Recursion Relations Research Articles

Maintaining Agricultural Production Profitability—A Simulation Approach to Wheat Market Dynamics

Profitability is a complex notion, intertwined with theoretical, socio-economic, and modern economic considerations. While traditionally linked to monopoly advantages, contemporary views broaden this to include shareholder value creation. In agriculture, profitability faces impediments such as rising input costs, market volatility, and economic disparities, emphasizing technological innovation, market conditions, and policy as crucial determinants. This study presents an econometric simulation model to analyze and forecast wheat production profitability in Poland from 2023 to 2027, providing insights into production efficiencies, market dynamics, and policy impacts. Using a system of recursive equations, the model forecasts profitability, integrating econometric techniques with expert insights. It examines variables like resource use, production levels, and price changes, validated through FADN data. The findings reveal that price relations and production efficiencies are the key to profitability. The model highlights market volatility, particularly through “price scissors”, as the main factor influencing profitability. Favorable price conditions significantly boost profitability and incentivize production. The model is a critical tool for analyzing wheat profitability, highlighting the influence of market and policy changes. Future work could extend the model’s use to other regions or crops, incorporating advanced technologies to improve accuracy. This study offers valuable insights for agricultural economics, aiding stakeholders in strategic decision-making.

The Value of Fractal Analysis in Ultrasound Imaging: Exploring Intricate Patterns

Fractal analysis is a mathematical approach employed to study and describe complex patterns and structures across various disciplines, including mathematics, physics, computer science, biology and finance. Introduced by mathematician Benoit Mandelbrot in the 1970s, fractals are intricate, self-similar patterns that repeat at different scales, exhibiting consistent structures upon magnification or reduction. This analysis involves generating fractals through iterative processes or recursive equations, resulting in highly detailed and complex formations. Fractal analysis enhances medical images by removing noise while preserving details and improving diagnostic quality in magnetic resonance and computed tomography scans. However, there is a lack of comprehensive studies on its application in ultrasound imaging, prompting this narrative review to investigate its use and methodology in this context. Selected papers on the use of fractal analysis in ultrasound imaging were analyzed. Out of 186 records screened, 60 duplicates were removed and 28 were discarded. The text content of 98 potentially eligible papers was checked, with 65 not meeting inclusion criteria. Finally, 33 studies were included in the review. Fractal analysis enhances ultrasound imaging by providing detailed tissue texture characterization, aiding in the diagnosis of conditions like breast and lung cancer, osteoporosis and hypertensive disorders in pregnancy. It quantifies biological structure complexity and improves diagnostic accuracy and reliability. This technique supports clinicians in making informed decisions by offering critical insights into various medical conditions.

Space in project organising: Insights from planning within and between construction projects

Projects are discussed as social processes that are bounded in both time and space. Elaborating on space is still scarce in studies on project organising. The aim in this paper is to explore space influence on project planning, to extend our understanding of the relationship between space and project organising. Through two illustrative examples, construction project planning practices were followed within and between projects as the actors sought to handle space. Contribution develops current understanding of how projects are embedded in space and its influence on project planning practices, by shedding light on the recursive relationship between space and project organising. Furthermore, to trace planning practice both within a project and between parallel projects visualise how a broader perspective of the embeddedness is necessary. The findings nuance the current understanding of project's embeddedness, by visualising how planning practices can be directed to both changing space or to maintain space by changing practices.

Exponential series approximation of the SIR epidemiological model

IntroductionThe SIR (Susceptible-Infected-Recovered) model is one of the simplest and most widely used frameworks for understanding epidemic outbreaks.MethodsA second-order dynamical system for the R variable is formulated using an infinite exponential series expansion, and a recursion relation is established between the series coefficients. A numerical approximation scheme for the R variable is also developed.ResultsThe proposed numerical method is compared to a double exponential (DE) nonlinear approximate analytic solution, which reveals two coupled timescales: a relaxation timescale, determined by the ratio of the model’s time constants, and an excitation timescale, dictated by the population size. The DE solution is applied to estimate model parameters for a well-known epidemiological dataset—the boarding school flu outbreak.DiscussionFrom a theoretical standpoint, the primary contribution of this work is the derivation of an infinite exponential, Dirichlet, series for the model variables. Truncating the series yields a finite approximation, known as a Prony series, which can be interpreted as a sequence of coupled exponential relaxation processes, each with a distinct timescale. This apparent complexity can be approximated well by the DE solution, which appears to be of main practical interest.

