LICHEN DATA FROM THE ATHABASCA OIL SANDS REGION
|
|
|
- ĒΔανιήλ Θεοδωρίδης
- 8 χρόνια πριν
- Προβολές:
Transcript
1 LICHEN DATA FROM THE ATHABASCA OIL SANDS REGION STATISTICAL REPORT Prepared for Janet Marsh Woods Buffalo Environmental Association Okotoks, Alberta, Canada June 2005 by Gregory Brenner Pacific Analytics PO Box 219 Albany, OR (541)
2 Table of Contents LICHEN DATA FROM THE ATHABASCA OIL SANDS REGION STATISTICAL REPORT I. TABLE OF CONTENTS I. Table of Contents... 1 II. Executive Summary... 2 III. Introduction... 3 Questions of Interest... 4 Species of Interest... 4 Elements... 4 IV. Statistical Procedures... 5 V. Quality Assurance Analysis VI. Variance Components Evernia mesomorpha VII VIII. Summary Statistics IX. Ordinations X. Species Diversity XI. Literature Cited Statistical Report by Pacific Analytics, L.L.C. 1
3 Executive Summary II. EXECUTIVE SUMMARY This is a report of statistical analysis of the apportionment of variance within the Lichen Data from the Athabasca Oil Sands Region. The report answers three questions of interest. They are: 1. What is the relative error due to laboratory analysis, as measured with laboratory replicates? 2. What is the error due to field collections, as measured by field replicates? 3. What is the error due to pollution deposition among sites? 4. Do the concentrations of elements in lichens change with distance from mine sites? The report includes an introduction to the analysis, a description of the statistical procedures, and the results of the analyses. The results are presented in three chapters, one dealing with each question of interest. Statistical Report by Pacific Analytics, L.L.C. 2
4 Introduction III. INTRODUCTION Lichens are a unique life form, consisting of a relationship between a fungus and a photosynthetic partner, a cyanobacterium or a green alga. The association is said to be symbiotic, such that the fungus provides moisture and shelter for the algal cells allowing them live even in places that otherwise would be unsuitable for them. Due to this symbiotic relationship, lichens are able to live in some of the harshest habitats on earth. Lichens are extremely widespread in nature; they occur from arid desert regions to the Arctic and grow on bare soil, tree trunks, and rocks. Lichens grow very slowly, often less than a millimeter per year. Lichens lack any outside covering, or cuticle, and consequently are directly exposed to the atmosphere, which they depend upon for their nutrients and water. Moistened lichen tissues act as blotters, soaking up chemicals or materials deposited on their surfaces. This feature has also made them highly susceptible to air pollutants; and lichens are perhaps the plant species most susceptible to sulfur dioxide, heavy metals, and acid rain. Since lichens are very sensitive to pollutants, they are sometimes used as indicators of air and water pollution. Lichens are investigated at a number of locations surrounding a point or area pollution source, or at a number of locations within an area of interest. Appropriate lichen metrics are recorded at each location and are related to known or inferred pollution levels. The metrics include distribution of individual indicator species, frequency or abundance of individual species, species richness (total number of different species) at each study location, total lichen cover, and element content of lichen samples. Statistical Report by Pacific Analytics, L.L.C. 3
5 Introduction When assessing pollution with lichens it is appropriate to apportion the variance of the data into its various sources. Variability in element content is dependent upon the ability to collect a representative sample, the precision of laboratory measurement, and the natural variability among sites due to environmental variables such as air pollution, rainfall, temperature, and substrate. Questions of Interest 1. What is the relative error due to laboratory analysis, as measured with laboratory replicates? 2. What is the error due to field collections, as measured by field replicates? 3. What is the error due to elemental deposition among sites? 4. Do the concentrations of elements in lichens change with distance from mine sites? Species of Interest Element content was measured from two lichen species: 1 Evemes = Evernia mesomorpha 2 Hypphy = Elements Twenty-eight elements were detected in laboratory analysis: Percent Nitrogen, Percent Sulfur, parts per million (ppb for Hg) of Al, B, Ba, Be, Ca, Cd, Co, Cr, Cu, Fe, Hg, K, Li, Mg, Mn, Mo, Na, Ni, P, Pb, Rb, Si, Sr, Ti, V, Zn. Statistical Report by Pacific Analytics, L.L.C. 4
6 Statistical Procedures IV. STATISTICAL PROCEDURES The data were compiled and delivered to Pacific Analytics on April 14, 2005 for analysis. The element content of two lichen species were delivered in spreadsheet format with columns for Lab ID # and Sample Name that was coded for Site, Direction to Mine, Distance to Mine, Species acronym, and replicate code. Estimation of Components of Variance Variance components models are used when there is interest in variability of one or more variables other than the residual error. One of the goals of this study was to estimate components of variation due to field measurement and to laboratory analysis. For this purpose Sampling Sites are regarded as fixed. When there are several samples within a Site, the model for the response variable for Site (S), and sample (replicate), is: y = μ + + ij where ξ is the fixed effect of Site, and ε is an independent random variable with ξ i ε ij zero mean and variance σ 2 S (variance of replicate samples within Sites) (Montgomery 1991). A maximum likelihood method was used to estimate the variance components. The maximum likelihood process constructs a likelihood function, which is a function of the model parameters. The maximum likelihood method makes use of a Newton-Raphson computing algorithm that iterates until the log-likelihood objective function converges (Searle et al., 1992). The maximum likelihood estimators that result are those values of the parameters from the parameter space that maximize the value of the likelihood function (Milliken and Johnson Statistical Report by Pacific Analytics, L.L.C. 5
7 Statistical Procedures 1992). The restricted maximum likelihood method is similar to the maximum likelihood method, but it first separates the likelihood into two parts; one that contains the fixed effects and one that does not (Patterson and Thompson 1971). A brief review of the restricted maximum likelihood estimators appears in Anderson et al. (1986). For the tasks presented in this report, restricted maximum likelihood estimators were obtained for each of the data sets. Software used for all statistical analyses was S-Plus 2000 (MathSoft ). Data Reduction The sampling units in this study are the sites at which lichen samples were collected. In most cases more than one sample of each species was taken at a site. These field replicate samples are sub-samples of the sampling unit and are not appropriate for analysis without accounting for the structure of the sampling. For this study, the site mean response of the sub-samples for each element for each species was calculated and used as the response variable for that site. Twenty-eight elements were detected in laboratory analysis. In each of the species, some of the samples had element concentrations below the detectable limit. Statistical analysis was not conducted for those elements that had greater than about 50% of the samples below detectable limits. These include Beryllium (Be), Cadmium (Cd), Cobalt (Co), Lead (Pb), and Rubidium (Rb) for E. mesomorpha. For the same reason, statistical analysis was not performed for Cobalt (Co) and Rubidium (Rb) for H. physodes. Statistical Report by Pacific Analytics, L.L.C. 6
8 Statistical Procedures Linear Regression Regression analysis describes statistical relationships between a response variable and several explanatory variables. In the case of lichen data, the response variables are the measurements of element concentration in lichen samples taken at several sites. The explanatory variables are cardinal directions and distance from mine sites. Knowledge about the statistical relationship between variables enables one to determine certain characteristics of the response variable from the measured explanatory variables. In mathematical terms the relationship looks like μ = β 0 + β 1 X 1 + β 2 X 2 where μ = the mean of the response distribution, β 0 is the intercept coefficient, β 1 is the coefficient for the first explanatory variable, X 1, and β 2 is the coefficient for the next explanatory variable, X 2. The regression coefficients are calculated using Least Squares Estimation. These parameters are estimated and each has its own associated standard error. An estimate for the value of the response variable can be calculated by inserting the values of the explanatory variables into the equation. The difference between the estimated value and the observed measured value is called the residual. The Least Squares Estimation procedure minimizes the squared residuals while estimating the regression coefficients. There are several conditions under which Least Squares Estimation is most efficient. The first is that the response distributions for each set of explanatory values have approximately the same standard deviations. The next is that the distributions of the response variables are approximately Normal (Gaussian). Statistical Report by Pacific Analytics, L.L.C. 7
9 Statistical Procedures The third is that each response is drawn independently of all the other responses. Least Squares Regression is useful for modeling the fit of a response variable to several continuous explanatory variables. In this study, the distance from the mine is one such continuous variable. Least Squares Regression can also be used to distinguish between two or more groups or categories. Indicator (or Dummy) variables are set up for each of the groups (or levels of a factor) but one. The indicator variables take on values of 1 or 0, indicating the attribute is present or absent. In the previous AOS Statistical Report, this method was used for the analysis of the effect of direction on the concentration of elements in lichens. Because most sampling was done in only one direction the method was not necessary for the analyses in the current report The fit of the model to the assumptions can be assessed by examination of the distribution of points in residual plots. These plots are the graph of the residuals on the Y axis versus the fitted values on the X axis. Inequalities of standard error are easily detected from these graphs. Usually transformations (e.g., log or square root transformations) will correct for departures from equality. In other cases, it is necessary to explore transformation of the explanatory variables. All determinations for transformation were made after examination of the distribution of the points in residual plots. Statistical Report by Pacific Analytics, L.L.C. 8
10 Statistical Procedures Ordination in Element Space Non-metric multidimensional scaling (NMS) ordination was used to ordinate the lichen tissue samples in elemental space (20 elements) for both lichen species combined. Ordination summarizes complex relationships among samples based on their elemental content. NMS is an iterative technique that is capable of extracting non-linear gradients in elemental space (Kruskal 1964; Mather 1976). Sørensen distance measure was used with the Slow-and-Thorough autopilot settings in PC-ORD 4.0 (40 runs of 400 iterations; McCune & Mefford 1999). The NMS ordination was rotated to maximize the correlation of distance from the mine sites with axis 1. Only 20 elements were ordinated; elements were not excluded when a high percentage of samples were below the MDL (see Table C2). Elemental concentrations in lichens were log-transformed for the ordination analysis to reduce noise in the data. Multivariate outlier analysis found no extreme outliers (lichen tissue samples > 3 standard deviations from the grand mean) at either locality. The Pearson s correlations of the individual elements and distance from the oil sands facilities with the ordination axes are reported. Ordination in Lichen Species Space We used non-metric multidimensional scaling (NMS) ordination to ordinate stands in lichen species space. The ordination was used to assess gradients in lichen community composition and their relationship to air pollution, topographic features and forest stand characteristics. NMS is an iterative technique that is capable of extracting non-linear gradients in species space (Kruskal 1964; Mather 1976). Sørensen distance measure was used with the Slow-and-Thorough autopilot settings in PCORD 4.0 (40 runs of 400 iterations; Statistical Report by Pacific Analytics, L.L.C. 9
11 Statistical Procedures McCune & Mefford 1999). Lichen abundance codes (described above) were converted to a scale of 1 to 10 for data analysis. Lichen species present in < 5% of the stands were excluded from the ordination analysis, eliminating 24 rare species to reduce noise in the dataset. After deletion of rare species, multivariate outlier analysis of all Muskeg stands found no stands that were potential outliers. The correlations of environmental variables (topographic and stand characteristics, species diversity measures, and concentration of elements in ) were assessed with the ordination axes (using Pearson s correlation). Distance from the mine sites and element concentrations in H. physodes were used to represent the potential pollution gradient. Statistical Report by Pacific Analytics, L.L.C. 10
12 Quality Assurance Analysis V. QUALITY ASSURANCE ANALYSIS Detection Limits The method detection limit (MDL) is 2 times the standard deviation of eleven replicates of a reagent water sample (blank). The percent of samples below the MDL was determined for each element by lichen species. Many elements were below the MDL in lichen samples (Table C2). All Evernia mesomorpha samples were below the MDL for Rubidium (Rb) and Cobalt (Co). Beryllium (Be), Cadmium (Cd), and Lead (Pb) concentrations were below the MDL for > 50% of E. mesomorpha samples. Consequently, none of these elements were evaluated in the statistical analyses for the elemental data. Although a large percentage of E. mesomorpha samples were below the MDL for Lithium (Li 48%) and Molybdenum (Mo 18%) these elements were included in statistical analyses. Almost all samples were below the MDL for Rubidium (Rb 98%) and Cobalt (Co 98%). Consequently, none of these elements were evaluated in the statistical analyses for the elemental data. No other elements were below the MDL for > 50% of H. physodes samples. Although a large percentage of H. physodes samples were below the MDL for Lithium (Li 44%) and Beryllium (Be 48%) these elements were included in statistical analyses. Statistical Report by Pacific Analytics, L.L.C. 11
13 Quality Assurance Analysis Table C2. The percentage of samples with element concentrations below the MDL, reported by element for each lichen species. Only elements with samples below the MDL are shown. Element Evernia Mesomorpha Beryllium 92% 48% Cadmium 74% 6% Cobalt 100% 98% Lead 88% 0% Lithium 48% 44% Molybdenum 18% 6% Rubidium 100% 98% Laboratory contamination The laboratory contamination was assessed using acid blanks. Element concentrations in blanks were above the MDL for Calcium and Silicon. Concentration of most elements in blanks was < 1% of the grand mean for field samples with the exception of Beryllium, Boron, Cadmium, Cobalt, Copper, Chromium, Molybdenum, Nickel, Rubidium, Sodium, Titanium, and Vanadium (Table C3). Statistical Report by Pacific Analytics, L.L.C. 12
14 Quality Assurance Analysis Table C3. Contamination in acid blanks measured by ICP-AES at the UMRAL. Values are in µg/g dry weight. Average values are reported for 2 acid blanks and the grand mean for that element is reported for the lichen samples across all species (n = 125). Percent of the grand mean is: (blank/grand mean) *100. MDL Units (dry wt.) % of Grand Mean Average Grand Element Symbol Blank Mean Aluminum Al 3.58 µ/g Barium Ba 0.12 µ/g Beryllium Be 0.04 µ/g Boron B 0.46 µ/g Cadmium Cd 0.12 µ/g Calcium Ca 0.82 µ/g Chromium Cr 0.28 µ/g Cobalt Co 0.24 µ/g Copper Cu 0.52 µ/g Iron Fe 0.34 µ/g Lead Pb 1.68 µ/g Lithium Li 0.40 µ/g Magnesium Mg 3.80 µ/g Manganese Mn 0.06 µ/g Mercury Hg µ/g Molybdenum Mo 0.22 µ/g Nickel Ni 0.44 µ/g Phosphorus P 0.70 µ/g Potassium K µ/g Rubidium Rb 53.0 µ/g Silicon Si 1.00 µ/g Sodium Na 3.60 µ/g Strontium Sr 0.06 µ/g Titanium Ti 0.30 µ/g Vanadium V 0.36 µ/g Zinc Zn 0.14 µ/g Statistical Report by Pacific Analytics, L.L.C. 13
15 Quality Assurance Analysis Laboratory replicates. Replicate analyses of twelve selected sample digests were run. This determined the laboratory precision for repeated measures of the same sample. Relative percent difference (RPD) between the laboratory replicates was determined to assess laboratory precision using the equation: RPD = ABS (x1 x2) / (mean x1, x2) *100 where ABS is the absolute value; x1 is the first lab measurement and x2 is the repeated lab measurement. Re-runs of lichen samples were also considered lab replicates and were used to estimate laboratory precision. Statistical Report by Pacific Analytics, L.L.C. 14
16 Quality Assurance Analysis Table C5. Laboratory precision is measured by the average relative percent difference, comparing two measurements of the same sample. The mean, median, minimum and maximum relative percent differences are reported (RPD). Sulfur and Nitrogen comparisons were made with 12 lab replicates; and results for all other elements were made with comparisons of 11 lab replicates. RPD was not calculated for samples near or at the MDL or for mercury (Hg). Element Units Mean RPD Median RPD Min. RPD Max. RPD Nitrogen % Sulphur % Aluminum ppm Barium ppm Beryllium ppm Boron ppm Cadmium ppm Calcium ppm Chromium ppm Copper ppm Iron ppm Lead ppm Lithium ppm Magnesium ppm Manganese ppm Molybdenum ppm Nickel ppm Phosphorous ppm Potassium ppm Silicon ppm Sodium ppm Strontium ppm Titanium ppm Vanadium ppm Zinc ppm Statistical Report by Pacific Analytics, L.L.C. 15
17 Variance Components VI. VARIANCE COMPONENTS Presented in Tables F6 and F7 are the estimated (REML) variance components for field replication for Evernia mesomorpha and respectively. Reported for each element in Part a. of each table are the Variances of Sites and Field Duplicates, a Total (Sum) of the two variances, and the proportion of the total variance for each component. Reported for each element in Part b. of each table are the Variances of Sites and Laboratory Duplicates, a Total (Sum) of the two variances, and the proportion of the total variance for each component. Statistical Report by Pacific Analytics, L.L.C. 16
18 Table F6. Part a. Field Replicate Variation of Evernia mesomorpha. ELEMENT SOURCE OF VARIATION N (%) S (%) Al (ppm) B (ppm) Ba (ppm) Ca (ppm) Cr (ppm) Cu (ppm) Sample Site Field Duplicate TOTAL VARIATION PROPORTION Site PROPORTION Field Duplicate SOURCE OF VARIATION Fe (ppm) K (ppm) Li (ppm) Mg (ppm) Mn (ppm) Mo (ppm) Na (ppm) Ni (ppm) Sample Site Field Duplicate TOTAL VARIATION PROPORTION Site PROPORTION Field Duplicate SOURCE OF VARIATION P (ppm) Si (ppm) Sr (ppm) Ti (ppm) V (ppm) Zn (ppm) Hg (ppb) Sample Site Field Duplicate TOTAL VARIATION PROPORTION Site PROPORTION Field Duplicate Statistical Report by Pacific Analytics, L.L.C. 17
19 Table F6. Part b. Laboratory Replicate Variation of Evernia mesomorpha. ELEMENT SOURCE OF VARIATION N (%) S (%) Al (ppm) B (ppm) Ba (ppm) Ca (ppm) Cr (ppm) Cu (ppm) Sample Site Laboratory Duplicate TOTAL VARIATION PROPORTION Site PROPORTION Laboratory Duplicate SOURCE OF VARIATION Fe (ppm) K (ppm) Li (ppm) Mg (ppm) Mn (ppm) Mo (ppm) Na (ppm) Ni (ppm) Sample Site Laboratory Duplicate TOTAL VARIATION PROPORTION Site PROPORTION Laboratory Duplicate SOURCE OF VARIATION P (ppm) Si (ppm) Sr (ppm) Ti (ppm) V (ppm) Zn (ppm) Sample Site Laboratory Duplicate TOTAL VARIATION PROPORTION Site PROPORTION Laboratory Duplicate Statistical Report by Pacific Analytics, L.L.C. 18
