β)-nonexpansive mappings to illustrate the major outcomes. One example was constructed over a subset of a real line while the other one was on the two dimensional space with a taxicab norm. We considered both these examples in our numerical computations to show that our iterative algorithm was more effective in the rate of convergence corresponding to other fixed point algorithms of the literature. Some 2D and 3D graphs were obtained that supported graphically our results and claims. As applications of our major results, we solved a class of fractional differential equations, 2D Voltera differential equation, and a convex minimization problem. Our findings improved and extended the corresponding results of the current literature [ABSTRACT FROM AUTHOR]

In this paper we investigate the polynomial-like iterative equation on Riesz spaces. Since a Riesz space does not need to have a metric space structure, neither the Schauder fixed point theorem nor the Banach fixed point theorem is available. Using the Knaster–Tarski fixed point theorem, we first obtain the existence and uniqueness of order-preserving solutions on convex complete sublattices of Riesz spaces. Then, restricting to R and R n , special cases of Riesz space, we obtain semi-continuous solutions and integrable solutions, respectively. Finally, we present more special cases of Riesz space in which solutions to the iterative equation can be discussed. [ABSTRACT FROM AUTHOR]

In this work, we consider the properties of the two-term Machin-like formula and develop an algorithm for computing digits of π by using its rational approximation. In this approximation, both terms are constructed by using a representation of 1 / π in the binary form. This approach provides the squared convergence in computing digits of π without any trigonometric functions and surd numbers. The Mathematica codes showing some examples are presented. [ABSTRACT FROM AUTHOR]

In this paper, we studied the AA-iterative algorithm for finding fixed points of the class of nonlinear generalized $ (\alpha, \beta) $-nonexpansive mappings. First, we proved weak convergence and then proved several strong convergence results of the scheme in a ground setting of uniformly convex Banach spaces. We gave a few numerical examples of generalized $ (\alpha, \beta) $-nonexpansive mappings to illustrate the major outcomes. One example was constructed over a subset of a real line while the other one was on the two dimensional space with a taxicab norm. We considered both these examples in our numerical computations to show that our iterative algorithm was more effective in the rate of convergence corresponding to other fixed point algorithms of the literature. Some 2D and 3D graphs were obtained that supported graphically our results and claims. As applications of our major results, we solved a class of fractional differential equations, 2D Voltera differential equation, and a convex minimization problem. Our findings improved and extended the corresponding results of the current literature.

In this work, we consider the properties of the two-term Machin-like formula and develop an algorithm for computing digits of π by using its rational approximation. In this approximation, both terms are constructed by using a representation of 1/π in the binary form. This approach provides the squared convergence in computing digits of π without any trigonometric functions and surd numbers. The Mathematica codes showing some examples are presented.

To address the issue of inadequate control effect resulting from the challenge of measuring state feedback information comprehensively, this paper proposes an iterative output feedback energy-to-peak control method that solely depends on partial external observation data. This paper presents the computational steps for achieving a suboptimal solution to the output feedback bilinear matrix inequality constrained problem using an iterative linear matrix inequality approach. The proposed method overcomes the challenge of numerically solving the optimization problem. The unknown variables in the output feedback linear matrix inequality optimization problem are transformed equivalently to obtain a new linear matrix inequality optimization problem. The numerical results of the two optimization problems are then used to iterate with each other and obtain a suboptimal solution. A comprehensive analysis was conducted on an 8-story building structure, utilizing state feedback, output feedback, and iterative output feedback energy-to-peak control techniques. The results of the study indicate that the proposed iterative output feedback energy-to-peak control approach efficiently reduces the displacement and acceleration response of the structure, exhibiting superior control effectiveness than both the state feedback and output feedback energy-to-peak control methods. The findings demonstrate the practicality and versatility of the suggested method.

Background. Image processing is used in machine vision measurement systems, which are widely used in industrial applications. One of the important tasks in processing is image superposition. Registration methods must fulfill two basic requirements: satisfactory registration quality and practical processing time. One of the methods that meets these requirements is iterative superposition. Aim. The aim is to study the size of the area (region of convergence) for the values of the parameters of the initial approximation, which ensures satisfactory superposition. The size of the region determines the performance of the iterative algorithm. Methods. The size of the region of convergence was determined experimentally: correlation analysis and statistical simulation. Results. Experiments have shown if a sampling step is no more than 1/10 of the size of the image fragment, then the probability of correct registration is almost equal to one. If this threshold is exceeded, then the probability decreases. Conclusion. The size of the region of convergence of the iterative image registration method has been established. It is possible to design processing algorithms and predict processing time by obtaining results. The superposition method was introduced into a machine vision system to recognize contact wire clamps on the railway. Image superposition in this system is carried out in real time.

