Mathematical Perspective Research Articles

MATHEMATICAL MODELLING OF FOOD MANAGEMENT FOR WILD LIFE POPULATION WITH MILD ENVIRONMENTAL EFFECT

In this paper we constructed a Mathematical Model of food management for animal species interacting with natural environment. The mathematical framework has been generated with generations as the time scale. Efforts have been made to mathematically formalize the environmental changes dependent food availability and consequent changes. The aim to develop a mathematical perspective to understand the environmental impact on wild life population and its food management. The carrying capacity of environment in terms of primary food has been assumed to be limited. The environmental changes lead to changes in availability of vegetation for animal species. A Mathematical model is constructed in terms of a system of nonlinear difference equations. The solutions have been worked out for some special cases. These solutions can be expressed as finite polynomials. Graphical patterns have been worked out as examples

A perturbation-based approach for continuous network design problem with link capacity expansion

This paper formulates a continuous network design problem (CNDP) as a nonlinear mathematical program with complementarity constraints (NLMPCC) and then a perturbation-based approach is proposed to overcome the NLMPCC problem and the lack of constraint qualifications. This formulation permits a more general route cost structure and every stationary point of it corresponds to a global optimal solution of the perturbed problem. The contribution of this paper from the mathematical perspective is that, instead of using the conventional nonlinear programming methodology, variational analysis is taken as a tool to analyse the convergence of the perturbation-based method. From the practical point of view, a convergent algorithm is proposed for the CNDP and employs the sequential quadratic program (SQP) solver to obtain the solution of the perturbed problem. Numerical experiments are carried out in both 16 and 76-link road networks to illustrate the capability of the perturbation-based approach to the CNDP with elastic demand. Results showed that the proposed model will solve a wider class of transportation equilibrium problems than the existing ones.

A generalized European option pricing model with risk management

Risk control systems in financial markets with numerous innovative financial products are characterized by infrequent and significant fluctuations (e.g., financial crises and minor disturbances occurring anytime and anywhere). Given that the traditional Black–Scholes (BS) model is difficult to adapt to ever-changing financial markets, to better describe real financial markets, this paper presents a generalized European option-pricing model with stochastic volatility and stochastic interest rates and pure jumps under Levy processes, which are stochastic processes with both stationary and independent increments. We use the Levy–Ito formula and measurement tools to transform logarithmic stock prices into conditions under risk neutral measures, and the characteristic functions of logarithmic stock prices are obtained using the decomposed characteristic function form. We in turn obtain a characteristic function solution based on the Fourier and inverse Fourier transform. Finally, we conduct a Monte Carlo (MC) simulation which highlight the adaptability, accuracy and efficiency of the FFT algorithm. The proposed model is superior from an economic and mathematics perspective, as it not only inherits advantages of the BS model but also better depicts the leptokurtosis and jump phenomenon in option markets.

An Understanding of Artificial Bee Colony Algorithm from the Perspective of Computation and Applied Mathematics: A Comparative Study

In the recent past, one of the swarm-based algorithms that have been introduced is Artificial Be Colony (ABC) algorithms. The role of ABC lies in the stimulation of honeybee swarms’ intelligent foraging behavior. This study applied the ABC algorithm toward large numerical test function optimization. Also, the results were compared with those that had been reported by experimental studies employing evolution strategies, differential evolution algorithm, particle swarm optimization algorithm, and genetic algorithm. From the findings, the study established that ABC exhibits superior performance compared to population-based algorithms, with other situations also witnessing the algorithm’s performance likened to or similar to the population-based algorithms. The factor that explained the superiority of the ABC algorithm was that it employs fewer control parameters.

Applying Isotropic Fractional-Rational Curves Toward Surface Modeling: New Insights from the Applied Mathematics Perspective

Given curves or points, one of the problems that have been documented in the recent past entails building smooth surfaces. The problem is pronounced due to computer technology and industry developments. Initially, zero Gaussian curvature shells and minimal surfaces were used. These surfaces relied on isotropic analytic curves. However, consumer properties restrict these curves. Hence, there is a growing need to steer expansions in surface shaping. In response to this trend, this paper proposed a technique for surface construction based on the role of isotropic fractional-rational curves. In the framework, the building of surfaces involved the use of flat orthogonal and isothermal grids, a process governed by the Weierstrass technique. Indeed, the latter approach was adopted due to the associated trend of demanding minimal surfaces.

