Symétrisation de la longueur et du temps dans un espace de Lorentz C3 en algèbre lineaire, pouvant servir en théorie trichromatique des couleurs

1975 ◽  
Vol 53 (17) ◽  
pp. 1687-1688 ◽  
Author(s):  
Pierre Demers
Keyword(s):  
Quadratic Function ◽  
The Other ◽  
Auxiliary Variables ◽  
Lorentzian Form

It is proposed to express time as a composition of three auxiliary variables tx, ty, tz. which will be named components of vector t. Event P is expressed as a composition of six variables x, y, z, tx, ty, tz in R6 or of three coordinates ξ = x + itx, η = y + ity, and ζ = z + itz in C3. A quadratic function is defined, called 'carré simple', of P, which comes to the same as taking the square of the Lorentzian form of P in R4, equalling.s2. In this formalism, length r(x, y, z) and time t (tx, ty, tz) play roles exactly symmetrical and are exchangeable one for the other. This formalism will be applied to trichromatic theory.

scholarly journals Effects of Bonding Parameters on Free Air Ball Properties and Bonded Strength of Ag-10Au-3.6Pd Alloy Bonding Wire

Micromachines ◽  
2020 ◽  
Vol 11 (8) ◽  
pp. 777 ◽  
Author(s):  
Jun Cao ◽  
Junchao Zhang ◽  
John Persic ◽  
Kexing Song
Keyword(s):  
Quadratic Function ◽  
Golf Ball ◽  
The Other ◽  
Bonding Wire ◽  
Small Ball ◽  
Ball Bond ◽  
Bonding Parameters ◽  
Optimal Geometry ◽  
Other Hand ◽  
Free Air

Free air ball (FAB) and bonded strength were performed on an Ag-10Au-3.6Pd alloy bonding wire (diameter of 0.025 mm) for different electronic flame-off (EFO) currents, times and bonding parameters. The effects of the EFO and bonding parameters on the characteristics of the FAB as well as the bonded strength were investigated using scanning electron microscopy. The results showed that, for a constant EFO time, the FAB of the Ag-10Au-3.6Pd alloy bonding wire transitioned from a pointed defined ball to an oval one, then to a perfectly shaped one, and finally to a golf ball with an increase in the EFO current. On the other hand, when the EFO current was constant and the EFO time was increased, the FAB changed from a small ball to a perfect one, then to a large one, and finally to a golf ball. The FAB exhibited the optimal geometry at an EFO current of 0.030 A and EFO time of 0.8 ms. Further, in the case of the Ag-10Au-3.6Pd alloy bonding wire, for an EFO current of 0.030 A, the FAB diameter exhibited a nonlinear relationship with the EFO time, which could be expressed by a quadratic function. Finally, the bonded strength decreased when the bonding power and force were excessively high, causing the ball bond to overflow. This led to the formation of neck cracks and decrease in the bonded strength. On the other hand, the bonded strength was insufficiently when the bonding power and force were small. The bonded strength was of the desired level when the bonding power and force were 70 mW and 0.60 N (for the ball bonded) and 95 mW and 0.85 N (for the wedge bonded), respectively.

Seed Bank Dynamics of Three Co-Occurring Banksias in South Coastal Western Australia: the Role of Plant Age, Cockatoos, Senescence and Interfire Establishment.

1991 ◽  
Vol 39 (4) ◽  
pp. 385 ◽  
Author(s):  
ETF Witkowski ◽  
BB Lamont ◽  
SJ Connell
Keyword(s):  
Western Australia ◽  
Seed Bank ◽  
Quadratic Function ◽  
Seed Storage ◽  
Plant Age ◽  
The Other ◽  
Age Cohorts ◽  
Seed Bank Dynamics ◽  
Order Of Magnitude

