Nkeh Oma Nfor, Akoni Brikly Njinabo, Francois Marie Moukam Kakmeni
We investigate the spatial profiles of periodic localized modes in attractive Bose-Einstein condensates, by solving the mean-field Gross-Pitaevskii equation in the presence of elliptic-type periodic potential. By considering a one-dimensional time independent linearized Gross-Pitaevskii equation, we obtained three bound state solutions and energies emanating from the first order Lamé equation. When the nonlinearity induced by the two body inter-atomic interactions are fully activated, spatially localized trivial phase periodic solutions of the attractive condensates are analytically obtained using the ansatz technique coupled with the direct integral method. Results of numerical simulation depicts trivial phase solutions, which are uniform train of spatially localized modes that are insensitive to variation of the elliptic modulus. However in the non-trivial phase regime, the spatially localized trains of soliton become very structurally unstable. This work underscores the spontaneous generation of periodic potential by the condensate wave function, determine the band structure of the lattice and basic properties of periodic matter waves under linear conditions, and highlight various spatial nonlinear periodic modes in the condensate. Finally, our investigation provides a solid theoretical framework that finds potential application in the fabrication of atomic lasers, periodic matter-wave gratings and quantum logic gates.
S. Sabarinathan, M. Sivashankar, Kottakkaran Sooppy Nisar
et al.
Chemical kinetics is the study of the rates of chemical reactions and the mechanisms by which they occur. This field is critical for optimizing industrial processes, such as fertilizer and pharmaceutical production, by increasing efficiency and yield. In environmental science, understanding reaction rates is crucial for modeling pollution dynamics and assessing environmental impacts. In biochemistry, chemical kinetics reveals the intricacies of cellular processes, aiding in the understanding of disease mechanisms and the development of new drugs. This article focuses on the stability analysis of fractal–fractional derivatives for enzyme kinetics. The primary objective is to examine the criteria for existence and uniqueness using the fixed-point technique. The study explores Hyers–Ulam stability results and discusses other significant findings for the proposed model and also employs numerical schemes using the Lagrange polynomial interpolation method. Finally, generate simulated graphical representations for various fractal–fractional order values, and the simulation results confirm the effectiveness and practical applicability of the theoretical findings.
Armin Shoushtarizadeh, Michele Cerminara, Corinne Chureau
et al.
Quantitative imaging of subcellular processes in living embryos, stem-cell systems, and organoid models requires microscopy platforms that combine high spatial resolution, fast volumetric acquisition, long-term stability, and minimal phototoxicity. Single-objective light-sheet approaches based on oblique plane microscopy (OPM) are well suited for live imaging in standard sample geometries, but most existing implementations lack the optical calibration, timing precision, and end-to-end integration required for reproducible quantitative measurements. Here we present a fully integrated and quantitatively characterized OPM platform engineered for dynamic studies of transcription and nuclear organization in embryos, embryonic stem cells, and three-dimensional culture systems. The system combines high numerical aperture remote refocusing with tilt-invariant light-sheet scanning and hardware-timed synchronization of laser excitation, galvo scanning, and camera readout. We provide a comprehensive characterization of the optical performance, including point spread function, sampling geometry, usable field of view, and system stability, establishing a well-defined framework for quantitative volumetric imaging. To support high-throughput operation, we developed a unified acquisition and reconstruction pipeline that enables real time volumetric imaging at hardware-limited rates while preserving deterministic timing and reproducible geometry. Using this platform, we demonstrate quantitative three-dimensional imaging of MS2-labeled transcription sites in living Drosophila embryos, cultured mouse embryonic stem cells, and mESC-derived gastruloids, enabling extraction of transcriptional intensity traces across diverse biological contexts. This work establishes OPM as a robust and quantitatively calibrated single-objective light-sheet platform for transcription imaging in complex living systems.
A new type of experiment with joint considerations of quantitative and sequence factors is recently drawing much attention in medical science, bio-engineering, and many other disciplines. The input spaces of such experiments are semi-discrete and often very large. Thus, efficient and economical experimental designs are required. Based on the transformations and aggregations of good lattice point sets, we construct a new class of optimal quantitative-sequence (QS) designs that are marginally coupled, pair-balanced, space-filling, and asymptotically orthogonal. The proposed QS designs have a certain flexibility in run and factor sizes and are especially appealing for high-dimensional cases.