Gaussian states as minimum uncertainty states

In bosonic fields, Gaussian states, which consist of a rather wide family of states including coherent states, squeezed states, thermal states, etc., have many classical-like features, and are usually defined from the mathematical perspective in terms of characteristic functions. It is well known that some special Gaussian states, such as coherent states, are minimum uncertainty states for the conventional Heisenberg uncertainty relation involving canonical pair of position and momentum observables. A natural question arises as whether all Gaussian states can be characterized as minimum uncertainty states. In this work, we show that indeed Gaussian states coincide with minimum uncertainty states for an information-theoretic refinement of the conventional uncertainty relation established in Luo (2005) [40]. This characterization puts Gaussian states on a novel basis of physical significance.

Lingko: Interweaving Manggarai Culture, and Mathematics

This research was conducted to explore the relationship between formal mathematics and Lingko, a system of traditional agricultural land distribution in Pocoleok, Manggarai-NTT Regency shaped like a spider web. Lingko was interesting to study concerning mathematics because of the philosophical values contained in Lingko and the Lingko sharing ceremony. This research focused on two things, namely: (1) how the distribution of ulayat land, Lingko, was mathematically reviewed while still paying attention to cultural values, and (2) how the community practiced mathematical concepts in the distribution of Lingko. The first focus of the problem was to uncover the mathematical activity of the distribution of ulayat land, Lingko, which was unknowingly carried out by the Pocoleok, Manggarai peoples. Knowledge gained from this first study might produce a new approach to learning mathematics, both from a mathematical or mathematical education perspective. The second focus of the problem sought to reveal the extent to which the basic concepts of Manggarai culture (following understanding) to solve mathematical problems faced in the reality of life. This second study provided more space for cultural-based mathematics learning, namely how to comprehend mathematical concepts based on contextual issues that arise in Manggarai culture.

Design of problem-solving questions for measuring mathematical thinking type mathematization

Mathematical thinking is a thought process in developing a mathematical perspective that involves other mathematical abilities such as modeling, reasoning, proving, symbolization, representation, abstraction, and mathematization. This study aims to describe the design results of problem-solving question that can be used to measure mathematical thinking type mathematization. This research is design research consisting of five stages, namely: preliminary design, focus group discussions, trials, observations and interviews, and retrospective analysis. The instrument consisted of test, observation, and interview. Data analysis uses qualitative methods. Based on data analysis, the problem-solving questions that are designed can already measure mathematical thinking type mathematization. This can be theoretically seen from the results of focus group discussions, which states the questions have been based on content, construct and language. Illustrated from the results of the trial, the strategies that have been used by the subject specifically on question number 1 is by making pictures and using certain mathematical formulas. Which solution illustrates that the subject has geometrization and formalization capabilities. Whereas in problem number 2, the mathematical ability that arises is connecting and formalization because in solving problems most subjects associate certain mathematical concepts and ideas with use facts, concepts and rules of mathematics.

Notes on Michio Morishima's Understanding of Marxian Economics

Michio Morishima's recapitulation and study of Marxian economics by means of mathematical methods focus primarily on the typical themes such as the labor theory of value, the theory of exploitation, the transformation problem, the theory of reproduction and so on, which provides a new mathematical perspective for understanding Marxian economics. However, Morishima's understanding of Marxian economics is full of contradictions: on the one hand, he speaks highly of Marxian economics, believing that Marx has conducted pioneering work in and made innovative contributions to general equilibrium theory, dynamic general equilibrium theory, contemporary economic growth theory, input–output analysis and the dual dualities of commodity production society and the like important fields and front subjects of modern economics, in particular Morishima, employing mathematical methods, has proved the objectivity of values and the sufficiency and necessity of exploitation to capitalism; on the other hand, Morishima attempts to integrate Marxian economics into orthodox economics, and finally contends abandoning the labor theory of value, the theory of exploitation (the theory of surplus value) and the theory of the breakdown of capitalism. The work of Morishima shows that formalized Marxian economics must follow the logic of Marxian economics, otherwise, replacing the logic of economics with the logic of mathematics will lead to erroneous results.

