The current study examines the numerical simulation of the nanoliquid boundary layer flow comprising gyrotactic microbes with mass and energy transmission across a stretching inclined cylinder. The ...consequences of chemical reaction, heat generation/absorption, buoyancy force and Arrhenius activation energy is also considered on the nanofluid flow. The flow mechanism has been modeled in the form of system of nonlinear partial differential equations (PDEs). That system of PDEs is further transform into the dimensionless set of ordinary differential equations (ODEs) through the similarity substitutions. The obtained set of differential equations are numerically computed through the parametric continuation method (PCM). The effects of the distinct physical constraints on the energy, velocity, mass and the motile microbe profiles are discoursed and evaluated through Tables and Figures. It has been noticed that the velocity curve drops with the influence of inclination angle and Richardson number, while enhances against the variation of curvature factor. Furthermore, the energy field boosts with the upshot of inclination angle and heat source term, while declines with the influence of Prandtl number and Richardson number.
Monkeypox (MPX) is a global public health concern. This infectious disease affects people all over the world, not just those in West and Central Africa. Various approaches have been used to study ...epidemiology, the source of infection, and patterns of transmission of MPX. In this article, we analyze the dynamics of MPX using a fractional mathematical model with a power law kernel. The human-to-animal transmission is considered in the model formulation. The fractional model is further reformulated via a generalized fractal-fractional differential operator in the Caputo sense. The basic mathematical including the existence and uniqueness of both fractional and fractal-fractional problems are provided using fixed points theorems. A numerical scheme for the proposed model is obtained using an efficient iterative method. Moreover, detailed simulation results are shown for different fractional orders in the first stage. Finally, a number of graphical results of fractal-fractional MPX transmission models are presented showing the combined effect of fractal and fractional orders on model dynamics. The resulting simulations conclude that the new fractal-fractional operator added more biological insight into the dynamics of illness.
The topic of convex and nonconvex mapping has many applications in engineering and applied mathematics. The Aumann and fuzzy Aumann integrals are the most significant interval and fuzzy operators ...that allow the classical theory of integrals to be generalized. This paper considers the well-known fuzzy Hermite–Hadamard (HH) type and associated inequalities. With the help of fuzzy Aumann integrals and the newly introduced fuzzy number valued up and down convexity (UD-convexity), we increase this mileage even further. Additionally, with the help of definitions of lower UD-concave (lower UD-concave) and upper UD-convex (concave) fuzzy number valued mappings (FNVMs), we have gathered a sizable collection of both well-known and new extraordinary cases that act as applications of the main conclusions. We also offer a few examples of fuzzy number valued UD-convexity to further demonstrate the validity of the fuzzy inclusion relations presented in this study.
We discuss the notion of fibration property of continuous functions in the theory of topological left almost semigroups. The concept of L-fibration is introduced and investigated. The restriction and ...composition properties of L-fibrations and the lifting property of L-fibrations are studied through the concepts of L-lifting function and L-regular lifting function. The study shows the uniqueness of L-regular lifting function of any L-fibration. Besides, the homotopically equivalent and preserving projection of L-regular lifting functions are also investigated. Finally, by using the idea of homotopy extension property in homotopy theory of topological spaces, the study provides the notion of L-homotopy extension property in the theory of topological left almost semigroups by giving L-homotopy extension theorem and the concepts of L-absolute retract and L-absolute neighborhood retract. Also, the role of L-absolute retract, L-absolute neighborhood retract and L-regular lifting functions in the theory of L-homotopy extension are revealed.
Convex bodies are naturally symmetrical. There is also a correlation between the two variables of symmetry and convexity. Their use, in either case, has been feasible in recent years because of their ...interchangeable and similar properties. The proposed analysis provides information on a new class for a convex function which is known as up and down X1,X2-convex fuzzy-Number valued mappings (UD-X1,X2-convex FNVM). Using this class, we disclosed a number of new versions of integral inequalities. Additionally, we give a number of new related integral inequalities connected to the well-known Hermite-Hadamard-type inequalities. In conclusion, some examples are given to back up and show the value of these new results.