Bootstrapping multi-wound twist effects in symmetric orbifold CFTs

We investigate the effects of the twist-2 operator in 2D symmetric orbifold CFTs. The twist operator can join together a twist-M state and a twist-N state, creating a twist-(M + N) state. This process involves three effects: pair creation, propagation, and contraction. We study these effects by using a Bogoliubov ansatz and conformal symmetry. In this multi-wound scenario, pair creation no longer decouples from propagation, in contrast to the previous study where M = N = 1. We derive equations for these effects, which organize themselves into recursion relations and constraints. Using the recursion relations, we can determine the infinite number of coefficients in the effects through a finite number of inputs. Moreover, the number of required inputs can be further reduced by applying constraints.

Study on the parameter identification of lithium-ion battery model under high-rate pulse discharge conditions

With the rapid development of the new energy sector and lithium-ion (Li-ion) battery technologies, using Li-ion batteries with high energy density and high discharge rate to form the primary energy subsystem can further improve the compactness and miniaturization level of pulsed power systems. In traditional electric power systems, Li-ion batteries normally operate under the discharge condition of low current and long time. However, as the main power source of pulsed power systems, it is required that Li-ion batteries should have the capability for high-rate pulse discharge. To ensure the safe and reliable operation of the battery energy storage system, it is necessary to conduct the parameter identification of the Li-ion battery model to establish an accurate pulse discharge model under such working conditions. This paper focuses on the discharge characteristics of a cylindrical high-rate single Li-ion battery with a capacity of 3 Ah. At a 20 C rate, the discharge data were obtained when the pulse repetition frequency was 10 Hz and the duty cycle was 90%. By using the mathematical expressions of the Thevenin equivalent circuit model, the recursive relationship of the circuit parameters was obtained, and the parameter identification of the battery model was conducted based on the experimental data by using the genetic algorithm. The results show that the fitting accuracy of the parameter identification reaches 0.9995, indicating the high precision of the model for the Li-ion battery. This work provides a significant reference for the modeling and parameter identification of Li-ion batteries under high-rate pulse discharge conditions.

Distribution of centrality measures on undirected random networks via the cavity method

The Katz centrality of a node in a complex network is a measure of the node's importance as far as the flow of information across the network is concerned. For ensembles of locally tree-like undirected random graphs, this observable is a random variable. Its full probability distribution is of interest but difficult to handle analytically because of its "global" character and its definition in terms of a matrix inverse. Leveraging a fast Gaussian Belief Propagation-Cavity algorithm to solve linear systems on tree-like structures, we show that i) the Katz centrality of a single instance can be computed recursively in a very fast way, and ii) the probability [Formula: see text] that a random node in the ensemble of undirected random graphs has centrality [Formula: see text] satisfies a set of recursive distributional equations, which can be analytically characterized and efficiently solved using a population dynamics algorithm. We test our solution on ensembles of Erdős-Rényi and Scale Free networks in the locally tree-like regime, with excellent agreement. The analytical distribution of centrality for the configuration model conditioned on the degree of each node can be employed as a benchmark to identify nodes of empirical networks with over- and underexpressed centrality relative to a null baseline. We also provide an approximate formula based on a rank-[Formula: see text] projection that works well if the network is not too sparse, and we argue that an extension of our method could be efficiently extended to tackle analytical distributions of other centrality measures such as PageRank for directed networks in a transparent and user-friendly way.

An application of recurrence relations to central force fields

By generalizing the relationships between auxiliary variables that appear in the works of A.E. Roy, we investigate the dynamics of non-interacting particles under the action of a central force field whose force function is a solution to a certain differential equation. The method used by A.E. Roy, R. Broucke, and later by G. Sitarski, was utilized in such a way that the obtained recursive equations can be used to describe the motion of a particle under such a field. The class of such fields includes both gravitational and non-gravitational force fields. Several numerical and historically essential examples and detailed discussions of various cases are given.

