Based at Thornton Science Park, the new Faculty of Science and Engineering is located in a major research and innovation hub for the North West which is only a 20-minute bus trip from the main Chester Campus. The Faculty offers degrees in engineering and science disciplines using a strongly interdisciplinary teaching philosophy.

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  • Weak convergence of the L1 scheme for a stochastic subdiffusion problem driven by fractionally integrated additive noise

    Hu, Ye; Li, Changpin; Yan, Yubin; University of Chester; Lvliang University; Shanghai University
    The weak convergence of a fully discrete scheme for approximating a stochastic subdiffusion problem driven by fractionally integrated additive noise is studied. The Caputo fractional derivative is approximated by the L1 scheme and the Riemann-Liouville fractional integral is approximated with the first order convolution quadrature formula. The noise is discretized by using the Euler method and the spatial derivative is approximated with the linear finite element method. Based on the nonsmooth data error estimates of the corresponding deterministic problem, the weak convergence orders of the fully discrete schemes for approximating the stochastic subdiffusion problem driven by fractionally integrated additive noise are proved by using the Kolmogorov equation approach. Numerical experiments are given to show that the numerical results are consistent with the theoretical results.
  • Numerical methods for Caputo-Hadamard fractional differential equations with graded and non-uniform meshes

    Green, Charles; Liu, Yanzhi; Yan, Yubin; University of Chester; Lvliang University
    We consider the predictor-corrector numerical methods for solving Caputo-Hadamard fractional differential equation with the graded meshes $\log t_{j} = \log a + \big ( \log \frac{t_{N}}{a} \big ) \big ( \frac{j}{N} \big )^{r}, \, j=0, 1, 2, \dots, N$ with $a \geq 1$ and $ r \geq 1$, where $\log a = \log t_{0} < \log t_{1} < \dots < \log t_{N}= \log T$ is a partition of $[\log t_{0}, \log T]$. We also consider the rectangular and trapezoidal methods for solving Caputo-Hadamard fractional differential equation with the non-uniform meshes $\log t_{j} = \log a + \big ( \log \frac{t_{N}}{a} \big ) \frac{j (j+1)}{N(N+1)}, \, j=0, 1, 2, \dots, N$. Under the weak smoothness assumptions of the Caputo-Hadamard fractional derivative, e.g., $\prescript{}{CH}D^\alpha_{a,t}y(t) \notin C^{1}[a, T]$ with $ \alpha \in (0, 2)$, the optimal convergence orders of the proposed numerical methods are obtained by choosing the suitable graded mesh ratio $r \geq 1$. The numerical examples are given to show that the numerical results are consistent with the theoretical findings.
  • 2D‐Hexagonal Boron Nitride Screen‐Printed Bulk‐Modified Electrochemical Platforms Explored towards Oxygen Reduction Reactions

    Khan, Aamar; Ferrari, Alejandro Garcia-Miranda; Hughes, Jack; Smith, Graham C; Banks, Craig E; Rowley-Neale, Samuel J; Manchester Metropolitan University; University of Chester (MDPI, 2022-04-26)
    A low‐cost, scalable and reproducible approach for the mass production of screen‐printed electrode (SPE) platforms that have varying percentage mass incorporations of 2D hexagonal boron nitride (2D‐hBN) (2D‐hBN/SPEs) is demonstrated herein. These novel 2D‐hBN/SPEs are explored as a potential metal‐free electrocatalysts towards oxygen reduction reactions (ORRs) within acidic media where their performance is evaluated. A 5% mass incorporation of 2D‐hBN into the SPEs resulted in the most beneficial ORR catalysis, reducing the ORR onset potential by ca. 200 mV in comparison to bare/unmodified SPEs. Furthermore, an increase in the achievable current of 83% is also exhibited upon the utilisation of a 2D‐hBN/SPE in comparison to its unmodified equivalent. The screen‐printed fabrication approach replaces the less‐reproducible and time‐consuming dropcasting technique of 2D‐hBN and provides an alternative approach for the large‐scale manufacture of novel electrode platforms that can be utilised in a variety of applications
  • Visualization for Epidemiological Modelling: Challenges, Solutions, Reflections & Recommendations