Yiting Liu, Anthony James El-helou, Bill Soderstrom
et al.
Extracellular vesicles (EVs) have drawn rapidly increasing attention as the next-generation diagnostic biomarkers and therapeutic agents. However, the heterogeneous nature of EVs necessitates advanced methods for profiling EVs at the single-particle level. While nanoparticle tracking analysis (NTA) is a widely used technique for quantifying particle size and concentration, conventional scattering-based systems are non-specific. In this study, we present an optimised protocol for quantitative profiling of EVs at the single-particle level by fluorescent NTA (F-NTA). The protocol integrates fluorescent immunolabeling of EVs with size-exclusion chromatography (SEC) to efficiently remove unbound labels, enabling the precise quantification of EV concentration, size distribution, and surface immunophenotype. We first validated this approach using biotinylated liposomes and EVs from cultured human cell lines, confirming effective removal of unbound labels and assessing labelling efficiency. We then demonstrated that F-NTA can distinguish EV subpopulations with distinct surface marker expression, exemplified by the differentiation of EpCAM-positive EVs derived from HT29 and HEK293 cells. Finally, we applied dual labelling to human plasma isolates to simultaneously profile EVs and non-vesicular extracellular particles, providing a quantitative quality assessment of EV purity at the single-particle level. The robustness of this method was further supported by comparative analysis with total internal reflection fluorescence microscopy. This validated workflow enables robust, quantitative profiling of EV subpopulations, providing a critical tool for diverse EV applications, including biomarker discovery, therapeutic monitoring, and quality control for engineered vesicles.
This study considers a two-species reaction–diffusion–advection (RDA) model in a heterogeneous advective environment with zero Neumann boundary conditions. We suppose that two species compete for the same food resource but have different diffusion and advection rates. The primary objective of this study is to investigate the global asymptotic stability and coexistence of steady state based on different and unequal diffusion and advection rates through theoretical and numerical analysis. We establish the local stability of two semi-trivial steady states of the competing species. Also, the non-existence of coexistence steady state is proved with the help of some non-trivial assumptions. Finally, we show the global stability with the help of monotone dynamical systems and combine the local stability and non-existence of coexistence steady state. If one species adopts a smaller diffusion and advection rate, the competition’s result depends on the advection and diffusion rate ratio. If the ratio is smaller, then the species will prevail. Also, the species with higher diffusion and smaller advection will win. Lastly, the effectiveness of the model in one and two-dimensional situations is shown by a series of numerical calculations, which is particularly important for environmental consideration.
Mesfin Teshome Beyene, Mitiku Daba Firdi, Tamirat Temesgen Dufera
Abstract In our present work, we study a coupled system of Caputo–Hadamard fractional differential equations supplemented with a novel set of initial value conditions involving the η = ( t d d t ) $\eta =(t\frac{d}{dt})$ derivatives. We provided sufficient criteria for the existence and stability of the solutions for a coupled system of fractional differential equations by applying the Hyers–Ulam stability theory, the fixed point theorems of Banach, Krasnoselskii, and the Leray–Schauder nonlinear alternative. When computing priori bounds in Leray–Schauder nonlinear alternative and stability of the solutions, a novel Gronwall type inequality related to Hadamard integral is employed. This study investigates the properties of a solution, such as existence, uniqueness, and stability, to a given problem without attempting to solve the exact solution, and its theoretical applications are illustrated by providing an example.
Seyed Mahdi Rouhani Poor, Ahmad Jafarnejad Chaghoshi, Hannan Amoozad Mahdiraji
et al.