General expressions for on-shell recursion relations for tree-level open string amplitudes

In this paper, we present a systematic derivation aimed at obtaining general expressions for on-shell recursion relations for tree-level open string amplitudes. Our approach involves applying the BCFW shift to an open string amplitude written in terms of multiple Gaussian hypergeometric functions. By employing binomial expansions, we demonstrate that the shifted amplitudes manifest simple poles, which correspond to scattering channels of intermediate states. Using the residue theorem, we thereby derive a general expression for these relations.

Recurrence formulae for spectral determinants

We develop a unified method to study spectral determinants for several different manifolds, including spheres and hemispheres, and projective spaces. This is a direct consequence of an approach based on deriving recursion relations for the corresponding zeta functions, which we are then able to solve explicitly. Apart from new applications such as hemispheres, we also believe that the resulting formulae in the cases for which expressions for the determinant were already known are simpler and easier to compute in general, when compared to those resulting from other approaches.

Note on holographic torus stress tensor correlators in AdS3 gravity

In the AdS3/CFT2 framework, the Euclidean BTZ black hole corresponds to the dominant high-temperature phase of its dual field theory. We initially employ perturbative methods to solve the Einstein equations as boundary value problems, providing correlators for the energy-momentum tensor operator at low points. Utilizing operator equations established in our previous work, we further compute arbitrary high-point correlators for the energy-momentum tensor operator in the high-temperature phase and recursive relations for these high-point functions. Concurrently, we employ the Chern-Simons formalism to derive consistent results. Further, using the cut-off AdS/TT¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ T\\overline{T} $$\\end{document}-deformed CFT duality, we calculate the energy-momentum tensor correlators, contributing to the comprehensive understanding of the system’s dynamics. Finally, stress tensor correlators enable us to ascertain the corresponding KdV operator correlators at low-temperature.

Recurrent Relationships as an Important Class of Mathematical Equations in Chemistry

The unique potential and different areas of applications of recurrent (synonymous: recursive) relationships in chemistry and chromatography are considered. Recurrent relations can be used in two forms: as functions of integer arguments, y(x+ 1) = ay(x) + b, and as functions of equidistant argument values, A(x+ Δx) = aA(x)+ b, Δx= const. The first form applies to all physicochemical properties of homologs in organic chemistry, because the number of carbon (and other) atoms in a molecule can be integer only. The second one applies to chemical variables depending on temperature, pressure, concentrations, etc., when the chemists should provide equal “steps” of their variations. Recurrent relations combine the properties of arithmetic and geometric progressions, which accounts for their unique approximation abilities. This was illustrated by approximating the number of isomers of alkanes, the boiling points of homologs (nonlinear dependencies), the melting points of homologs (alternation effects), the temperature dependence of the solubility of inorganic salts in water, and by revealing the anomalies of gas chromatographic retention indices and retention times in reversed-phase high performance liquid chromatography.

The Protective Role of Supportive Relationships in Mitigating Bullying Victimization and Psychological Distress in Adolescents

AbstractSupportive relationships have been hypothesized to protect against psychological distress in general and to reduce the impacts of adversity on distress. Bullying victimization by peers is a salient adverse experience for many adolescents. Being bullied increases the risk of psychological distress which in turn increases the risk of further bullying victimization. There is minimal previous research on whether and how supportive relationships protect adolescents from bullying victimization, psychological distress and the recursive relationships between victimization and distress. This study investigated the direct and moderating effects of supportive relationships with parents, peers, and teachers on later psychological distress and bullying victimization of adolescents. This longitudinal study involved 1425 Australian adolescents aged 12–18 years (mostly male, 74.3%), using questionnaires on bullying victimization, psychological distress, and supportive relationships at two-time points, 6 months apart. All types of supportive relationships reduced the risk of later psychological distress predicted from earlier psychological distress, suggesting a direct compensatory effect. Support from classmates and parents also protected adolescents against ongoing bullying victimization and mitigated the impact of bullying victimization on later psychological distress, consistent with a stress-buffering hypothesis. The pattern of results confirms the important role that supportive relationships play in protecting adolescents from psychological distress and bullying victimization. Persistent bullying victimization and later psychological distress are less likely to occur for victimized adolescents supported by parents and classmates. Strategies and programs that improve parental support may enhance the effectiveness of programs to prevent bullying and improve outcomes for victims.

