Ratio Of Sum Research Articles

Differential pressure, bypass chilled water systems: Capacity ratios between on-off and modulating units

An analysis is presented concerning the relative proportion betwen the sums of rated capacities of on-off controlled and modulating controlled terminal units in differential-pressure-bypass type chilled water distribution systems. In these systems, there is the chance that differential temperature across the supply and return mains at system part-load conditions could be lower than the system design value. The ratio of the sum of rated capacities of on-off controlled terminal units to the sum of the rated capacities of all terminal units should be smaller than the smallest value of the ratios of the pressure difference across the mains at the distribution end (when all the connected terminal units are receiving their rated water flows) to the constant supply differential pressure for all distribution circuits. This excludes units designed for precooling intake outdoor air to or above the design room air temperature.

Applications and limitations of Mango's light hydrocarbon parameters in petroleum correlation studies

Mango (1987) reported on the remarkable invariance of four isoheptanes in petroleums: regardless of the absolute concentration, the ratio of sums of concentration of (2-methylhexane + 2,3-dimethylpentane)/(3-methylhexane +2,4-dimethylpentane) remains constant, the K 1 ratio value being around unity. Gas chromatographic analyses of an additional 500 oils contradict this invariance, as a suite of oils from the Cretaceous Northwest Basin (Argentina) deviate significantly by having a ratio of 1.67. Still, oils derived from the same structural kerogen have invariant ratios that can vary from a lowest value of 0.79 found for the Midland oil set (Mango, 1990) up to a highest value of 1.67 found for the Cretaceous Northwest Basin. Mango (1990) postulated so-called parent-daughter schemes having an invariance in the ratio of isoheptanes and dimethylcyclopentanes, an invariance unique for a homologous set of oils, but possibly distinctly different from another suite of homologous oils. It will be shown here that this difference in invariance can be used in oil/oil correlation studies, and that this technique is especially powerful for oil/condensate correlation, condensates in which the concentration of biological markers is quite often below the limit of detection. Further, the concentration of light hydrocarbons, needed for this approach, can be determined from whole-oil gas chromatography without any pre-treatment, thus providing a rapid and cheap tool for correlation studies.

Modifying Cluster-Based Segments to Enhance Agreement with an Exogenous Response Variable

K-means clustering programs are frequently used to group buyers into market segments. Segment members exhibit similar background profiles, based on such characteristics as psychographics, benefits seeking, conjoint-based partworths, and so on. In addition, researchers also may use data on one or more exogenous variables for the same respondents. The authors describe and apply an algorithm for systematically modifying the original K-means segmentation to enhance prediction of an exogenous variable (either continuous or categorical). The modification is designed to respect a user-specified constraint on the permissible percentage decrease in the initial partition's ratio of among-groups sums of squares to total-groups sums of squares. The authors compare this approach with models drawn from the highly popular clusterwise regression literature.

A Greedy-heuristic for 3-partitioning with similar elements

For a given list of 3m items with positive lengths we look for a partition intom subsets containing 3 elements each, such that the ratio of the largest sum of lengths to the smallest sum of lengths is as small as possible. Let ρG be the value of this ratio using a Greedy-heuristic and ρ* the optimal value of this ratio; furthermore let β be the ratio of the largest length of an item to the smallest length. Then we will show that for 1≤β≤4 the inequality ρG/ρ*≤(4β+7)(2β+5) holds and this bound is tight.

Ratios of Trimmed Sums and Order Statistics

Let $X_i$ be independent and identically distributed random variables with distribution $F$. Let $M^{(n)}_n \leq \cdots \leq M^{(1)}_n$ be the sample $X_1, X_2,\ldots, X_n$ arranged in increasing order, with a convention for the breaking of ties, and let $X^{(n)}_n,\ldots, X^{(1)}_n$ be the sample arranged in increasing order of modulus, again with a convention to break ties. Let $S_n = X_1 + \cdots + X_n$ be the sample sum. We consider sums trimmed by large values, $^{(r)}S_n = S_n - M^{(1)}_n - \cdots - M^{(r)}_n, r = 1,2,\ldots, n, ^{(0)}S_n = S_n,$ and sums trimmed by values large in modulus, $^{(r)}\tilde{S}_n = S_n - X^{(1)}_n - \cdots - X^{(r)}_n, r = 1,2,\ldots, n, ^{(0)}\tilde{S}_n = S_n.$ In this paper we give necessary and sufficient conditions for $^{(r)}\tilde{S}_n/|X^{(r)}_n| \rightarrow \infty$ and $^{(r)}S_n/M^{(r)}_n \rightarrow \infty$ to hold almost surely or in probability, when $r = 1,2,\ldots$. These express the dominance of the sum over the large values in the sample in various ways and are of interest in relation to the law of large numbers and to central limit behavior. Our conditions are related to the relative stability almost surely or in probability of the trimmed sum and, hence, to analytic conditions on the tail of the distribution of $X_i$ which give relative stability.

Measurement of Mueller matrices

A technique that allows Mueller matrix components to be measured and involves the use of two phase modulators instead of the usual method that uses four modulators is discussed. It allows true matrix components to be measured instead of the ratio of sums of matrix components, which are measured using a single modulator.

Mechanically Induced Pendelluft Flow in a Model Airway Bifurcation During High Frequency Oscillation

A single bifurcation with adjustable branch compliances, resistances and inertances was used to study the generation of pendelluft flows during ventilation at tidal volumes of 5-15 ml and frequencies of 6-26 Hz, corresponding to parent branch Reynolds numbers of 400-8000 and Womersley parameter values of 12-25. Pendelluft was quantified by the ratio of tidal volume sum in sibling branches to tidal volume in the parent branch. This tidal volume fraction being greater than one in all experiments where an asymmetry in branch mechanics was imposed, indicated that some degree of pendelluft was always present. Asymmetries in compliance and in inertance produced much greater pendelluft than an asymmetry in resistance. The largest tidal volume fraction, equal to 2.75, was recorded when inertance in both sibling branches was high, resistance was low, and compliances differed by a factor of five. Tidal volume fraction always peaked at an optimal frequency between 12-24 Hz, similar to the frequencies at which physiologic transport optima have previously been observed.

Fatty acids as biomarkers of planktonic inputs in the stratified estuary of the Krka River, Adriatic Sea: relationship with pigments

Fatty acids (FA) associated with particles were quantitatively determined at several stations in the Krka Estuary in March 1987 and May 1988. Particles were sampled from riverine stations (E 0 and E 2) down to the open sea (C 2). Two intermediate stations (E 3 and E 4a) were sampled on both sides of the freshwater-seawater interface (FSI) and as close as possible to the interfacial layer. In winter (March 1987), total FA concentrations were highest at station E 4a, located off the city of Šibenik (75.9 μg l −1 at the surface). Total FA concentrations found at stations E 0 (7.0 μg l −1) and C 2 (2.6 μg l −1) were low and of the same range as usually encountered in non-productive waters. A net decrease of terrigenous inputs was observed between riverine station E 0 and marine station C 2 (FA > C 24=9.7% and 0.3% of total FA, respectively). In spring (May 1988), the total FA maxima were found at the FSI at stations E 4a and E 3 (26.6 and 11.2 μg l −1). