Two Legendre-Dual-Petrov-Galerkin Algorithms for Solving the Integrated Forms of High Odd-Order Boundary Value Problems

Two numerical algorithms based on dual-Petrov-Galerkin method are developed for solving the integrated forms of high odd-order boundary value problems (BVPs) governed by homogeneous and nonhomogeneous boundary conditions. Two different choices of trial functions and test functions which satisfy the underlying boundary conditions of the differential equations and the dual boundary conditions are used for this purpose. These choices lead to linear systems with specially structured matrices that can be efficiently inverted, hence greatly reducing the cost. The various matrix systems resulting from these discretizations are carefully investigated, especially their complexities and their condition numbers. Numerical results are given to illustrate the efficiency of the proposed algorithms, and some comparisons with some other methods are made

Alternative epidemic indicators for COVID-19 in three settings with incomplete death registration systems

Not all COVID-19 deaths are officially reported, and particularly in low-income and humanitarian settings, the magnitude of reporting gaps remains sparsely characterized. Alternative data sources, including burial site worker reports, satellite imagery of cemeteries, and social media-conducted surveys of infection may offer solutions. By merging these data with independently conducted, representative serological studies within a mathematical modeling framework, we aim to better understand the range of underreporting using examples from three major cities: Addis Ababa (Ethiopia), Aden (Yemen), and Khartoum (Sudan) during 2020. We estimate that 69 to 100%, 0.8 to 8.0%, and 3.0 to 6.0% of COVID-19 deaths were reported in each setting, respectively. In future epidemics, and in settings where vital registration systems are limited, using multiple alternative data sources could provide critically needed, improved estimates of epidemic impact. However, ultimately, these systems are needed to ensure that, in contrast to COVID-19, the impact of future pandemics or other drivers of mortality is reported and understood worldwide

Impact of fruit peels extract on the shelf-life of minced beef

Fourteen kilograms of minced meat were divided into 4 groups (about 3.5 Kg for each group). All samples were examined to study the effect of the addition of 1% fruit peel extracts (banana, orange, and pomegranate) on the extension of the shelf life of such food article. Reduction of APC after 6 days in samples treated with banana, orange, and pomegranate peel reached 83.9 %, 91.6 %, and 95.4%, respectively and reduction of articles coliform reached 75.8%, 90.3 %, and 93% while S. aureus count reduced by 77.5%, 89%, and 96.5 %, respectively. Fruit peels decreased pH values compared with the control sample during storage at 4ËšC for 10 days. pH values of samples treated with banana peel decreased from 5.63 to 5.61 at zero time and from 6.71 to 5.84 on the 6th day and orange peel decreased to 5.58 and to 5.70 while pomegranate to 5.56 and to 5.67 at zero time and at 6th day of storage, respectively. TVB-N values of samples treated with banana decreased from 1.97 to 1.89 at zero time and from 29.58 to 9.83 on the 6th day and orange peel decreased to 1.84 and to 7.90 while pomegranate to 1.81 and to 6.88 at zero time and at 6th day. TBA values of samples treated with banana peel decreased from 1.22 to 0.25 on the 6th day but orange peel decreased to 0.02 and to 0.19 and with pomegranate to 0.02 and to 0.14 at zero time and on the 6th day of storage, respectively. In general, the incorporation of banana, orange, and pomegranate peel powder into minced meat as natural preservatives improved color, odor, appearance, consistency, and overall acceptability and extended their shelf life during storage

New Algorithm for the Numerical Solutions of Nonlinear Third-Order Differential Equations Using Jacobi-Gauss Collocation Method

A new algorithm for solving the general nonlinear third-order differential equation is developed by means of a shifted Jacobi-Gauss collocation spectral method. The shifted Jacobi-Gauss points are used as collocation nodes. Numerical examples are included to demonstrate the validity and applicability of the proposed algorithm, and some comparisons are made with the existing results. The method is easy to implement and yields very accurate results

Impact of fruit peels extract on the shelf-life of minced beef

Fourteen kilograms of minced meat were divided into 4 groups (about 3.5 Kg for each group). All samples were examined to study the effect of the addition of 1% fruit peel extracts (banana, orange, and pomegranate) on the extension of the shelf life of such food article. Reduction of APC after 6 days in samples treated with banana, orange, and pomegranate peel reached 83.9 %, 91.6 %, and 95.4%, respectively and reduction of articles coliform reached 75.8%, 90.3 %, and 93% while S. aureus count reduced by 77.5%, 89%, and 96.5 %, respectively. Fruit peels decreased pH values compared with the control sample during storage at 4˚C for 10 days. pH values of samples treated with banana peel decreased from 5.63 to 5.61 at zero time and from 6.71 to 5.84 on the 6th day and orange peel decreased to 5.58 and to 5.70 while pomegranate to 5.56 and to 5.67 at zero time and at 6th day of storage, respectively. TVB-N values of samples treated with banana decreased from 1.97 to 1.89 at zero time and from 29.58 to 9.83 on the 6th day and orange peel decreased to 1.84 and to 7.90 while pomegranate to 1.81 and to 6.88 at zero time and at 6th day. TBA values of samples treated with banana peel decreased from 1.22 to 0.25 on the 6th day but orange peel decreased to 0.02 and to 0.19 and with pomegranate to 0.02 and to 0.14 at zero time and on the 6th day of storage, respectively. In general, the incorporation of banana, orange, and pomegranate peel powder into minced meat as natural preservatives improved color, odor, appearance, consistency, and overall acceptability and extended their shelf life during storage

Monitoring of Helicobacter pylori in chicken products

A total of 200 samples of chicken products collected randomly from Quesna and El-Bagour in Menoufia governorate. The collected samples were represented by chicken breast, thigh, gizzard and liver (50 of each) and subjected to bacteriological examination for detection of Helicobacter species particularly, Helicobacter pylori. Further, the effect of L. rhamnosus culture to control such serious pathogen contaminating chicken products was studied. Helicobacter spp detected in 4%, 6%, 12% and 20% of breast, thigh, gizzard and liver, respectively and H. pylori represent 4%, 4% 6% and 10% from this examined samples, respectively. H. pylori inoculated chicken fillet (1×106 /g) which are not treated with  Lactobacillus rhamnosus (control +ve) showed increase  in  prevalence  of H. pylori 1.0×106, 1.3×106, 1.9×106 and 2.4×106 at zero time, 1st day, 2nd day and 3rd day, respectively.  While chicken fillets treated with L. rhamnosus (1x106 /g) Effect on prevalence of H. pylori inoculated into chicken fillets with a reduction percent of  35%, 52% and 69%  but  L. rhamnosus (1x107 /g) showed remarkable reduction of H. pylori prevalence  with a reduction percent of  54%, 67% and 81% at 1st day, 2nd day and 3rd day, respectively. L. rhamnosus effected on virulence genes of H. pylori isolated from treated chicken fillet as L. rhamnosus (1x106/g) destructed cagA gene and L. rhamnosus (1x107/g) destructed cagA and vacA genes so using of Lactobacillus rhamnosus culture as a method of control has a good effect on prevalence of H. pylori and its virulence genes in chicken fillets and L. rhamnosus (1x107 /g) more effective than L. rhamnosus (1x106 /g).Â