Hasil untuk "Applied mathematics. Quantitative methods"

Michele Antonio Fino, Carmine Garzia

In the context of strategies for the promotion of a sustainable wine industry, the utilization of production regulations under the European Geographical Indications system is seldom contemplated. Furthermore, when such texts are considered, the focus is typically on rules for viticulture or winemaking, rather than on articles governing the boundaries of a PDO or PGI. The present study examines the manner in which regulatory innovation, when viewed from a strictly geographical perspective, can promote the sustainable growth of the sparkling wine districts of Franciacorta and Oltrepò Pavese, which are located in the Italian Lombardy region. Through a comparative analysis of Franciacorta and Oltrepò Pavese, we explore how regulatory frameworks, land-use constraints, and production capacities interact to shape environmental, social, and economic sustainability. Franciacorta’s premium positioning and global reputation are constrained by its limited geographic area, making expansion environmentally and socially challenging. In contrast, Oltrepò Pavese has substantial production potential, particularly for Pinot Noir-based classic-method sparkling wines but suffers from a fragmented identity and weak market recognition. Benchmarking the Prosecco PDO evolution, we propose a sustainability-oriented growth model integrating multiple territories under harmonized rules, termed “Grande Franciacorta”. This framework would enable controlled growth, reduce land pressure in high-density areas, enhance regional competitiveness, and support long-term ecological stewardship. This study outlines managerial implications for producers, emphasizing multi-tier product architectures, dynamic capabilities, and coordinated governance mechanisms. Policy recommendations highlight the need for regulatory frameworks that embed sustainability criteria, optimize land use, and consolidate regional reputation to ensure the long-term viability of high-quality sparkling wine production.

Allen Love, Omar Alejandro Valdez Pastrana, Saeed Behseresht et al.

Metal additive manufacturing (AM) techniques such Direct Energy Deposition (DED), Powder Bed Fusion (PBF), and Wire Arc Additive Manufacturing (WAAM) enable the production of complex metal components built at rapid rates. Because of the complexity of the process, including high thermal gradients, residual stress, and parameter optimization, these techniques pose significant challenges necessitating the need for advanced computational modeling. A powerful technique to reduce or, in some cases, eliminate these challenges at a much lower cost compared to trial-and-error experiments, is Finite Element Analysis (FEA). This study provides a comprehensive review of the FEA techniques being used and developed to model metal AM processes focusing on the thermal, mechanical, and coupled thermo-mechanical models in DED, PBF, and WAAM. Key topics include heat transfer, residual stress and distortion prediction, microstructure evolution and parameter optimization. Recent advancements in FEA have improved the accuracy of AM process simulations, reducing the need for costly experimental testing, though there is still room for improvement and further development of FEA in metal AM. This review serves as a foundation for future work in the metal AM modeling field, enabling the development of optimized process parameters, defect reduction strategies and improved computational methodologies for high-fidelity simulations.

Safieddine Bouali

I investigate how partial prey migration cycles, analogous to a non-autonomous harmonic oscillator, force the classical Lotka-Volterra model and reshape predator-prey interactions. A 3D nonlinear system is introduced, into which the external forcing replicates the entry and exit of partial migrants from the ecosystem, devoid feedback loops. Numerical simulations reveal an elusive resilience contour of the species interplay under stationary migration cycles. Thus, quasi-periodic and chaotic fluctuations appear at a minimum migration magnitude, vanishing beyond a bifurcation-induced tipping point. However, resilient interactions surge in localized hotspots, i.e., narrow regions of phase space and forcing intensity. It is striking to note that the detected chaos exhibits a threefold complexity related to migration magnitude, initial conditions, and a functional response parameter, implying a basin of attraction intertwined at fractal boundaries. In contrast, the resilience non-monotonicity fades due to ascending cycles of partial prey migration involving recruitment of a cohort of migrants by its resident species. In this case, chaos is suppressed, leading to predictable oscillations and phase-locking. Even extreme predator-prey ratios (e.g., 10:1) do not endanger prey. Despite its parsimony, the framework offers a tractable prototype with broader ecological applicability for studying how exogenous forcings (e.g., climate-driven phenology), can alter ecosystems.