20 Table F7. Part a. Field Replicate Variation of. ELEMENT SOURCE OF VARIATION N (%) S (%) Al (ppm) B (ppm) Ba (ppm) Be (ppm) Ca (ppm) Cd (ppm) Cr (ppm) Sample Site Field Duplicate TOTAL VARIATION PROPORTION Site PROPORTION Field Duplicate SOURCE OF VARIATION Cu (ppm) Fe (ppm) K (ppm) Li (ppm) Mg (ppm) Mn (ppm) Mo (ppm) Na (ppm) Ni (ppm) Sample Site Field Duplicate TOTAL VARIATION PROPORTION Site PROPORTION Field Duplicate SOURCE OF VARIATION P (ppm) Pb (ppm) Si (ppm) Sr (ppm) Ti (ppm) V (ppm) Zn (ppm) Hg (ppb) Sample Site Field Duplicate TOTAL VARIATION PROPORTION Site PROPORTION Field Duplicate Statistical Report by Pacific Analytics, L.L.C. 19
21 Table F7. Part b. Laboratory Replicate Variation of. ELEMENT SOURCE OF VARIATION N (%) S (%) Al (ppm) B (ppm) Ba (ppm) Be (ppm) Ca (ppm) Cd (ppm) Cr (ppm) Sample Site Laboratory Duplicate TOTAL VARIATION PROPORTION Site PROPORTION Laboratory Duplicate SOURCE OF VARIATION Cu (ppm) Fe (ppm) K (ppm) Li (ppm) Mg (ppm) Mn (ppm) Mo (ppm) Na (ppm) Ni (ppm) Sample Site Laboratory Duplicate TOTAL VARIATION PROPORTION Site PROPORTION Laboratory Duplicate SOURCE OF VARIATION P (ppm) Pb (ppm) Si (ppm) Sr (ppm) Ti (ppm) V (ppm) Zn (ppm) Sample Site Laboratory Duplicate TOTAL VARIATION PROPORTION Site PROPORTION Laboratory Duplicate Statistical Report by Pacific Analytics, L.L.C. 20
22 VII. REGRESSIONS All regressions were run with natural log-transformed elemental concentrations and natural log-transformed Distance from mine measurements. Transformations were necessary to stabilize the variance. The need for transformation was determined through visual inspection of the residual graphs from the regression analyses. Potential outliers (i.e., lichen tissue samples) were assessed; however, no outliers were severe enough to affect any of the regression analyses. Consequently, all samples above the MDL were included in the analyses. Results from regression analyses are reported for each species by element. Statistically significant terms in the models were those coefficients with p- values = All regression coefficients with p-values between 0.05 and 0.10 were indicative of suggestive evidence. The intercept and slope are reported for each regression analysis with associated standard errors. The p-values are reported for the distance coefficient in the regression analysis. The tables also include the R-Squared value for the regressions. The R-Squared value is a measure of how well the model fit the data and is generally interpreted as the amount of variation in the data explained by the model. Software used for all regression analyses was S-Plus version 2000 (MathSoft 1999). Statistical Report by Pacific Analytics, L.L.C. 21
23 Table D2. Results from regression analyses of the effects of distance on elemental concentrations in Evernia mesomorpha on the Firebag transect. Results are reported by element. The intercept and slope are also reported for the model, with associated standard errors (SE). The p-values for the Distance coefficient and regression R-Squared values are reported. Element Intercept SE Distance SE T- statistic P-Value R- Squared N S Al B Ba Ca Cr Cu Fe K Mg Mo Mn Na Ni P Si Sr Ti V Zn Hg Statistical Report by Pacific Analytics, L.L.C. 22
24 Table D3. Results from regression analyses of the effects of distance on elemental concentrations in Evernia mesomorpha on the Muskeg a and b transects. Results are reported by element. The intercept and slope are also reported for the model, with associated standard errors (SE). The p-values for the Distance coefficient and regression R-Squared values are reported. Element Intercept SE Distance SE T- statistic P-Value R- Squared N S Al B Ba Ca Cr Cu Fe K Li Mg Mo Mn Na Ni P Si Sr Ti V Zn Hg Statistical Report by Pacific Analytics, L.L.C. 23
25 Table D4. Results from regression analyses of the effects of distance on elemental concentrations in on the Firebag transect. Results are reported by element. The intercept and slope are also reported for the model, with associated standard errors (SE). The p-values for the Distance coefficient and regression R-Squared values are reported. Element Intercept SE Distance SE T- statistic P-Value R- Squared N S Al B Ba Ca Cd Cr Cu Fe K Mg Mo Mn Na Ni P Pb Si Sr Ti V Zn Hg Statistical Report by Pacific Analytics, L.L.C. 24
26 Table D5. Results from regression analyses of the effects of distance on elemental concentrations in on the Muskeg a and b transects. Results are reported by element. The intercept and slope are also reported for the model, with associated standard errors (SE). The p-values for the Distance coefficient and regression R-Squared values are reported. Element Intercept SE Distance SE T- statistic P-Value R- Squared N S Al B Ba Be Ca Cd Cr Cu Fe K Li Mg Mo Mn Na Ni P Pb Si Sr Ti V Zn Hg Statistical Report by Pacific Analytics, L.L.C. 25
27 Scatter plots Graphs show the variation of element concentrations in tissue samples of the three lichen species with distance from the mines. Sites with field duplicate lichen samples are shown as the average value for the two samples. Linear lines are drawn in the graphs to show correlations of element concentrations with distance from the mines by species. Lichen samples are symbol and color coded by species: and Evernia mesomorpha. Values for the element concentrations and distance are shown on the natural log-scale. The interpretation of the Distance coefficients are provided below the graphs in which the slope was significantly different from zero and where the R-Squared value was greater than Statistical Report by Pacific Analytics, L.L.C. 26
28 natural log N (%) -0.4 Evernia mesomorpha R-Squared = R-Squared = Figure G1. Total percent nitrogen (dry weight) in relation to distance (m) from the mines along the Firebag Transect for and Evernia mesomorpha samples. Statistical Report by Pacific Analytics, L.L.C. 27
29 natural log N (%) Evernia mesomorpha R-Squared = R-Squared = Figure G2. Total percent nitrogen (dry weight) in relation to distance (m) from the mines along the Muskeg a and b Transects for and Evernia mesomorpha samples. Statistical Report by Pacific Analytics, L.L.C. 28
30 natural log S (%) -2.8 Evernia mesomorpha R-Squared = R-Squared = Figure G3. Total percent sulfur (dry weight) in relation to distance (m) from the mines along the Firebag Transect for and Evernia mesomorpha samples. Statistical Report by Pacific Analytics, L.L.C. 29
31 natural log S (%) Evernia mesomorpha R-Squared = R-Squared = Figure G4. Total percent sulfur (dry weight) in relation to distance (m) from the mines along the Muskeg a and b Transects for and Evernia mesomorpha samples. Statistical Report by Pacific Analytics, L.L.C. 30
32 natural log Al (ppm) Evernia mesomorpha R-Squared = R-Squared = Figure G5. Total Aluminum (ppm) in relation to distance (m) from the mines along the Firebag Transect for and Evernia mesomorpha samples. For E. mesomorpha, as the distance from the mine doubles the concentration of Al decreases by about 14%. For H. physodes, as the distance from the mine doubles the concentration of Al decreases by 13%. For both lichen species, the concentration of Al is much higher within 500 m of the mines. Statistical Report by Pacific Analytics, L.L.C. 31
33 natural log Al (ppm) 7 Evernia mesomorpha R-Squared = R-Squared = Figure G6. Total Aluminum (ppm) in relation to distance (m) from the mines along the Muskeg a and b Transects for and Evernia mesomorpha samples. For H. physodes, as the distance from the mine doubles the concentration of Al decreases by 12%. For both lichen species, the concentration of Al is much higher within 100 m of the mines. Statistical Report by Pacific Analytics, L.L.C. 32
34 natural log B (ppm) Evernia mesomorpha R-Squared = R-Squared < Figure G7. Total Boron (ppm) in relation to distance (m) from the mines along the Firebag Transect for and Evernia mesomorpha samples. Statistical Report by Pacific Analytics, L.L.C. 33
35 2.2 2 natural log B (ppm) Evernia mesomorpha R-Squared = R-Squared = Figure G8. Total Boron (ppm) in relation to distance (m) from the mines along the Muskeg a and b Transects for and Evernia mesomorpha samples. For E. mesomorpha, as the distance from the mine doubles the concentration of B decreases by 11%. For H. physodes, as the distance from the mine doubles the concentration of B decreases by 8%. Statistical Report by Pacific Analytics, L.L.C. 34
36 natural log Ba (ppm) Evernia mesomorpha R-Squared = R-Squared = Figure G9. Total Barium (ppm) in relation to distance (m) from the mines along the Firebag Transect for and Evernia mesomorpha samples. Statistical Report by Pacific Analytics, L.L.C. 35
37 4 3.5 natural log Ba (ppm) Evernia mesomorpha R-Squared = R-Squared = Figure G10. Total Barium (ppm) in relation to distance (m) from the mines along the Muskeg a and b Transects for and Evernia mesomorpha samples. For E. mesomorpha, as the distance from the mine doubles the concentration of Ba decreases by 13%. For both lichen species, the concentration of Ba is much higher within 100 m of the mines. Statistical Report by Pacific Analytics, L.L.C. 36
38 Figure G11. Total Beryllium (ppm) in relation to distance (m) from the mines along the Firebag Transect for and Evernia mesomorpha samples. All samples were below MDL therefore no regression was analyzed. Statistical Report by Pacific Analytics, L.L.C. 37
39 natural log Be (ppm) R-Squared = Figure G12. Total Beryllium (ppm) in relation to distance (m) from the mines along the Muskeg a and b Transects for. All samples of Evernia mesomorpha were below the MDL and no regression was analyzed. For H. physodes, as the distance from the mine doubles the concentration of Be decreases by 12%, and the concentration of Be is much higher within 100 m of the mines. Statistical Report by Pacific Analytics, L.L.C. 38
40 natural log Ca (ppm) Evernia mesomorpha R-Squared = R-Squared = Figure G13. Total Calcium (ppm) in relation to distance (m) from the mines along the Firebag Transect for and Evernia mesomorpha samples. Statistical Report by Pacific Analytics, L.L.C. 39
41 natural log Ca (ppm) Evernia mesomorpha R-Squared = R-Squared = Figure G14. Total Calcium (ppm) in relation to distance (m) from the mines along the Muskeg a and b Transects for and Evernia mesomorpha samples. For E. mesomorpha, as the distance from the mine doubles the concentration of Ca decreases by 24%. Statistical Report by Pacific Analytics, L.L.C. 40