Faraday instability of viscous liquid films on a heated substrate with Maxwell–Cattaneo heat flux

Faraday instability of viscous liquid films with Maxwell–Cattaneo (MC) heat flux on an infinite, heated horizontal substrate subject to vertical time-varying periodic vibration is investigated theoretically. The MC effect means that the response of the heat flux to a temperature gradient obeys a relaxation time law rather than a classical Fourier time law. Applying the classic Floquet theory to linear analysis, a recursive relation is obtained. When considering the MC effect, a new phenomenon appears at a large wave number k. The neutral stability curves branch new tongues that turn left rather than right as before, but the tongues still move up and right as the wave number increases. Furthermore, typical harmonic (H) and subharmonic (SH) alternation behavior continues to exist. Interestingly, the first tongue of a branch is H or SH, implying that there is a transition following the branches. However, near the critical wave number kc of a branch, the SH and H almost overlap. As Cattaneo number C increases, the tongue-like unstable zones of branches become wider, and the critical wave number kc of the appeared branch becomes small. As the driving frequency ω decreases, the branch tongues become elongated and the critical wave number kc of the appeared branch becomes small.

Evolutional behavior of viscoelastic materials: A formulation based on logarithmic approach

In this paper, a new formulation for large deformation of visco-elastometic materials is derived. The formulation is based on logarithmic strain, and the internal variable is defined as the viscous part of the logarithmic strain. A derivation of thermodynamically consistent formulation for visco-elastomeric materials is provided. The evolution equation which is related to the deviatoric part of the strain for viscoelastic formulation is solved by the implicit trapezoidal integration rule which leads to a recursive relation.

Forced vibration characteristics of viscoelastic variable stiffness laminated composite plates using time and frequency domain approaches

The linear forced vibration characteristics of viscoelastic variable stiffness laminated composite plates (VVSLC) are studied using a generalized Maxwell model and finite element method. The integral form of the viscoelastic constitutive relation is converted to the incremental form for finite element formulation based on the Reissner–Mindlin plate theory. The recursive relations are developed to compute the current time-step solution using only the previous time-step solution. The periodic response directly in the time domain is obtained using shooting technique coupled with Newmark’s time integration method. The implementation of shooting technique for Boltzmann integral-based viscoelasticity for curvilinear fibre composite plates is done for the first time in this study. For the comparison purpose, the response/resonance frequency/modal loss factor is also obtained using equivalent complex modulus based viscoelastic correspondence principle. It is observed that the variation in fibre orientation and boundary conditions leads to significant variations in response, stress/moment resultant amplitude and the damping factor of the VVSLC plates. Further, the present time domain based approach is capable of predicting damping factor at all forcing frequencies whereas complex eigenvalue analysis can predict damping factor only at discrete resonance frequency. Based on the detailed studies, it is found that the curvilinear fibre composite plates depict a significant reduction in response/moment resultants compared to straight fibre composite plates.

A New Notion of Convergence Defined by The Fibonacci Sequence: A Novel Framework and Its Tauberian Conditions

The Fibonacci sequence has broad applications in mathematics, where its inherent patterns and properties are utilized to solve various problems. The sequence often emerges in areas involving growth patterns, series, and recursive relationships. It is known for its connection to the golden ratio, which appears in numerous natural phenomena and mathematical constructs. In this research paper, we introduce new concepts of convergence and summability for sequences of real and complex numbers by using Fibonacci sequences, called Δ-Fibonacci statistical convergence, strong Δ-Fibonacci summability, and Δ-Fibonacci statistical summability. And, these new concepts are supported by several significant theorems, properties, and relations in the study. Furthermore, for this type of convergence, we introduce one-sided Tauberian conditions for sequences of real numbers and two-sided Tauberian conditions for sequences of complex numbers.