Here determination of the level dimensions regularity of the multicomponent contamination zones (by heavy metals and petroleum products) of the soils adjacent to the municipal solid waste landfill. The dependences of the mercury, copper and zinc concentrations in the soil on the distance to the landfill of municipal solid waste were determined, similar dependence was specified for petroleum products for a distance of up to 500 m. The research employed the regression analysis technique for investigating single-factor experiments and other paired patterns. The selection of a suitable function was based on commonly utilized options, determined by the criterion of achieving the maximum correlation coefficient value. Regression analyses were conducted by employing linearizing transformations, facilitating the conversion of non-linear regularities into linear forms. Graphical dependences, describing the change in the concentrations of individual soil pollutants with the distance from the municipal solid waste landfill have been built, they enable to demonstrating the satisfactory convergence of theoretical outcomes with empirical observations was achieved. The level regularity of multicomponent soil contamination (with petroleum products and heavy metals) at the distance from the municipal solid waste landfill has been obtained, it’s required for determining the dimentions of the zones of multicomponent soil contamination. Applying the method of iterations, the dimensions of the multicomponent contamination zones (with petroleum products and heavy metals) of the soils, adjacent to the landfill of municipal solid waste have been determined: very heavy pollution – 22.93 m, heavy pollution – 81.77 m, average pollution – 474.9 m from the foot of the landfill.

Passive acoustic monitoring (PAM) – autonomously recording ambient sound – could dramatically increase the scale and robustness of species monitoring in rainforest ecosystems. PAM generates large volumes of data that require automated methods of target species detection. Species-specific recognisers, which often use supervised machine learning, can achieve this goal. However, they require a large training dataset of target and non-target signals, which is time-consuming and challenging to create. Unfortunately, very little information about creating training datasets for supervised machine learning recognisers is available, especially for tropical ecosystems. Here, we show an iterative approach to creating a training dataset that improved recogniser precision from 0.12 to 0.55. By sampling background noise using an initial small recogniser, we can address one of the significant challenges of training dataset creation in acoustically diverse environments. Our work demonstrates that recognisers will likely fail in real-world settings unless the training dataset size is large enough and sufficiently representative of the ambient soundscape. We outline a workflow that can provide users with an accessible way to create a species-specific PAM recogniser that addresses these issues for tropical rainforest environments. Our work provides important lessons for PAM practitioners wanting to develop species-specific recognisers for acoustically diverse ecosystems. [ABSTRACT FROM AUTHOR]

Imposing some conditions on derivatives of the known functions, using the Fiber Contraction Theorem we prove the existence of C 1 solutions of a class of iterative functional equations which involves iterates of the unknown functions and a nonlinear term. [ABSTRACT FROM AUTHOR]

The note is concerned with the functional equation λ 1 H 1 (f (x)) + λ 2 H 2 (f 2 (x)) + ⋯ + λ n H n (f n (x)) = F (x) , which is a generalised form of the so-called polynomial-like iterative equation. We investigate the existence of nondecreasing convex (both usual and higher order) solutions to this equation on open intervals using the Schauder fixed point theorem. The results supplement those proved by Trif (Aquat Math, 79:315–327, 2010) for the polynomial-like iterative equation by generalising them to a greater extent. This assertion is supported by some examples illustrating their applicability. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the existence of a positive solution for a class of nonvariational fractional elliptic system with concave and convex nonlinearities in two cases. The paper is divided in two parts: In the first one, for general nonlinearity with subcritical or critical growth, we use Galerkin's method and an approximation argument to show the existence of a solution for the system considered. In the second part, for special cases (which include the power case), we remove the restriction on the growth of the nonlinearity and use sub-supersolution, monotone iteration and a comparison argument to obtain a solution for the system considered. [ABSTRACT FROM AUTHOR]

