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LetAandBbe commutative rings with unity,f:A → Ba ring homomorphism, andJan ideal ofB. Then the subringA ⋈fJ: = {(a,f(a) + j)|a ∈ Aandj ∈ J} ofA × Bis called the amalgamation ofAwithBalongJwith respect tof. In this article, among other things, we investigate the Cohen–Macaulay and (quasi-)Gorenstein properties on the ringA ⋈fJ. [ABSTRACT FROM PUBLISHER]

In this article, we present the uniform convergence analysis and accuracy estimation of hybrid functions (HFs) method for finding the solution of nonlinear Volterra and Fredholm integral equations. The properties of HFs which consist of block-pulse functions (BPFs) and Legendre polynomials are used to reduce the solution of nonlinear integral equations to the solution of algebraic equations. The superiority and accuracy of the HFs method to BPF and Legendre polynomial methods are illustrated through some numerical examples. [ABSTRACT FROM PUBLISHER]

An approximation method is developed for the solution of high-order non-linear Volterra-Fredholm integro-differential (NVFID) equations under the mixed conditions. The approach is based on the orthogonal Chebyshev polynomials. The operational matrices of integration and product together with the derivative operational matrix are presented and are utilized to reduce the computation of Volterra-Fredholm integro-differential equations to a system of non-linear algebraic equations. Numerical examples illustrate the pertinent features of the method. [ABSTRACT FROM AUTHOR]

In this paper, we analyse the iterated collocation method for the nonlinear Urysohn operator equation x=y+K(x) with K a singular kernel. The paper extends the study [H. Kaneko, R.D. Noren, and P.A. Padilla, J. Comput. Appl. Math. 80 (1997), pp. 335-349] in which the convergence of the iterated collocation method for Urysohn equations is considered. [ABSTRACT FROM AUTHOR]