scholarly journals Application of the partitioning method to specific Toeplitz matrices

2013 ◽  
Vol 23 (4) ◽  
pp. 809-821 ◽  
Author(s):  
Predrag Stanimirović ◽  
Marko Miladinović ◽  
Igor Stojanović ◽  
Sladjana Miljković
Keyword(s):  
Toeplitz Matrices ◽  
Motion Blur ◽  
Computational Time ◽  
Linear Motion ◽  
Column Matrix ◽  
Arbitrary Size ◽  
Convolution Kernels ◽  
Time Required ◽  
Block Column

Abstract We propose an adaptation of the partitioning method for determination of theMoore-Penrose inverse of a matrix augmented by a block-column matrix. A simplified implementation of the partitioning method on specific Toeplitz matrices is obtained. The idea for observing this type of Toeplitz matrices lies in the fact that they appear in the linear motion blur models in which blurring matrices (representing the convolution kernels) are known in advance. The advantage of the introduced method is a significant reduction in the computational time required to calculate the Moore-Penrose inverse of specific Toeplitz matrices of an arbitrary size. The method is implemented in MATLAB, and illustrative examples are presented.

Is Hydraulics Over-Used or Under-Used in Storm Drainage?

1994 ◽  
Vol 29 (1-2) ◽  
pp. 53-61
Author(s):  
Ben Chie Yen
Keyword(s):  
Unsteady Flow ◽  
Computational Time ◽  
Time Step ◽  
Flow Routing ◽  
Kinematic Wave Equation ◽  
Storm Drainage ◽  
Saint Venant Equations ◽  
Unsteady Flow Routing ◽  
Selection Of

Urban drainage models utilize hydraulics of different levels. Developing or selecting a model appropriate to a particular project is not an easy task. Not knowing the hydraulic principles and numerical techniques used in an existing model, users often misuse and abuse the model. Hydraulically, the use of the Saint-Venant equations is not always necessary. In many cases the kinematic wave equation is inadequate because of the backwater effect, whereas in designing sewers, often Manning's formula is adequate. The flow travel time provides a guide in selecting the computational time step At, which in turn, together with flow unsteadiness, helps in the selection of steady or unsteady flow routing. Often the noninertia model is the appropriate model for unsteady flow routing, whereas delivery curves are very useful for stepwise steady nonuniform flow routing and for determination of channel capacity.

scholarly journals Stiffness Estimation and Equivalence of Boundary Conditions in FEM Models

2021 ◽  
Vol 11 (4) ◽  
pp. 1482
Author(s):  
Róbert Huňady ◽  
Pavol Lengvarský ◽  
Peter Pavelka ◽  
Adam Kaľavský ◽  
Jakub Mlotek
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Boundary Conditions ◽  
Model Updating ◽  
Element Model ◽  
Computational Time ◽  
Stiffness Coefficients ◽  
First Case ◽  
Numerical Approaches

The paper deals with methods of equivalence of boundary conditions in finite element models that are based on finite element model updating technique. The proposed methods are based on the determination of the stiffness parameters in the section plate or region, where the boundary condition or the removed part of the model is replaced by the bushing connector. Two methods for determining its elastic properties are described. In the first case, the stiffness coefficients are determined by a series of static finite element analyses that are used to obtain the response of the removed part to the six basic types of loads. The second method is a combination of experimental and numerical approaches. The natural frequencies obtained by the measurement are used in finite element (FE) optimization, in which the response of the model is tuned by changing the stiffness coefficients of the bushing. Both methods provide a good estimate of the stiffness at the region where the model is replaced by an equivalent boundary condition. This increases the accuracy of the numerical model and also saves computational time and capacity due to element reduction.