    Dykes, Jason; Abdul-Rahman, Alfie; Archambault, Daniel; Bach, Benjamin; Borgo, Rita; Chen, Min; Enright, Jessica; Fang, Hui; Firat, Elif E.; Freeman, Euan; et al.
    We report on an ongoing collaboration between epidemiological modellers and visualization researchers by documenting and reflecting upon knowledge constructs – a series of ideas, approaches and methods taken from existing visualization research and practice – deployed and developed to support modelling of the COVID-19 pandemic. Structured independent commentary on these efforts is synthesized through iterative reflection to develop: evidence of the effectiveness and value of visualization in this context; open problems upon which the research communities may focus; guidance for future activity of this type; and recommendations to safeguard the achievements and promote, advance, secure and prepare for future collaborations of this kind. In describing and comparing a series of related projects that were undertaken in unprecedented conditions, our hope is that this unique report, and its rich interactive supplementary materials, will guide the scientific community in embracing visualization in its observation, analysis and modelling of data as well as in disseminating findings. Equally we hope to encourage the visualization community to engage with impactful science in addressing its emerging data challenges. If we are successful, this showcase of activity may stimulate mutually beneficial engagement between communities with complementary expertise to address problems of significance in epidemiology and beyond.
  • Multi-metric Evaluation of the Effectiveness of Remote Learning in Mechanical and Industrial Engineering During the COVID-19 Pandemic: Indicators and Guidance for Future Preparedness, 2021

    Behera, Amar Kumar; de Sousa, Ricardo Alves; Oleksik, Valentin; Dong, Jingyan; Fritzen, Daniel; University of Chester; University of Aveiro; Lucian Blaga University of Sibiu; North Carolina State University; SATC College, Criciuma
    This data set is a follow on study from a study on remote learning conducted in 2020 during the first year of the COVID-19 pandemic. It contains data collected from 5 universities in 5 countries about the effectiveness of e-learning during the COVID-19 pandemic in 2021, specifically tailored to mechanical and industrial engineering students. A survey was administered in August 2021 at these universities simultaneously, using Google Forms. The survey had 41 questions, including 24 questions on a 5-point Likert scale. The survey questions gathered data on their program of study, year of study, university of enrolment and mode of accessing their online learning content. The Likert scale questions on the survey gathered data on the effectiveness of digital delivery tools, student preferences for remote learning and the success of the digital delivery tools during the pandemic. All students enrolled in modules taught by the authors of this study were encouraged to fill the survey up. Additionally, remaining students in the departments associated with the authors were also encouraged to fill up the form through emails sent on mailing lists. The survey was also advertised on external websites such as survey circle and facebook. Crucial insights have been obtained after analysing this data set that link the student demographic profile (gender, program of study, year of study, university) to their preferences for remote learning and effectiveness of digital delivery tools. This data set can be used for further comparative studies and was useful to get a snapshot of the evolution of the student preferences and e-learning effectiveness during the COVID-19 pandemic from 2020 to 2021 by comparing with the dataset from 2020.
  • A survey of modern deep learning based object detection models

    Zaidi, Syed Sahil Abbas; Ansari, Mohammad Samar; Aslam, Asra; Kanwal, Nadia; Asghar, Mamoona; Lee, Brian; Technological University of the Shannon; University of Chester; National University of Ireland; Keele University; Lahore College for Women University (Elsevier, 2022-03-08)
    Object Detection is the task of classification and localization of objects in an image or video. It has gained prominence in recent years due to its widespread applications. This article surveys recent developments in deep learning based object detectors. Concise overview of benchmark datasets and evaluation metrics used in detection is also provided along with some of the prominent backbone architectures used in recognition tasks. It also covers contemporary lightweight classification models used on edge devices. Lastly, we compare the performances of these architectures on multiple metrics.
  • Immersive Virtual Reality for the Cognitive Rehabilitation of Stroke Survivors

    Chatterjee, Kausik; Buchanan, Alastair; Cottrell, Katy; Hughes, Sara; Day, Thomas W.; John, Nigel W.; Countess of Chester Hospital NHS Foundation Trust; Cadscan Limited; University of Chester (IEEE, 2022-03-10)
    We present the results of a double-blind phase 2b randomized control trial that used a custom built virtual reality environment for the cognitive rehabilitation of stroke survivors. A stroke causes damage to the brain and problem solving, memory and task sequencing are commonly affected. The brain can recover to some extent, however, and stroke patients have to relearn how to carry out activities of daily living. We have created an application called VIRTUE to enable such activities to be practiced using immersive virtual reality. Gamification techniques enhance the motivation of patients such as by making the level of difficulty of a task increase over time. The design and implementation of VIRTUE is described together with the results of the trial conducted within the Stroke Unit of a large hospital. We report on the safety and acceptability of VIRTUE. We have also observed particular benefits of VR treatment for stroke survivors that experienced more severe cognitive impairment, and an encouraging reduction in time spent in the hospital for all patients that received the VR treatment.
  • Insights into the Analysis of Fractional Delay Differential Equations

