In this study, we set up and analyze a cancer growth model that integrates a chemotherapy drug with the impact of vitamins in boosting and strengthening the immune system. The aim of this study is to determine the minimal amount of treatment required to eliminate cancer, which will help to reduce harm to patients. It is assumed that vitamins come from organic foods and beverages. The chemotherapy drug is added to delay and eliminate tumor cell growth and division. To that end, we suggest the tumor-immune model, composed of the interaction of tumor and immune cells, which is composed of two ordinary differential equations. The model’s fundamental mathematical properties, such as positivity, boundedness, and equilibrium existence, are examined. The equilibrium points’ asymptotic stability is analyzed using linear stability. Then, global stability and persistence are investigated using the Lyapunov strategy. The occurrence of bifurcations of the model, such as of trans-critical or Hopf type, is also explored. Numerical simulations are used to verify the theoretical analysis. The Runge–Kutta method of fourth order is used in the simulation of the model. The analytical study and simulation findings show that the immune system is boosted by regular vitamin consumption, inhibiting the growth of tumor cells. Further, the chemotherapy drug contributes to the control of tumor cell progression. Vitamin intake and chemotherapy are treated both individually and in combination, and in all situations, the minimal level required to eliminate the cancer is determined.
Let R be a ring with 1 and W is a left Module over R. A Submodule D of an R-Module W is small in W(D ≪ W) if whenever a Submodule V of W s.t W = D + V then V = W. A proper Submodule Y of an R-Module W is semismall in W(Y ≪_S W) if Y = 0 or Y/F ≪ W/F ∀ nonzero Submodules F of Y. A Submodule U of an R-Module E is essentially semismall(U ≪es E), if for every non zero semismall Submodule V of E, V∩U ≠ 0. An R-Module E is essentially semismall quasi-Dedekind(ESSQD) if Hom(E/W, E) = 0 ∀ W ≪es E. A ring R is ESSQD if R is an ESSQD R-Module. An R-Module E is a scalar R-Module if, ∀ , ∃ s.t V(e) = ze ∀ . In this paper, we study the relationship between ESSQD Modules with scalar and multiplication Modules. We show that
... Show MoreCoupling reaction of 2-amino benzoic acid with phenol gave the new bidentate azo ligand. The prepared ligand was identified by Microelemental Analysis, FT-IR and UV-Vis spectroscopic technique. Treatment of the prepared ligand with the following metal ions (CoII, NiII, CuII and ZnII) in aqueous ethanol with a 1:2 M:L ratio and at optimum pH, yielded a series of neutral complexes of the general formula [M(L)2]. The prepared complexes were characterized using flame atomic absorption, (C.H.N) Analysis, FT-IR and UV-Vis spectroscopic methods as well as magnetic susceptibility and conductivity measurements. The nature of the complexes formed were studied following the mole ratio and continuous variation methods, Beer's law obeyed over a concentr
... Show MoreCoupling reaction of 4-amino antipyrene with 2,6-dimethyl phenol gave bidentate azo ligand. The prepared ligand was identified by Microelemental Analysis, 1HNMR, FT-IR and UV-Vis spectroscopic techniques. Treatment of the prepared ligand with the following metal ions (CoII, NiII, CuII, ZnII, CdII, and HgII) in aqueous ethanol with a 1:2 M:L ratio and at optimum pH, yielded a series of neutral complexes of the general formula [M(L)2Cl2]. The prepared complexes were characterized using flame atomic absorption, (C.H.N) Analysis, FT-IR and UVVis spectroscopic methods as well as magnetic susceptibility and conductivity measurements. Chloride ion content was also evaluated by (Mohr method). The nature of the complexes formed were studied followin
... Show MoreMalnutrition, anemia, and micronutrient deficits may be associated with Enterobius vermicularis infection. Hence, the subject has recently received a lot of attention. The goal of this study was to analyse the nutritional, hematological and micronutrient status of children infected with E. vermicularis. This research was carried out in Baghdad from October 2021 to the end of March 2022. The study comprised 100 children of both sexes, ranging in age from 3-16 years. All individuals nutritional status was assessed using the weight-for-age Z score and the height-for-age Z score. As well as cellophane tape samples and blood samples were collected from all individuals. The cellophane tape samples were examined under microscope f
... Show MoreThis investigation deals with the use of orange peel (OP) waste as adsorbent for removal of nitrate (NO3) from simulated wastewater. Orange peel prepared in two conditions dried at 60C° (OPD) and burning at 500 °C (OPB). The effect of pH: 2-10, contact time: 30- 180 min, sorbent weight: 0.5- 3.0 g were considered. The optimal pH value for NO3 adsorption was found to be 2.0 for both adsorbents. The equilibrium data were analyzed using Langmuir and Freundlich isotherm models. Freundlich model was found to fit the equilibrium data very well with high-correlation coefficient (R2). The adsorption kinetics was found to follow pseudo-second-order rate kinetic model, with a good correlation (R2
... Show MoreEverybody is connected with social media like (Facebook, Twitter, LinkedIn, Instagram…etc.) that generate a large quantity of data and which traditional applications are inadequate to process. Social media are regarded as an important platform for sharing information, opinion, and knowledge of many subscribers. These basic media attribute Big data also to many issues, such as data collection, storage, moving, updating, reviewing, posting, scanning, visualization, Data protection, etc. To deal with all these problems, this is a need for an adequate system that not just prepares the details, but also provides meaningful analysis to take advantage of the difficult situations, relevant to business, proper decision, Health, social media, sc
... Show MoreA new hetrocyclic liquid crystal compounds containing 1,3,4-oxadiazole with different substituted in para position (Bromo, Chloro, Nitro and Methyl) were synthesized and characterized by melting points, FTIR Spectroscopy and 1HNMR spectroscopy for [Cl-SR6] and [NO2-SR6] compounds. The liquid crystalline properties of the synthesized compounds were studied by using hot-stage polarizing optical microscopy (POM), so they determined the transition enthalpies and entropies by using differential scanning calorimetery (DSC). All of the compounds show mesomorphic properties. The compounds [Br-SR6], [Cl-SR6] and [NO2SR6] exhibit an enantiotropic dimorphism smectic (Sm) phase, while the compounds [MeSR6] showed nematic (N) phase throw cooli
... Show MoreBackground: The aim of this study was to evaluate the expression of fibroblast growth factor-2 and Heparanase in salivary pleomorphic adenoma, and to correlate the two studied markers with each other and with clinicopathological parameters including: age, sex, tumor site and histopathological presentation. Methods: Sections of twenty five formalin-fixed paraffin embedded tissue blocks specimens of salivary pleomorphic adenoma were immunostained using monoclonal antibodies (Fibroblast growth factor-2 and Heparanase) to assess their expression in this tumor. Results: The expression of fibroblast growth factor-2 and Heparanase were positive in all pleomorphic adenoma cases (100%). The positive expression of fibroblast growth factor-2 was signi
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