Mercury-204 Determination by Emission Spectroscopy

1965 ◽  
Vol 19 (3) ◽  
pp. 87-89 ◽  
Author(s):  
F. M. Smith
Keyword(s):  
Coefficient Of Variation ◽  
Isotope Shift ◽  
Emission Spectroscopy ◽  
Electrodeless Discharge ◽  
Discharge Lamp ◽  
Isotope Concentration ◽  
Single Determination ◽  
Time Required

The determination of mercury-204 was made by using the isotope shift of the 3984 A mercury line excited by electrodeless discharge. Densitometric traces were made from film recordings of the 3984 A line and the areas under the component peaks were determined. Ratios of each of these areas to the sum of the areas from all the line components are plotted against the isotope concentration to produce a working curve. The coefficient of variation for this method is approximately 11 percent The time required for a single determination (after fabrication of the discharge lamp) is about two hours.

scholarly journals THE EFFECTS ON BIOLOGICAL MATERIALS OF FREEZING AND DRYING BY VACUUM SUBLIMATION

1954 ◽  
Vol 100 (1) ◽  
pp. 81-88 ◽  
Author(s):  
Donald Greiff ◽  
Henry Pinkerton
Keyword(s):  
Influenza Virus ◽  
Biological Materials ◽  
Continuous Operation ◽  
Virus Suspension ◽  
Vacuum Sublimation ◽  
End Point ◽  
Different Temperatures ◽  
Time Required

A vacuum sublimation apparatus is described which will permit, (a) the removal of water from virus suspensions at temperatures ranging down to –80°C., (b) continuous operation with a minimum of attention from the investigator, (c) sealing off of samples at operating pressures (10–5 mm. Hg), (d) simultaneous lyophilization of aliquot samples at different temperatures, (e) isolation of a portion of the apparatus without disturbing the remainder of the system, and (f) determination of the end-point of sublimation without disturbing the samples. The time required for drying 0.1 ml. of influenza virus suspension was shown to increase markedly with decrease of temperature, 8 days being required for dehydration at –80°C. in contrast to 2 days at –30°C. and 1 day at 0°C.

Developing and Comparing Alternative Design Optimization Formulations for a Vibration Absorber Example

2017 ◽  
Author(s):  
Siyao Luan ◽  
Deborah L. Thurston ◽  
Madhav Arora ◽  
James T. Allison
Keyword(s):  
Design Problem ◽  
Mathematical Optimization ◽  
Computational Time ◽  
Vibration Absorber ◽  
Solution Quality ◽  
Design Representation ◽  
Core Elements ◽  
Improved Design ◽  
Time Required ◽  
Level Of Effort

In some cases, the level of effort required to formulate and solve an engineering design problem as a mathematical optimization problem is significant, and the potential improved design performance may not be worth the excessive effort. In this article we address the tradeoffs associated with formulation and modeling effort. Here we define three core elements (dimensions) of design formulations: design representation, comparison metrics, and predictive model. Each formulation dimension offers opportunities for the design engineer to balance the expected quality of the solution with the level of effort and time required to reach that solution. This paper demonstrates how using guidelines can be used to help create alternative formulations for the same underlying design problem, and then how the resulting solutions can be evaluated and compared. Using a vibration absorber design example, the guidelines are enumerated, explained, and used to compose six alternative optimization formulations, featuring different objective functions, decision variables, and constraints. The six alternative optimization formulations are subsequently solved, and their scores reflecting their complexity, computational time, and solution quality are quantified and compared. The results illustrate the unavoidable tradeoffs among these three attributes. The best formulation depends on the set of tradeoffs that are best in that situation.

Evaluation of a Multi-Goal Solver for Use in a Blackboard Architecture

2014 ◽  
Vol 6 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Jeremy Straub
Keyword(s):  
Multiple Solutions ◽  
Computational Time ◽  
Problem Analysis ◽  
Robotic Control ◽  
Operating Environment ◽  
Blackboard Architecture ◽  
Rule Based ◽  
Multiple Levels ◽  
Time Required ◽  
Naive Approach

This article presents a multi-goal solver for problems that can be modeled using a Blackboard Architecture. The Blackboard Architecture can be used for data fusion, robotic control and other applications. It combines the rule-based problem analysis of an expert system with a mechanism for interacting with its operating environment. In this context, numerous control or domain (system-subject) problems may exist which can be solved through reaching one of multiple outcomes. For these problems which have multiple solutions, any of which constitutes an end-goal, a solving mechanism which is solution-choice-agnostic and finds the lowest-cost path to the lowest-cost solution is required. Such a solver mechanism is presented and characterized herein. The performance of the solver (including both the computational time required to ascertain a solution and execute it) is compared to the naïve Blackboard approach. This performance characterization is performed across multiple levels of rule counts and rule connectivity. The naïve approach is shown to generate a solution faster, but the solutions generated by this approach, in most cases, are inferior to those generated by the solver.