An infinite system of integral equations with power nonlinearity on the positive half-line is considered. A number of particular cases of this system arise in many branches of mathematical physics. In particular, systems of this nature are encountered in the theory of radiative transfer in spectral lines, in the dynamic theory of -adic open-closed strings, in the mathematical theory of the spread of epidemic diseases, and in econometrics. The existence of a nonnegative (in coordinates) nontrivial and bounded solution is proved. Under an additional constraint on the matrix kernel, we also study the asymptotic behavior at infinity. In the case of strong symmetry (symmetry both in coordinates and in indices) of the matrix kernel, we also prove a uniqueness theorem for a solution in a certain class of infinite and bounded vector functions. At the end, concrete examples of an infinite matrix kernel are given that are of practical interest in the above applications. [ABSTRACT FROM AUTHOR]

In recent years of the literature, fixed point iteration schemes have been studied theoretically for many nonlinear problems, including differential and integral equations; however, numerically, there has been a little work on these iterative schemes for finding numerical solutions of differential equations. The main purpose of this paper is to propose a new numerically efficient iterative approach based on fixed point theory and Green's function. First, we compute a Green's function for a wider class fourth order BVPs and express the sought solution as a fixed point of a certain integral operator. We show by Banach Contraction Principle that this new integral operator admits a unique fixed point which is the solution for a given BVP. We embed the integral operator into our iterative scheme and obtain a generalized iterative scheme. We prove the convergence of our new scheme under possible mild assumptions. Instead of stability, we prove a weak w 2 -stability result for our scheme which is a natural and weak notion of the stability for any given iterative scheme. To support numerically the convergence of our scheme, we provide two different examples. Using these examples, we compare the high accuracy of our new scheme with the classical approaches of the literature. As an application of our scheme, we show that the scheme can be used for finding solutions for the Bratu's problem in a Banach space setting. At the end of the paper, we include some interesting discussion about the main results of the paper. [ABSTRACT FROM AUTHOR]

For large classes of (finite and) infinite dimensional complex Banach spaces Z, B its open unit ball and f : B → B a compact holomorphic fixed-point free map, we introduce and define the Wolff hull, W(f), of f in ∂ B and prove that W(f) is proximal to the images of all subsequential limits of the sequences of iterates (f n) n of f. The Wolff hull generalises the concept of a Wolff point, where such a point can no longer be uniquely determined, and coincides with the Wolff point if Z is a Hilbert space. Recall that (f n) n does not generally converge even in finite dimensions, compactness of f (i.e. f(B) is relatively compact) is necessary for convergence in the infinite dimensional Hilbert ball and all accumulation points Γ (f) of (f n) n map B into ∂ B (for any topology finer than the topology of pointwise convergence on B). The target set of f is T (f) = ⋃ g ∈ Γ (f) g (B). To locate T(f), we use a concept of closed convex holomorphic hull, Ch (x) ⊂ ∂ B for each x ∈ ∂ B and define a distinguished Wolff hull W(f). We show that the Wolff hull intersects all hulls from T(f), namely W (f) ∩ Ch (x) ≠ ∅ for all x ∈ T (f). If B is the Hilbert ball, W(f) is the Wolff point, and this is the usual Denjoy–Wolff result. Our results are for all reflexive Banach spaces having a homogeneous ball (or equivalently, for all finite rank J B ∗ -triples). These include many well-known operator spaces, for example, L(H, K), where either H or K is finite dimensional. [ABSTRACT FROM AUTHOR]

Museum educators play a major role in how visitors' experience failure moments during STEM-related activities. The purpose of this study was to explore how museum educators co-constructed iteration through failure moments with visitors during an engineering activity. Utilizing an instrumental case study, we analyzed video data and one-on-one reflective meetings from five museum educators. Through our analysis, we highlight how educators and visitors are able to jointly attend, interpret, and respond to failures that leads to continuous improvements of the prototype and/or design process (i.e., iteration). The significance of this study lies in providing informal educators with approaches they can incorporate to support visitors during the failure-learning process, namely, strategies that develop visitors' noticing skills around failure. [ABSTRACT FROM AUTHOR]

A binary operation # on Z + is said to be an associative arithmetic if both # and its iteration — the binary operation ∗ defined recursively by: x∗1 = x and x∗y = [x ∗ (y −1)]#x — are associative. E. Rosinger [6] showed that under reasonable conditions an associative arithmetic must be ordinary addition. However, in the general case, there are associative arithmetics that are not ordinary addition. This paper gives examples of these as well as results towards a structure theorem for associative arithmetics. The paper also describes the role that this particular math problem has played in my mathematical life. [ABSTRACT FROM AUTHOR]