    Ford, Neville; Osborne, Neil (University of Chester, 2021-07)
    This thesis is concerned with determining the analytic solution, using the method of steps, of the following fractional delay differential equation initial interval problem (FDDE IIP), c Dαy(s) = −y(t − τ ) for t > 0, τ > 0, 0 < α < 1, and y ∈ A1(0, T ] 0 t y(t) = ϕ(t) for t ∈ (−τ, 0] The properties of the analytic solution obtained are a surprise but they do sit comfortably when compared with those of the analytic solutions of an ordinary differential equation initial value problem (ODE IVP), a delay differential equation initial interval problem (DDE IIP) and an fractional ordinary differential equation initial value problem (FODE IVP). Further the analytic solution formula obtained is closely related to that of the analytic solution formula of the DDE IIP. However, these insights into the analytic solution of the FDDE IIP we have not seen before, and differ from those published elsewhere.
  • Towards Effective Project Management and Knowledge Transfer Enhancement: A Novel System Capturing and Modelling Knowledge Acquired in a Software Development Practice

    Kerins, John; Rayner, Linda; John, Nigel; Fannoun, Sufian (University of Chester, 2021-03)
    The practice of software project management evolves alongside emerging new technologies such as advances in new tools and resources in Application Programming Interfaces (APIs) and machine learning applications. This thesis evaluates the ways in which a small software development unit, characteristics of other small enterprises, has embraced emerging trends in the development of digital technologies in order to establish and maintain successful practice. A qualitative research approach was adopted to elicit an understanding of the critical knowledge acquired as the unit developed and its members become effective practitioners. The research identifies and analyses the acquired knowledge that underpins successful practice, and uses the results of this analysis to propose a support system to enhance future practice. This is a challenge is that there is limited evidence of Small and Medium Enterprises (SMEs) engaging in knowledge management (KM) or in organisational learning (OL) initiatives. In developing projects, smaller software development organisations rely on implicit knowledge and Agile to resolve complexity. Consequently, and specifically in a small business, the development of this bespoke system, represents a novel approach to Knowledge Management (KM) and Organisational Learning (OL). Projects were identified as key sources and locus of development, innovation knowledge, skills, know-how and learning within the unit. This outcome has reinforced the proposal for a links-based system around individual projects. As in Chapter Nine, the system is as a web-based repository of project templates. The templates capture key insights into critical decisions and significant advances in current practice that arise from work within individual projects. The proposed system captures the unit’s knowledge. In addition, it provides an accessible resource that not only supports critical reflection and decision making but also retains key aspects of organisational learning (OL) and know-how. Further, while complementing continuing implicit learning, it has the further benefit of maintaining organisational resilience where individuals’ skills may be lost or where the unit faces high staff turnover. Moreover, the system can serve to induct newcomers to the unit. Accordingly, for a small software development unit with no prior knowledge management initiative or system in place, the research’s immediate contribution is through modelling, capturing and representing the acquired knowledge. This thesis provides insights into the management of software project knowledge through web technology. The prototype was successfully designed, implemented, evaluated and made available to the research unit working group. Such a system provides an effective measure for application at organisational and project levels, the evaluation of practice and the reuse of project knowledge to improve performance and effective practice. A further contribution made by this research is in revealing the range of the acquired knowledge, the know-how and the soft skills that complement the technical skills of software development within the research unit. The set of know-how and soft skills could be valuable where measures for effective professional practice are required. The analysed data revealed the range of capabilities the members developed to enable the application of implicit knowledge. Such insights, perceptions, and understanding enabled them to engage with clients, as well as manage risks and changes, assist key business processes and, importantly, deliver projects successfully. These skills contribute to the members’ individual professional development and capabilities. These might be termed Confidence, Relationships, Communication and Self-Management, Cooperation and Teamwork. Similarly, the research revealed the range of Know-How the members have developed. This range would include Understanding of Business Processes, Experimentation and Problem Solving, Reusing of Project Knowledge, Establishing and Marinating Quality, Project Time Estimates, and Learning from Project Failure the thesis also highlights the additional range of critical knowledge encapsulated within projects. This knowledge specifically related to Business Processes, Business Domains, Client and Working Environment. Such contextual implicit knowledge is part of the critical knowledge the practitioners acquired. Consequently, a model of successful practice within the unit was then built upon facets of this salient knowledge. An evaluation provided feedback on the system and assessed its suitability for the research unit. The unit members were satisfied with how the prototype restricted the key elements related to their knowledge and practice without duplicating information and acknowledged that it was the knowledge management system that best suits their needs. A focus group meeting with another similar software development unit highlighted and validated commonalities and differences in experience and in the nature of the individual organisations. The findings suggest that the proposed approach to recognising and utilising knowledge for transfer, reuse and consolidating effective practice is, potentially, extendable to similar domains. Continued research would explore the wider generalisability of this approach. Further research would explore extensions or revisions of the prototype that might further clarify the benefits and limitations of such an approach as well as providing a model for knowledge management in similar small-scale environments. This research might also serve as a template or road map for the implementation of KM initiatives elsewhere, such as start-up companies where there is a lack of software development expertise. Furthermore, the proposed system could serve as a model for the development of comparable systems in organisations where projects form the core of their work.
  • Terahertz Characterisation of Lead-Free Dielectrics for Different Applications

