Numerical solutions of nonlinear evolution equations using variational iteration method

AbstractThe variational iteration method is used to solve three kinds of nonlinear partial differential equations, coupled nonlinear reaction diffusion equations, Hirota–Satsuma coupled KdV system and Drinefel’d–Sokolov–Wilson equations. Numerical solutions obtained by the variational iteration method are compared with the exact solutions, revealing that the obtained solutions are of high accuracy. He's variational iteration method is introduced to overcome the difficulty arising in calculating Adomian polynomial in Adomian method. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics

Toeplitz matrix method and nonlinear integral equation of Hammerstein type

AbstractThe existence and uniqueness solution of the nonlinear integral equation of Hammerstein type with discontinuous kernel are discussed. The normality and continuity of the integral operator are proved. Toeplitz matrix method is used, as a numerical method, to obtain a nonlinear system of algebraic equations. Also, many important theorems related to the existence and uniqueness of the produced algebraic system are derived. Finally, numerical examples, when the kernel takes a logarithmic and Carleman forms, are discussed and the estimate error, in each case, is calculated

EFFECT OF SOME OF ORGANIC AND BIO AND/OR MINERAL FERTILIZATION ON VEGETATIVE GROWTH AND CHEMICAL COMPOSITION OF DELONIX REGIA

This work wasexecuted during two successive seasons of 2018 and 2019 in the nursery and laboratory of Fac. Agric., Minia Univ., Egypt to investigate the response of vegetative and root growthand some chemical composition of Delonix regia seedlings to four percentages of humic acid (0, 1, 2 and 4%) and four bio- and/or mineral NPK fertilization treatments (control, 100% NPK, Minia Azotein and 75% NPK plus Minia Azotein), as well as, the interaction between them. All used three percentages of humic acid significantly increased vegetative growth (plant height, stem diameter, the aerial part dry weight), root growth (root number and roots dry weight) and chemical composition (photosynthetic pigments, NPK%, total phenolic and total flavonoids contents) over control. Humic acid at 4% more was effective treatment. All used bio-and/or mineral NPK fertilization treatments significantly increased all studied characters over control. The best treatments were 100% NPK or 75% NPK plus Minia Azotein. It could be recommended to add humic acid at 4% in combination with 100% NPK or 75% NPK plus Minia Azotein to improve growth of Delonix regia

The Landscape of Immune Microenvironments in Racially Diverse Breast Cancer Patients

Background: Immunotherapy is a rapidly evolving treatment option in breast cancer; However, the breast cancer immune microenvironment is understudied in Black and younger (<50 years) patients. Methods: We used histologic and RNA-based immunoprofiling methods to characterize the breast cancer immune landscape in 1,952 tumors from the Carolina Breast Cancer Study (CBCS), a population-based study that oversampled Black (n ¼ 1,030) and young women (n ¼ 1,039). We evaluated immune response leveraging markers for 10 immune cell populations, compared profiles to those in The Cancer Genome Atlas (TCGA) Project [n ¼ 1,095 tumors, Black (n ¼ 183), and young women (n ¼ 295)], and evaluated in association with clinical and demographic variables, including recurrence. Results: Consensus clustering identified three immune clusters in CBCS (adaptive-enriched, innate-enriched, or immune-quiet) that varied in frequency by race, age, tumor grade and subtype; however, only two clusters were identified in TCGA, which were predominantly comprised of adaptive-enriched and innate-enriched tumors. In CBCS, the strongest adaptive immune response was observed for basal-like, HER2-positive (HER2þ), triple-negative breast cancer (TNBC), and high-grade tumors. Younger patients had higher proportions of adaptive-enriched tumors, particularly among estrogen receptor (ER)-negative (ER-) cases. Black patients had higher frequencies of both adaptive-enriched and innate-enriched tumors. Immune clusters were associated with recurrence among ER- tumors, with adaptive-enriched showing the best and innate-enriched showing the poorest 5-year recurrence-free survival. Conclusions: These data suggest that immune microenvironments are intricately related to race, age, tumor subtype, and grade. Impact: Given higher mortality among Black and young women, more defined immune classification using cell-type–specific panels could help explain higher recurrence and ultimately lead to target-able interventions

Reducing the environmental impact of surgery on a global scale: systematic review and co-prioritization with healthcare workers in 132 countries

