Background Intestinal viability is crucial before commencement of any anastomoses or establishment of stomas after resection of the gut for any surgical reason, and depending on the clinical sense and subjective methods alone may result in disastrous results and complications affecting the outcomes of the surgical procedures. There are many techniques available nowadays for assessing bowel viability, but most of them are technically demanding and not usually available in the operating theater, besides the cost of many of them, which may represent another added burden. For all the aforementioned reasons, the wireless pulse oximeter (PO) has emerged as a possible new method which can aid in assessment of bowel viability during surgeries with the advantages of availability, low cost, and simple rapid way of gut viability assessment. Purpose The aim of this study was to evaluate the capability of the wireless PO in discrimination between viable and nonviable intestine intraoperatively before establishment of stomas or intestinal anastomoses. Study design This was a prospective study that included 40 patients who were evaluated intraoperatively by the wireless PO to assess the viability of the proximal and distal ends of the intestine. The intestinal viability in the first 10 patients was also evaluated by the fluorescein dye in addition to the PO. Here, fluorescein was used as a well-established method to validate the new technique of the PO. All the readings were recorded, and patients were followed up for 2 weeks postoperatively to detect any complications related to intestinal ischemia. Results Three cases were complicated: two cases of failed anastomosis with leakage and the third case was ischemic end colostomy stoma. The mean values of PO readings in the noncomplicated group (37 cases) were 95.65 and 96.32% in the proximal and distal segments, respectively, whereas in the complicated group (three cases), mean values were 89 and 87% in the proximal and distal segments, respectively. Conclusion The PO device is safe, portable, and nonsophisticated, which can be used easily by surgeons in assessment of bowel viability during surgery. It takes less time to assess the intestinal viability and is very cost-effective, as one device can be used in multiple patients.

Function expansion in terms of finite Sinc bases is considered. For finite intervals, we considered proper transformation and weighted barycentric methods. We adjusted the transformation function to comply with the truncation of the expansion. This removes the unbounded behavior of the terminal derivatives and yields accurate results. Efficient weighted barycentric expansions are presented to improve the accuracies of function and derivative estimations. A new expression for the estimation of the second derivative is derived. The derived expressions are successfully applied to accurately locate the minimum of the solution and solve a singularly-perturbed problem.

We propose an accurate and computationally efficient numerical technique for solving the biharmonic eigenvalue problem. The technique is based on the sinc-Galerkin approximation method to solve the clamped plate problem. Numerical experiments for plates with various aspect ratios are reported, and comparisons are made with other methods in literature. The calculated results accord well with those published earlier, which proves the accuracy and validity of the proposed method.

Background and purpose The functional outcomes of incontinence and high stool frequency resulting from restorative surgery are often criticised. The aim of this study was to assess the taeniectomy pouch in comparison with other pouches described in the literature. Material and methods This was a prospective cohort study. All patients who were candidate for low rectal resection presenting to the colorectal unit at Cairo University hospitals during the period February 2013 to February 2015 were included in the study (90 patients). Safety and feasibility of the new technique were assessed, including operative time, leakage, postoperative urgency, incontinence, number of daily motions and difficulty in evacuation. These parameters were assessed clinically, by means of defecography and anorectal manometry. Results The mean age of patients was 49.6 years. Percentages of postoperative mortality and leakage were 2.2% and 3.4%, respectively. Mean operative time was 117 minutes. Mean numbers of daily motions were 3.04 and 1.52 at 3 and 12 months, respectively. Mean Wexner score for continence at 3 and 12 months were 3.21 and 1.32, respectively. Mean resting pressure was 51.63 mmHg, squeeze pressure was 130.42 mmHg and mean threshold volume was 118.68 ml. Conclusions Taeniectomy is a novel technique for pouch formation after low rectal resection, which can be used as an alternative to other pouches, especially the widely used transverse coloplasty.

A numerical method based on sinc approximation is developed to solve linear and nonlinear Volterra-Fredholm integro-differential equations. Sinc approximation are typified by errors of the form O ( e−k/h ) , where k > 0 is a constant and h is a step size. The equations are reduced to systems of linear and nonlinear algebraic equations. Numerical examples are provided to illustrate the accuracy and computational efficiency of the method. The examples include convolution type, singular as well as singularly-perturbed problems. 2010 Mathematics Subject Classification: 65L60; 45J05.

Sinc methods are frequently used in treating mathematical physics problems such as in interpolation, quadrature and solving integral and differential equations. However, for finite intervals the function derivatives become unbounded. This unbounded behavior is addressed. The choice of proper weights and the use of the Sinc expansion of the function F(x) = x are used to provide improved expansions and to eliminate the unbounded behavior of the derivatives at the terminal points. (C) 2015 Published by Elsevier Inc.

There are many techniques available to numerically solve the biharmonic equation. In this paper we show that the sinc-Galerkin method is a very effective tool in numerically solving this equation. Hermite interpolation is used to treat the nonhomogeneous boundary conditions. Our method is tested on examples and comparisons with other methods are made. It is shown that the sinc-Galerkin method yields good results even when singularities occur at the boundaries.

This paper is concerned with the numerical solution using sinc-collocation method of nonlinear Fredholm integro-differential equations. The algorithm is based on replacing the exact solution by a linear combination of sinc functions. The resulting nonlinear equations are treated using Newton method. Numerical examples illustrate the pertinent features of the method and its applicability to a large variety. The examples include convolution type, singular as well as singularly-perturbed problems.