This article is devoted to showing the existence and uniqueness (EU) of a solution with non-Lipschitz coefficients (NLC) of fractional Itô-Doob stochastic differential equations driven by countably ...many Brownian motions (FIDSDECBMs) of order ϰ∈(0,1) by using the Picard iteration technique (PIT) and the semimartingale local time (SLT).
The new computational approach has been incorporated for modeling the nanofluid flow through a cavity involving a wavy inner wall which experiences uniform flux. The fluid was created by loading ...alumina powders with various shapes within the water. The stream function formulation was applied after employing Darcy law and final equations have been generated. The container is under the impact of Lorentz force in addition to buoyancy forces. With loading additives, Nu enhances about 17.07% and 41.57% depending on the amount of Ha. The greater value of Ha makes the effect of adding nanoparticles become more sensible. With increasing the value of shape factor, Nu increases about 11.76%. As Ha grows, the rate of cooling decreases about 41.31%. With augment of Ra, Nu enhances about 50.41% in absence of Ha.
•Intar-tumoral and peri-tumoural rCBV (rCBVt and rCBVp) were measured to evaluate the glioma grade.•Each of rCBVt and rCBVp significantly distinguished between low and high-grade glioma.•Integration ...of both rCBVt and rCBVp provided better overall diagnostic accuracy for the preoperative glioma grading.
To assess the usefulness of intra-tumor and peri-tumoral relative cerebral blood volume (rCBV) in preoperative glioma grading.
21 patients with histopathologically confirmed glioma were included. Imaging was achieved on a 1.5T MRI scanner. Dynamic susceptibility contrast (DSC) MRI was performed using T2* weighted gradient echo-planner imaging (EPI). Multiple regions of interest (ROIs) have been drawn in the hotspots regions, the highest ROI has been selected to represent the rCBV of each intra-tumoral and peri-tumoral regions. Based on histopathology, tumors were subdivided into low grade and high grade. Receiver operating characteristic analysis (ROC) of rCBV, of both intra-tumoral and peri-tumoral regions, was performed to find cut-off values between high and low-grade tumors. The resulting sensitivity, specificity, positive predictive value, negative predictive value, and accuracy were calculated.
Based on the histopathology, high-grade glioma (HGG) represented 76.2% whereas low-grade glioma (LGG) represented 23.8%. Both intra-tumoral and peri-tumoral rCBV of HGG were significantly higher than those of LGG. A cut-off value >2.9 for intra-tumoral rCBV provided sensitivity, specificity, and accuracy of 80%, 100%, and 85.7% respectively to differentiate between HGG and LGG. Additionally, the cut-off value >0.7 for peri-tumoral rCBV provided sensitivity, specificity, and accuracy of 100%, 66.6%, and 90.5% respectively to differentiate between HGG and LGG.
rCBV of each of intra-tumoral and peri-tumoral rCBV are significantly reliable for the preoperative distinction between HGG and LGG. Combined intra-tumoral and peri-tumoral rCBV provides overall better diagnostic accuracy and helps to decrease the invasive intervention for non-surgical candidates.
In this article, we discuss the existence and uniqueness of proportional Itô–Doob stochastic fractional order systems (PIDSFOS) by using the Picard iteration method. The paper provides new results ...using the proportional fractional integral and stochastic calculus techniques. We have shown the convergence of the solution of the averaged PIDSFOS to that of the standard PIDSFOS in the context of the mean square and also in probability. One example is given to illustrate our results.
To evaluate the efficiency of a system involving wavy shapes of wall, numerical technique has been utilized in this article. The region between two wavy complex surfaces was fabricated from porous ...material and the working fluid is nanofluid (mixture of water with various shapes of alumina nanoparticles). The new terms related to porous media have been added according to Darcy law. The pressure terms were removed with defining stream function. The last form of equations contains two variables (θ and Ψ) which were solved via CVFEM. The results from the present code have been compared with previous article and good agreement was reported. With augmenting Ha, the speed of nanofluid decreases and Nu drops about 50.48% when Ra = 700. Considering greater buoyancy force makes Nu to increase about 61.36% when Ha = 0. The shape factor has a direct relation with the amount of conductivity, thus, Nu enhances about 11.97% with an increase of this factor when Ha = 15, Ra = 150.