    Zhang, Man; Zhang, Hangfeng; Jiang, Qinghui; Gao, Feng; Chen, Riqing; Zhang, Dou; Reece, Michael J.; Yang, Bin; Viola, Giuseppe; Yan, Haixue; et al. (American Chemical Society, 2021-11-02)
    In this Spotlight on Applications, we describe our recent progress on the terahertz (THz) characterization of linear and non-linear dielectrics for broadening their applications in different electrical devices. We begin with a discussion on the behavior of dielectrics over a broadband of frequencies and describe the main characteristics of ferroelectrics, as an important category of non-linear dielectrics. We then move on to look at the influence of point defects, porosity and interfaces, including grain boundaries and domain walls, on the dielectric properties at THz frequencies. Based on our studies on linear dielectrics, we show that THz characterization is able to probe the effect of porosities, point defects, shear planes and grain boundaries to improve dielectric properties for telecommunication applications. Further, we demonstrate that THz measurements on relaxor ferroelectrics can be successfully used to study the reversibility of the electric field-induced phase transitions, providing guidance for improving their energy storage efficiency in capacitors. Finally, we show that THz characterization can be used to characterize the effect of domain walls in ferroelectrics. In particular, our studies indicate that the dipoles located within domain walls provide a lower contribution to the permittivity at THz frequencies than the dipoles present in domains. The new findings could help develop a new memory device based on non-destructive reading operations using a THz beam.
  • Terahertz probing of low temperature degradation in zirconia bioceramics

    Ahmed, Shafique; Zhang, Man; Koval, Vladimir; Zou, Lifong; Shen, Zhijian; Chen, Riqing; Yang, Bin; Yan, Haixue; Queen Mary University of London; Mehran University of Engineering and Technology; Institute of Materials Research; Stockholm University; Fujian Agriculture and Forestry University; University of Chester (Wiley, 2021-09-19)
    ZrO2 based ceramics are widely used in biomedical applications due to its colour, biocompatibility, and excellent mechanical properties. However, low temperature degradation (LTD) introduces a potential risk for long-term reliability of these materials. The development of innovative non-destructive techniques, which can explore LTD in zirconia-derived compounds, is strongly required. Yttria stabilised zirconia, 3Y-TZP, is one of the well-developed ZrO2 based ceramics with the improved resistance to LTD for dental crown and implant applications. Here, 3Y-TZP ceramic powders were pressed and sintered to study the LTD phenomenon by phase transition behaviour. The LTD driven tetragonal-to-monoclinic phase transition was confirmed by XRD. XPS analysis demonstrated the LTD induced the reduction of oxygen vacancies to support these findings. It is proved that after the degradation the 3Y-TZP ceramics show the decreased dielectric permittivity at terahertz frequencies due to the crystallographic phase transformation. Terahertz non-destructive probe is a promising method to investigate LTD in zirconia ceramics.
  • LevelEd SR: A Substitutional Reality Level Design Workflow