Picard iteration is on the basis of a great number of numerical methods and applications of mathematics. However, it has been known since the 1950s that this method of fixed-point approximation may not converge in the case of nonexpansive mappings. In this paper, an extension of the concept of nonexpansiveness is presented in the first place. Unlike the classical case, the new maps may be discontinuous, adding an element of generality to the model. Some properties of the set of fixed points of the new maps are studied. Afterwards, two iterative methods of fixed-point approximation are analyzed, in the frameworks of b-metric and Hilbert spaces. In the latter case, it is proved that the symmetrically averaged iterative procedures perform well in the sense of convergence with the least number of operations at each step. As an application, the second part of the article is devoted to the study of fractal mappings on Hilbert spaces defined by means of nonexpansive operators. The paper considers fractal mappings coming from φ -contractions as well. In particular, the new operators are useful for the definition of an extension of the concept of α -fractal function, enlarging its scope to more abstract spaces and procedures. The fractal maps studied here have quasi-symmetry, in the sense that their graphs are composed of transformed copies of itself. [ABSTRACT FROM AUTHOR]

In this paper, we extend SMSNS [Pourbagher M, Salkuyeh DK. On the solution of a class of complex symmetric linear systems. Appl Math Lett. 2018;76:14–20.] iteration method for solving a class of complex symmetric system of linear equations. We propose a successive-overrelaxation (SOR) acceleration scheme for SMSNS (SMSNSSOR), discuss the convergence conditions of it and give the optimal parameters which make the fast convergence. Numerical results demonstrate that SMSNSSOR iteration method is feasible and effective for solving complex symmetric systems, and performs better than some other usually used iteration methods. [ABSTRACT FROM AUTHOR]

The purpose of this study is to evaluate the effect of the number of diffusers placed in the same room, as well as the effect of diffusers with a flat area (8.4, 13.2, and 18 m2) on the calculated sound absorption coefficient in a reverberation room, when an iterative procedure based on the evaluation of the sound power level is applied (this is done by using the sound power equation and substituting with different values of equivalent absorption area on both sides of the transformed equation to reach the correct value for absorption area, which achieves equality on both sides of the equation in order to achieve the goal). The sound absorption coefficient at random incident of three materials having different degrees of absorption—has been measured in a reverberation room according to ISO 345: a highly absorbent material (sponge) a medium absorbent material (rubber) and a low absorbent material (wood).There is a noticeable convergence between the calculated and measured sound absorption coefficient from the usual ISO 354 procedure and from the sound power level equation from ISO 3741,when diffusers are present. The difference in sound power level is close to 1.0 dB depending on the position of the source with the diffuser area. Thanks to the diffusers effect, the difference between the measured and the calculated sound absorption coefficient can be considerably reduced. [ABSTRACT FROM AUTHOR]

Here determination of the level dimensions regularity of the multicomponent contamination zones (by heavy metals and petroleum products) of the soils adjacent to the municipal solid waste landfill. The dependences of the mercury, copper and zinc concentrations in the soil on the distance to the landfill of municipal solid waste were determined, similar dependence was specified for petroleum products for a distance of up to 500 m. The research employed the regression analysis technique for investigating single-factor experiments and other paired patterns. The selection of a suitable function was based on commonly utilized options, determined by the criterion of achieving the maximum correlation coefficient value. Regression analyses were conducted by employing linearizing transformations, facilitating the conversion of non-linear regularities into linear forms. Graphical dependences, describing the change in the concentrations of individual soil pollutants with the distance from the municipal solid waste landfill have been built, they enable to demonstrating the satisfactory convergence of theoretical outcomes with empirical observations was achieved. The level regularity of multicomponent soil contamination (with petroleum products and heavy metals) at the distance from the municipal solid waste landfill has been obtained, it's required for determining the dimentions of the zones of multicomponent soil contamination. Applying the method of iterations, the dimensions of the multicomponent contamination zones (with petroleum products and heavy metals) of the soils, adjacent to the landfill of municipal solid waste have been determined: very heavy pollution - 22.93 m, heavy pollution - 81.77 m, average pollution - 474.9 m from the foot of the landfill. [ABSTRACT FROM AUTHOR]