42 natural log Cd (ppm) -1.2 R-Squared = Figure G15. Total Cadmium (ppm) in relation to distance (m) from the mines along the Firebag Transect for. More than 50% of the samples of Evernia mesomorpha had Cd concentrations below the MDL therefore regression was not analyzed. Statistical Report by Pacific Analytics, L.L.C. 41
43 natural log Cd (ppm) R-Squared = Figure G16. Total Cadmium (ppm) in relation to distance (m) from the mines along the Muskeg a and b Transects for. More than 50% of the samples of Evernia mesomorpha had Cd concentrations below the MDL therefore regression was not analyzed. Statistical Report by Pacific Analytics, L.L.C. 42
44 natural log Cr (ppm) Evernia mesomorpha R-Squared = R-Squared = Figure G17. Total Chromium (ppm) in relation to distance (m) from the mines along the Firebag Transect for and Evernia mesomorpha samples. For H. physodes, as the distance from the mine doubles the concentration of Cr decreases by 14%. For both lichen species, the concentration of Al is much higher within 500 m of the mines. Statistical Report by Pacific Analytics, L.L.C. 43
45 natural log Cr (ppm) Evernia mesomorpha R-Squared = R-Squared = Figure G18. Total Chromium (ppm) in relation to distance (m) from the mines along the Muskeg a and b Transects for and Evernia mesomorpha samples. For H. physodes, as the distance from the mine doubles the concentration of Cr decreases by 11%. For both lichen species, the concentration of Al is much higher within 500 m of the mines. Statistical Report by Pacific Analytics, L.L.C. 44
46 natural log Cu (ppm) Evernia mesomorpha R-Squared = R-Squared = Figure G19. Total Copper (ppm) in relation to distance (m) from the mines along the Firebag Transect for and Evernia mesomorpha samples. For E. mesomorpha, as the distance from the mine doubles the concentration of Cu decreases by 8%. For both lichen species, the concentration of Cu is much higher within 500 m of the mines. Statistical Report by Pacific Analytics, L.L.C. 45
47 natural log Cu (ppm) Evernia mesomorpha R-Squared = R-Squared = Figure G20. Total Copper (ppm) in relation to distance (m) from the mines along the Muskeg a and b Transects for and Evernia mesomorpha samples. For H. physodes, as the distance from the mine doubles the concentration of Cu decreases by 8%. Statistical Report by Pacific Analytics, L.L.C. 46
48 natural log Fe (ppm) Evernia mesomorpha R-Squared = R-Squared = Figure G21. Total Iron (ppm) in relation to distance (m) from the mines along the Firebag Transect for and Evernia mesomorpha samples. For E. mesomorpha, as the distance from the mine doubles the concentration of Fe decreases by 20%. For H. physodes, as the distance from the mine doubles the concentration of Fe decreases by 15%. For both lichen species, the concentration of Fe is much higher within 500 m of the mines. Statistical Report by Pacific Analytics, L.L.C. 47
49 natural log Fe (ppm) Evernia mesomorpha R-Squared = R-Squared = Figure G22. Total Iron (ppm) in relation to distance (m) from the mines along the Muskeg a and b Transects for and Evernia mesomorpha samples. For H. physodes, as the distance from the mine doubles the concentration of Fe decreases by 12%. Statistical Report by Pacific Analytics, L.L.C. 48
50 natural log Pb (ppm) R-Squared = Figure G23. Total Lead (ppm) in relation to distance (m) from the mines along the Firebag Transect for. More than 50% of the samples of Evernia mesomorpha had Pb concentrations below the MDL therefore regression was not analyzed. Statistical Report by Pacific Analytics, L.L.C. 49
51 natural log Pb (ppm) R-Squared = Figure G24. Total Lead (ppm) in relation to distance (m) from the mines along the Muskeg a and b Transects for. More than 50% of the samples of Evernia mesomorpha had Pb concentrations below the MDL therefore regression was not analyzed. Statistical Report by Pacific Analytics, L.L.C. 50
52 Figure G25. Total Lithium (ppm) in relation to distance (m) from the mines along the Firebag Transect for and Evernia mesomorpha samples. More than 50% of the samples of both lichens had Li concentrations below the MDL therefore regressions were not analyzed. Statistical Report by Pacific Analytics, L.L.C. 51
53 natural log Li (ppm) Evernia mesomorpha R-Squared = R-Squared = Figure G26. Total Lithium (ppm) in relation to distance (m) from the mines along the Muskeg a and b Transects for and Evernia mesomorpha samples. For H. physodes, as the distance from the mine doubles the concentration of Li decreases by 15%. For E. mesomorpha, the concentration of Li is much higher within 100 m of the mines. Statistical Report by Pacific Analytics, L.L.C. 52
54 natural log Mg (ppm) Evernia mesomorpha R-Squared = R-Squared = Figure G27. Total Magnesium (ppm) in relation to distance (m) from the mines along the Firebag Transect for and Evernia mesomorpha samples. For E. mesomorpha, as the distance from the mine doubles the concentration of Mg decreases by 11%. Statistical Report by Pacific Analytics, L.L.C. 53
55 natural log Mg (ppm) Evernia mesomorpha R-Squared = R-Squared = Figure G28. Total Magnesium (ppm) in relation to distance (m) from the mines along the Muskeg a and b Transects for and Evernia mesomorpha samples. Statistical Report by Pacific Analytics, L.L.C. 54
56 natural log Mn (ppm) Evernia mesomorpha R-Squared = R-Squared = Figure G29. Total Manganese (ppm) in relation to distance (m) from the mines along the Firebag Transect for and Evernia mesomorpha samples. Statistical Report by Pacific Analytics, L.L.C. 55
57 natural log Mn (ppm) Evernia mesomorpha R-Squared = R-Squared = Figure G30. Total Manganese (ppm) in relation to distance (m) from the mines along the Muskeg a and b Transects for and Evernia mesomorpha samples. Statistical Report by Pacific Analytics, L.L.C. 56
58 natural log Hg (ppb) Evernia mesomorpha R-Squared = R-Squared = Figure G31. Total Mercury (ppb) in relation to distance (m) from the mines along the Firebag Transect for and Evernia mesomorpha samples. Statistical Report by Pacific Analytics, L.L.C. 57
59 natural log Hg (ppm) Evernia mesomorpha R-Squared = R-Squared = Figure G32. Total Mercury (ppb) in relation to distance (m) from the mines along the Muskeg a and b Transects for and Evernia mesomorpha samples. Statistical Report by Pacific Analytics, L.L.C. 58
60 natural log Mo (ppm) Evernia mesomorpha R-Squared = R-Squared = Figure G33. Total Molybdenum (ppm) in relation to distance (m) from the mines along the Firebag Transect for and Evernia mesomorpha samples. For E. mesomorpha, as the distance from the mine doubles the concentration of Mo decreases by 12%. For H. physodes, as the distance from the mine doubles the concentration of Mo decreases by 15%. For both lichen species, the concentration of Mo is much higher within 100 m of the mines. Statistical Report by Pacific Analytics, L.L.C. 59
61 natural log Mo (ppm) Evernia mesomorpha R-Squared = R-Squared = Figure G34. Total Molybdenum (ppm) in relation to distance (m) from the mines along the Muskeg a and b Transects for and Evernia mesomorpha samples. Statistical Report by Pacific Analytics, L.L.C. 60
62 natural log Ni (ppm) Evernia mesomorpha R-Squared = R-Squared = Figure G35. Total Nickel (ppm) in relation to distance (m) from the mines along the Firebag Transect for and Evernia mesomorpha samples. Statistical Report by Pacific Analytics, L.L.C. 61
63 natural log Ni (ppm) Evernia mesomorpha R-Squared = R-Squared = Figure G36. Total Nickel (ppm) in relation to distance (m) from the mines along the Muskeg a and b Transects for and Evernia mesomorpha samples. Statistical Report by Pacific Analytics, L.L.C. 62
64 natural log P (ppm) Evernia mesomorpha R-Squared < R-Squared = Figure G37. Total Phosphorous (ppm) in relation to distance (m) from the mines along the Firebag Transect for and Evernia mesomorpha samples. Statistical Report by Pacific Analytics, L.L.C. 63
65 natural log P (ppm) 6.4 Evernia mesomorpha R-Squared = R-Squared = Figure G38. Total Phosphorous (ppm) in relation to distance (m) from the mines along the Muskeg a and b Transects for and Evernia mesomorpha samples. Statistical Report by Pacific Analytics, L.L.C. 64
66 natural log K (ppm) Evernia mesomorpha R-Squared = R-Squared = Figure G39. Total Potassium (ppm) in relation to distance (m) from the mines along the Firebag Transect for and Evernia mesomorpha samples. Statistical Report by Pacific Analytics, L.L.C. 65
67 natural log K (ppm) Evernia mesomorpha R-Squared = R-Squared = Figure G40. Total Potassium (ppm) in relation to distance (m) from the mines along the Muskeg a and b Transects for and Evernia mesomorpha samples. Statistical Report by Pacific Analytics, L.L.C. 66
68 natural log Si (ppm) Evernia mesomorpha R-Squared = R-Squared = Figure G41. Total Silicon (ppm) in relation to distance (m) from the mines along the Firebag Transect for and Evernia mesomorpha samples. For both lichen species, the concentration of Si is much higher within 500 m of the mines. Statistical Report by Pacific Analytics, L.L.C. 67
69 natural log Si (ppm) Evernia mesomorpha R-Squared = R-Squared = Figure G42. Total Silicon (ppm) in relation to distance (m) from the mines along the Muskeg a and b Transects for and Evernia mesomorpha samples. For E. mesomorpha, as the distance from the mine doubles the concentration of Si decreases by 6%. For H. physodes, as the distance from the mine doubles the concentration of Si decreases by 8%. For both lichen species, the concentration of Si is much higher within 100 m of the mines. Statistical Report by Pacific Analytics, L.L.C. 68
REGRESSION ANALYSIS OF LICHEN DATA FROM THE ATHABASCA OIL SANDS REGION
REGRESSION ANALYSIS OF LICHEN DATA FROM THE ATHABASCA OIL SANDS REGION STATISTICAL REPORT Prepared for Shanti Berryman Woods Buffalo Environmental Association Moab, Utah May 2003 by Pacific Analytics PO
5.4 The Poisson Distribution.
The worst thing you can do about a situation is nothing. Sr. O Shea Jackson 5.4 The Poisson Distribution. Description of the Poisson Distribution Discrete probability distribution. The random variable
the total number of electrons passing through the lamp.