Nested formulation paradigms for induced ordered weighted averaging aggregation for decision‐making and evaluation

Existing extensions to Yager's ordered weighted averaging (OWA) operators enlarge the application range and to encompass more principles and properties related to OWA aggregation. However, these extensions do not provide a strict and convenient way to model evaluation scenarios with complex or grouped preferences. Based on earlier studies and recent evolutionary changes in OWA operators, we propose formulation paradigms for induced OWA aggregation and a related weight function with self-contained properties that make it possible to model such complex preference-involved evaluation problems in a systematic way. The new formulations have some recursive forms that provide more ways to apply OWA aggregation and deserve further study from a mathematical perspective. In addition, the new proposal generalizes almost all of the well-known extensions to the original OWA operators. We provide an example showing the representative use of such paradigms in decision-making and evaluation problems.

DẠY HỌC KHÁI NIỆM TÍCH PHÂN Ở TRƯỜNG PHỔ THÔNG TỪ QUAN ĐIỂM LIÊN MÔN TOÁN – VẬT LÍ: MỘT GIẢI PHÁP GIÚP VƯỢT QUA NHỮNG BẤT CẬP ĐẶT RA BỞI CÁC CÁCH TIẾP CẬN TRUYỀN THỐNG

DẠY HỌC KHÁI NIỆM TÍCH PHÂN Ở TRƯỜNG PHỔ THÔNG TỪ QUAN ĐIỂM LIÊN MÔN TOÁN – VẬT LÍ: MỘT GIẢI PHÁP GIÚP VƯỢT QUA NHỮNG BẤT CẬP ĐẶT RA BỞI CÁC CÁCH TIẾP CẬN TRUYỀN THỐNG

Which Needle in which Trocar? A Mathematical-Theoretical Approach

Aim-Background: Needles used in surgery come in various sizes and shapes, and with varying properties. In lapa-roscopic surgery, the trocars create the communication ports to the operative environment, and these ports are used for the introduction of instruments into the surgical field. Needles also need to be passed through these cannulas, which creates constraints regarding the needle size. The aim of this study was to describe the correlation between trocar size and needle size/shape. Methods: In order to estimate the maximum needle length that can be introduced through trocars of different calibers, we approached this problem from the mathematical and theoretical perspective, based on the four most commonly used needle types and the six most frequently used trocars. Results: The results are summarized in a table which determines the maximum needle length the surgeon may choose, given the specific needle type and trocar. Conclusions: Introduction of needles into the abdomen through laparoscopic trocars poses the risk of needle distortion or trocar dysfunction. In order to avoid these complications, the type and length of the needle to be introduced should be compatible with the diameter of the trocar.

Mathematical Aspects in Combining Network Coding With Transmission Range Adjustment

Combining topology control with network coding has been recently noticed which provides essential advantages, such as lower energy consumption and higher lifetime. In this letter, we utilize optimization and graph theory to propose a mathematical perspective for combining network coding with transmission range adjustment in wireless sensor network (WSN). For this aim, we define an extended optimization problem based on two vectors of variables, including transmission range and network flow. In particular, it is proved that there is a coding solution if and only if the extended optimization problem has at least an optimal solution. Due to this theorem, a new objective function is provided which is more practical to prolong the lifetime of WSNs. Simulation results demonstrate that the proposed model could adjust transmission range efficiently to obtain the optimal lifetime for network-coding-based WSNs.

