Bulletin of The Chemical Society of Ethiopia, 2002
Guinea pig haemoglobin has six sulfhydryl groups, one at each of the positions F9[93], G11[104] a... more Guinea pig haemoglobin has six sulfhydryl groups, one at each of the positions F9[93], G11[104] and H3[125], which appear in pairs. Titration with p-hydroxymercuri(II)- benzoic acid and with 5,5'-dithiobis(2-nitrobenzoic acid) (DTNB) indicate that four of the six sulfhydryls are reactive. The time course of the DTNB reaction is triphasic at pH > 7. The fast phase is about 2 orders of magnitude faster than the intermediate phase and can be clearly separated from it. The intermediate phase, where it exists, is about 3-4 times faster than the slow phase. However, the amplitude of the intermediate phase, which has a maximum of about 15% of the total signal amplitude, becomes negligible as it approaches pH 7, so that the kinetics eventually becomes biphasic. The pH dependence profile of kapp, the apparent second-order rate constant, for the fast phase resembles the titration curve of a diprotic acid. Quantitative analysis indicates that the reactivity of the sulfhydryl group to wh...
Assessing performance of employees is an important process for achieving excellence. In many, eva... more Assessing performance of employees is an important process for achieving excellence. In many, evaluation processes, an employee’s annual composite score is a weighted average of performance scores on several roles and weights chosen by the employee within bounds stipulated by the administration for each role. In this process, the composite score depends not on merit alone, but also on employee's choice of weights. In this paper, we propose a modified process-based on Linear Programming (LP) that assigns to employees the optimal weights that are compatible with their supervisor-assigned scores in each role. The LP model is designed to assign role weights, within predefined ranges, such that the composite score is maximized. The overall score depends on the supervisor’s assessment of performance alone, eliminating the need for the employee to “correctly” choose weights. The modified approach should lead to more valid evaluations of performance and improved employee satisfaction wi...
Abstract. Let A be a matrix such that the diagonal matrix D with the same diagonal as A is invert... more Abstract. Let A be a matrix such that the diagonal matrix D with the same diagonal as A is invertible. It is well known that if (1) A satisfies the Sassenfeld condition then its Gauss-Seidel scheme is convergent, and (2) if D −1 A certifies certain classical diagonal dominance conditions then the Jacobi iterations for A are convergent. In this paper we generalize the second result and extend the first result to irreducible matrices satisfying a weak Sassenfeld condition.
We study a one-step intermediate method for the iterative computation of a zero of the sum of two... more We study a one-step intermediate method for the iterative computation of a zero of the sum of two nonlinear operators. The proposed method contains Newton scheme and the Modified Newton scheme as special cases and therefore provides a unified setting for the study of both methods.
Let A be a matrix such that the diagonal matrix D with the same diagonal as A is invertible. It i... more Let A be a matrix such that the diagonal matrix D with the same diagonal as A is invertible. It is well known that if (1) A satisfles the Sassenfeld condition then its Gauss-Seidel scheme is convergent, and (2) if D i1 A certifles certain classical diagonal dominance conditions then the Jacobi iterations for A are convergent. In this paper we generalize the second result and extend the flrst result to irreducible matrices satisfying a weak Sassenfeld condition.
We revisit a one-step intermediate Newton iterative scheme that was used by Uko and Velásquez in ... more We revisit a one-step intermediate Newton iterative scheme that was used by Uko and Velásquez in [17] for the constructive solution of nonlinear equations of the type f(u) + g(u) = 0 . By utilizing weaker hypotheses of the Zabrejko-Nguen kind and a modified majorizing sequence we perform a semilocal convergence analysis which yields finer error bounds and more precise information on the location of the solution that the ones obtained in [17]. We also give two generalizations of the well-known Kantorovich theorem on the solvability of nonlinear equations and the convergence of Newton’s method. Illustrative examples are provided in the paper. MSC 2010. 65H99, 49M15.