    Beever, Lee; John, Nigel W.; University of Chester
    Virtual reality (VR) and augmented reality (AR) have continued to increase in popularity over the past decade. However, there are still issues with how much space is required for room-scale VR and experiences are still lacking from haptic feedback. We present LevelEd SR, a substitutional reality level design workflow that combines AR and VR systems and is built for consumer devices. The system enables passive haptics through the inclusion of physical objects from within a space into a virtual world. A validation study (17 participants) has produced quantitative data that suggests players benefit from passive haptics in entertainment VR games with an improved game experience and increased levels of presence. Including objects, such as real-world furniture that is paired with a digital proxy in the virtual world, also opens up more spaces to be used for room-scale VR. We evaluated the workflow and found that participants were accepting of the system, rating it positively using the System Usability Scale questionnaire and would want to use it again to experience substitutional reality.
  • Application of Virtual Reality and Electrodermal Activity for the Detection of Cognitive Impairments

    Patient, Rebecca; Ghali, Fawaz; Kolivand, Hoshang; Hurst, William; John, Nigel W.; Liverpool John Moores; Wageningen University; University of Chester (IEEE, 2022-03-01)
    Mild Cognitive Impairment (MCI) is a definition of the diagnosis of early memory loss and disorientation. This study aims to identify people’s symptoms through technology. However, machine learning (ML) can classify Cognitive Normal (CN) and Mild Cognitive Impairment (MCI) and Early Mild Cognitive Impairment (EMCI) using standard assessments from the Alzheimer’s Disease Neuroimaging Initiative (ADNI); Montreal Cognitive (MoCA), Mini-Mental State Examination (MMSE), Functional Activities Questionnaire (FAQ). Consequently, a Multilayer Perceptron (MLP) model was assembled into tables; MCI vs CN, MCI vs EMCI, and CN vs MCI. Additionally, an MLP model was developed for CN vs MCI vs EMCI. As a result, of advanced model performance, a cascade 3-path categorisation approach was created. Similarly, the exploitation of meta-analysis indicated a combination of MLP models (MCI vs CN, MCI vs EMCI, and CN vs MCI) with an overall accuracy within an acceptable limit. In addition, better results were found when assessments were combined rather than individually. Furthermore, applying class weights and probability thresholds could improve the MLP framework by performance achieving a balanced specificity and sensitivity ratio. Altering class weights and probability thresholds when training the MLP neuro network model, the sensitivity and Accuracy could be progressed further. In conclusion, ML, VR and electrodermal activity are constrained. Introducing the possibility of activity-based applications to enhance innovative solutions for cognitive impairment diagnosis and treatment.
  • Structural speciation in chemical reactivity profiling of binary-ternary systems of Ni(II) with iminodialcohol and aromatic chelators

    Salifoglou, Athanasios; Papadopoulos, Theodoros; Reimann, M. K.; Pöttgen, R.; Salifoglou, A.; Matsia, S.; Kaoulla, A.; Menelaou, M.; Hatzidimitriou, A.; Aristotle University of Thessaloniki; University of Chester; Universität Münster; Cyprus University of Technology (Elsevier, 2021-11-10)
    The importance of structural speciation in the control of chemical reactivity in Ni(II) binary-ternary systems, involving (O,O,N)-containing substrates (1,1’-iminodi-2-propanol), and aromatic chelators (2,2’-bipyridine, 1,10-phenanthroline), prompted the systematic synthesis of new crystalline materials characterized by elemental analysis, FT-IR, UV-Visible, Luminescence, TGA, magnetic susceptibility, and X-ray crystallography. The structures contain mononuclear octahedral assemblies, the lattice architecture of which exemplifies reaction conditions under which conformational variants and solvent-associated lattice-imposed complexes are assembled. Transformations between complex species denote their association with reactivity pathways, suggesting alternate synthetic methodologies for their isolation. Theoretical work (Hirshfeld, Electrostatic Potential, DFT) signifies the impact of crystal structure on energy profiles of the generated species. The arisen physicochemical profiles of all compounds portray a well-configured interwoven network of pathways, projecting strong connection between structural speciation and Ni(II) reactivity patterns in organic-solvent media. The collective results provide well-defined parameterized profiles, poised to influence the synthesis of new Ni(II)-iminodialcohol materials with specified structural-magneto-optical properties.
  • Experimental exploration of cryogenic CO2 capture utilising a moving bed