A polynomial f(x) over a field K is said to be stable if all its iterates are irreducible over K. L. Danielson and B. Fein have shown that over a large class of fields K, if f(x) is an irreducible monic binomial, then it is stable over K. In this paper it is proved that this result no longer holds over finite fields. Necessary and sufficient conditions are provided under which a given binomial is stable over Fq. These conditions are used to construct a table listing the stable binomials over Fq of the form f(x) = xd - a, a ∈ Fq \ {0, 1}, for q ≤ 27 and d ≤ 10. The paper ends with a brief link to Mersenne primes. [ABSTRACT FROM AUTHOR]

Individual survival and evolutionary selection require biological organisms to maximize reward. Economic choice theories define the necessary and sufficient conditions, and neuronal signals of decision variables provide mechanistic explanations. Reinforcement learning (RL) formalisms use predictions, actions, and policies to maximize reward. Midbrain dopamine neurons code reward prediction errors (RPE) of subjective reward value suitable for RL. Electrical and optogenetic self-stimulation experiments demonstrate that monkeys and rodents repeat behaviors that result in dopamine excitation. Dopamine excitations reflect positive RPEs that increase reward predictions via RL; against increasing predictions, obtaining similar dopamine RPE signals again requires better rewards than before. The positive RPEs drive predictions higher again and thus advance a recursive reward-RPE-prediction iteration toward better and better rewards. Agents also avoid dopamine inhibitions that lower reward prediction via RL, which allows smaller rewards than before to elicit positive dopamine RPE signals and resume the iteration toward better rewards. In this way, dopamine RPE signals serve a causal mechanism that attracts agents via RL to the best rewards. The mechanism improves daily life and benefits evolutionary selection but may also induce restlessness and greed. [ABSTRACT FROM AUTHOR]

The aim of the paper is to (re-)evaluate the treatment of reduplicative expressions as compound words in nearly all previous work on English. Examples of reduplicative expressions are listed, out of context, and they are labelled as compound words, without providing proper motivations as to why it makes sense to treat them as compounds, in the sense of lexical items that are formed of other lexical items. The paper provides plenty of examples of how the reduplicatives listed in previous work are actually used in present-day English and examines the functions and interpretations of such expressions. The paper shows that most reduplicative expressions are not compound words. Some of them are words in their own right that cannot be divided into meaningful constituents. Some may have a more compound-like reading, alongside a clearly non-compound-like reading; for most such items, the latter function and interpretation seem to be most common. A large majority of alleged reduplicative compounds display clear non-compound-like behaviour. It will be shown that these expressions are likely to be sequences of words that are created by the same (syntactic) process/es that iterate or stack ‘ordinary’ nouns, adjectives and verbs in English. [ABSTRACT FROM AUTHOR]

In the medical field, computed tomography (CT) is a commonly used examination method, but the radiation generated increases the risk of illness in patients. Therefore, low-dose scanning schemes have attracted attention, in which noise reduction is essential. We propose a purposeful and interpretable decomposition iterative network (DISN) for low-dose CT denoising. This method aims to make the network design interpretable and improve the fidelity of details, rather than blindly designing or using deep CNN architecture. The experiment is trained and tested on multiple data sets. The results show that the DISN method can restore the low-dose CT image structure and improve the diagnostic performance when the image details are limited. Compared with other algorithms, DISN has better quantitative and visual performance, and has potential clinical application prospects. [ABSTRACT FROM AUTHOR]

Let f(z), g(z), h(z) be three entire functions of non zero finite order and fn(z) the iterations of f(z) with respect to g(z) and h(z) also T (r, f), T (r, g), T (r, h), T (r, fn) are there respective characteristic functions. In this paper we study comparative growth properties of T(r, fn) with respect to T (r, f), T (r, g) and T (r, h) in terms of generalist order. [ABSTRACT FROM AUTHOR]

Experimental designs in the social sciences have received increasing attention due to their power to produce causal inferences. Nevertheless, experimental research faces limitations, including limited external validity and unrealistic treatments. We propose combining qualitative fieldwork and experimental design iteratively—moving back-and-forth between elements of a research design—to overcome these limitations. To properly evaluate the strength of experiments researchers need information about the context, data, and previous knowledge used to design the treatment. To support our argument, we analyze 338 pre-analysis plans submitted to the Evidence in Governance and Politics repository in 2019 and the design of a study on public opinion support for punitive policing practices in Montevideo, Uruguay. The paper provides insights about using qualitative fieldwork to enhance the external validity, transparency and replicability of experimental research, and a practical guide for researchers who want to incorporate iteration to their research designs. [ABSTRACT FROM AUTHOR]

