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Recent years have seen the significant developments in theoretical, experimental and clinical approaches to understand the dynamics of cancer cells, the mechanism, cancer evolution and treatment resistances. Within the last five years, attention has been given on intensively investigating the evolution of cancer cells through model-based approach. In order to rationalize the treatment personalization and address the treatment failure, the use of mathematical modelling is widely accepted to support drug and treatment decision making. By now, several mathematical models for the cancer cell growth process have been formulated in the literature. It is clear that cancer evolution operates in a highly uncertain environment as a result of the noisy behaviour in the human body. To reflect the realistic behaviour of the cancerous cell growth, a mathematical model that describes this process should take into account the stochastic effects. To the fact that the stochastic models incorporate the random effects that may influence the behaviour of physical systems, mathematical models which is a stochastic differential equation (SDE) known as stochastic Gompertz model have been developed to understand the cancer growth process and its response to the cancer treatment methods. The objective of this paper is to investigate the performance of stochastic Gompertz model in predicting the growth of cervical cancer cells compared to the performance of deterministic model and the forecasting model of cervical cancer cell growth. The stochastic and deterministic Gompertz model will be solved via numerical method and the result will be presented together with the forecasting model of cervical cancer cell growth. The performance of stochastic Gompertz model, deterministic model and cervical cancer forecasting model in predicting the growth of cervical cancer cells will be analysed by using Root Mean-squared error (RMSE) and Global error. The present result will suggest the best model representing the growth of cancer cells, hence provide the better understanding of cancer evolution to overcome the treatment resistance. This useful clinical knowledge may help oncologists to design better treatment strategies and brings opportunities to treat cancer patients. [ABSTRACT FROM AUTHOR]

In this paper, steady two-dimensional magnetohydrodynamics mixed convective flow of non-Newtonian power-law nanofluid with the presence of heat generation/absorption and chemical reaction effects is investigated. The nanofluid incorporates the effects of Brownian motion and thermophoresis using Buongiorno's model. The flow is studied in a cavity with a moving top wall and contains isothermal solid circular cylinder at the center. The governing dimensional equations in a vector form are transformed into non-dimensional form. Then, the dimensionless equations are solved numerically by finite element method (FEM) using automated solution technique which is FEniCS. The influence of various parameters such as Richardson number, power-law index, magnetic field, heat generation/absorption, chemical reaction and size of solid circular cylinder on velocity, temperature, and concentration profiles are presented and discussed in this study. The results show that increasing Richardson number and power-law index has enhanced the velocity and the temperature profiles (left side of cavity). Meanwhile, both profiles reduce when the magnetic parameter and the size of solid circular cylinder are added. The temperature profile is increased with the rising of heat generation/absorption parameter. Besides that, declining trend is observed on the concentration profile with increasing chemical reaction parameter. [ABSTRACT FROM AUTHOR]

The numerical study presents the effect of heat generation and chemical reaction on the problem of magnetohydrodynamics mixed convective flow of power-law nanofluid using Buongiorno's model. Adiabatic non-conducting solid square block is located at the center of the cavity and both vertical walls are moving with uniform velocity. The governing dimensional equations in vector form are transformed into non-dimensional form. Then, the dimensionless equations are solved numerically by finite element method (FEM) using automated solution technique which is FEniCS. The effects of different parameters such as Richardson number, power-law index, magnetic field, heat generation/absorption, chemical reaction and size of square block on velocity, temperature, and concentration profiles are performed and discussed in this paper. It is found that rising both Richardson number and power-law index lead to increase the velocity and temperature profiles (right side of cavity). Besides, rising both magnetic parameter and size of square block lead to decrease the velocity and temperature profiles (right side of cavity). Adding the heat generation/absorption parameter has increased the temperature profile. In addition, increasing chemical reaction parameter has reduced the concentration profile. [ABSTRACT FROM AUTHOR]