Purpose: Product quality includes three variables: design, conformance and use. Measuring the quality of products with respect to all three quality variables is one of the important challenges of the country. Therefore, the present study was an attempt to figure out how quality factors are related to each other and to determine the relative weight of these factors and to provide a product quality measurement model using hesitant fuzzy linguistic terms.Methodology: The present study falls into the category of applied studies in terms of objective and can be recognized as a quantitative study in terms of methodology. The population of the study incorporates academic experts and university-industry experts. Sample size (n=10) was determined using the purposeful and snowball sampling method. Due to the uncertainty of experts' in determining the mutual impact of product quality factors, the DEMATEL technique was combined with hesitant fuzzy logic, the resulting technique was then integrated with the Network Analysis Process (ANP), and the final model was extracted (DEMATEL based ANP (DANP)). Thanks to this procedure, the present study can be deemed innovative.Findings: The cause and effect relationships between the main factors of product quality were identified and extracted using DEMATEL technique. Then, taking into account the intensity of the mutual impact of quality factors on each other and using the DNAP technique, the product quality factors were ranked in three dimensions: design quality, conformance and use. According to the findings, management factors and resources (employees-infrastructure-environment) were identified as causal factors that affect other factors. On the other hand, the DANP output showed that "design quality" is the most important factor in product quality. So, with the relative weights of the factors, the product quality measurement model was obtained.Originality/Value: Researchers and industrial managers at the national level will be able to identify the relationship between quality factors and use this model to measure product quality or the quality rate of goods according to relative weight of each factor.
M.M. Endang Susetyawati, Bintang Wicaksono, Lisa Oktavia
et al.
The ability to count is part of mathematics which can develop children's cognitive abilities. It is very important to develop the ability to count in children, because counting can be used in children's daily lives. The problem faced by children in their ability to count is that children lack skills in doing calculations. Lack of numeracy skills can cause low mathematics learning achievement. This research aims to examine the snakes and ladders game as a medium to help elementary school children improve their numeracy skills to solve math problems. The method used in this research is descriptive qualitative with data collection through observation, interviews and documentation. It was tested in three stages and involved nine children who had different numeracy abilities. The results of this research are that children become more skilled at doing calculations, learning becomes fun, learning activities become interactive, and motivation to learn to count increases. The snakes and ladders learning media can increase motivation to learn to count and solve math problems.
Keywords: Snakes and Ladders Game, Numeracy Skills, Media
We present here the classical Schwarz method with a time domain decomposition applied to unconstrained parabolic optimal control problems. Unlike Dirichlet-Neumann and Neumann-Neumann algorithms, we find different properties based on the forward-backward structure of the optimality system. Variants can be found using only Dirichlet and Neumann transmission conditions. Some of these variants are only good smoothers, while others could lead to efficient solvers.
O presente trabalho tem como objetivo analisar sobre a abordagem do pensamento algébrico nos conteúdos de Álgebra apresentados nos Currículos disponíveis ao longo do tempo, em especial, aqueles adotados pelo estado de São Paulo no segmento do Ensino Fundamental nos Anos Finais. Em seguida, apresentamos os estudos de alguns autores que discorrem sobre o pensamento algébrico que justificam a pertinência da pesquisa, como, Blanton e Kaput (2005), Ponte, Branco e Matos (2009), Lima e Bianchini (2017), Gomes e Noronha (2020), Lins e Gimenez (2001). Para isso foi desenvolvida uma pesquisa de caráter qualitativo com análise dos documentos curriculares disponíveis no Brasil ao longo do tempo, dentre eles, os Guias Curriculares (1975), a Proposta Curricular de Matemática (1992), os Parâmetros Curriculares Nacionais - PCN (1998), a Base Nacional Comum Curricular - BNCC (2017) e o Currículo Paulista (2019). Nos resultados esperados consideramos que cada vez mais se torna eficaz para o entendimento do processo ensino aprendizagem da Álgebra, os estudos e o acompanhamento da manifestação do pensamento algébrico dos estudantes em sala de aula, assim como, o acompanhamento de suas respectivas aprendizagens em prol de documentos curriculares coesos e que buscam entender o que os alunos aprenderam ao sair da escola.
Special aspects of education, Applied mathematics. Quantitative methods
This paper is devoted to derive periodic solutions of a generalized Chaffee–Infante equation. This will be attained by employing several periodic ansatz methods so as to obtain a variety of exact solutions of distinct physical structures. In addition, other analytical solutions for the aforesaid equation, will be established via the symmetry reduction approach. It will be shown that a generalized Chaffee–Infante equation admits four principal Lie algebra. It will be further shown that the principal Lie algebra admits only one possible extension. The obtained results show that a generalized Chaffee–Infante equation reveals the richness of explicit periodic and traveling wave solutions.
Mukhtar Ahmad, Saddam Hussain, Ulfat Parveen
et al.
In this paper, we adequately describe the generalised petersen graph, expanding to the categories of graphs. We created a petersen graph, which is cyclic and has vertices that are arranged in the centre and nine gons plus one vertex, leading to the factorization of regular graphs. Petersen graph is still shown in graph theory literature, nevertheless.
