Toeplitz Matrix Method and Volterra-Hammerstien Integral Equation with a Generalized Singular Kernel

In this work, the existence of a unique solution of Volterra-Hammerstein integral equation of the second kind (V-HIESK) is discussed. The Volterra integral term (VIT) is considered in time with a continuous kernel, while the Fredholm integral term (FIT) is considered in position with a generalized singular kernel. Using a numerical technique, V-HIESK is reduced to a nonlinear system of Fredholm integral equations (SFIEs). Using Toeplitz matrix method we have  a nonlinear algebraic system of equations. Also, many important theorems related to the existence and uniqueness of the produced algebraic system are derived. Finally, some numerical examples when the kernel takes the logarithmic, Carleman, and Cauchy forms, are considered

Error Analysis for Numerical Solutions of Hammerstein Integral Equation With A Generalized Singular Kernel

In this work, the existence and uniqueness solution of the Hammerstein integral equation (HIE), with a generalized singular kernel, is discussed and solved numerically using Toeplitz matrix method and Product Nyström method. Moreover, the error analysis for these methods is discussed. Finally, numerical results when the kernel takes a generalized logarithmic form, Carleman function and Cauchy kernel function are investigated. Also the error, in each case, is estimated

Some Numerical Methods for Solving Linear Two-Dimensional Volterra Integral Equation

In this paper, the existence and uniqueness of solution of the linear twodimensional Volterra integral equation of the second kind(LT-DVIE) with Continuous Kernel are discussed and proved. Trapezoidal rule and Simpson's rule are used to solve this type of two dimensional Volterra integral equation of the second kind. Numerical examples are considered to illustrate the effectiveness of the proposed methods and the error is estimated

Two-Dimensional Fredholm Integro-Differential Equation with Singular Kernel and Its Numerical Solutions

In this paper, we introduce the nonlinear Fredholm integro-differential equation of the second kind with singular kernel in two-dimensional NT-DFIDE. Furthermore, we study this new equation numerically. The existence of a unique solution of the equation is proved. The numerical results of NT-DFIDE are obtained by the following methods: Toeplitz matrix method (TMM) and product Nystrom method (PNM). The given applications showed the efficiency of these methods

Everolimus with Reduced Calcineurin Inhibitor Exposure in Renal Transplantation

Background Everolimus permits reduced calcineurin inhibitor (CNI) exposure, but the efficacy and safety outcomes of this treatment after kidney transplant require confirmation.Methods In a multicenter noninferiority trial, we randomized 2037 de novo kidney transplant recipients to receive, in combination with induction therapy and corticosteroids, everolimus with reduced-exposure CNI (everolimus arm) or mycophenolic acid (MPA) with standard-exposure CNI (MPA arm). The primary end point was treated biopsy-proven acute rejection or eGFR<50 ml/min per 1.73 m2 at post-transplant month 12 using a 10% noninferiority margin.Results In the intent-to-treat population (everolimus n=1022, MPA n=1015), the primary end point incidence was 48.2% (493) with everolimus and 45.1% (457) with MPA (difference 3.2%; 95% confidence interval, -1.3% to 7.6%). Similar between-treatment differences in incidence were observed in the subgroups of patients who received tacrolimus or cyclosporine. Treated biopsy-proven acute rejection, graft loss, or death at post-transplant month 12 occurred in 14.9% and 12.5% of patients treated with everolimus and MPA, respectively (difference 2.3%; 95% confidence interval, -1.7% to 6.4%). De novo donor-specific antibody incidence at 12 months and antibody-mediated rejection rate did not differ between arms. Cytomegalovirus (3.6% versus 13.3%) and BK virus infections (4.3% versus 8.0%) were less frequent in the everolimus arm than in the MPA arm. Overall, 23.0% and 11.9% of patients treated with everolimus and MPA, respectively, discontinued the study drug because of adverse events.Conclusions In kidney transplant recipients at mild-to-moderate immunologic risk, everolimus was noninferior to MPA for a binary composite end point assessing immunosuppressive efficacy and preservation of graft function

Updated Recommendations for the Diagnosis and Management of Osteoporosis: A Local Perspective

Postmenopausal osteoporosis and osteoporosis in elderly men are major health problems, with a significant medical and economic burden. Although osteopenia and osteoporosis are more common locally than in the West, fracture rates are generally less than in Western countries. Vitamin D deficiency is common in the region and contributes adversely to bone health. Vitamin D deficiency should be suspected and treated in all subjects with ostopenia or osteoporosis. The use of risk factors to determine fracture risk has been adopted by the World Health Organization and many international societies. Absolute fracture risk methodology improves the use of resources by targeting subjects at higher risk of fractures for screening and management. The King Faisal Specialist Hospital Osteoporosis Working Group recommends screening for women 65 years and older and for men 70 years and older. Younger subjects with clinical risk factors and persons with clinical evidence of osteoporosis or diseases leading to osteoporosis should also be screened. These guidelines provide recommendations for treatment for postmenopausal women and men older than 50 years presenting with osteoporotic fractures for persons having osteoporosis—after excluding secondary causes—or for persons having low bone mass and a high risk for fracture. The Working Group has suggested an algorithm to use at King Faisal Specialist Hospital that is based on the availability, cost, and level of evidence of various therapeutic modalities. Adequate calcium and vitamin D supplement are recommended for all. Weekly alendronate (in the absence of contraindications) is recommended as first-line therapy. Alternatives to alendronate are raloxifene or strontium ranelate. Second-line therapies are zoledronic acid intravenously once yearly, when oral therapy is not feasible or complicated by side effects, or teriparatide in established osteoporosis with fractures

Safety of Everolimus With Reduced Calcineurin Inhibitor Exposure in De Novo Kidney Transplants: An Analysis From the Randomized TRANSFORM Study

BACKGROUND: The safety profiles of standard therapy versus everolimus with reduced-exposure calcineurin inhibitor (CNI) therapy using contemporary protocols in de novo kidney transplant recipients have not been compared in detail. METHODS: TRANSFORM was a randomized, international trial in which de novo kidney transplant patients were randomized to everolimus with reduced-exposure CNI (N = 1014) or mycophenolic acid (MPA) with standard-exposure CNI (N = 1012), both with induction and corticosteroids. RESULTS: Within the safety population (everolimus 1014, MPA 1012), adverse events with a suspected relation to study drug occurred in 62.9% versus 59.2% of patients given everolimus or MPA, respectively (P = 0.085). Hyperlipidemia, interstitial lung disease, peripheral edema, proteinuria, stomatitis/mouth ulceration, thrombocytopenia, and wound healing complications were more frequent with everolimus, whereas diarrhea, nausea, vomiting, leukopenia, tremor, and insomnia were more frequent in the MPA group. The incidence of viral infections (17.2% versus 29.2%; P < 0.001), cytomegalovirus (CMV) infections (8.1% versus 20.1%; P < 0.001), CMV syndrome (13.6% versus 23.0%, P = 0.044), and BK virus (BKV) infections (4.3% versus 8.0%, P < 0.001) were less frequent with everolimus. CMV infection was less common with everolimus versus MPA after adjusting for prophylaxis therapy in the D+/R- subgroup (P < 0.001). Study drug was discontinued more frequently due to rejection or impaired healing with everolimus, and more often due to BKV infection or BKV nephropathy with MPA. CONCLUSIONS: De novo everolimus with reduced-exposure CNI yielded a comparable incidence, though a distinctly different pattern, of adverse events versus current standard of care. Both regimens are safe and effective, yet their distinct profiles may enable tailoring for individual kidney transplant recipients.status: publishe