Analytical method for solving a set of inhomogeneous infinite simultaneous equations

A purely analytical method has been developed for the kinetic (force or kinetostatic) analysis of frictionless planar mechanisms. It employs polar notation of vectors, the principle of conservation of energy and the force equilibrium of the links. Unlike many other methods which lead to a system of several simultaneous equations, it leads to only one algebraic or one vectorial equation at a time and, interestingly, it is less time consuming that the conventional graphical methods. The method is general, comprehensive and systematic such that it could also serve as a suitable teaching technique for manual approach to the problem. It easily lends itself to automation too.

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Renewing Assets with Uncertain Revenues and Operating Costs

Journal of Financial and Quantitative Analysis ◽

10.1017/s0022109010000815 ◽

2010 ◽

Vol 46 (3) ◽

pp. 785-813 ◽

Cited By ~ 33

Author(s):

Roger Adkins ◽

Dean Paxson

Keyword(s):

Significant Influence ◽

Analytical Method ◽

Real Option ◽

Operating Cost ◽

Simultaneous Equations ◽

Relative Influence ◽

Operating Costs ◽

Implicit Representation ◽

Optimal Replacement ◽

Real Assets

AbstractWe study optimal replacement and abandonment decisions for real assets, when both revenues and costs are uncertain and deteriorate with age. We develop an implicit representation of the renewal boundary as the solution to a set of simultaneous equations. This quasi-analytical method has the merit of computational ease and transparency. We show that the correlation between revenues and operating costs has a significant influence on the renewal boundary, and that the increase in revenue immediately following a renewal has a greater relative influence on the boundary than either operating cost or renewal cost. The quasi-analytical method is sufficiently flexible to deal with other real option models involving 2 variables.

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A Simple Analytical Method for Teaching Force Analysis of Planar Frictionless Mechanisms

Innovations in Engineering Education: Mechanical Engineering Education, Mechanical Engineering/Mechanical Engineering Technology Department Heads ◽

10.1115/imece2005-79097 ◽

2005 ◽

Author(s):

Kazem Abhary

Keyword(s):

Algebraic Equation ◽

Analytical Method ◽

Kinematic Analysis ◽

Simultaneous Equations ◽

Degree Of Freedom ◽

Force Analysis ◽

Equilibrium Equations ◽

Planar Mechanisms ◽

Joint Force ◽

Teaching Force

A purely analytical method for teaching force analysis of one degree-of-freedom planar frictionless mechanisms has been developed herein. The method uses the vectorial illustration of mechanisms, which is widely used for kinematic analysis of mechanisms too. In this method, a joint-force is determined either via its decomposition into the direction of its adjacent links or from the equilibrium equations of one of these links. Unlike the conventional analytical method which leads to a system of simultaneous equations, this method leads to only one simple algebraic-equation or one simple vectorial-equation at a time. Force analysis of planar mechanisms has always been tedious and time consuming but this method has proved to be simple, straightforward and quick. It is therefore a most suitable tool for teaching mechanisms as it downgrades the project-type problems to the level of classroom tutorials.

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Densitometric Identification of Primitive Erythroblasts After Reaction With Diaminobenzidine

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100072083 ◽

1973 ◽

Vol 31 ◽

pp. 328-329

Author(s):

John A. Trotter

Keyword(s):

Red Blood Cells ◽

Analytical Method ◽

Blood Cells ◽

Guinea Pigs ◽

Specific Protein ◽

Visual Examination ◽

Hemoglobin Synthesis ◽

Peroxidatic Activity ◽

Small Density

Hemoglobin is the specific protein of red blood cells. Those cells in which hemoglobin synthesis is initiated are the earliest cells that can presently be considered to be committed to erythropoiesis. In order to identify such early cells electron microscopically, we have made use of the peroxidatic activity of hemoglobin by reacting the marrow of erythropoietically stimulated guinea pigs with diaminobenzidine (DAB). The reaction product appeared as a diffuse and amorphous electron opacity throughout the cytoplasm of reactive cells. The detection of small density increases of such a diffuse nature required an analytical method more sensitive and reliable than the visual examination of micrographs. A procedure was therefore devised for the evaluation of micrographs (negatives) with a densitometer (Weston Photographic Analyzer).

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Bulk standards for low-temperature biological x-ray microanalysis

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100111525 ◽

1984 ◽

Vol 42 ◽

pp. 282-283

Author(s):

P. Echlin ◽

M. McKoon ◽

E.S. Taylor ◽

C.E. Thomas ◽

K.L. Maloney ◽

...

Keyword(s):

Phase Separation ◽

Low Temperature ◽

Analytical Method ◽

Salt Solutions ◽

Absolute Concentration ◽

Cooling Process ◽

X Ray ◽

The Absolute ◽

Analytical Procedures ◽

Electrical Conductors

Although sections of frozen salt solutions have been used as standards for x-ray microanalysis, such solutions are less useful when analysed in the bulk form. They are poor thermal and electrical conductors and severe phase separation occurs during the cooling process. Following a suggestion by Whitecross et al we have made up a series of salt solutions containing a small amount of graphite to improve the sample conductivity. In addition, we have incorporated a polymer to ensure the formation of microcrystalline ice and a consequent homogenity of salt dispersion within the frozen matrix. The mixtures have been used to standardize the analytical procedures applied to frozen hydrated bulk specimens based on the peak/background analytical method and to measure the absolute concentration of elements in developing roots.

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