Seed bank dynamics of three co-occurring, non-sprouting Banksia species (B. baxteri, B. speciosa and B. coccinea) in patch-burnt scrub-heath (aged 10 and 21 years) were studied in the southern sandplains of Western Australia. In the younger plants, canopy seed storage was highest in B. coccinea. However, 21-year-old B. coccinea stored an order of magnitude fewer seeds than the other species and no more than young B. coccinea. Seed storage per year increased exponentially with plant age in B. speciosa and B. baxteri, whereas a quadratic function, peaking at 16 years, best described seed storage in B. Coccinea. Degree of serotiny was lowest in B. coccinea. Seed abortion did not vary between age cohorts but was highest in B. coccinea. Granivory ranged from 18 to 42% and was highest in the older plants and in B. baxteri. Cockatoos removed about 20% of cones in B. baxteri and B. coccinea and 10% in B. speciosa. Experimental cone removal accelerated follicle opening, especially in B. coccinea, irrespective of whether cones were placed on the ground (simulating cockatoo removal) or reattached to the plant (simulating plant death). Half the 21-year-old B. coccinea were dead and the remainder were considered senescent, as most branches showed dieback and cone fertility had fallen to 8%. Death of the other species was negligible, with cone fertility rising to a mean of 45% (B. speciosa) and 66% (B. baxteri). Interfire establishment was significant only in B. coccinea. The build-up of a viable seed bank with time occurred at a slower rate than for non-sprouting banksias in the northern sandplains.

scholarly journals A note on the turning point for the quadratic trend

2019 ◽  
Vol 5 (2) ◽  
pp. 39-48
Author(s):  
Vedran Kojić ◽  
Tihana Škrinjarić
Keyword(s):  
Statistical Model ◽  
Unemployment Rate ◽  
Differential Calculus ◽  
Turning Point ◽  
Quadratic Function ◽  
The Other ◽  
New Method ◽  
Quadratic Trend ◽  
Function Finding

AbstractThe quadratic trend is a statistical model described by the quadratic function. Finding its extremum (also called the vertex or the turning point) using differential calculus or completing the square method is very well known in the literature. In this paper, a new method for finding the extremum of the quadratic function, based on a simple mathematical inequality is proposed. In comparison with the other two known methods, our method does not require the differentiability assumption and it takes fewer steps than completing the square method. Also, it is shown how the turning point for the quadratic trend can be applied in forecasting the unemployment rate in Croatia in the first quarter of 2019. The obtained conclusions are equal to the conclusions obtained in the usual way by using forecasting software.

scholarly journals Source apportionment of ambient particle number concentrations in central Los Angeles using positive matrix factorization (PMF)

2016 ◽  
Author(s):  
M. H. Sowlat ◽  
S. Hasheminassab ◽  
C. Sioutas
Keyword(s):  
Los Angeles ◽  
Matrix Factorization ◽  
Particle Number ◽  
Road Dust ◽  
Positive Matrix Factorization ◽  
The Other ◽  
Auxiliary Variables ◽  
Positive Matrix ◽  
Urban Background ◽  
Secondary Aerosol

Abstract. In this study, the Positive Matrix Factorization (PMF) receptor model (version 5.0) was used to identify and quantify major sources contributing to particulate matter (PM) number concentrations, using PM number size distributions in the range of 13 nm to 10 μm combined with several auxiliary variables, including black carbon (BC), elemental and organic carbon (EC/OC), PM mass concentrations, gaseous pollutants, meteorological, and traffic counts data, collected for about 9 months between August 2014 and 2015 in central Los Angeles, CA. Several parameters, including particle number and volume size distribution profiles, profiles of auxiliary variables, contributions of different factors in different seasons to the total number concentrations, diurnal variations of each of the resolved factors in the cold and warm phases, weekday/weekend analysis for each of the resolved factors, and correlation between auxiliary variables and the relative contribution of each of the resolved factors, were used to identify PM sources. A six-factor solution was identified as the optimum for the aforementioned input data. The resolved factors comprised nucleation, traffic 1, traffic 2 (having a larger mode diameter than traffic 1 factor), urban background aerosol, secondary aerosol, and soil/road dust. Traffic sources (1 and 2) were the major contributor to PM number concentrations, collectively making up to above 60 % (60.8–68.4 %) of the total number concentrations during the study period. Their contribution was also significantly higher in the cold phase compared to the warm phase. Nucleation was another major factor significantly contributing to the total number concentrations (an overall contribution of 17 %, ranging from 11.7 % to 24 %), having a larger contribution during the warm phase than in the cold phase. The other identified factors were urban background aerosol, secondary aerosol, and soil/road dust, with relative contributions of approximately 12 % (7.4–17.1), 2.1 % (1.5–2.5 %), and 1.1 % (0.2–6.3 %), respectively, overall accounting for about 15 % (15.2–19.8 %) of PM number concentrations. As expected, PM number concentrations were dominated by factors with smaller mode diameters, such as traffic and nucleation. On the other hand, PM volume and mass concentrations in the study area were mostly affected by sources having larger mode diameters, including secondary aerosols and soil/road dust. Results from the present study can be used as input parameters in future epidemiological studies to link PM sources to adverse health effects as well as by policy makers to set targeted and more protective emission standards for PM.

A balanced sampling and calibration

2016 ◽  
Vol 61 (3) ◽  
pp. 38-60
Author(s):  
Arkadiusz Kozłowski
Keyword(s):  
Sampling Design ◽  
The Other ◽  
General Idea ◽  
Auxiliary Variables ◽  
Numerical Examples ◽  
Balanced Sampling ◽  
Other Hand ◽  
Design Weights

A balanced sampling design is a design in which Horvitz-Thompson estimators of population totals for a set of auxiliary variables equal the known totals of these variables. On the other hand, calibration is a technique where the modification of design weights occurs in such a way that the new weights, when applied to auxiliary variables, reproduce, i.e. estimate withouterror, the known totals for these variables. The general idea behind balanced sampling and calibration is thus the same — both techniques tend to reproduce known totals of the auxiliary variables. The purpose of the paper is to describe and compare both techniques, considering them as alternatives in achieving the same goal. More attention was devoted to balanced sampling. The algorithm for selecting a sample was illustrated with two numerical examples. The comparison between balanced sampling and calibration, as alternatives, indicates calibration, but the best strategy is to use both methods simultaneously.

scholarly journals A Generalized Class of Exponential Type Estimators for Population Mean under Systematic Sampling Using Two Auxiliary Variables

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Mursala Khan
Keyword(s):  
Exponential Type ◽  
Secondary Data ◽  
Estimation Procedure ◽  
The Other ◽  
Systematic Sampling ◽  
Auxiliary Variables ◽  
Population Mean ◽  
First Order ◽  
Class Of Estimators ◽  
The Mean

We have proposed a generalized class of exponential type estimators for population mean under the framework of systematic sampling using the knowledge of two auxiliary variables. The expressions for the mean square error of the proposed class of estimators have been corrected up to first order of approximation. Comparisons of the efficiency of the proposed class of estimators under the optimal conditions with the other existing estimators have been presented through a real secondary data. The statistical study provides strong evidence that the proposed class of estimators in survey estimation procedure results in substantial efficiency improvements over the other existing estimation approaches.

scholarly journals Source apportionment of ambient particle number concentrations in central Los Angeles using positive matrix factorization (PMF)

2016 ◽  
Vol 16 (8) ◽  
pp. 4849-4866 ◽  
Author(s):  
Mohammad Hossein Sowlat ◽  
Sina Hasheminassab ◽  
Constantinos Sioutas
Keyword(s):  
Los Angeles ◽  
Matrix Factorization ◽  
Particle Number ◽  
Road Dust ◽  
Positive Matrix Factorization ◽  
The Other ◽  
Auxiliary Variables ◽  
Positive Matrix ◽  
Urban Background ◽  
Secondary Aerosol

Abstract. In this study, the positive matrix factorization (PMF) receptor model (version 5.0) was used to identify and quantify major sources contributing to particulate matter (PM) number concentrations, using PM number size distributions in the range of 13 nm to 10 µm combined with several auxiliary variables, including black carbon (BC), elemental and organic carbon (EC/OC), PM mass concentrations, gaseous pollutants, meteorological, and traffic counts data, collected for about 9 months between August 2014 and 2015 in central Los Angeles, CA. Several parameters, including particle number and volume size distribution profiles, profiles of auxiliary variables, contributions of different factors in different seasons to the total number concentrations, diurnal variations of each of the resolved factors in the cold and warm phases, weekday/weekend analysis for each of the resolved factors, and correlation between auxiliary variables and the relative contribution of each of the resolved factors, were used to identify PM sources. A six-factor solution was identified as the optimum for the aforementioned input data. The resolved factors comprised nucleation, traffic 1, traffic 2 (with a larger mode diameter than traffic 1 factor), urban background aerosol, secondary aerosol, and soil/road dust. Traffic sources (1 and 2) were the major contributor to PM number concentrations, collectively making up to above 60 % (60.8–68.4 %) of the total number concentrations during the study period. Their contribution was also significantly higher in the cold phase compared to the warm phase. Nucleation was another major factor significantly contributing to the total number concentrations (an overall contribution of 17 %, ranging from 11.7 to 24 %), with a larger contribution during the warm phase than in the cold phase. The other identified factors were urban background aerosol, secondary aerosol, and soil/road dust, with relative contributions of approximately 12 % (7.4–17.1), 2.1 % (1.5–2.5 %), and 1.1 % (0.2–6.3 %), respectively, overall accounting for about 15 % (15.2–19.8 %) of PM number concentrations. As expected, PM number concentrations were dominated by factors with smaller mode diameters, such as traffic and nucleation. On the other hand, PM volume and mass concentrations in the study area were mostly affected by sources with larger mode diameters, including secondary aerosols and soil/road dust. Results from the present study can be used as input parameters in future epidemiological studies to link PM sources to adverse health effects as well as by policymakers to set targeted and more protective emission standards for PM.

