scholarly journals Comprehensive derivation of bond-valence parameters for ion pairs involving oxygen

2015 ◽  
Vol 71 (5) ◽  
pp. 562-578 ◽  
Author(s):  
Olivier Charles Gagné ◽  
Frank Christopher Hawthorne
Keyword(s):  
Ion Pairs ◽  
Valence Bond ◽  
Bond Valence ◽  
Data Set ◽  
Coordination Polyhedra ◽  
Reduced Gradient Method ◽  
Advantages And Disadvantages ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient ◽  
Two Parameter

Published two-body bond-valence parameters for cation–oxygen bonds have been evaluatedviathe root mean-square deviation (RMSD) from the valence-sum rule for 128 cations, using 180 194 filtered bond lengths from 31 489 coordination polyhedra. Values of the RMSD range from 0.033–2.451 v.u. (1.1–40.9% per unit of charge) with a weighted mean of 0.174 v.u. (7.34% per unit of charge). The set of best published parameters has been determined for 128 ions and used as a benchmark for the determination of new bond-valence parameters in this paper. Two common methods for the derivation of bond-valence parameters have been evaluated: (1) fixingBand solving forRo; (2) the graphical method. On a subset of 90 ions observed in more than one coordination, fixingBat 0.37 Å leads to a mean weighted-RMSD of 0.139 v.u. (6.7% per unit of charge), while graphical derivation gives 0.161 v.u. (8.0% per unit of charge). The advantages and disadvantages of these (and other) methods of derivation have been considered, leading to the conclusion that current methods of derivation of bond-valence parameters are not satisfactory. A new method of derivation is introduced, the GRG (generalized reduced gradient) method, which leads to a mean weighted-RMSD of 0.128 v.u. (6.1% per unit of charge) over the same sample of 90 multiple-coordination ions. The evaluation of 19 two-parameter equations and 7 three-parameter equations to model the bond-valence–bond-length relation indicates that: (1) many equations can adequately describe the relation; (2) a plateau has been reached in the fit for two-parameter equations; (3) the equation of Brown & Altermatt (1985) is sufficiently good that use of any of the other equations tested is not warranted. Improved bond-valence parameters have been derived for 135 ions for the equation of Brown & Altermatt (1985) in terms of both the cation and anion bond-valence sums using the GRG method and our complete data set.

Synthesis of a Large Oscillation Four-Bar Mechanism

1997 ◽  
Author(s):  
Gloria K. Starns ◽  
Donald R. Flugrad
Keyword(s):  
Reduced Gradient Method ◽  
Large Oscillation ◽  
Oscillation Mechanism ◽  
Straight Line ◽  
Transmission Angle ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient ◽  
Angular Oscillations ◽  
Four Bar Linkage ◽  
Effective Transmission

Abstract This paper demonstrates procedures implemented for the synthesis of a four-bar mechanism that produces large angular oscillations of the output member while maintaining effective transmission angles. The mechanisms are modeled as being driven by a force applied at the coupler link. Additionally this force’s line of action is constrained to occur along an approximate straight line. This research was conducted out of the need for a device that is capable of retraction of the horizontal tool bar housed on the back of a tractor. The tool bars accommodate the implements required to accomplish the numerous tasks of the farmer, i.e. row markers, sprayer arms, planters, etc. Upon retraction of the tool bar so that it is parallel to ground, the appropriate tools are lowered to their working position. As the length of these bars increases, a savings of time and increased productivity is realized. Kurt Hain makes the following observation regarding large oscillation mechanisms in [1]: “It would be very difficult to solve this problem with one four-bar linkage, because it is difficult to design a four-bar linkage having such a large oscillation of a crank without running into problems of poor transmission angle characteristics; it might be possible to use linkages in combinations with gears, but this would make the mechanism more expensive, less efficient, and probably noisier.” In this study simulated annealing, a genetic algorithm and the generalized reduced gradient method are used to produce mechanisms with large angular oscillations of the output member and transmission angles that vary by as little as 20° from 90°. A comparative analysis of each of the optimization procedures is presented with observations regarding the efficacy of each method in the solution of the large oscillation mechanism.

