A mathematical definition of choking phenomenon and a mathematical model for predicting choking velocity and choking voidage

AIChE Journal ◽  
1975 ◽  
Vol 21 (5) ◽  
pp. 1013-1015 ◽  
Author(s):  
Wen-Ching Yang
Keyword(s):  
Mathematical Model ◽  
Mathematical Definition ◽  
Definition Of

A Hull Normal Based Approach for Cylindrical Size Assessment

2011 ◽  
Vol 133 (1) ◽  
Author(s):  
Steven Turek ◽  
Sam Anand
Keyword(s):  
New York ◽  
Least Squares ◽  
Measured Data ◽  
Size Determination ◽  
Mathematical Definition ◽  
Dimensioning And Tolerancing ◽  
Normal Method ◽  
Computational Metrology ◽  
American Society ◽  
Definition Of

Digital measurement devices, such as coordinate measuring machines, laser scanning devices, and digital imaging, can provide highly accurate and precise coordinate data representing the sampled surface. However, this discrete measurement process can only account for measured data points, not the entire continuous form, and is heavily influenced by the algorithm that interprets the measured data. The definition of cylindrical size for an external feature as specified by ASME Y14.5.1M-1994 [The American Society of Mechanical Engineers, 1995, Dimensioning and Tolerancing, ASME Standard Y14.5M-1994, ASME, New York, NY; The American Society of Mechanical Engineers, 1995, Mathematical Definition of Dimensioning and Tolerancing Principles, ASME Standard Y14.5.1M-1994, ASME, New York, NY] matches the analytical definition of a minimum circumscribing cylinder (MCC) when rule no. 1 [The American Society of Mechanical Engineers, 1995, Dimensioning and Tolerancing, ASME Standard Y14.5M-1994, ASME, New York, NY; The American Society of Mechanical Engineers, 1995, Mathematical Definition of Dimensioning and Tolerancing Principles, ASME Standard Y14.5.1M-1994, ASME, New York, NY] is applied to ensure a linear axis. Even though the MCC is a logical choice for size determination, it is highly sensitive to the sampling method and any uncertainties encountered in that process. Determining the least-sum-of-squares solution is an alternative method commonly utilized in size determination. However, the least-squares formulation seeks an optimal solution not based on the cylindrical size definition [The American Society of Mechanical Engineers, 1995, Dimensioning and Tolerancing, ASME Standard Y14.5M-1994, ASME, New York, NY; The American Society of Mechanical Engineers, 1995, Mathematical Definition of Dimensioning and Tolerancing Principles, ASME Standard Y14.5.1M-1994, ASME, New York, NY] and thus has been shown to be biased [Hopp, 1993, “Computational Metrology,” Manuf. Rev., 6(4), pp. 295–304; Nassef, and ElMaraghy, 1999, “Determination of Best Objective Function for Evaluating Geometric Deviations,” Int. J. Adv. Manuf. Technol., 15, pp. 90–95]. This work builds upon previous research in which the hull normal method was presented to determine the size of cylindrical bosses when rule no. 1 is applied [Turek, and Anand, 2007, “A Hull Normal Approach for Determining the Size of Cylindrical Features,” ASME, Atlanta, GA]. A thorough analysis of the hull normal method’s performance in various circumstances is presented here to validate it as a superior alternative to the least-squares and MCC solutions for size evaluation. The goal of the hull normal method is to recreate the sampled surface using computational geometry methods and to determine the cylinder’s axis and radius based upon it. Based on repetitive analyses of random samples of data from several measured parts and generated forms, it was concluded that the hull normal method outperformed all traditional solution methods. The hull normal method proved to be robust by having a lower bias and distributions that were skewed toward the true value of the radius, regardless of the amount of form error.

Mathematical definition of the curve of Spee in permanent healthy dentitions in man

1992 ◽  
Vol 37 (9) ◽  
pp. 691-694 ◽  
Author(s):  
V.F. Ferrario ◽  
C. Sforza ◽  
A. Miani ◽  
A. Colombo ◽  
G. Tartaglia
Keyword(s):  
Mathematical Definition ◽  
Curve Of Spee ◽  
Definition Of

scholarly journals Immediately mathematical model of maneuverability of the items of the administration

2019 ◽  
Vol 9 (3) ◽  
Author(s):  
Volodymyr Kotsyuruba ◽  
Ruslan Cherevko
Keyword(s):  
Mathematical Model ◽  
Traditional Approach ◽  
Armed Forces ◽  
Control Points ◽  
Military Operations ◽  
The Reformation ◽  
Definition Of ◽  
The Cost ◽  
Military Units ◽  
Current Stage