1. A 12 V 36 W lamp is lit to normal brightness using a 12 V car battery of negligible internal resistance. The lamp is switched on for one hour (3600 s). For the time of 1 hour, calculate (i) the energy
Statistics 104: Quantitative Methods for Economics Formula and Theorem Review
Harvard College Statistics 104: Quantitative Methods for Economics Formula and Theorem Review Tommy MacWilliam, 13 tmacwilliam@college.harvard.edu March 10, 2011 Contents 1 Introduction to Data 5 1.1 Sample
Si + Al Mg Fe + Mn +Ni Ca rim Ca p.f.u
.6.5. y = -.4x +.8 R =.9574 y = - x +.14 R =.9788 y = -.4 x +.7 R =.9896 Si + Al Fe + Mn +Ni y =.55 x.36 R =.9988.149.148.147.146.145..88 core rim.144 4 =.6 ±.6 4 =.6 ±.18.84.88 p.f.u..86.76 y = -3.9 x
Αξιολόγηση των Φασματικού Διαχωρισμού στην Διάκριση Διαφορετικών Τύπων Εδάφους ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ. Σπίγγος Γεώργιος
ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ ΤΜΗΜΑ ΑΓΡΟΝΟΜΩΝ ΤΟΠΟΓΡΑΦΩΝ ΜΗΧΑΝΙΚΩΝ ΤΟΜΕΑΣ ΤΟΠΟΓΡΑΦΙΑΣ-ΕΡΓΑΣΤΗΡΙΟ ΤΗΛΕΠΙΣΚΟΠΗΣΗΣ Αξιολόγηση των Φασματικού Διαχωρισμού στην Διάκριση Διαφορετικών Τύπων Εδάφους ΔΙΠΛΩΜΑΤΙΚΗ
DOUGLAS FIR BEETLE TRAP-SUPPRESSION STUDY STATISTICAL REPORT
DOUGLAS FIR BEETLE TRAP-SUPPRESSION STUDY STATISTICAL REPORT Prepared for Dr. Robert Progar U.S. Forest Service Forest Sciences Laboratory Corvallis, Oregon January 2005 By Greg Brenner Pacific Analytics
Queensland University of Technology Transport Data Analysis and Modeling Methodologies
Queensland University of Technology Transport Data Analysis and Modeling Methodologies Lab Session #7 Example 5.2 (with 3SLS Extensions) Seemingly Unrelated Regression Estimation and 3SLS A survey of 206
ΑΚΑ ΗΜΙΑ ΕΜΠΟΡΙΚΟΥ ΝΑΥΤΙΚΟΥ ΜΑΚΕ ΟΝΙΑΣ ΣΧΟΛΗ ΜΗΧΑΝΙΚΩΝ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΟΝΟΜΑΤΕΠΩΝΥΜΟ: ΓΕΩΡΓΙΟΣ ΙΩΑΝΝΟΥ Α.Μ.: 4674 ΟΝΟΜΑΤΕΠΩΝΥΜΟ ΚΑΘΗΓΗΤΡΙΑΣ: ρ.ελευθερια ΜΠΑΚΟΓΙΑΝΝΗ ΘΕΜΑ: ΟΙ ΕΠΙΠΤΩΣΕΙΣ ΤΗΣ ΠΑΡΟΥΣΙΑΣ ΧΗΜΙΚΩΝ
Επιδημιολογική μελέτη για την εκτίμηση των επιπτώσεων έκθεσης παιδιών σε υψηλές συγκεντρώσεις βαρέων μετάλλων
Επιδημιολογική μελέτη για την εκτίμηση των επιπτώσεων έκθεσης παιδιών σε υψηλές συγκεντρώσεις βαρέων μετάλλων Επιστημονικό Εγχειρίδιο Επιδημιολογικής Εκτίμησης Θεμελίωση οριακών τιμών βαρέων μετάλλων και
ΠΟΛΥΤΕΧΝΕΙΟ ΚΡΗΤΗΣ ΣΧΟΛΗ ΜΗΧΑΝΙΚΩΝ ΠΕΡΙΒΑΛΛΟΝΤΟΣ
ΠΟΛΥΤΕΧΝΕΙΟ ΚΡΗΤΗΣ ΣΧΟΛΗ ΜΗΧΑΝΙΚΩΝ ΠΕΡΙΒΑΛΛΟΝΤΟΣ Τομέας Περιβαλλοντικής Υδραυλικής και Γεωπεριβαλλοντικής Μηχανικής (III) Εργαστήριο Γεωπεριβαλλοντικής Μηχανικής TECHNICAL UNIVERSITY OF CRETE SCHOOL of
HOMEWORK 4 = G. In order to plot the stress versus the stretch we define a normalized stretch:
HOMEWORK 4 Problem a For the fast loading case, we want to derive the relationship between P zz and λ z. We know that the nominal stress is expressed as: P zz = ψ λ z where λ z = λ λ z. Therefore, applying
Math 6 SL Probability Distributions Practice Test Mark Scheme
Math 6 SL Probability Distributions Practice Test Mark Scheme. (a) Note: Award A for vertical line to right of mean, A for shading to right of their vertical line. AA N (b) evidence of recognizing symmetry
[1] P Q. Fig. 3.1
![[1] P Q. Fig. 3.1](/thumbs/79/80362156.jpg "[1] P Q. Fig. 3.1")
1 (a) Define resistance....... [1] (b) The smallest conductor within a computer processing chip can be represented as a rectangular block that is one atom high, four atoms wide and twenty atoms long. One
ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 19/5/2007
Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Αν κάπου κάνετε κάποιες υποθέσεις να αναφερθούν στη σχετική ερώτηση. Όλα τα αρχεία που αναφέρονται στα προβλήματα βρίσκονται στον ίδιο φάκελο με το εκτελέσιμο
ANALYSIS REPORT CONTACT: Ann Eastman
DATE of Analysis: 5 March 23 BC RESEARCH INC DATE of Report: 7 March 23 365 Westbrook Mall PROJECT No.: 8-3-124 Vancouver, B.C. APPROVED BY: Anna Becalska TEL: (64) 224-4331 FAX: (64) 224-54 Advanced Nutrients
519.22(07.07) 78 : ( ) /.. ; c (07.07) , , 2008
.. ( ) 2008 519.22(07.07) 78 : ( ) /.. ;. : -, 2008. 38 c. ( ) STATISTICA.,. STATISTICA.,. 519.22(07.07),.., 2008.., 2008., 2008 2 ... 4 1...5...5 2...14...14 3...27...27 3 ,, -. " ", :,,,... STATISTICA.,,,.
Mean bond enthalpy Standard enthalpy of formation Bond N H N N N N H O O O
Q1. (a) Explain the meaning of the terms mean bond enthalpy and standard enthalpy of formation. Mean bond enthalpy... Standard enthalpy of formation... (5) (b) Some mean bond enthalpies are given below.
Bayesian statistics. DS GA 1002 Probability and Statistics for Data Science.
Bayesian statistics DS GA 1002 Probability and Statistics for Data Science http://www.cims.nyu.edu/~cfgranda/pages/dsga1002_fall17 Carlos Fernandez-Granda Frequentist vs Bayesian statistics In frequentist
Strain gauge and rosettes
Strain gauge and rosettes Introduction A strain gauge is a device which is used to measure strain (deformation) on an object subjected to forces. Strain can be measured using various types of devices classified
Approximation of distance between locations on earth given by latitude and longitude
Approximation of distance between locations on earth given by latitude and longitude Jan Behrens 2012-12-31 In this paper we shall provide a method to approximate distances between two points on earth
CHAPTER 25 SOLVING EQUATIONS BY ITERATIVE METHODS
CHAPTER 5 SOLVING EQUATIONS BY ITERATIVE METHODS EXERCISE 104 Page 8 1. Find the positive root of the equation x + 3x 5 = 0, correct to 3 significant figures, using the method of bisection. Let f(x) =
ΕΙΣΑΓΩΓΗ ΣΤΗ ΣΤΑΤΙΣΤΙΚΗ ΑΝΑΛΥΣΗ
ΕΙΣΑΓΩΓΗ ΣΤΗ ΣΤΑΤΙΣΤΙΚΗ ΑΝΑΛΥΣΗ ΕΛΕΝΑ ΦΛΟΚΑ Επίκουρος Καθηγήτρια Τµήµα Φυσικής, Τοµέας Φυσικής Περιβάλλοντος- Μετεωρολογίας ΓΕΝΙΚΟΙ ΟΡΙΣΜΟΙ Πληθυσµός Σύνολο ατόµων ή αντικειµένων στα οποία αναφέρονται
ΤΜΗΜΑ ΦΥΣΙΚΩΝ ΠΟΡΩΝ & ΠΕΡΙΒΑΛΛΟΝΤΟΣ
ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙ ΕΥΤΙΚΟ Ι ΡΥΜΑ ΚΡΗΤΗΣ ΠΑΡΑΡΤΗΜΑ ΧΑΝΙΩΝ ΤΜΗΜΑ ΦΥΣΙΚΩΝ ΠΟΡΩΝ & ΠΕΡΙΒΑΛΛΟΝΤΟΣ ΤΟΜΕΑΣ ΠΕΡΙΒΑΛΛΟΝΤΙΚΗΣ ΤΕΧΝΟΛΟΓΙΑΣ ΕΡΓΑΣΤΗΡΙΟ ΠΕΡΙΒΑΛΛΟΝΤΙΚΗΣ ΧΗΜΕΙΑΣ & ΒΙΟΧΗΜΙΚΩΝ ΙΕΡΓΑΣΙΩΝ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ
Nuclear Physics 5. Name: Date: 8 (1)
Name: Date: Nuclear Physics 5. A sample of radioactive carbon-4 decays into a stable isotope of nitrogen. As the carbon-4 decays, the rate at which the amount of nitrogen is produced A. decreases linearly
«ΑΓΡΟΤΟΥΡΙΣΜΟΣ ΚΑΙ ΤΟΠΙΚΗ ΑΝΑΠΤΥΞΗ: Ο ΡΟΛΟΣ ΤΩΝ ΝΕΩΝ ΤΕΧΝΟΛΟΓΙΩΝ ΣΤΗΝ ΠΡΟΩΘΗΣΗ ΤΩΝ ΓΥΝΑΙΚΕΙΩΝ ΣΥΝΕΤΑΙΡΙΣΜΩΝ»
I ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΣΧΟΛΗ ΝΟΜΙΚΩΝ ΟΙΚΟΝΟΜΙΚΩΝ ΚΑΙ ΠΟΛΙΤΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΤΜΗΜΑ ΟΙΚΟΝΟΜΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΣΤΗΝ «ΔΙΟΙΚΗΣΗ ΚΑΙ ΟΙΚΟΝΟΜΙΑ» ΚΑΤΕΥΘΥΝΣΗ: ΟΙΚΟΝΟΜΙΚΗ
6.3 Forecasting ARMA processes
122 CHAPTER 6. ARMA MODELS 6.3 Forecasting ARMA processes The purpose of forecasting is to predict future values of a TS based on the data collected to the present. In this section we will discuss a linear
FORMULAS FOR STATISTICS 1
FORMULAS FOR STATISTICS 1 X = 1 n Sample statistics X i or x = 1 n x i (sample mean) S 2 = 1 n 1 s 2 = 1 n 1 (X i X) 2 = 1 n 1 (x i x) 2 = 1 n 1 Xi 2 n n 1 X 2 x 2 i n n 1 x 2 or (sample variance) E(X)
4.6 Autoregressive Moving Average Model ARMA(1,1)
84 CHAPTER 4. STATIONARY TS MODELS 4.6 Autoregressive Moving Average Model ARMA(,) This section is an introduction to a wide class of models ARMA(p,q) which we will consider in more detail later in this
Μηχανική Μάθηση Hypothesis Testing
ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ Μηχανική Μάθηση Hypothesis Testing Γιώργος Μπορμπουδάκης Τμήμα Επιστήμης Υπολογιστών Procedure 1. Form the null (H 0 ) and alternative (H 1 ) hypothesis 2. Consider
HISTOGRAMS AND PERCENTILES What is the 25 th percentile of a histogram? What is the 50 th percentile for the cigarette histogram?
HISTOGRAMS AND PERCENTILES What is the 25 th percentile of a histogram? The point on the horizontal axis such that of the area under the histogram lies to the left of that point (and to the right) What
Εργαστήριο Ανάπτυξης Εφαρμογών Βάσεων Δεδομένων. Εξάμηνο 7 ο
Εργαστήριο Ανάπτυξης Εφαρμογών Βάσεων Δεδομένων Εξάμηνο 7 ο Procedures and Functions Stored procedures and functions are named blocks of code that enable you to group and organize a series of SQL and PL/SQL
ΑΚΑ ΗΜΙΑ ΕΜΠΟΡΙΚΟΥ ΝΑΥΤΙΚΟΥ ΜΑΚΕ ΟΝΙΑΣ ΣΧΟΛΗ ΜΗΧΑΝΙΚΩΝ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΘΕΜΑ : ΧΗΜΙΚΑ ΠΡΟΣΘΕΤΑ ΠΟΥ ΠΡΟΟΡΙΖΟΝΤΑΙ ΓΙΑ ΤΟ ΝΕΡΟ ΤΟΥ ΑΤΜΟΛΕΒΗΤΑ
ΑΚΑ ΗΜΙΑ ΕΜΠΟΡΙΚΟΥ ΝΑΥΤΙΚΟΥ ΜΑΚΕ ΟΝΙΑΣ ΣΧΟΛΗ ΜΗΧΑΝΙΚΩΝ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΘΕΜΑ : ΧΗΜΙΚΑ ΠΡΟΣΘΕΤΑ ΠΟΥ ΠΡΟΟΡΙΖΟΝΤΑΙ ΓΙΑ ΤΟ ΝΕΡΟ ΤΟΥ ΑΤΜΟΛΕΒΗΤΑ ΣΠΟΥ ΑΣΤΗΣ : ΑΓΟΡΑΣΤΟΣ ΧΡΥΣΟΒΑΛΑΝΤΗΣ ΕΠΙΒΛΕΠΟΥΣΑ ΚΑΘΗΓΗΤΡΙΑ :
Correction Table for an Alcoholometer Calibrated at 20 o C
An alcoholometer is a device that measures the concentration of ethanol in a water-ethanol mixture (often in units of %abv percent alcohol by volume). The depth to which an alcoholometer sinks in a water-ethanol
Other Test Constructions: Likelihood Ratio & Bayes Tests
Other Test Constructions: Likelihood Ratio & Bayes Tests Side-Note: So far we have seen a few approaches for creating tests such as Neyman-Pearson Lemma ( most powerful tests of H 0 : θ = θ 0 vs H 1 :
Biostatistics for Health Sciences Review Sheet
Biostatistics for Health Sciences Review Sheet http://mathvault.ca June 1, 2017 Contents 1 Descriptive Statistics 2 1.1 Variables.............................................. 2 1.1.1 Qualitative........................................
EPL 603 TOPICS IN SOFTWARE ENGINEERING. Lab 5: Component Adaptation Environment (COPE)
EPL 603 TOPICS IN SOFTWARE ENGINEERING Lab 5: Component Adaptation Environment (COPE) Performing Static Analysis 1 Class Name: The fully qualified name of the specific class Type: The type of the class
Capacitors - Capacitance, Charge and Potential Difference
Capacitors - Capacitance, Charge and Potential Difference Capacitors store electric charge. This ability to store electric charge is known as capacitance. A simple capacitor consists of 2 parallel metal
Repeated measures Επαναληπτικές μετρήσεις
ΠΡΟΒΛΗΜΑ Στο αρχείο δεδομένων diavitis.sav καταγράφεται η ποσότητα γλυκόζης στο αίμα 10 ασθενών στην αρχή της χορήγησης μιας θεραπείας, μετά από ένα μήνα και μετά από δύο μήνες. Μελετήστε την επίδραση
«ΑΝΑΠΣΤΞΖ ΓΠ ΚΑΗ ΥΩΡΗΚΖ ΑΝΑΛΤΖ ΜΔΣΔΩΡΟΛΟΓΗΚΩΝ ΓΔΓΟΜΔΝΩΝ ΣΟΝ ΔΛΛΑΓΗΚΟ ΥΩΡΟ»
ΓΔΩΠΟΝΗΚΟ ΠΑΝΔΠΗΣΖΜΗΟ ΑΘΖΝΩΝ ΣΜΗΜΑ ΑΞΙΟΠΟΙΗΗ ΦΤΙΚΩΝ ΠΟΡΩΝ & ΓΕΩΡΓΙΚΗ ΜΗΥΑΝΙΚΗ ΣΟΜΕΑ ΕΔΑΦΟΛΟΓΙΑ ΚΑΙ ΓΕΩΡΓΙΚΗ ΥΗΜΕΙΑ ΕΙΔΙΚΕΤΗ: ΕΦΑΡΜΟΓΕ ΣΗ ΓΕΩΠΛΗΡΟΦΟΡΙΚΗ ΣΟΤ ΦΤΙΚΟΤ ΠΟΡΟΤ «ΑΝΑΠΣΤΞΖ ΓΠ ΚΑΗ ΥΩΡΗΚΖ ΑΝΑΛΤΖ ΜΔΣΔΩΡΟΛΟΓΗΚΩΝ
Statistical Inference I Locally most powerful tests
Statistical Inference I Locally most powerful tests Shirsendu Mukherjee Department of Statistics, Asutosh College, Kolkata, India. shirsendu st@yahoo.co.in So far we have treated the testing of one-sided
Inverse trigonometric functions & General Solution of Trigonometric Equations. ------------------ ----------------------------- -----------------
Inverse trigonometric functions & General Solution of Trigonometric Equations. 1. Sin ( ) = a) b) c) d) Ans b. Solution : Method 1. Ans a: 17 > 1 a) is rejected. w.k.t Sin ( sin ) = d is rejected. If sin
Phys460.nb Solution for the t-dependent Schrodinger s equation How did we find the solution? (not required)
Phys460.nb 81 ψ n (t) is still the (same) eigenstate of H But for tdependent H. The answer is NO. 5.5.5. Solution for the tdependent Schrodinger s equation If we assume that at time t 0, the electron starts
Section 8.3 Trigonometric Equations
99 Section 8. Trigonometric Equations Objective 1: Solve Equations Involving One Trigonometric Function. In this section and the next, we will exple how to solving equations involving trigonometric functions.
Potential Dividers. 46 minutes. 46 marks. Page 1 of 11
Potential Dividers 46 minutes 46 marks Page 1 of 11 Q1. In the circuit shown in the figure below, the battery, of negligible internal resistance, has an emf of 30 V. The pd across the lamp is 6.0 V and
Summary of the model specified
Program: HLM 7 Hierarchical Linear and Nonlinear Modeling Authors: Stephen Raudenbush, Tony Bryk, & Richard Congdon Publisher: Scientific Software International, Inc. (c) 2010 techsupport@ssicentral.com
EE512: Error Control Coding
EE512: Error Control Coding Solution for Assignment on Finite Fields February 16, 2007 1. (a) Addition and Multiplication tables for GF (5) and GF (7) are shown in Tables 1 and 2. + 0 1 2 3 4 0 0 1 2 3
ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ
ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΨΥΧΟΛΟΓΙΚΕΣ ΕΠΙΠΤΩΣΕΙΣ ΣΕ ΓΥΝΑΙΚΕΣ ΜΕΤΑ ΑΠΟ ΜΑΣΤΕΚΤΟΜΗ ΓΕΩΡΓΙΑ ΤΡΙΣΟΚΚΑ Λευκωσία 2012 ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ
SUPPLEMENTAL INFORMATION. Fully Automated Total Metals and Chromium Speciation Single Platform Introduction System for ICP-MS
Electronic Supplementary Material (ESI) for Journal of Analytical Atomic Spectrometry. This journal is The Royal Society of Chemistry 2018 SUPPLEMENTAL INFORMATION Fully Automated Total Metals and Chromium
Instruction Execution Times
1 C Execution Times InThisAppendix... Introduction DL330 Execution Times DL330P Execution Times DL340 Execution Times C-2 Execution Times Introduction Data Registers This appendix contains several tables
Figure 1 T / K Explain, in terms of molecules, why the first part of the graph in Figure 1 is a line that slopes up from the origin.
Q1.(a) Figure 1 shows how the entropy of a molecular substance X varies with temperature. Figure 1 T / K (i) Explain, in terms of molecules, why the entropy is zero when the temperature is zero Kelvin.
PENGARUHKEPEMIMPINANINSTRUKSIONAL KEPALASEKOLAHDAN MOTIVASI BERPRESTASI GURU TERHADAP KINERJA MENGAJAR GURU SD NEGERI DI KOTA SUKABUMI
155 Lampiran 6 Yayan Sumaryana, 2014 PENGARUHKEPEMIMPINANINSTRUKSIONAL KEPALASEKOLAHDAN MOTIVASI BERPRESTASI GURU TERHADAP KINERJA MENGAJAR GURU SD NEGERI DI KOTA SUKABUMI Universitas Pendidikan Indonesia
2 Composition. Invertible Mappings
Arkansas Tech University MATH 4033: Elementary Modern Algebra Dr. Marcel B. Finan Composition. Invertible Mappings In this section we discuss two procedures for creating new mappings from old ones, namely,
Solution Series 9. i=1 x i and i=1 x i.
Lecturer: Prof. Dr. Mete SONER Coordinator: Yilin WANG Solution Series 9 Q1. Let α, β >, the p.d.f. of a beta distribution with parameters α and β is { Γ(α+β) Γ(α)Γ(β) f(x α, β) xα 1 (1 x) β 1 for < x
ST5224: Advanced Statistical Theory II
ST5224: Advanced Statistical Theory II 2014/2015: Semester II Tutorial 7 1. Let X be a sample from a population P and consider testing hypotheses H 0 : P = P 0 versus H 1 : P = P 1, where P j is a known
Code Breaker. TEACHER s NOTES
TEACHER s NOTES Time: 50 minutes Learning Outcomes: To relate the genetic code to the assembly of proteins To summarize factors that lead to different types of mutations To distinguish among positive,
ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙ ΕΥΤΙΚΟ Ι ΡΥΜΑ ΚΡΗΤΗΣ ΤΜΗΜΑ ΦΥΣΙΚΩΝ ΠΟΡΩΝ & ΠΕΡΙΒΑΛΛΟΝΤΟΣ ΤΟΜΕΑΣ ΠΕΡΙΒΑΛΛΟΝΤΙΚΗΣ ΤΕΧΝΟΛΟΓΙΑΣ ΕΡΓΑΣΤΗΡΙΟ ΕΛΕΓΧΟΥ ΠΟΙΟΤΗΤΑΣ Υ ΑΤΙΚΩΝ & Ε ΑΦΙΚΩΝ ΠΟΡΩΝ ΕΠΙΒΑΡΥΝΣΗ ΜΕ ΒΑΡΕΑ ΜΕΤΑΛΛΑ Ε ΑΦΩΝ ΤΗΣ
Aquinas College. Edexcel Mathematical formulae and statistics tables DO NOT WRITE ON THIS BOOKLET
Aquinas College Edexcel Mathematical formulae and statistics tables DO NOT WRITE ON THIS BOOKLET Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Mathematics and Further Mathematics Mathematical
ΠΑΝΔΠΗΣΖΜΗΟ ΠΑΣΡΩΝ ΣΜΖΜΑ ΖΛΔΚΣΡΟΛΟΓΩΝ ΜΖΥΑΝΗΚΩΝ ΚΑΗ ΣΔΥΝΟΛΟΓΗΑ ΤΠΟΛΟΓΗΣΩΝ ΣΟΜΔΑ ΤΣΖΜΑΣΩΝ ΖΛΔΚΣΡΗΚΖ ΔΝΔΡΓΔΗΑ
ΠΑΝΔΠΗΣΖΜΗΟ ΠΑΣΡΩΝ ΣΜΖΜΑ ΖΛΔΚΣΡΟΛΟΓΩΝ ΜΖΥΑΝΗΚΩΝ ΚΑΗ ΣΔΥΝΟΛΟΓΗΑ ΤΠΟΛΟΓΗΣΩΝ ΣΟΜΔΑ ΤΣΖΜΑΣΩΝ ΖΛΔΚΣΡΗΚΖ ΔΝΔΡΓΔΗΑ Γηπισκαηηθή Δξγαζία ηνπ Φνηηεηή ηνπ ηκήκαηνο Ζιεθηξνιόγσλ Μεραληθώλ θαη Σερλνινγίαο Ζιεθηξνληθώλ
Assalamu `alaikum wr. wb.