A New Algorithm and Computation Approach for Economic Dispatch with Prohibited Operating Zones in Power Systems

2005 ◽  
Vol 23 (4) ◽  
pp. 267-275
Author(s):  
Nurettin Çetinkaya ◽  
Abdullah Ürkmez ◽  
İsmet Erkmen ◽  
Tankut Yalçinöz
Keyword(s):  
Power Systems ◽  
Electrical Power ◽  
Quadratic Function ◽  
Power Production ◽  
Standard Test ◽  
The Other ◽  
Economic Load Dispatch ◽  
Electrical Power Systems ◽  
Prohibited Operating Zones ◽  
Cost Curves

This paper presents a new algorithm and computation approach to solve the economic load dispatch (ELD) in electrical power systems. We applied a new power formula to solve the ELD problem. If production units cost curves are represented properly then ELD becomes more correct. In this respect we assumed that production units have prohibited operating zones. Cost curves of the production units are generally accepted as piece-wise quadratic function. The power production is cheaper since we do not use the production units in the prohibited operating zones. The proposed method and algorithm are compared to other ELD methods on the standard test systems. The proposed method solve the dispatch problem faster than the other ELD methods.

scholarly journals Revisiting Graph Width Measures for CNF-Encodings

2020 ◽  
Vol 67 ◽  
pp. 409-436
Author(s):  
Romain Wallon ◽  
Stefan Mengel
Keyword(s):  
Communication Complexity ◽  
The Other ◽  
Auxiliary Variables ◽  
Design Of Algorithms ◽  
Bounded Treewidth ◽  
Graph Classes ◽  
Stark Contrast ◽  
Bounded Width ◽  
Cnf Formulas

We consider bounded width CNF-formulas where the width is measured by popular graph width measures on graphs associated to CNF-formulas. Such restricted graph classes, in particular those of bounded treewidth, have been extensively studied for their uses in the design of algorithms for various computational problems on CNF-formulas. Here we consider the expressivity of these formulas in the model of clausal encodings with auxiliary variables. We first show that bounding the width for many of the measures from the literature leads to a dramatic loss of expressivity, restricting the formulas to such of low communication complexity. We then show that the width of optimal encodings with respect to different measures is strongly linked: there are two classes of width measures, one containing primal treewidth and the other incidence cliquewidth, such that in each class the width of optimal encodings only differs by constant factors. Moreover, between the two classes the width differs at most by a factor logarithmic in the number of variables. Both these results are in stark contrast to the setting without auxiliary variables where all width measures we consider here differ by more than constant factors and in many cases even by linear factors.

scholarly journals Bounds on the size of PC and URC formulas

2020 ◽  
Vol 69 ◽  
pp. 1395-1420
Author(s):  
Petr Kučera ◽  
Petr Savický
Keyword(s):  
The Other ◽  
Auxiliary Variables ◽  
Similar Statement ◽  
Partial Assignment ◽  
Other Hand ◽  
Polynomial Size ◽  
Exponential Separation ◽  
Unit Propagation

In this paper, we investigate CNF encodings, for which unit propagation is strong enough to derive a contradiction if the encoding is not consistent with a partial assignment of the variables (unit refutation complete or URC encoding) or additionally to derive all implied literals if the encoding is consistent with the partial assignment (propagation complete or PC encoding). We prove an exponential separation between the sizes of PC and URC encodings without auxiliary variables and strengthen the known results on their relationship to the PC and URC encodings that can use auxiliary variables. Besides of this, we prove that the sizes of any two irredundant PC formulas representing the same function differ at most by a factor polynomial in the number of the variables and present an example of a function demonstrating that a similar statement is not true for URC formulas. One of the separations above implies that a q-Horn formula may require an exponential number of additional clauses to become a URC formula. On the other hand, for every q-Horn formula, we present a polynomial size URC encoding of the same function using auxiliary variables. This encoding is not q-Horn in general.

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