Subject adaptation network for EEG data analysis

Biosignals tend to display manifest intra- and cross-subject variance, which generates numerous challenges for electroencephalograph (EEG) data analysis. For instance, in the context of classification, the discrepancy between EEG data can make the trained model generalising poorly for new test subjects. In this paper, a subject adaptation network (SAN) inspired by the generative adversarial network (GAN) to mitigate different variances is proposed for analysing EEG data. First the challenges faced by traditional approaches employed for EEG signal processing are emphasised. Then the problem is formulated from mathematical perspective to highlight the key points in resolving such discrepancies. Third, the motivation behind and design principle of the SAN are described in an intuitive manner to reflect its suitability for analysing EEG data. Then after depicting the overall architecture of the SAN, several experiments are used to justify the practicality and efficiency of using the proposed model from different perspectives. For instance, an EEG dataset captured during a stereotypical neurophysiological experiment called the VEP oddball task is utilised to demonstrate the performance improvement achieved by running the SAN.

Fatalities by traffic in Maryland and Massachusetts evaluated in the context of a probabilistic random walk.

Introduction: The analysis of injuries caused by traffic from a physical and mathematical perspective can help improve road safety strategies. Objective: Predict the dynamics of traffic fatalities in the states of Maryland and Massachusetts for the years 2004 and 2014 in the context of probabilistic random walk. Methods: An analysis was made of the number of total fatalities caused by traffic per year, in the states of Maryland and Massachusetts between the years 1994-2003 and 1994-2013. The behavior of these values was analyzed as a probabilistic random walk; for this, the probabilistic lengths were found for each year, during the period studied and four probability spaces were analyzed, with which it was possible to analyze their behavior, to establish a prediction of the number of total fatalities caused by traffic for the years 2004 and 2014. Results: The predictions for the years 2014 and 2004 for Maryland and Massachusetts when compared with the real values, the percentage of success was 98%. Main conclusion: The predictions for the years 2014 and 2004 for Maryland and Massachusetts when compared with the real values, the percentage of success was 98%. Conclusions: the behavior of traffic fatalities in Maryland and Massachusetts presented a predictable self-organization from the context of probabilistic random walk, constituting a useful tool for analyzing the operation of road safety strategies.

Sliding mode control for Markovian jump repeated scalar nonlinear systems with packet dropouts: The uncertain occurrence probabilities case

This paper studies the sliding-mode-based control problem for a class of delayed Markovian jump repeated scalar nonlinear systems (RSNSs) subject to packet dropouts (PDs) and randomly occurring uncertainties (ROUs). Here, the phenomenon of the Markovian PDs is modeled by utilizing a random variable obeying Markov process. By using the Bernoulli distributed random variables, the ROUs under uncertain occurrence probabilities (UOPs) are characterized from the mathematical perspective. In addition, the time-delay considered is bounded time-varying with known upper and lower bounds. The attention is on designing a sliding-mode-based control method for Markovian jump RSNSs in the simultaneous presence of Markovian PDs, ROUs and time-varying delays. Specifically, the robustly asymptotically mean-square stability is ensured for corresponding sliding mode dynamics by proposing new sufficient criterion. Moreover, the reachability in discrete setting is analyzed, i.e., the state trajectories of the system from any initial condition are globally driven onto a small region nearby the pre-designed sliding surface in mean square sense by synthesizing a robust sliding mode control (SMC) law. Finally, the effectiveness of developed control method is verified by some simulations.

Towards a Materialist Vision of ‘Learning as Making’: the Case of 3D Printing Pens in School Mathematics

In this paper, we build on a previously developed notion of ‘learning as Making’ to examine mathematics thinking and learning in a highly transformative and technological Making environment: one that involves a handheld 3D printing technology which enables 3D models to be created instantly via one’s moving hand. In particular, we present two examples of Maker-centred lessons for teaching and learning of primary mathematics. In these lessons, the students actively constructed artefacts with 3D Printing Pens while engaging in inquiry-based learning activities, where the target concepts were properties of prisms and cross-sections at the primary 5 (age 10–11) and primary 6 (age 11–12) levels respectively. We use diffractive analysis to capture the fine details in students’ body-material interactions while engaging in the tasks with or without the 3D Printing Pens during the lessons. Through the lens of Making as a material act of creation and seeking to update Papert’s constructionist view of learning, we propose to rethink Making in school mathematics according to a four-fold characterisation: Making is co-constructing meanings, Making is mathematising, Making is assembling with technology and Making is inventing. We discuss our contribution towards advancing a materialist perspective of learning mathematics and implications for a ‘learning as Making’ pedagogy and curriculum.