LUMP SUM Assalamu `alaikum wr. wb. LUMP SUM Wassalamu alaikum wr. wb. Assalamu `alaikum wr. wb. LUMP SUM Wassalamu alaikum wr. wb. LUMP SUM Lump sum lump sum lump sum. lump sum fixed price lump sum lump
Conductivity Logging for Thermal Spring Well
/.,**. 25 +,1- **-- 0/2,,,1- **-- 0/2, +,, +/., +0 /,* Conductivity Logging for Thermal Spring Well Koji SATO +, Tadashi TAKAYA,, Tadashi CHIBA, + Nihon Chika Kenkyuusho Co. Ltd., 0/2,, Hongo, Funabashi,
ΕΚΤΙΜΗΣΗ ΤΟΥ ΚΟΣΤΟΥΣ ΤΩΝ ΟΔΙΚΩΝ ΑΤΥΧΗΜΑΤΩΝ ΚΑΙ ΔΙΕΡΕΥΝΗΣΗ ΤΩΝ ΠΑΡΑΓΟΝΤΩΝ ΕΠΙΡΡΟΗΣ ΤΟΥ
ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΠΟΛΥΤΕΧΝΙΚΗ ΣΧΟΛΗ ΤΜΗΜΑ ΠΟΛΙΤΙΚΩΝ ΜΗΧΑΝΙΚΩΝ ΕΚΤΙΜΗΣΗ ΤΟΥ ΚΟΣΤΟΥΣ ΤΩΝ ΟΔΙΚΩΝ ΑΤΥΧΗΜΑΤΩΝ ΚΑΙ ΔΙΕΡΕΥΝΗΣΗ ΤΩΝ ΠΑΡΑΓΟΝΤΩΝ ΕΠΙΡΡΟΗΣ ΤΟΥ ΔΙΑΤΡΙΒΗ ΔΙΠΛΩΜΑΤΟΣ ΕΙΔΙΚΕΥΣΗΣ ΔΗΜΗΤΡΙΟΥ Ν. ΠΙΤΕΡΟΥ
(1) Describe the process by which mercury atoms become excited in a fluorescent tube (3)
Q1. (a) A fluorescent tube is filled with mercury vapour at low pressure. In order to emit electromagnetic radiation the mercury atoms must first be excited. (i) What is meant by an excited atom? (1) (ii)
Λιμνοποτάμιο Περιβάλλον και Οργανισμοί
ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΑΝΟΙΧΤΑ ΑΚΑΔΗΜΑΙΚΑ ΜΑΘΗΜΑΤΑ Λιμνοποτάμιο Περιβάλλον και Οργανισμοί Ενότητα 14: Επίδραση ρύπανσης στα ψάρια Επίκ. Καθηγήτρια Δήμητρα Μπόμπορη Άδειες Χρήσης Το παρόν
ΚΥΠΡΙΑΚΟΣ ΣΥΝΔΕΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY 21 ος ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ Δεύτερος Γύρος - 30 Μαρτίου 2011
Διάρκεια Διαγωνισμού: 3 ώρες Απαντήστε όλες τις ερωτήσεις Μέγιστο Βάρος (20 Μονάδες) Δίνεται ένα σύνολο από N σφαιρίδια τα οποία δεν έχουν όλα το ίδιο βάρος μεταξύ τους και ένα κουτί που αντέχει μέχρι
3.4 SUM AND DIFFERENCE FORMULAS. NOTE: cos(α+β) cos α + cos β cos(α-β) cos α -cos β
3.4 SUM AND DIFFERENCE FORMULAS Page Theorem cos(αβ cos α cos β -sin α cos(α-β cos α cos β sin α NOTE: cos(αβ cos α cos β cos(α-β cos α -cos β Proof of cos(α-β cos α cos β sin α Let s use a unit circle
«Χρήσεις γης, αξίες γης και κυκλοφοριακές ρυθμίσεις στο Δήμο Χαλκιδέων. Η μεταξύ τους σχέση και εξέλιξη.»
ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ ΣΧΟΛΗ ΑΓΡΟΝΟΜΩΝ ΚΑΙ ΤΟΠΟΓΡΑΦΩΝ ΜΗΧΑΝΙΚΩΝ ΤΟΜΕΑΣ ΓΕΩΓΡΑΦΙΑΣ ΚΑΙ ΠΕΡΙΦΕΡΕΙΑΚΟΥ ΣΧΕΔΙΑΣΜΟΥ ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ: «Χρήσεις γης, αξίες γης και κυκλοφοριακές ρυθμίσεις στο Δήμο Χαλκιδέων.
TABLES AND FORMULAS FOR MOORE Basic Practice of Statistics
TABLES AND FORMULAS FOR MOORE Basic Practice of Statistics Exploring Data: Distributions Look for overall pattern (shape, center, spread) and deviations (outliers). Mean (use a calculator): x = x 1 + x
ΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ. ΘΕΜΑ: «ιερεύνηση της σχέσης µεταξύ φωνηµικής επίγνωσης και ορθογραφικής δεξιότητας σε παιδιά προσχολικής ηλικίας»
ΠΑΝΕΠΙΣΤΗΜΙΟ ΑΙΓΑΙΟΥ ΣΧΟΛΗ ΑΝΘΡΩΠΙΣΤΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΤΜΗΜΑ ΕΠΙΣΤΗΜΩΝ ΤΗΣ ΠΡΟΣΧΟΛΙΚΗΣ ΑΓΩΓΗΣ ΚΑΙ ΤΟΥ ΕΚΠΑΙ ΕΥΤΙΚΟΥ ΣΧΕ ΙΑΣΜΟΥ «ΠΑΙ ΙΚΟ ΒΙΒΛΙΟ ΚΑΙ ΠΑΙ ΑΓΩΓΙΚΟ ΥΛΙΚΟ» ΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ που εκπονήθηκε για τη
Lecture 34 Bootstrap confidence intervals
Lecture 34 Bootstrap confidence intervals Confidence Intervals θ: an unknown parameter of interest We want to find limits θ and θ such that Gt = P nˆθ θ t If G 1 1 α is known, then P θ θ = P θ θ = 1 α
Homework 3 Solutions
Homework 3 Solutions Igor Yanovsky (Math 151A TA) Problem 1: Compute the absolute error and relative error in approximations of p by p. (Use calculator!) a) p π, p 22/7; b) p π, p 3.141. Solution: For
APPENDICES APPENDIX A. STATISTICAL TABLES AND CHARTS 651 APPENDIX B. BIBLIOGRAPHY 677 APPENDIX C. ANSWERS TO SELECTED EXERCISES 679
APPENDICES APPENDIX A. STATISTICAL TABLES AND CHARTS 1 Table I Summary of Common Probability Distributions 2 Table II Cumulative Standard Normal Distribution Table III Percentage Points, 2 of the Chi-Squared
Estimation for ARMA Processes with Stable Noise. Matt Calder & Richard A. Davis Colorado State University
Estimation for ARMA Processes with Stable Noise Matt Calder & Richard A. Davis Colorado State University rdavis@stat.colostate.edu 1 ARMA processes with stable noise Review of M-estimation Examples of
Section 9.2 Polar Equations and Graphs
180 Section 9. Polar Equations and Graphs In this section, we will be graphing polar equations on a polar grid. In the first few examples, we will write the polar equation in rectangular form to help identify
Main source: "Discrete-time systems and computer control" by Α. ΣΚΟΔΡΑΣ ΨΗΦΙΑΚΟΣ ΕΛΕΓΧΟΣ ΔΙΑΛΕΞΗ 4 ΔΙΑΦΑΝΕΙΑ 1
Main source: "Discrete-time systems and computer control" by Α. ΣΚΟΔΡΑΣ ΨΗΦΙΑΚΟΣ ΕΛΕΓΧΟΣ ΔΙΑΛΕΞΗ 4 ΔΙΑΦΑΝΕΙΑ 1 A Brief History of Sampling Research 1915 - Edmund Taylor Whittaker (1873-1956) devised a
Second Order RLC Filters
ECEN 60 Circuits/Electronics Spring 007-0-07 P. Mathys Second Order RLC Filters RLC Lowpass Filter A passive RLC lowpass filter (LPF) circuit is shown in the following schematic. R L C v O (t) Using phasor
CHAPTER 48 APPLICATIONS OF MATRICES AND DETERMINANTS
CHAPTER 48 APPLICATIONS OF MATRICES AND DETERMINANTS EXERCISE 01 Page 545 1. Use matrices to solve: 3x + 4y x + 5y + 7 3x + 4y x + 5y 7 Hence, 3 4 x 0 5 y 7 The inverse of 3 4 5 is: 1 5 4 1 5 4 15 8 3
The Simply Typed Lambda Calculus
Type Inference Instead of writing type annotations, can we use an algorithm to infer what the type annotations should be? That depends on the type system. For simple type systems the answer is yes, and
Supplementary figures
A Supplementary figures a) DMT.BG2 0.87 0.87 0.72 20 40 60 80 100 DMT.EG2 0.93 0.85 20 40 60 80 EMT.MG3 0.85 0 20 40 60 80 20 40 60 80 100 20 40 60 80 100 20 40 60 80 EMT.G6 DMT/EMT b) EG2 0.92 0.85 5
ΠΕΡΙΕΧΟΜΕΝΑ. Κεφάλαιο 1: Κεφάλαιο 2: Κεφάλαιο 3:
4 Πρόλογος Η παρούσα διπλωµατική εργασία µε τίτλο «ιερεύνηση χωρικής κατανοµής µετεωρολογικών µεταβλητών. Εφαρµογή στον ελληνικό χώρο», ανατέθηκε από το ιεπιστηµονικό ιατµηµατικό Πρόγραµµα Μεταπτυχιακών