An efficient recursive technique with Padé approximation for a kind of Lane–Emden type equations emerging in various physical phenomena

The study numerically examined a class of nonlinear singular differential problems known as the Lane–Emden differential equation, which emerges in numerous real-world situations. The primary goal of this work is to formulate a computationally efficient iterative technique for solving the nonlinear Lane–Emden initial value problems. The proposed approach is a hybrid of the homotopy perturbation method and the Padé approximation. The nonlinear singular Lane–Emden initial value problem (SLEIVP) is transformed into an equivalent recursive integral employing the Picard’s approach. To resolve the singularity and nonlinearity, the recursive integral equation is transformed into a system of integral equations by using the homotopy notion. Furthermore, to enhance the convergence rate of the technique, Padé approximation is taken into account. The convergence analysis for the proposed approach is also conducted. The present technique is tested on SLEIVPs and numerical findings are compared with the existing techniques, to demonstrate the accuracy, effectiveness and ease of use.

A new autonomous positioning method of Baseline-RFMDR and Kalman filter solution

The development of intelligent positioning requires a new method of low-cost to meet the needs of autonomous positioning or emergency positioning underground. A new method of Baseline Radio Frequency Magnetic Dead Reckoning (Baseline-RFMDR) autonomous positioning is constructed in this paper, to solve the problems of low accuracy of geomagnetic matching positioning and large cumulative errors in Pedestrian Dead Reckoning (PDR) positioning, which provides a new approach for high-precision and stable autonomous positioning of underground personnel. This method combines PDR positioning and geomagnetic matching positioning, with the constraint of baseline distance, which is the distance from the Tag Pair to the reader. The Kalman Filter solution equation for this model is constructed, and the recursive equation for the covariance matrix under baseline constraints is derived. An underground positioning test was conducted using the self-developed Baseline RFMDR positioning device, the results showed that the accuracy of this combined positioning method is significantly better than PDR positioning or geomagnetic matching positioning. At normal speed, the MAE and RMSE of Baseline-RFMDR combined positioning can be kept within 0.12 m in the X direction and within 0.2 m in the Y direction. It is 88% more accurate in the X direction than PDR, 60% more than geomagnetic matching, 70% more in the Y direction than PDR, and 75% more than geomagnetic matching. At fast speed, the MAE and RMSE of Baseline-RFMDR combined positioning can maintain 0.2 m in the X direction and 0.61 m in the Y direction. It is 79% more accurate in the X direction than PDR, 21% more than geomagnetic matching, 49% more than PDR in the Y direction, and 46% more than geomagnetic matching. At the same time, Baseline-RFMDR positioning has good robustness. When the initial coordinate error or initial covariance error or Baseline-RFMDR partial failure, the MAE and RMSE of Baseline-RFMDR combined positioning can still be maintained within 0.24 m.

Out-of-time-order asymptotic observables are quasi-isomorphic to time-ordered amplitudes

Asymptotic observables in quantum field theory beyond the familiar S-matrix have recently attracted much interest, for instance in the context of gravity waveforms. Such observables can be understood in terms of Schwinger-Keldysh-type ‘amplitudes’ computed by a set of modified Feynman rules involving cut internal legs and external legs labelled by time-folds.In parallel, a homotopy-algebraic understanding of perturbative quantum field theory has emerged in recent years. In particular, passing through homotopy transfer, the S-matrix of a perturbative quantum field theory can be understood as the minimal model of an associated (quantum) L∞-algebra.Here we bring these two developments together. In particular, we show that Schwinger-Keldysh amplitudes are naturally encoded in an L∞-algebra, similar to ordinary scattering amplitudes. As before, they are computed via homotopy transfer, but using deformation-retract data that are not canonical (in contrast to the conventional S-matrix). We further show that the L∞-algebras encoding Schwinger-Keldysh amplitudes and ordinary amplitudes are quasi-isomorphic (meaning, in a suitable sense, equivalent). This entails a set of recursion relations that enable one to compute Schwinger-Keldysh amplitudes in terms of ordinary amplitudes or vice versa.