Accurate estimation of the transmissibility of an infectious disease is critical to understanding disease transmission dynamics and designing effective control strategies. However, it has always been difficult to estimate the transmission rates due to the unobservability and multiple contributing factors. In this paper, we develop a data-driven inverse method based on discretizations of compartmental differential equation models for estimating time-varying transmission rates of infectious diseases. By developing iteration algorithms for three typical classes of infectious diseases, namely, a disease with seasonal cycles, a disease with nonseasonal cycles, and a disease with no obvious periodicity, we demonstrate that the discrete inverse method is a valuable tool for extracting information from available pandemic or epidemic incidence data. We also obtain insights for some epidemiological phenomena and issues of concern based on each application. Our method is highly intuitive and generates rapid implementation even with multiple years of data instances. In particular, it can be used in conjunction with other data-driven technologies, such as machine learning, to forecast future disease dynamics based on future weather conditions, policy decisions, or human mobility trends, providing guidance to public health authorities. [ABSTRACT FROM AUTHOR]

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

The present paper is mainly concerned with a balanced partial q-series. By the classical Abel lemma on summation by parts, we establish the q-contiguous relations for the partial sum whose iterating cases embrace many new summation and transformation formulae as well as some known results. Of particular interest are one identity of Rogers–Ramanujan type and two identities of partial theta functions. [ABSTRACT FROM AUTHOR]

It was found that a function with exactly one discontinuity may have a continuous iterate of second order, indicating that a discontinuity may be repaired to be a continuous one by its adjacent pair of functions of second order, called second order sui-repair. If a function has more than one discontinuities, examples show that some discontinuities may be repaired to be continuous ones by the other's adjacent pair of functions of second order, called second order C 0 homi-repair. In this paper we investigate second order C 0 homi-repairs of removable and jumping discontinuities for functions having more than one but finitely many discontinuities. We give necessary and sufficient conditions for removable and jumping discontinuities to be C 0 repaired by the second order iteration. [ABSTRACT FROM AUTHOR]

It is shown that removable and jumping discontinuities for functions having more than one but finitely many discontinuities have a second order C 0 homi-repair. In this paper we study second order C 0 homi-repair of oscillating discontinuities and pre-discontinuities for those functions and give necessary and sufficient conditions for C 0 repair by second order iteration. [ABSTRACT FROM AUTHOR]

Due to the restrictive growth and/or monotonicity requirements inherent in their employment, classical iterative fixed-point theorems are rarely used to approximate solutions to an integral operator with Green's function kernel whose fixed points are solutions of a boundary value problem. In this paper, we show how one can decompose a fixed-point problem into multiple fixed-point problems that one can easily iterate to approximate a solution of a differential equation satisfying one boundary condition, then apply a bisection method in an intermediate value theorem argument to meet a second boundary condition. Error estimates on the iterates are also established. The technique will be illustrated on a second-order right focal boundary value problem, with an example provided showing how to apply the results. [ABSTRACT FROM AUTHOR]

Since the topological properties of a b-metric space (which generalizes the concept of a metric space) seem sometimes counterintuitive due to the fact that the "open" balls may not be open sets, we review some aspects of these spaces concerning compactness, metrizability, continuity and fixed points. After doing so, we introduce new types of contractivities that extend the concept of Banach contraction. We study some of their properties, giving sufficient conditions for the existence of fixed points and common fixed points. Afterwards, we consider some iterative schemes in quasi-normed spaces for the approximation of these critical points, analyzing their convergence and stability. We apply these concepts to the resolution of a model of integral equation of Urysohn type. In the last part of the paper, we refine some results about partial contractivities in the case where the underlying set is a strong b-metric space, and we establish some relations between mutual weak contractions and quasi-contractions and the new type of contractivity. [ABSTRACT FROM AUTHOR]