This paper presents a Newton-type iterative scheme for finding the zero of the sum of a different... more This paper presents a Newton-type iterative scheme for finding the zero of the sum of a differentiable function and a multivalued maximal monotone function. Local and semi-local convergence results are proved for the Newton scheme, and an analogue of the Kantorovich theorem is proved for the associated modified scheme that uses only one Jacobian evaluation for the entire iteration. Applications in variational inequalities are discussed, and an illustrative numerical example is given. Abbreviated title: Generalized Newton method. Mathematics Subject Classification (1991): 47H15, 65H10, 65K05, 65K10, 49J40, 47H19
Abstract. We study a one-step intermediate method for the iterative compu-tation of a zero of the... more Abstract. We study a one-step intermediate method for the iterative compu-tation of a zero of the sum of two nonlinear operators. The proposed method contains Newton scheme and the Modified Newton scheme as special cases and therefore provides a unified setting for the study of both methods. Key words and phrases. Nonlinear equations, Newton’s method, intermediate Newton method, majorant error bounds. 1991 Mathematics Subject Classification. Primary 65H10. Let X and Y be Banach spaces, let u0 ∈ X and let f, g be continuous operators mapping a closed ball B[u0, T] into Y, assumed Fréchet differentiable on the open ball B(u0, T). We are interested in the equation f(u) + g(u) = 0. (1) The method of Newton, defined by the iterations um+1 = um − [f ′(um) + g′(um)]−1[f(um) + g(um)], m = 0, 1,... (2) This paper was supported by the Centro de Investigaciones (CIEN) of the Facultad de
A Magic Cube of order p is a p×p×p cubical array with non-repeated entries from the set {1, 2, . ... more A Magic Cube of order p is a p×p×p cubical array with non-repeated entries from the set {1, 2, . . . , p3} such that all rows, columns, pillars and space diagonals have the same sum. In this paper, we show that a formula introduced in The Mathematical Gazette 84(2000), by M. Trenkler, for generating odd order magic cubes is a special case of a more general class of formulas. We derive sufficient conditions for the formulas in the new class to generate magic cubes, and we refer to the resulting class as regular magic cubes. We illustrate these ideas by deriving three new formulas that generate magic cubes of odd order that differ from each other and from the magic cubes generated with Trenkler’s rule.
Bulletin of The Chemical Society of Ethiopia, 2002
Guinea pig haemoglobin has six sulfhydryl groups, one at each of the positions F9[93], G11[104] a... more Guinea pig haemoglobin has six sulfhydryl groups, one at each of the positions F9[93], G11[104] and H3[125], which appear in pairs. Titration with p-hydroxymercuri(II)- benzoic acid and with 5,5'-dithiobis(2-nitrobenzoic acid) (DTNB) indicate that four of the six sulfhydryls are reactive. The time course of the DTNB reaction is triphasic at pH > 7. The fast phase is about 2 orders of magnitude faster than the intermediate phase and can be clearly separated from it. The intermediate phase, where it exists, is about 3-4 times faster than the slow phase. However, the amplitude of the intermediate phase, which has a maximum of about 15% of the total signal amplitude, becomes negligible as it approaches pH 7, so that the kinetics eventually becomes biphasic. The pH dependence profile of kapp, the apparent second-order rate constant, for the fast phase resembles the titration curve of a diprotic acid. Quantitative analysis indicates that the reactivity of the sulfhydryl group to wh...
Assessing performance of employees is an important process for achieving excellence. In many, eva... more Assessing performance of employees is an important process for achieving excellence. In many, evaluation processes, an employee’s annual composite score is a weighted average of performance scores on several roles and weights chosen by the employee within bounds stipulated by the administration for each role. In this process, the composite score depends not on merit alone, but also on employee's choice of weights. In this paper, we propose a modified process-based on Linear Programming (LP) that assigns to employees the optimal weights that are compatible with their supervisor-assigned scores in each role. The LP model is designed to assign role weights, within predefined ranges, such that the composite score is maximized. The overall score depends on the supervisor’s assessment of performance alone, eliminating the need for the employee to “correctly” choose weights. The modified approach should lead to more valid evaluations of performance and improved employee satisfaction wi...