ΜΗΤΡΙΚΟΣ ΘΗΛΑΣΜΟΣ ΚΑΙ ΓΝΩΣΤΙΚΗ ΑΝΑΠΤΥΞΗ ΜΕΧΡΙ ΚΑΙ 10 ΧΡΟΝΩΝ
ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ ΜΗΤΡΙΚΟΣ ΘΗΛΑΣΜΟΣ ΚΑΙ ΓΝΩΣΤΙΚΗ ΑΝΑΠΤΥΞΗ ΜΕΧΡΙ ΚΑΙ 10 ΧΡΟΝΩΝ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ Ονοματεπώνυμο Κεντούλλα Πέτρου Αριθμός Φοιτητικής Ταυτότητας 2008761539 Κύπρος
ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΚΡΗΤΗΣ ΣΧΟΛΗ ΔΙΟΙΚΗΣΗΣ ΚΑΙ ΟΙΚΟΝΟΜΙΑΣ ΤΜΗΜΑ ΛΟΓΙΣΤΙΚΗΣ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ
ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΚΡΗΤΗΣ ΣΧΟΛΗ ΔΙΟΙΚΗΣΗΣ ΚΑΙ ΟΙΚΟΝΟΜΙΑΣ ΤΜΗΜΑ ΛΟΓΙΣΤΙΚΗΣ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΛΟΓΙΣΤΙΚΗ ΚΑΙ ΦΟΡΟΛΟΓΙΑ Ο.Ε. ΕΙΣΗΓΗΤΡΙΑ ΚΑΘΗΓΗΤΡΙΑ: κ. ΟΥΡΑΝΟΥ ΕΡΜΙΟΝΗ ΣΠΟΥΔΑΣΤΡΙΕΣ: ΔΕΜΕΤΖΟΥ ΑΓΛΑΪΑ
χ 2 test ανεξαρτησίας
χ 2 test ανεξαρτησίας Καθηγητής Ι. Κ. ΔΗΜΗΤΡΙΟΥ demetri@econ.uoa.gr 7.2 Το χ 2 Τεστ Ανεξαρτησίας Tο χ 2 τεστ ανεξαρτησίας (όπως και η παλινδρόμηση) είναι στατιστικά εργαλεία για τον εντοπισμό σχέσεων μεταξύ
SCHOOL OF MATHEMATICAL SCIENCES G11LMA Linear Mathematics Examination Solutions
SCHOOL OF MATHEMATICAL SCIENCES GLMA Linear Mathematics 00- Examination Solutions. (a) i. ( + 5i)( i) = (6 + 5) + (5 )i = + i. Real part is, imaginary part is. (b) ii. + 5i i ( + 5i)( + i) = ( i)( + i)
Aluminum Electrolytic Capacitors (Large Can Type)
Aluminum Electrolytic Capacitors (Large Can Type) Snap-In, 85 C TS-U ECE-S (U) Series: TS-U Features General purpose Wide CV value range (33 ~ 47,000 µf/16 4V) Various case sizes Top vent construction
ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΥΓΕΙΑΣ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΕΠΗΡΕΑΖΕΙ ΤΗΝ ΠΡΟΛΗΨΗ ΚΑΡΚΙΝΟΥ ΤΟΥ ΜΑΣΤΟΥ
ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΥΓΕΙΑΣ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΠΩΣ Η ΚΑΤΑΝΑΛΩΣΗ ΦΡΟΥΤΩΝ ΚΑΙ ΛΑΧΑΝΙΚΩΝ ΕΠΗΡΕΑΖΕΙ ΤΗΝ ΠΡΟΛΗΨΗ ΚΑΡΚΙΝΟΥ ΤΟΥ ΜΑΣΤΟΥ Όνομα φοιτήτριας ΚΑΛΑΠΟΔΑ ΜΑΡΚΕΛΛΑ
Solutions to Exercise Sheet 5
Solutions to Eercise Sheet 5 jacques@ucsd.edu. Let X and Y be random variables with joint pdf f(, y) = 3y( + y) where and y. Determine each of the following probabilities. Solutions. a. P (X ). b. P (X
Probability and Random Processes (Part II)
Probability and Random Processes (Part II) 1. If the variance σ x of d(n) = x(n) x(n 1) is one-tenth the variance σ x of a stationary zero-mean discrete-time signal x(n), then the normalized autocorrelation
Problem Set 3: Solutions
CMPSCI 69GG Applied Information Theory Fall 006 Problem Set 3: Solutions. [Cover and Thomas 7.] a Define the following notation, C I p xx; Y max X; Y C I p xx; Ỹ max I X; Ỹ We would like to show that C
* ** *** *** Jun S HIMADA*, Kyoko O HSUMI**, Kazuhiko O HBA*** and Atsushi M ARUYAMA***
J. Jpn. Soc. Soil Phys. No. +*2, p. +3,2,**2 * ** *** *** Influence Area of Stem Flow on a Soil of Deciduous Forest Floor by Electric Resistivity Survey and the Evaluation of Groundwater Recharge through
CE 530 Molecular Simulation
C 53 olecular Siulation Lecture Histogra Reweighting ethods David. Kofke Departent of Cheical ngineering SUNY uffalo kofke@eng.buffalo.edu Histogra Reweighting ethod to cobine results taken at different
ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΤΜΗΜΑ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΚΑΙ ΤΕΧΝΟΛΟΓΙΑΣ ΥΠΟΛΟΓΙΣΤΩΝ ΤΟΜΕΑΣ ΣΥΣΤΗΜΑΤΩΝ ΗΛΕΚΤΡΙΚΗΣ ΕΝΕΡΓΕΙΑΣ
ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΤΜΗΜΑ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΚΑΙ ΤΕΧΝΟΛΟΓΙΑΣ ΥΠΟΛΟΓΙΣΤΩΝ ΤΟΜΕΑΣ ΣΥΣΤΗΜΑΤΩΝ ΗΛΕΚΤΡΙΚΗΣ ΕΝΕΡΓΕΙΑΣ ιπλωµατική Εργασία του φοιτητή του τµήµατος Ηλεκτρολόγων Μηχανικών και Τεχνολογίας Ηλεκτρονικών
Οι απόψεις και τα συμπεράσματα που περιέχονται σε αυτό το έγγραφο, εκφράζουν τον συγγραφέα και δεν πρέπει να ερμηνευτεί ότι αντιπροσωπεύουν τις
Οι απόψεις και τα συμπεράσματα που περιέχονται σε αυτό το έγγραφο, εκφράζουν τον συγγραφέα και δεν πρέπει να ερμηνευτεί ότι αντιπροσωπεύουν τις επίσημες θέσεις των εξεταστών. i ΠΡΟΛΟΓΟΣ ΕΥΧΑΡΙΣΤΙΕΣ Η παρούσα
Supplementary Appendix
Supplementary Appendix Measuring crisis risk using conditional copulas: An empirical analysis of the 2008 shipping crisis Sebastian Opitz, Henry Seidel and Alexander Szimayer Model specification Table
1. Ηλεκτρικό μαύρο κουτί: Αισθητήρας μετατόπισης με βάση τη χωρητικότητα
IPHO_42_2011_EXP1.DO Experimental ompetition: 14 July 2011 Problem 1 Page 1 of 5 1. Ηλεκτρικό μαύρο κουτί: Αισθητήρας μετατόπισης με βάση τη χωρητικότητα Για ένα πυκνωτή χωρητικότητας ο οποίος είναι μέρος
Quantitative chemical analyses of rocks with X-ray fluorescence analyzer: major and trace elements in ultrabasic rocks
98 Scientific Note X : Quantitative chemical analyses of rocks with X-ray fluorescence analyzer: major and trace elements in ultrabasic rocks Kimiko Seno and Yoichi Motoyoshi,**- +, +, ;,**. -,/ Abstract:
6.1. Dirac Equation. Hamiltonian. Dirac Eq.
6.1. Dirac Equation Ref: M.Kaku, Quantum Field Theory, Oxford Univ Press (1993) η μν = η μν = diag(1, -1, -1, -1) p 0 = p 0 p = p i = -p i p μ p μ = p 0 p 0 + p i p i = E c 2 - p 2 = (m c) 2 H = c p 2
Quantifying the Financial Benefits of Chemical Inventory Management Using CISPro
of Chemical Inventory Management Using CISPro by Darryl Braaksma Sr. Business and Financial Consultant, ChemSW, Inc. of Chemical Inventory Management Using CISPro Table of Contents Introduction 3 About
Optimizing Microwave-assisted Extraction Process for Paprika Red Pigments Using Response Surface Methodology
2012 34 2 382-387 http / /xuebao. jxau. edu. cn Acta Agriculturae Universitatis Jiangxiensis E - mail ndxb7775@ sina. com 212018 105 W 42 2 min 0. 631 TS202. 3 A 1000-2286 2012 02-0382 - 06 Optimizing
ΥΠΕΥΘΥΝΟΣ ΚΑΘΗΓΗΤΗΣ: ΜΟΥΣΙΟΠΟΥΛΟΣ ΝΙΚΟΛΑΟΣ ΑΡΜΟΔΙΟΙ ΠΑΡΑΚΟΛΟΥΘΗΣΗΣ: ΦΡΑΓΚΟΥ ΕΥΑΓΓΕΛΙΑ, ΝΤΟΥΡΟΣ ΙΩΑΝΝΗΣ
ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΤΜΗΜΑ ΜΗΧΑΝΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΕΝΕΡΓΕΙΑΚΟΣ ΤΟΜΕΑΣ ΕΡΓΑΣΤΗΡΙΟ ΜΕΤΑΔΟΣΗΣ ΘΕΡΜΟΤΗΤΑΣ & ΠΕΡΙΒΑΛΛΟΝΤΙΚΗΣ ΜΗΧΑΝΙΚΗΣ ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ ΑΠΟΤΙΜΗΣΗ ΕΚΠΟΜΠΩΝ ΣΩΜΑΤΙΔΙΑΚΩΝ ΡΥΠΩΝ