Breast cancer arises when cells develop uncontrollably in the breast to form tumour cells. The risk of having breast cancer rises as a woman continues to age. Thus, details about the early stages of cancer progression can help a woman make early treatment choices, preventing them from being diagnosed with these harmful cancers. It is believed that cytotoxic T lymphocytes (CTLs) act as effector cells to eradicate cancer cells. CTLs and tumor cells were discovered to be around a "predator-prey" relationship, with CTL acting as the predator along with tumor cells acting as the prey. In this paper, we examined steady-state solutions for two numerical differentiation using the Jacobian matrix. We will also examine the stability region of breast cancer cells in two different phases to describe its progress in different types of the human body at various phases. Also, compare tumour cells population development in the duration of interphase and metaphase in the presence and the absence of immune response, which is dependent on the CTL population, will be observed by applying Fourth Order Runge Kutta (RK4) method. We can see that the Runge-Kutta method is an important method for approximate solutions to ordinary systems with known initial conditions. We achieved populations value of tumour cells throughout interphase and mitosis as well as the population of the immune system using the method. Based on our observations, we draw the conclusion that persons with a higher immune system are more likely to be able to fight cancer for for a period of time than cancer sufferers with a poor immune system. We may observe that the cancer cells were reduced in a shorter period of time with a high immune response population compared to other lower CTL values. [ABSTRACT FROM AUTHOR]

This paper introduces the hybrid of Potential Method (PM) and Graph Theory and Matrix Approach (GTMA) to surmount the issues in the existing hybrid of Analytic Hierarchy Process (AHP) and Graph Theory and Matrix Approach (GTMA) concerning the complexity of the calculation of the weight of the attributes when involving many attributes, no visualization of the relationship between attributes and complex calculation of ranking order of attributes for missing information. Subsequently, the implementation of the proposed method is utilized in the fuel selection problem in solving two issues namely complexity in pairwise comparison and missing information. Besides, the proposed method could surmount the complexity in pairwise comparison and deal well with missing information in providing the ranking order of alternatives. Finally, the results obtained indicate that the method could be utilized for ranking purposes in Multi-Criteria Decision Making (MCDM) problem. [ABSTRACT FROM AUTHOR]

A typical problem in additive combinatorics is to find the structure of a set given an additive assumption about the set. Sárközy's conjecture is one such problem. The conjecture posits the nonexistence of a nontrivial 2-decomposition of the set Qp of quadratic residue modulo p. In this paper, we review the history and formulation of the conjecture. Then we survey the progress made towards this conjecture in which we first suppose that a 2-decomposition Qp = A+B exists, with │A│, │B│ ≥2. Next, we find bounds for the cardinalities of sets A and B while showcasing the techniques used in obtaining them. Finally, we suggest further problems by discussing the case for a 3-decomposition of Qp and other related problems. [ABSTRACT FROM AUTHOR]

Numerous models have been proposed over time to study the behavior and properties of hybrid nanofluids. In this paper, a modified Buongiorno nanofluid model (MBNM) is used to investigate the stagnation-point flow of a hybrid nanofluid past a linearly stretching surface. The model combined Buongiorno's nanofluid model with Devi and Devi's hybrid nanofluid model. Compared to other models, it is still not widely used in the literature. It took into consideration the effect of Brownian motion and thermophoresis and the effective properties of the hybrid nanofluid. This paper also imposed the zero normal flux condition at the stretching surface instead of the usual constant nanoparticle concentration. The governing partial differential equations are transformed into ordinary differential equations using appropriate similarity variables. The problem is then solved numerically using the MATLAB function bvp4c. Results indicate that the stagnation parameter can significantly influence the magnitude of the skin friction coefficient. There is no skin friction when the surface moves at the same velocity as the fluid. The Brownian motion parameter is insignificant to both skin friction coefficient and the heat transfer rate of the fluid. It can also be seen that hybrid nanofluid indeed has a higher heat transfer rate as compared to mono-nanofluid. [ABSTRACT FROM AUTHOR]