A brief survey of the properties and different treatments of the one-dimensional (1D) planar Bratu problem is presented. The treatment using Green’s function is considered. Different iterative treatments of the resulting nonlinear system of equations are discussed. Starting the solution with simple sinusoidal function having appropriate amplitude is recommended. Then the resulting system is solved using a nonlinear conjugate-gradient (NL-CG) method. The importance of the proper choice of the starting function as well as the stopping criterion of the iterative solution are stressed.

A brief survey of the properties and different treatments of the one-dimensional (1D) and (2D) Bratu problems is presented. Different iterative treatments of the resulting nonlinear system of equations are discussed. The finite-difference treatment of the problem is considered. Nonstandard finite-difference methods with a simple sinusoidal starting function having an appropriate amplitude are recommended. Bounds on the amplitude for yielding both lower and upper solutions are given.

The problem of non-uniqueness (NU) of the solution of exterior acoustic problems when using the boundary element method (BEM) is well known. Methods like the Burton-Miller technique or the CHIEF method are used to solve this challenge at the expense of more complex procedures for handling hypersingular integrals and/or higher computing times due to higher complexity of the algorithm or additional equations. The dual surface method, commonly used for electromagnetic problems, was adapted for acoustic radiation and scattering problems. The basic principles of methods to solve the NU problem are outlined and results for different models and solution procedures are presented, taking into account quality, solution time and the numerical advantages when using iterative solvers.

The problem of nonuniqueness (NU) of the solution of exterior acoustic problems via boundary integral equations (BIEs) is studied. The application of the dual surface method, used in electromagnetic problems, to exterior acoustic problems is studied. The dual surface integral equations, although identical in form and comparable in complexity to the original surface integral equations, provide a unique solution at all real frequencies. The conditions and the proof of uniqueness are outlined. Applications of the method are given for the scattering as well as the radiation from three different structures. We consider normalized frequencies up to ka similar to 22, where "a" is a typical dimension of the structure.

Sinc bases are developed to approximate the solutions of linear and nonlinear Volterra integral and integro-differential equations. Properties of these sinc bases and some operational matrices are first presented. These properties are then used to reduce the integral and integro-differential equations to systems of linear or nonlinear algebraic equations. Numerical examples illustrate the pertinent features of the method and its applicability to a large variety of problems. The examples include convolution type, singular as well as singularly-perturbed problems.

The solution of acoustic problems via integral equations (IEs) is considered. Symmetrical evaluation of the resulting integrals is proposed. The possible reduction of the system matrix to complex symmetric form is considered. Applications of the proposed method to scattering by a soft as well as a hard sphere are presented. Another application to radiation from a uniformly vibrating sphere is also considered. To overcome the nonuniqueness problem, CHIEF method is used and Lagrange multipliers are employed to deal with the resulting overdetermined system to preserve the symmetry of the system matrix. The application of CHIEF via a close interior surface of a hard sphere with ka = 22.602185 illustrates the success of CHIEF at high frequencies (HF).

Matrix LU decomposition has six ijk forms. Different forms have different computational complexities and storage requirements, particularly on vector and parallel computers. Other factors governing the choice of a particular form are considered. For treating Fredholm integral equations of the first kind, the truncated LU decomposition of the resulting system matrix is recommended. Required modifications to selected known ijk forms are presented.

This paper presents a study of the performance of the collocation and Galerkin methods using sinc basis functions for solving linear and nonlinear second-order two-point boundary value problems. The two methods have the linear systems solved by the Q-R method and have the nonlinear systems solved by Newton's method. This study shows that the collocation method performs better than the Galerkin method for the cases considered.

In this paper, we present more investigations of the numerical solution of the 2D Bratu equation to obtain the second solution on the upper branch by Multigrid. Classical smoothers such as Gauss–Seidel and weighted Jacobi have proven ineffective for obtaining the second solution due to the loss of diagonal dominance and the presence of indefinite Jacobian system at some parameter values. In this paper, we modify the Multigrid algorithms by adding and combining some Krylov methods as smoothers to enhance the multigrid efficiency. Though the idea is not new but we could get new enhanced results compared to that presented by Hackbusch [W. Hackbusch, Comparison of different multi-grid variants for nonlinear equations, ZAMM Z. Angew. Math. Mech. 72 (1992) 148–151] and Washio and Oosterlee [T. Washio, C.W. Oosterlee, Krylov subspace acceleration for nonlinear multigrid schemes, Electron. Trans. Numer. Anal. 6 (1997) 271–290].

A Sinc–Collocation method for solving linear integro-differential equations of the Fredholm type is discussed. The integro-differential equations are reduced to a system of algebraic equations and Q-R method is used to establish numerical procedures. The convergence rate of the method is \(O{\left( {e^{{ - k{\sqrt N }}} } \right)}\). Numerical results are included to confirm the efficiency and accuracy of the method even in the presence of singularities and a comparison with the rationalized Haar wavelet method is made.

The solution of the linear system Ax = b with an m x n-matrix A of maximal rank mu := min(m, n) is considered. The method generates a sequence of n x m-matrices H(k) and vectors x(k) so that the AH(k) are positive semidefinite, the H(k) approximate the pseudoinverse of A and x(k) approximate the least squares solution of Ax = b. The method is of the type of Broyden's rank-one updates and yields the pseudoinverse in mu steps.

The problem of acoustic wave scattering by closed objects via second kind integral equations, is considered. Based on, combined Helmholtz integral equation formulation (CHIEF) method, an efficient method for choosing and utilizing interior field relations is suggested for solving the non-uniqueness problem at the characteristic frequencies. The implementation of the algorithm fully utilizes previous computation and thus significantly reduces the CPU time compared to the usual least-squares treatment. The method is tested for acoustic wave scattering by both acoustically hard and soft spheres. Accurate results compared to the known exact solutions are obtained. Copyright (C) 2006 John Wiley & Sons, Ltd.