Paola Pia Foligno, Daniele Boffi, Fabio Credali et al.

Standard Virtual Element Methods (VEM) are based on polynomial projections and require a stabilization term to evaluate the contribution of the non-polynomial component of the discrete space. However, the stabilization term is not uniquely defined by the underlying variational formulation and is typically introduced in an ad hoc manner, potentially affecting the numerical response. Stabilization-free and self-stabilized formulations have been proposed to overcome this issue, although their theoretical analysis is still less mature. This paper provides an in-depth numerical investigation into different stabilized and self-stabilized formulations for the p-version of VEM. The results show that self-stabilized and stabilization-free formulations achieve optimal accuracy while suffering from worse conditioning. Moreover, a new projection operator, which explicitly accounts for variable coefficients, is introduced within the framework of standard virtual element spaces. Numerical results show that this new approach is more robust than the existing ones for large values of p.

Wenshu Zhou, Xiaodan Wei

We consider a diffusive predator–prey model of Leslie–Gower type, and obtain a new global stability result by combining the Lyapunov function method and the transformation technique used in Qi and Zhu, (2016). Our result partially answers the question proposed in [Y. H. Du and S. B. Hsu, J. Differential Equations 203(2004) 331–364]. In addition, we extend the result to a class of diffusive systems with a more general type of reaction-terms.

Yue Wang

In this short review, I will summarize my research experience in three fields in applied mathematics: mathematical biology, applied probability, and applied discrete mathematics. Specifically, I will show how each project was initiated, and what wrong approaches were applied. Such details are important in learning how to do research, but they cannot be read out from research papers. I wish that students and junior researchers in applied mathematics could learn a lesson from this summary.

Nicolas Balacheff

It is nowadays common to consider that proof must be part of the learning of mathematics from Kindergarten to University1. As it is easy to observe, looking back to the history of mathematical curricula, this has not always been the case either because following an old pedagogical tradition of rote learning proof was reduced to the formalism of a text and deprived from its meaning or, despiteits acknowledged presence anywhere in mathematics, proof did not get the status of something to learn for what it is. On the long way from its absence as such in the past to its contemporary presence as a content to be taught at all grades, proof has had to go through a process of didactical transposition to satisfy a number of different constraints either of an epistemic, didactical, logical ormathematical nature. I will follow a chronological order to outline the main features of this process with the objective to better understand the didactical problem that our current research is facing.

Porntip Dechpichai, Nuttawadee Jinapang, Pariyakorn Yamphli et al.

The purpose of this research is to study the spatial and temporal groupings of 124 meteorological stations in Thailand under ENSO. The multivariate climate variables are rainfall, relative humidity, temperature, max temperature, min temperature, solar downwelling, and horizontal wind from the conformal cubic atmospheric model (CCAM) in years of El Niño (1987, 2004, and 2015) and La Niña (1999, 2000, and 2011). Euclidean distance timed and spaced with average linkage for clustering and silhouette width for cluster validation were employed. Five spatial clusters (SCs) and three temporal clusters (TCs) in each SC with different average precipitation were compared by El Niño and La Niña. The pattern of SCs and TCs was similar for both events except in the case when severe El Niño occurred. This method could be applied using variables forecasted in the future to be used for planning and managing crop cultivation with the climate change in each area.

M. Dehghan Banadaki, H. Navidi

The Tau method based on the Bernoulli polynomials is implemented efficiently to approximate the Nash equilibrium of open-loop kind in non-linear differential games over a finite time horizon. By this treatment, the system of two-point boundary value problems of differential game ex-tracted from Pontryagin’s maximum principle is transferred to a system of algebraic equations that Newton’s iteration method can be used for solving it. Also, for the mentioned approximation by the Bernoulli polynomials, the convergence analysis and the error upper bound are discussed. To demonstrate the applicably and accuracy of the proposed approach, some illustrated examples are presented at the final.