    Font-Palma, Carolina; Willson, Paul; Cann, David G. (University of Chester, 2021-04)
    It is widely accepted that climate change is a result of the increase in greenhouse gases in the atmosphere. The continued combustion of fossil fuels and subsequent emission of CO2 is leading to an increase in global temperatures, which has led to interest in decarbonising the energy sector. Carbon capture and storage (CCS) is a method of reducing carbon emissions from fossil fuel power plants by capturing CO2 from exhaust gases and storing it in underground gas stores. Carbon capture using chemical solvents is the most matured technology for capturing emissions from the energy sector, however as the energy sector continues to decarbonise with the arrival of renewable sources focus is shifting to other industries to reduce their carbon footprint. Solvent carbon capture has disadvantages including requiring large equipment and large amounts of heat to regenerate solvent for capture, meaning it would be difficult to scale the technology down and apply it to other industrial applications. Cryogenic carbon capture (CCC) is one proposed method of CCS at smaller scale, which captures CO2 by freezing CO2 out of the exhaust gases as CO2 forms a frost on a heat transfer surface. One disadvantage of CCC is the accumulation of CO2 frost reduces the efficiency of the capture process. The process must be periodically shut down to regenerate the heat transfer surface and collect CO2 that has been frozen out of exhaust gases. This thesis proposes to overcome the frost accumulation through the use of a moving packed bed of small spherical metal beads as the heat transfer surface. As CO2 is fed into a capture column and freezes onto the metal beads, the metal beads are removed from the column, regenerated to recover the CO2, then cooled and recirculated back into the capture column. This prevents the accumulation of frost and allows continuous CO2 capture. There are many difficulties identified in this project, primarily a lack of knowledge on CO2 frost formation and how heat transfer in a moving bed affects frost formation. The research done on a purpose built experimental rig is critical in improving the future design work of a next generation moving bed CCC system. The frost accumulation in a capture column is known as a frost front, which advanced through the capture column at a fixed velocity until the column is saturated with frost. Experimental results had shown that the frost front velocity is predictable for varying CO2 concentrations and gas flow rates, with frost front velocities between 0.46-0.78 mm/s for CO2 concentrations between 4-18% v/v and 0.36-0.98 mm/s for gas flow rates between 50-120 LPM. These frost front velocity experiments in a fixed packed bed allowed the design of a moving packed bed column to set the bed flow rate to match the frost front velocity. The moving bed experiments show that the excessive accumulation of CO2 frost within the capture column can be prevented by utilising the moving bed. The successful development of a moving bed CCC system would result in a cost effective solution to the requirements of certain smaller applications that need to capture CO2, which make up a significant portion of emissions. In particular this technology is very economical for biogas upgrading, where the CO2 content of biogas must be removed before the gas can be introduced to the UK’s larger gas network. There is also a growing interest for use in shipping and other maritime applications, capturing CO2 from ship exhaust emissions during transit.
  • A Novel Averaging Principle Provides Insights in the Impact of Intratumoral Heterogeneity on Tumor Progression

    Hatzikirou, Haralampos; orcid: 0000-0002-1270-7885; email:; Kavallaris, Nikos I.; Leocata, Marta; orcid: 0000-0002-5261-3699; email: (MDPI, 2021-10-09)
    Typically stochastic differential equations (SDEs) involve an additive or multiplicative noise term. Here, we are interested in stochastic differential equations for which the white noise is nonlinearly integrated into the corresponding evolution term, typically termed as random ordinary differential equations (RODEs). The classical averaging methods fail to treat such RODEs. Therefore, we introduce a novel averaging method appropriate to be applied to a specific class of RODEs. To exemplify the importance of our method, we apply it to an important biomedical problem, in particular, we implement the method to the assessment of intratumoral heterogeneity impact on tumor dynamics. Precisely, we model gliomas according to a well-known Go or Grow (GoG) model, and tumor heterogeneity is modeled as a stochastic process. It has been shown that the corresponding deterministic GoG model exhibits an emerging Allee effect (bistability). In contrast, we analytically and computationally show that the introduction of white noise, as a model of intratumoral heterogeneity, leads to monostable tumor growth. This monostability behavior is also derived even when spatial cell diffusion is taken into account.
  • Oscillatory and stability of a mixed type difference equation with variable coefficients