Network control of autonomous robotic devices involves a vast number of secured data coding, verification, and identification procedures to provide reliable work of distant agents. Blockchain scheme provides here the model of the extended linked list for the verification of critical data, approved by quasi-random hash values assigned by external network nodes. And quantum lines are the source of high-quality quasi-random keys used as hash values. Discrete multiple-valued logic in such procedures is a simple and flexible tool to form the logic linked list, combining critical internal parameters of agents with data taken from external nodes. Such combination enlarges the set of possible schemes for data protection from illegal modifications and for data restoration.
A cornerstone of the classical view of tolerance is the elimination of self-reactive T cells during negative selection in the thymus. However, high-throughput T-cell receptor sequencing data has so far failed to detect substantial signatures of negative selection in the observed repertoires. In addition, quantitative estimates as well as recent experiments suggest that the elimination of self-reactive T cells is at best incomplete. We discuss several recent theoretical ideas that can explain tolerance while being consistent with these observations, including collective decision making through quorum sensing, and sensitivity to change through dynamic tuning and adaptation. We propose that a unified quantitative theory of tolerance should combine these elements to explain the plasticity of the immune system and its robustness to autoimmunity.
Fatuh Inayaturohmat, Nursanti Anggriani, Asep K. Supriatna
In this research, we developed a coinfection model of tuberculosis and COVID-19 with the effect of isolation and treatment. We obtained two equilibria, namely, disease-free equilibrium and endemic equilibrium. Disease-free equilibrium is a state in which no infection of tuberculosis and COVID-19 occurs. Endemic equilibrium is a state in which there occurs not only the infection of tuberculosis and COVID-19 but also the coinfection of tuberculosis and COVID-19. We assumed that the parameters follow the uniform distribution, and then, we took 1,000 samples of each parameter using Latin hypercube sampling (LHS). Next, the samples were sorted by ranking. Finally, we used the partial rank correlation coefficient (PRCC) to find the correlation between the parameters with compartments. We analyzed the PRCC for three compartments, namely, individuals infected with COVID-19, individuals infected with tuberculosis, and individuals coinfected with COVID-19 and tuberculosis. The most sensitive parameters are the recovery rate and the infection rate of each COVID-19 and tuberculosis. We performed the optimal control in the form of prevention for COVID-19 and tuberculosis. The numerical simulation shows that these controls effectively reduce the infected population. We also concluded that the effect of isolation has an immediate impact on reducing the number of COVID-19 infections, while the effect of treatment has an impact that tends to take a longer time.
We investigate time complexities of finite difference methods for solving the high-dimensional linear heat equation, the high-dimensional linear hyperbolic equation and the multiscale hyperbolic heat system with quantum algorithms (hence referred to as the "quantum difference methods"). For the heat and linear hyperbolic equations we study the impact of explicit and implicit time discretizations on quantum advantages over the classical difference method. For the multiscale problem, we find the time complexity of both the classical treatment and quantum treatment for the explicit scheme scales as $\mathcal{O}(1/\varepsilon)$, where $\varepsilon$ is the scaling parameter, while the scaling for the multiscale Asymptotic-Preserving (AP) schemes does not depend on $\varepsilon$. This indicates that it is still of great importance to develop AP schemes for multiscale problems in quantum computing.
Rory Humphries, Kieran Mulchrone, Jamie Tratalos
et al.
Abstract We present a modelling framework for the spreading of epidemics on temporal networks from which both the individual-based and pair-based models can be recovered. The proposed temporal pair-based model that is systematically derived from this framework offers an improvement over existing pair-based models by moving away from edge-centric descriptions while keeping the description concise and relatively simple. For the contagion process, we consider the susceptible–infected–recovered (SIR) model, which is realized on a network with time-varying edges. We show that the shift in perspective from individual-based to pair-based quantities enables exact modelling of Markovian epidemic processes on temporal tree networks. On arbitrary networks, the proposed pair-based model provides a substantial increase in accuracy at a low computational and conceptual cost compared to the individual-based model. From the pair-based model, we analytically find the condition necessary for an epidemic to occur, otherwise known as the epidemic threshold. Due to the fact that the SIR model has only one stable fixed point, which is the global non-infected state, we identify an epidemic by looking at the initial stability of the model.