A.K. Pal, Anindita Bhattacharyya, Ashok Mondal

In this paper, an eco-epidemiological model has been studied where disease of prey population is modelled by a Susceptible–Infected (SI) scheme. Prey switching strategy is adopted by predator population when they are provided with two types of prey, susceptible and infected prey. However switching may happen due to several reasons such as shortage of preferable prey or risk in hunting the plentiful prey. In this work, we have proposed a prey–predator system with a particular type of switching functional response where a predator feeds on susceptible and infected prey but it switches from one type of prey to another when a particular prey population becomes lower. Both the species are supposed to be commercially viable and undergo constant non-selective harvesting. The stability aspects of the switching models around the infection-free state from a local as well as a global perspective has been investigated. Our aim is to study the role of harvesting and refuge of susceptible population on the dynamics of disease propagation and/or annihilation of an epidemiological model under consideration of switching phenomena. Numerical simulations are done to demonstrate our analytical results.

Stefan Schmollinger, Si Chen, Sabeeha S. Merchant

All organisms, fundamentally, are made from the same raw material, namely the elements of the periodic table. Biochemical diversity is achieved with how these elements are utilized, for what purpose and in which physical location. Determining elemental distributions, especially those of trace elements that facilitate metabolism as cofactors in the active centers of essential enzymes, can determine the state of metabolism, the nutritional status or the developmental stage of an organism. Photosynthetic eukaryotes, especially algae, are excellent subjects for quantitative analysis of elemental distribution. These microbes utilize unique metabolic pathways that require various trace nutrients at their core to enable its operation. Photosynthetic microbes also have important environmental roles as primary producers in habitats with limited nutrient supply or toxin contaminations. Accordingly, photosynthetic eukaryotes are of great interest for biotechnological exploitation, carbon sequestration and bioremediation, with many of the applications involving various trace elements and consequently affecting their quota and intracellular distribution. A number of diverse applications were developed for elemental imaging allowing subcellular resolution, with X-ray fluorescence microscopy (XFM) being at the forefront, enabling quantitative descriptions of intact cells in a non-destructive method. This Tutorial Review summarizes the workflow of a quantitative, single-cell elemental distribution analysis of a eukaryotic alga using XFM.

Ingo Blechschmidt

Toposes can be pictured as mathematical universes. Besides the standard topos, in which most of mathematics unfolds, there is a colorful host of alternate toposes in which mathematics plays out slightly differently. For instance, there are toposes in which the axiom of choice and the intermediate value theorem from undergraduate calculus fail. The purpose of this contribution is to give a glimpse of the toposophic landscape, presenting several specific toposes and exploring their peculiar properties, and to explicate how toposes provide distinct lenses through which the usual mathematical objects of the standard topos can be viewed.

Yurii Nesterov, Mihai I. Florea

In this paper, we consider gradient methods for minimizing smooth convex functions, which employ the information obtained at the previous iterations in order to accelerate the convergence towards the optimal solution. This information is used in the form of a piece-wise linear model of the objective function, which provides us with much better prediction abilities as compared with the standard linear model. To the best of our knowledge, this approach was never really applied in Convex Minimization to differentiable functions in view of the high complexity of the corresponding auxiliary problems. However, we show that all necessary computations can be done very efficiently. Consequently, we get new optimization methods, which are better than the usual Gradient Methods both in the number of oracle calls and in the computational time. Our theoretical conclusions are confirmed by preliminary computational experiments.

Alexandre Borovik

The classical platonist / formalist dilemma in philosophy of mathematics can be expressed in lay terms as a deceptively naive question: \emph{Is new mathematics discovered or invented? Using examples from my own mathematical work during the Coronavirus lockdown, I argue that there is also a third way: new mathematics can also be inherited. And entering into possession, making it your own, could be great fun.

Shih-Hsien Tseng, Tien Son Nguyen

In the “Age of the Internet”, fake news and rumor-mongering have emerged as some of the most critical factors that affect our online social lives. For example, in the workplace, rumor spreading runs rampant during times when employees may be plagued with uncertainty about the nature and consequences of major changes. Positive information should be widely propagated as much as possible; however, we must limit the spread of rumors in an effort to reduce their inherently harmful effects. The purpose of this research is to explain the mechanisms for controlling rumors and suggest an approach for dispelling the rumor effect in the workplace. In this study, we will present a simple simulation framework of agent-based modeling and apply Social Impact Theory to explain rumor propagation within social networks. Based on our results, we have found that organizations can significantly reduce the spread of the rumors by improving the workplace environment and instituting counseling for those in management positions.