Rapid Measurement of Nutation NQR Spectra in Powders Using an RF Pulse Train

1996 ◽  
Vol 51 (5-6) ◽  
pp. 363-367 ◽  
Author(s):  
Nicolai Sinyavsky ◽  
Michał Ostafin ◽  
Mariusz Maćkowiak
Keyword(s):  
Asymmetry Parameter ◽  
Pulse Train ◽  
Pulse Action ◽  
Rf Pulses ◽  
Time Saving ◽  
Long Time ◽  
The Asymmetry ◽  
Rf Pulse ◽  
Time Required

Abstract The method of two-dimensional nutation NQR spectroscopy, introduced by Harbison in 1989, has been successfully used for determining of the asymmetry parameter of the EFG tensor for spin-3/2 nuclei in both powdered and monocrystal samples in the absence of an external magnetic field. The inconvenience inherent in the method, however, is the long time required, because data acquisition must be repeated for various RF pulse lengths. We discuss a method to reduce the time of the nutation experiment by using a sequence of identical short RF pulses of length r w and distance τ. It is shown that for an NQR frequency ω0 , frequency offset Δω, and pulse parameters satisfying the relation ω0τ + Δωtw = 2πk (k = 1, 2, 3,..., n) a synchronism of pulse action takes place and the nutation interferogram can be measured "stroboscopically" between the pulses. The maximum time saving factor that can be obtained as compared to the conventional nutation experiment is of the order of the number of pulses used in a pulse train. The method has been successfully applied for determination of the asymmetry parameter for one of the two 3 5 Cl sites in polycrystalline 2,4,6-trichloro-1,3,5-triazine (cyanuric chloride).

DETERMINATION OF URANIUM IN FLOTATION CONCENTRATES AND IN LEACH LIQUORS BY X-RAY FLUORESCENCE

1959 ◽  
Vol 37 (1) ◽  
pp. 20-28 ◽  
Author(s):  
G. L. Smithson ◽  
R. L. Eager ◽  
A. B. VanCleave
Keyword(s):  
Direct Measurement ◽  
Pilot Plant ◽  
Internal Standard ◽  
Liquid Extraction ◽  
X Ray ◽  
Liquid Liquid Extraction ◽  
Northern Saskatchewan ◽  
Plant Operations ◽  
Time Required

X-Ray fluorescence has been applied to the analysis of flotation concentrates obtained from pegmatitic uranium ores occurring in Northern Saskatchewan. Approximate uranium analyses can be obtained by direct measurement on flotation concentrates but more accurate results are obtained by using an internal standard such as strontium or yttrium. The time required for an analysis, as compared to that of conventional chemical or fluorimetric methods, is considerably reduced and flotation pilot plant operations can therefore be more effectively controlled. The method has been extended to include the analysis of sulphate leach liquors obtained from the leaching of pegmatitic ores and their flotation concentrates. Organic phases obtained in liquid – liquid extraction studies can also be rapidly analyzed for uranium by X-ray fluorescence.

scholarly journals XXXIII.—I. On the Estimation of Carbon in Organic Substances by the Kjeldahl Method. II. Its Application to the Analysis of Potable Waters

1895 ◽  
Vol 37 (4) ◽  
pp. 743-757
Author(s):  
Charles Hunter Stewart
Keyword(s):  
Accurate Method ◽  
Great Accuracy ◽  
Organic Substances ◽  
Applied Chemistry ◽  
Carbon And Nitrogen ◽  
Kjeldahl Method ◽  
The Will ◽  
Time Required

An easy and yet accurate method of determining carbon and nitrogen in organic substances has long been a desideratum, especially among those engaged in the application of chemistry to biological, hygienic, and agricultural questions. For the determination of nitrogen the method of Dumas, with its numerous modifications, is still the only one applicable in all cases, but the time required for it, and the manipulative dexterity necessary, has prevented its wide application for the above-named purposes. The method of Will and Varrentrap, though less generally applicable, is easier, and, until the publication of Kjeldahl's method, was most frequently used in applied chemistry. Kjeldahl claims for his method the same applicability and as great accuracy as the Will and Varrentrap method, with the added advantage of greater ease in working.

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