Renal-related perinephric fluid collections: MRI findings

We retrospectively reviewed MR studies on 10 patients with renal-related perinephric fluid collections who underwent MRI in three institutions between January 2001 and August 2004. All patients underwent MRI of the abdomen and T1-weighted, T2-weighted and serial contrast-enhanced images, including delayed-phase contrast-enhanced images 10-12 min after contrast injection, were obtained. Perinephric fluid collections in 5 patients revealed MRI findings of simple fluid content (i.e., hypointense on T1-weighted images and hyperintense on T2-weighted images). In another 5 patients, a complex perinephric fluid content (i.e., mixed hyper/hypointense on T1-weighted images and mixed hypo/hyperintense on T2-weighted images compatible with blood breakdown products and pus) was observed. In 5 patients, contrast extravasation on late-phase images that was compatible with urine leak was demonstrated. Our results suggest that MRI may determine the content of perinephric fluid collections on noncontrast T1-weighted and T2-weighted images and that contrast extravasation on late-phase images is associated with urine extravasation from renal collecting systems.     

Discrete Gradient Method: Derivative-Free Method for Nonsmooth Optimization

A new derivative-free method is developed for solving unconstrained nonsmooth optimization problems. This method is based on the notion of a discrete gradient. It is demonstrated that the discrete gradients can be used to approximate subgradients of a broad class of nonsmooth functions. It is also shown that the discrete gradients can be applied to find descent directions of nonsmooth functions. The preliminary results of numerical experiments with unconstrained nonsmooth optimization problems as well as the comparison of the proposed method with the nonsmooth optimization solver DNLP from CONOPT-GAMS and the derivative-free optimization solver CONDOR are presented.     

A taylor collocation method for solving high‐order linear pantograph equations with linear functional argument

A numerical method based on the Taylor polynomials is introduced in this article for the approximate solution of the pantograph equations with constant and variable coefficients. Some numerical examples, which consist of the initial conditions, are given to show the properties of the method. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27:1628–1638, 2011     

Preparation and properties of a new solid state borate ion selective electrode and its application

A new borate ion selective electrode using solid salts of Ag₃BO₃, Ag₂S and Cu₂S has been developed. Detailed information is provided concerning the composition, working pH and conditioning of the electrode. An analytically useful potential change occurred from 1 × 10⁻⁶ to 1 × 10⁻¹ M borate ion. The slope of the linear portion was 31 ± 2 mV/10-fold changes in borate concentration. The measurements were made at constant ionic strength (0.1 M NaNO₃) and at room temperature. The effect of Cl⁻, Br⁻, NO₃⁻, SO⁼₄, H₂PO₄⁻ anions and K⁺, Na⁺, Cu²⁺, Ag⁺, Ca²⁺ cations on borate response is evaluated and it was found that only Ag⁺ had a small interference effect. The lifetime of the electrode was more than two years, when used at least 4-5 times a day, and the response time was about 20-30 s. Borate content in waste water of borax factory, tap water of a town situated near to the borax factory and city tap water far from these mines were also determined. The validation was made with differential pulse polarography for the same water sample, and high consistency was obtained.     

A rational approximation based on Bernstein polynomials for high order initial and boundary values problems

We introduce a new method to solve high order linear differential equations with initial and boundary conditions numerically. In this method, the approximate solution is based on rational interpolation and collocation method. Since controlling the occurrence of poles in rational interpolation is difficult, a construction which is found by Floater and Hormann [1] is used with no poles in real numbers. We use the Bernstein series solution instead of the interpolation polynomials in their construction. We find that our approximate solution has better convergence rate than the one found by using collocation method. The error of the approximate solution is given in the case of the exact solution f ∈ C^d+2[a, b].     

The regularized trace of a self adjoint differential operator of higher order with unbounded operator coefficient

Let L₀ and L be operators which are formed by the differential expressions.

?₀(y)=(-1)^my^(2m)(x)+Ay(x)     

A collocation approach for the numerical solution of certain linear retarded and advanced integrodifferential equations with linear functional arguments

This article presents a Taylor collocation method for the approximate solution of high‐order linear Volterra‐Fredholm integrodifferential equations with linear functional arguments. This method is essentially based on the truncated Taylor series and its matrix representations with collocation points. Some numerical examples, which consist of initial and boundary conditions, are given to show the properties of the technique. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

A Hermite collocation method for the approximate solutions of high‐order linear Fredholm integro‐differential equations

In this study, a Hermite matrix method is presented to solve high‐order linear Fredholm integro‐differential equations with variable coefficients under the mixed conditions in terms of the Hermite polynomials. The proposed method converts the equation and its conditions to matrix equations, which correspond to a system of linear algebraic equations with unknown Hermite coefficients, by means of collocation points on a finite interval. Then, by solving the matrix equation, the Hermite coefficients and the polynomial approach are obtained. Also, examples that illustrate the pertinent features of the method are presented; the accuracy of the solutions and the error analysis are performed. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1707–1721, 2011