Copyright of Actas de Diseño is the property of Facultad de Diseno y Comunicacion, Fundacion Universidad de Palermo and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Accurate dosimetric calculations are essential to enhance therapeutic efficacy in Yttrium-90 (Y-90) microsphere therapy, which rely significantly on the three-dimensional imaging parameters used. This study aims to evaluate the reconstruction parameters used to generate three-dimensional images from SPECT data obtained for dosimetric calculations, and to determine the optimal reconstruction parameters. This retrospective study evaluated Single Photon Emission Computed Tomography/Computed Tomography (SPECT/CT) images of 30 patients (8 women and 22 men) who underwent Transarterial Radioembolization (TARE) treatment at our clinic between 2018 and 2019 using Technetium 99mTc-labeled macroaggregated albumin (99mTc-MAA). The SPECT images were reconstructed using 20 different iterations and subset values. The perfused areas were identified using 5% and 10% threshold values. At the 5% threshold, the maximum difference from the average was 20.7% at 2 iterations and 2 subsets. For other parameters, the difference from the average was less than 2.8%. At the 10% threshold, the maximum difference from the average was 14.8% at 2 iterations and 2 subsets, with other parameters again showing a difference of less than 2.8%. For effective TARE treatment, it is recommended to set the SPECT image reconstruction parameters to higher than 5 iterations and 5 subsets following the administration of 99mTc-MAA. [ABSTRACT FROM AUTHOR]

The process of complex formation in the heterogeneous system Cu(Hg)–Cu(II)–L-Ala–H2O is studied using the classical Clark–Nikolsky oxidation potential method at a temperature of 298.15 K and a solution ionic strength of 1.0 mol/L. It is shown that coordination compounds [Cu(H2A)4]2+; [CuHL(H2A)3]2+; [Cu(HL)(OH)(H2A)2]+; [Cu(OH)2(H2A)2]0; and [Cu(HL)(L)(H2A)2]+ are formed in this system. The process of complex formation occurs in a fairly wide range from pH 1.0 to 8.8. Using the method of successive approximation (iteration) of the oxidative function, the formation constants of complexes are calculated, the areas of their dominance and maximum degrees of accumulation are determined, and diagrams of their distribution as a function of pH are constructed. [ABSTRACT FROM AUTHOR]

In this work, we develop a new iterative method for computing the digits of π by argument reduction of the tangent function. This method combines a modified version of the iterative formula for π with squared convergence that we proposed in a previous work and a leading arctangent term from the Machin-like formula. The computational test we performed shows that algorithmic implementation can provide more than 17 digits of π per increment. Mathematica codes, showing the convergence rate for computing the digits of π , are presented. [ABSTRACT FROM AUTHOR]

Iterative procedures have been proved as a milestone in the generation of fractals. This paper presents a novel approach for generating and visualizing fractals, specifically Mandelbrot and Julia sets, by utilizing complex polynomials of the form Q C (p) = a p n + m p + c , where n ≥ 2 . It establishes escape criteria that play a vital role in generating these sets and provides escape time results using different iterative schemes. In addition, the study includes the visualization of graphical images of Julia and Mandelbrot sets, revealing distinct patterns. Furthermore, the study also explores the impact of parameters on the deviation of dynamics, color, and appearance of fractals. [ABSTRACT FROM AUTHOR]

We study and solve some class of infinite systems of algebraic equations with monotone nonlinearity and Toeplitz-type matrices. Such systems for the specific representations of nonlinearities arise in the discrete problems of dynamic theory of clopen -adic strings for a scalar field of tachyons, the mathematical theory of spatio-temporal spread of an epidemic, radiation transfer theory in inhomogeneous media, and the kinetic theory of gases in the framework of the modified Bhatnagar–Gross–Krook model. The noncompactness of the corresponding operator in the bounded sequence space and the criticality property (the presence of trivial nonphysical solutions) is a distinctive feature of these systems. For these reasons, the use of the well-known classical principles of existence of fixed points for such equations do not lead to the desired results. Constructing some invariant cone segments for the corresponding nonlinear operator, we prove the existence and uniqueness of a nontrivial nonnegative solution in the bounded sequence space. Also, we study the asymptotic behavior of the solution at . In particular, we prove that the limit at of a solution is finite. Also, we show that the difference between this limit and a solution belongs to . By way of illustration, we provide some special applied examples. [ABSTRACT FROM AUTHOR]

The present work is devoted to finding numerical solutions of two types of nonlinear integral equations on half line with kernels depending on the sum and difference of arguments. These equations arise in various fields of mathematical physics: kinetic theory of gases, theoretical astrophysics, p-adic string theory, etc. The main result of the work is the derivation of an uniform estimate of the norm of difference between two successive approximations of solutions, which plays an important role for the control of the convergence of iterative schemes and number of iterations. The obtained results have been applied to determine numerical solutions of models from different areas of applications. [ABSTRACT FROM AUTHOR]