Background Healthcare cannot achieve net-zero carbon without addressing operating theatres. The aim of this study was to prioritize feasible interventions to reduce the environmental impact of operating theatres. Methods This study adopted a four-phase Delphi consensus co-prioritization methodology. In phase 1, a systematic review of published interventions and global consultation of perioperative healthcare professionals were used to longlist interventions. In phase 2, iterative thematic analysis consolidated comparable interventions into a shortlist. In phase 3, the shortlist was co-prioritized based on patient and clinician views on acceptability, feasibility, and safety. In phase 4, ranked lists of interventions were presented by their relevance to high-income countries and low–middle-income countries. Results In phase 1, 43 interventions were identified, which had low uptake in practice according to 3042 professionals globally. In phase 2, a shortlist of 15 intervention domains was generated. In phase 3, interventions were deemed acceptable for more than 90 per cent of patients except for reducing general anaesthesia (84 per cent) and re-sterilization of ‘single-use’ consumables (86 per cent). In phase 4, the top three shortlisted interventions for high-income countries were: introducing recycling; reducing use of anaesthetic gases; and appropriate clinical waste processing. In phase 4, the top three shortlisted interventions for low–middle-income countries were: introducing reusable surgical devices; reducing use of consumables; and reducing the use of general anaesthesia. Conclusion This is a step toward environmentally sustainable operating environments with actionable interventions applicable to both high– and low–middle–income countries

The evolving SARS-CoV-2 epidemic in Africa: Insights from rapidly expanding genomic surveillance

INTRODUCTION Investment in Africa over the past year with regard to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) sequencing has led to a massive increase in the number of sequences, which, to date, exceeds 100,000 sequences generated to track the pandemic on the continent. These sequences have profoundly affected how public health officials in Africa have navigated the COVID-19 pandemic. RATIONALE We demonstrate how the first 100,000 SARS-CoV-2 sequences from Africa have helped monitor the epidemic on the continent, how genomic surveillance expanded over the course of the pandemic, and how we adapted our sequencing methods to deal with an evolving virus. Finally, we also examine how viral lineages have spread across the continent in a phylogeographic framework to gain insights into the underlying temporal and spatial transmission dynamics for several variants of concern (VOCs). RESULTS Our results indicate that the number of countries in Africa that can sequence the virus within their own borders is growing and that this is coupled with a shorter turnaround time from the time of sampling to sequence submission. Ongoing evolution necessitated the continual updating of primer sets, and, as a result, eight primer sets were designed in tandem with viral evolution and used to ensure effective sequencing of the virus. The pandemic unfolded through multiple waves of infection that were each driven by distinct genetic lineages, with B.1-like ancestral strains associated with the first pandemic wave of infections in 2020. Successive waves on the continent were fueled by different VOCs, with Alpha and Beta cocirculating in distinct spatial patterns during the second wave and Delta and Omicron affecting the whole continent during the third and fourth waves, respectively. Phylogeographic reconstruction points toward distinct differences in viral importation and exportation patterns associated with the Alpha, Beta, Delta, and Omicron variants and subvariants, when considering both Africa versus the rest of the world and viral dissemination within the continent. Our epidemiological and phylogenetic inferences therefore underscore the heterogeneous nature of the pandemic on the continent and highlight key insights and challenges, for instance, recognizing the limitations of low testing proportions. We also highlight the early warning capacity that genomic surveillance in Africa has had for the rest of the world with the detection of new lineages and variants, the most recent being the characterization of various Omicron subvariants. CONCLUSION Sustained investment for diagnostics and genomic surveillance in Africa is needed as the virus continues to evolve. This is important not only to help combat SARS-CoV-2 on the continent but also because it can be used as a platform to help address the many emerging and reemerging infectious disease threats in Africa. In particular, capacity building for local sequencing within countries or within the continent should be prioritized because this is generally associated with shorter turnaround times, providing the most benefit to local public health authorities tasked with pandemic response and mitigation and allowing for the fastest reaction to localized outbreaks. These investments are crucial for pandemic preparedness and response and will serve the health of the continent well into the 21st century

Thermoelastic Problem for an Infinite Plate with a Curvilinear Hole Having Finite Poles

In the present paper, Muskhelishvili\u27s complex variable method of solving two-dimensional elasticity problems has been applied to derive exact expressions for Goursat\u27s functions for the boundary value problems of the infinite plate weakened by a hole having many poles and arbitrary shape which is conformally mapped n the dorhain outside a unit circle by means of general rational mapping function. Also the components of stress are obtained, when a stationary heat is flowing uniformly in the perpendicular direction of the hole. Some applications are considered. The interesting cases when the shape of the hole takes different shapes are included as special cases

New exact travelling wave solutions for space-time fractional nonlinear equations describing nonlinear transmission lines

In this paper, we examines the effectiveness of newly developed algorithms called the exp(-ϕ(ξ))-expansion function method and generalized Kudryashov method for constructing new and important travelling wave solutions of space-time fractional nonlinear differential equations. The fractional differential equation is converted into ordinary differential equations with the help of fractional complex transform and the modified Riemann Liouville derivative sense. The validity and reliability the proposed methods are tested by its applications it for describe the nonlinear low-pass electrical transmission lines and pulse narrowing nonlinear transmission lines respectively. Keywords: Fractional calculus, Fractional complex transform, Nonlinear low-pass electrical lines, The exp(-ϕ(ξ))-expansion function method, Kudryashov method, Exact solution