At the current stage of the reformation of the Armed Forces of Ukraine in the context of the operation of the United Nations (Anti-Terrorist Operation (ATO)), there was a need to increase the effectiveness of the use of troops without increasing the cost of the resource. In the context of increasing capabilities of the armies of the leading countries in the world to investigate and defeat the forces of the opposite side, the problem of maintaining and restoring combat capability in the course of hostilities is very acute. One of the important components that determines combat capability is the maneuverability of the control points (PU). In the course of the defense, the problem of increasing the survivability of the PU system is important because the forces of the opposite side, with the onset of aggression, will try, first of all, to dismantle the PU using modern means of defeat and the massive use of high-precision weapons (WTZ), as well as aircraft and artillery strikes, electronic information and information fight, the use of sabotage and reconnaissance groups and tactical airborne troops to disrupt the control of defending troops. Important importance of the ability to timely carry out maneuver (organized movement) of PU and its elements into a new area in the preparation and in the course of military operations. The traditional approach to ensuring the survivability of PU does not allow to ensure the proper stability of their functioning. There is an objective necessity in the development of such a mathematical model of maneuverability, which in its characteristics would meet the dynamically increasing requirements of the control system of troops in the difficult conditions of projected operations. To ensure the quality management of military units, various measures to ensure the survivability of PU are considered. The article outlines approaches to the definition of indicators of estimation of maneuverability of PU and methods of their calculation. The research is carried out in modern conditions of combat operations, taking into account the movement of the line of the combat collision of the parties and the disclosure of the PU to the enemy's intelligence.

scholarly journals Development of a mathematical model for calculating the process of crushing hard rocks by explosions of cylindrical charges of explosives

2020 ◽  
Vol 5 ◽  
pp. 30-32
Author(s):  
Norov Yunus Dzhumaevich ◽  
Mehmonov Maksud Rabbonokul ugli
Keyword(s):  
Mathematical Model ◽  
Rock Mass ◽  
Mechanism Of Action ◽  
Mathematical Description ◽  
Granulometric Composition ◽  
Rock Fragmentation ◽  
Hard Rocks ◽  
Definition Of ◽  
The Relationship

The article presents a developed mathematical model for calculating the granulometric composition of the blasted rock mass based on the mechanism of action of an explosion in rocks, a mathematical description of the determination of natural units (blocks) in the rock mass, the relationship between the degree of rock fragmentation and the size of the units and the definition of sections of the controlled pressure zone.

scholarly journals Mathematical and Physical Continuity

2008 ◽  
Vol 6 ◽  
Author(s):  
Mark Colyvan ◽  
Kenny Easwaran
Keyword(s):  
Common Sense ◽  
Natural Question ◽  
Alternative Definition ◽  
Continuous Motion ◽  
Mathematical Definition ◽  
Definition Of ◽  
Point Of Departure

There is general agreement in mathematics about what continuity is. In this paper we examine how well the mathematical definition lines up with common sense notions. We use a recent paper by Hud Hudson as a point of departure. Hudson argues that two objects moving continuously can coincide for all but the last moment of their histories and yet be separated in space at the end of this last moment. It turns out that Hudson’s construction does not deliver mathematically continuous motion, but the natural question then is whether there is any merit in the alternative definition of continuity that he implicitly invokes.

A City is Not a Semilattice Either

1976 ◽  
Vol 8 (4) ◽  
pp. 375-384 ◽  
Author(s):  
F Harary ◽  
J Rockey
Keyword(s):  
Graphical Analysis ◽  
Theoretical Concept ◽  
Theoretical Terms ◽  
Natural Form ◽  
Mathematical Definition ◽  
Christopher Alexander ◽  
Structural Configurations ◽  
Definition Of ◽  
The Relationship ◽  
The City

In 1965 Christopher Alexander took the original step of analysing the city in graph theoretical terms and concluded that its historical or natural form is a semilattice and that urban planners of the future should adhere to this model. The idea was well received in architectural circles and has passed without serious challenge. In this paper, the value of such analysis is once again emphasized, although some of Alexander's arguments and his conclusions are refuted. Beginning with an exposition of the relationship between the graph theoretical concept of a tree, and the representation of a tree by a family of sets, we present a mathematical definition of a semilattice and discuss the ‘points’ and ‘lines’ of a graph in terms of a city, concluding that it is neither a tree nor a semilattice. This clears the ground for future graphical analysis. It seems that even general structural configurations, such as graphs or digraphs with certain specified properties, will fail to characterize a city, whose complexity, at this stage, may well continue to be understood more readily through negative rather than positive descriptions.

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