Abstract. Let A be a matrix such that the diagonal matrix D with the same diagonal as A is invert... more Abstract. Let A be a matrix such that the diagonal matrix D with the same diagonal as A is invertible. It is well known that if (1) A satisfies the Sassenfeld condition then its Gauss-Seidel scheme is convergent, and (2) if D −1 A certifies certain classical diagonal dominance conditions then the Jacobi iterations for A are convergent. In this paper we generalize the second result and extend the first result to irreducible matrices satisfying a weak Sassenfeld condition.
We study a one-step intermediate method for the iterative computation of a zero of the sum of two... more We study a one-step intermediate method for the iterative computation of a zero of the sum of two nonlinear operators. The proposed method contains Newton scheme and the Modified Newton scheme as special cases and therefore provides a unified setting for the study of both methods.
Let A be a matrix such that the diagonal matrix D with the same diagonal as A is invertible. It i... more Let A be a matrix such that the diagonal matrix D with the same diagonal as A is invertible. It is well known that if (1) A satisfles the Sassenfeld condition then its Gauss-Seidel scheme is convergent, and (2) if D i1 A certifles certain classical diagonal dominance conditions then the Jacobi iterations for A are convergent. In this paper we generalize the second result and extend the flrst result to irreducible matrices satisfying a weak Sassenfeld condition.
We revisit a one-step intermediate Newton iterative scheme that was used by Uko and Velásquez in ... more We revisit a one-step intermediate Newton iterative scheme that was used by Uko and Velásquez in [17] for the constructive solution of nonlinear equations of the type f(u) + g(u) = 0 . By utilizing weaker hypotheses of the Zabrejko-Nguen kind and a modified majorizing sequence we perform a semilocal convergence analysis which yields finer error bounds and more precise information on the location of the solution that the ones obtained in [17]. We also give two generalizations of the well-known Kantorovich theorem on the solvability of nonlinear equations and the convergence of Newton’s method. Illustrative examples are provided in the paper. MSC 2010. 65H99, 49M15.
This paper presents a Newton-type iterative scheme for finding the zero of the sum of a different... more This paper presents a Newton-type iterative scheme for finding the zero of the sum of a differentiable function and a multivalued maximal monotone function. Local and semi-local convergence results are proved for the Newton scheme, and an analogue of the Kantorovich theorem is proved for the associated modified scheme that uses only one Jacobian evaluation for the entire iteration. Applications in variational inequalities are discussed, and an illustrative numerical example is given. Abbreviated title: Generalized Newton method. Mathematics Subject Classification (1991): 47H15, 65H10, 65K05, 65K10, 49J40, 47H19
Abstract. We study a one-step intermediate method for the iterative compu-tation of a zero of the... more Abstract. We study a one-step intermediate method for the iterative compu-tation of a zero of the sum of two nonlinear operators. The proposed method contains Newton scheme and the Modified Newton scheme as special cases and therefore provides a unified setting for the study of both methods. Key words and phrases. Nonlinear equations, Newton’s method, intermediate Newton method, majorant error bounds. 1991 Mathematics Subject Classification. Primary 65H10. Let X and Y be Banach spaces, let u0 ∈ X and let f, g be continuous operators mapping a closed ball B[u0, T] into Y, assumed Fréchet differentiable on the open ball B(u0, T). We are interested in the equation f(u) + g(u) = 0. (1) The method of Newton, defined by the iterations um+1 = um − [f ′(um) + g′(um)]−1[f(um) + g(um)], m = 0, 1,... (2) This paper was supported by the Centro de Investigaciones (CIEN) of the Facultad de
A Magic Cube of order p is a p×p×p cubical array with non-repeated entries from the set {1, 2, . ... more A Magic Cube of order p is a p×p×p cubical array with non-repeated entries from the set {1, 2, . . . , p3} such that all rows, columns, pillars and space diagonals have the same sum. In this paper, we show that a formula introduced in The Mathematical Gazette 84(2000), by M. Trenkler, for generating odd order magic cubes is a special case of a more general class of formulas. We derive sufficient conditions for the formulas in the new class to generate magic cubes, and we refer to the resulting class as regular magic cubes. We illustrate these ideas by deriving three new formulas that generate magic cubes of odd order that differ from each other and from the magic cubes generated with Trenkler’s rule.
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