    Yan, Yubin; Pinelas, Sandra; Ramdani, Nedjem; Yenicerioglu, Ali Fuat; RUDN University; University of Saad Dahleb Blida; Kocaeli University; University of Chester (Inderscience, 2021-08-12)
    The goal of this paper is to study the oscillatory and stability of the mixed type difference equation with variable coefficients \[ \Delta x(n)=\sum_{i=1}^{\ell}p_{i}(n)x(\tau_{i}(n))+\sum_{j=1}^{m}q_{j}(n)x(\sigma_{i}(n)),\quad n\ge n_{0}, \] where $\tau_{i}(n)$ is the delay term and $\sigma_{j}(n)$ is the advance term and they are positive real sequences for $i=1,\cdots,l$ and $j=1,\cdots,m$, respectively, and $p_{i}(n)$ and $q_{j}(n)$ are real functions. This paper generalise some known results and the examples illustrate the results.
  • Spatial Discretization for Stochastic Semi-Linear Subdiffusion Equations Driven by Fractionally Integrated Multiplicative Space-Time White Noise

    Yan, Yubin; Hoult, James; Wang, Junmei; University of Chester; LuLiang University (MDPI, 2021-08-12)
    Spatial discretization of the stochastic semilinear subdiffusion driven by integrated multiplicative space-time white noise is considered. The spatial discretization scheme discussed in Gy\"ongy \cite{gyo_space} and Anton et al. \cite{antcohque} for stochastic quasi-linear parabolic partial differential equations driven by multiplicative space-time noise is extended to the stochastic subdiffusion. The nonlinear terms $f$ and $\sigma$ satisfy the global Lipschitz conditions and the linear growth conditions. The space derivative and the integrated multiplicative space-time white noise are discretized by using finite difference methods. Based on the approximations of the Green functions which are expressed with the Mittag-Leffler functions, the optimal spatial convergence rates of the proposed numerical method are proved uniformly in space under the suitable smoothness assumptions of the initial values.
  • Error estimates of a continuous Galerkin time stepping method for subdiffusion problem

    Yan, Yubin; Yan, Yuyuan; Liang, Zongqi; Egwu, Bernard; Jimei University; University of Chester (Springer, 2021-07-29)
    A continuous Galerkin time stepping method is introduced and analyzed for subdiffusion problem in an abstract setting. The approximate solution will be sought as a continuous piecewise linear function in time $t$ and the test space is based on the discontinuous piecewise constant functions. We prove that the proposed time stepping method has the convergence order $O(\tau^{1+ \alpha}), \, \alpha \in (0, 1)$ for general sectorial elliptic operators for nonsmooth data by using the Laplace transform method, where $\tau$ is the time step size. This convergence order is higher than the convergence orders of the popular convolution quadrature methods (e.g., Lubich's convolution methods) and L-type methods (e.g., L1 method), which have only $O(\tau)$ convergence for the nonsmooth data. Numerical examples are given to verify the robustness of the time discretization schemes with respect to data regularity.
  • A Comprehensive Review of the Composition, Nutritional Value, and Functional Properties of Camel Milk Fat

    Bakry, Ibrahim A; Yang, Lan; Farag, Mohamed A.; orcid: 0000-0001-5139-1863; email:; Korma, Sameh A; Khalifa, Ibrahim; orcid: 0000-0002-7648-2961; email:; Cacciotti, Ilaria; orcid: 0000-0002-3478-6510; Ziedan, Noha I.; Jin, Jun; Jin, Qingzhe; Wei, Wei; et al. (MDPI, 2021-09-13)
    Recently, camel milk (CM) has been considered as a health-promoting icon due to its medicinal and nutritional benefits. CM fat globule membrane has numerous health-promoting properties, such as anti-adhesion and anti-bacterial properties, which are suitable for people who are allergic to cow’s milk. CM contains milk fat globules with a small size, which accounts for their rapid digestion. Moreover, it also comprises lower amounts of cholesterol and saturated fatty acids concurrent with higher levels of essential fatty acids than cow milk, with an improved lipid profile manifested by reducing cholesterol levels in the blood. In addition, it is rich in phospholipids, especially plasmalogens and sphingomyelin, suggesting that CM fat may meet the daily nutritional requirements of adults and infants. Thus, CM and its dairy products have become more attractive for consumers. In view of this, we performed a comprehensive review of CM fat’s composition and nutritional properties. The overall goal is to increase knowledge related to CM fat characteristics and modify its unfavorable perception. Future studies are expected to be directed toward a better understanding of CM fat, which appears to be promising in the design and formulation of new products with significant health-promoting benefits.

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