Effective metric in fluid-gravity duality through parallel transport: A proposal

The incompressible Navier-Stokes (NS) equation is known to govern the hydrodynamic limit of essentially any fluid and its rich non-linear structure has critical implications in both mathematics and physics. The employability of the methods of Riemannian geometry to the study of hydrodynamical flows has been previously explored from a purely mathematical perspective. In this work, we propose a bulk metric in $(p+2)$-dimensions with the construction being such that the induced metric is flat on a timelike $r = r_c$ (constant) slice. We then show that the equations of {\it parallel transport} for an appropriately defined bulk velocity vector field along its own direction on this manifold when projected onto the flat timelike hypersurface requires the satisfaction of the incompressible NS equation in $(p+1)$-dimensions. Additionally, the incompressibility condition of the fluid arises from a vanishing expansion parameter $\theta$, which is known to govern the convergence (or divergence) of a congruence of arbitrary timelike curves on a given manifold. In this approach Einstein's equations do not play any role and this can be regarded as an {\it off-shell} description of fluid-gravity correspondence. We argue that {\it our metric effectively encapsulates the information of forcing terms in the governing equations as if a free fluid is parallel transported on this curved background}. We finally discuss the implications of this interesting observation and its potentiality in helping us to understand hydrodynamical flows in a probable new setting.

Implementing a Multidisciplinary Curriculum in a Finnish Lower Secondary School – The Perspective of Science and Mathematics

ABSTRACT Finland has recently reformed the national school curriculum, basing it on so-called twenty-first century skills. The curriculum prescribes that schools must organise at least one multidisciplinary learning module per year. In this case study, we investigate the implementation of such a module in secondary school (grade 9) from the perspective of the school headmaster and science and mathematics teachers. The data comprise interviews with the headmaster, teachers, and protocols from collegiate meetings. Despite some gains experienced by teachers concerning cooperation with colleagues, the results reveal challenges connected to diffusely defined learning goals, as well as to the vagueness of goals concerning the role of different subjects in the module. The study shows the importance of offering research-based support and time for shared sensemaking for stakeholders to avoid the problems identified when implementing multidisciplinary teaching.

Abatement of gaseous volatile organic compounds: A process perspective

Abstract Volatile organic compounds (VOCs) are a class of liquid compounds with low saturation vapor pressures, which enables them to change phases even at ambient conditions. This causes a huge problem when it comes to emissions. A large portion of VOCs cause catastrophic health effects such as cancer or liver damage even at very low concentrations (ppm), and the control of these compounds is vital in ensuring good air quality. Many VOCs are used in common household implements such as wood finishes or paints and can even be emitted off improperly ventilated cooking. This significantly alters indoor air quality, and as such, a large portion of research into these compounds have focused on indoor air. On the other hand, their widespread use as solvents in most industries along with their emission rates from vehicular exhausts results in contamination of outdoor air as well. The combination of these VOCs and NOx pollutants tends to cause ground level ozone formation, which has a large bio-toxicity and causes the formation of a smog. Densely populated cities have also seen a sharp rise in VOC emissions due to the increase in both vehicular traffic and industrialization. A myriad of options is available for the abatement of VOCs, and they are similar to other pollution control strategies. These methods can be broadly be classified into destruction, separation and hybrid methods. This review discusses the different perspectives to be considered for this scenario, along with descriptions of the different methods available to the industry, along with some novel technologies that have been introduced recently. The influential parameters for each method have been investigated, along with optimum catalyst/material selection. In addition to this, a mathematical modeling perspective has also been examined, with significance to simulation studies performed for the control of VOC emission technologies.