Alfredo Palomino I., Leighton Estrada R., Javier Valeriano M. et al.

In this work we carried out the mathematical modeling of the wound healing process, which is a well documented topic in medical and biological practice; but mathematically speaking there are still too much to be done for a clear understanding of the healing phenomom. Here we contribute to the mathematical modelling by using chemical kinetic concepts and mathematical tools, from which we have been able to formulate a system of ordinary differential equations of initial value, whose solution is presented graphically in front of a case study, where we have tested an active pharmaceutical principle with respect to its effectiveness. Finally, the speed of the healing process for such a case study produced an excellent agreement with experimental data that has been omitted due to confidentiality.

Dong Zhang, Xiang Lin, Xiang Chen

Network Function Virtualization addresses the defect of traditional middleboxes and enables operators to implement new services through a process named Service Function Chain mapping. Service Function Chain is composed by a sequence of Virtual Network Functions (VNFs) which is deployed in shared platforms. Service Function Chain with parallel VNFs is proposed to reduce the delivery latency. In this paper, a multiple instances mapping scheme named MIM is proposed to resolve the performance bottleneck introduced by the imbalance of parallel VNFs. A integer programing model is established to describe the multiple instances mapping problem based on queuing theory, and a double layer Genetic Algorithm is used to allocate parallel VNFs with multiple instances. Simulation results show that the multiple instances mapping scheme can improve the performance of Service Function Chain with parallel VNFs effectively.

Francesca Grassetti

This review analyses the influence of technologies and saving propensities of workers and shareholders on economic growth, considering the [1] model. We show how investing behaviors and production peculiarities condition the evolution of capital over time. We highlight that fluctuations and multiple equilibria arise only when the elasticity of substitution between capital and labor is lower than one. Moreover, only production functions with variable elasticity of substitution between inputs are able to describe the poverty trap phenomenon. Complex dynamics emerge when the difference between the saving propensity of the two income groups is sufficiently high.

Fiona R Macfarlane, Mark AJ Chaplain, Raluca Eftimie

Rheumatoid arthritis is a chronic autoimmune disease that is a major public health challenge. The disease is characterised by inflammation of synovial joints and cartilage erosion, which leads to chronic pain, poor life quality and, in some cases, premature mortality. Understanding the biological mechanisms behind the progression of the disease, as well as developing new methods for quantitative predictions of disease progression in the presence/absence of various therapies is important for the success of therapeutic approaches. The aim of this study is to review various quantitative predictive modelling approaches for understanding rheumatoid arthritis. To this end, we start by discussing briefly the biology of this disease and some current treatment approaches, as well as emphasising some of the open problems in the field. Then we review various mathematical mechanistic models derived to address some of these open problems. We discuss models that investigate the biological mechanisms behind the progression of the disease, as well as pharmacokinetic and pharmacodynamic models for various drug therapies. Furthermore, we highlight models aimed at optimising the costs of the treatments while taking into consideration the evolution of the disease and potential complications.

Ivica Pervan, Maja Pervan, Tamara Kuvek

Modelling firm failure, classically defined as bankruptcy, is problematic in the Croatian business environment since the bankruptcy procedure starts at a very late stage of crisis, when a firm liabilities are higher than assets. In order to overcome this problem, we propose an alternative definition of firm failure which is based on a firm's financial status, meaning financial distress, rather than its legal status. A firm is characterised as financially distressed when its EBITDA is lower than its interest expenses for two consecutive periods. Accordingly, we developed models based on three different failed firm statuses: (i) bankruptcy, (ii) rescue plan and (iii) financial distress. The application of logistic regression on a sample of Croatian firms has shown that a financial distress model has a high level of predictive power. Moreover, for the whole sample this model outperformed bankruptcy and rescue plan models in terms of overall accuracy and the prediction of failure status. Additional analysis has revealed that it is useful to develop a model for non-micro firms because such an estimation results in improved prediction power in comparison with a generic, one-size firm model. In the case of non-micro firms, the financial distress model outperformed the rescue plan model, while the hit rate was similar to the hit rate of the bankruptcy model. A developed financial distress model can be applied by investors and creditors in order to timely evaluate firm failure risks and undertake required business decisions.