An inventory model of a three parameter Weibull distributed deteriorating item with variable demand dependent on price and frequency of advertisement under trade credit

2019 ◽  
Vol 53 (3) ◽  
pp. 903-916 ◽  
Author(s):  
Ali Akbar Shaikh ◽  
Leopoldo Eduardo Cárdenas–Barrón ◽  
Asoke Kumar Bhunia ◽  
Sunil Tiwari
Keyword(s):  
Trade Credit ◽  
Inventory Model ◽  
Selling Price ◽  
Credit Policy ◽  
Variable Demand ◽  
Reduced Gradient Method ◽  
Deterioration Rate ◽  
Rate Dependent ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient

This paper develops an inventory model for a deteriorating item with variable demand dependent on the selling price and frequency of advertisement of the item under the financial trade credit policy. Shortages are allowed and these are partially backlogged with a variable rate dependent on the duration of waiting time until to the arrival of next order. In this inventory model, the deterioration rate follows a three-parameter Weibull distribution. The corresponding inventory model is formulated and solved by using the well-known generalized reduced gradient method along with an algorithm. To validate the inventory model, two numerical examples are considered and solved. Finally, based on one numerical example, the impacts of different parameters are studied by a sensitivity analysis considering one parameter at a time and leaving the other parameters fixed.

scholarly journals A Mathematical Model for Optimal Strength and Alignment of a Marine Shafting System

1985 ◽  
Vol 29 (03) ◽  
pp. 212-222
Author(s):  
Zissimos Mourelatos ◽  
Panos Papalambros
Keyword(s):  
Mathematical Model ◽  
Nonlinear Programming ◽  
Programming Formulation ◽  
Solution Strategy ◽  
Reduced Gradient Method ◽  
Trade Offs ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient ◽  
Optimal Strength ◽  
Vertical Positioning

The design of a marine shafting system is modeled mathematically in order to perform optimization studies with respect to shaft strength as well as longitudinal and vertical positioning of the bearings. The objective criteria used are minimization of the bearing reaction influence numbers and even distribution of the bearing loading. Design trade-offs can be thus established. The problem is posed in a nonlinear programming formulation and is solved using a standard generalized reduced gradient method (GRG2), but in a specialized solution strategy. Two examples from actual ship designs are presented.

The Method of Alternate Formulations Applied to Optimization Problems With Functionally Dependent State Equations

1989 ◽  
Author(s):  
C. R. Hammond ◽  
G. E. Johnson
Keyword(s):  
Optimization Problems ◽  
Functional Dependence ◽  
Numerical Approach ◽  
Upper And Lower Bounds ◽  
Decision Variable ◽  
State Equations ◽  
Reduced Gradient Method ◽  
Mathematical Properties ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient

Abstract The Method of Alternate Formulations (MAF) is a non-numerical approach to constrained optimal design. MAF requires that the problem statement be transformed into an objective function, a set of equality-constraints (i.e. state equations), and a set of upper and lower bounds on the variables. In this format, the design vector can be partitioned into decision variable and state variable components. This is the same format as used in the solution of such problems by the generalized reduced gradient method. The fact that there are usually several ways to effect the partition of the design vector gives rise to the existence of alternate formulations. Each alternate formulation contains all of the information about the physical system — and the constrained optima are invariant under the transformation from form to form. Yet all other mathematical properties (e.g., convexity, linearity, scaling, etc.) can change. In this paper, we consider the special case when the state equations are functionally dependent, hence some of the expected constraint intersections do not exist. Several examples are used to demonstrate the concept of functional dependence and to show how functional dependence affects the search for the solution.

Multi-objective traction optimization of vehicles in loose dry sand using the generalized reduced gradient method

2016 ◽  
Vol 64 ◽  
pp. 46-57 ◽  
Author(s):  
Joe D. Robinson ◽  
Farshid Vahedifard ◽  
Masoud Rais-Rohani ◽  
George L. Mason ◽  
Jody D. Priddy
Keyword(s):  
Gradient Method ◽  
Multi Objective ◽  
Reduced Gradient Method ◽  
Reduced Gradient ◽  
Dry Sand ◽  
Generalized Reduced Gradient
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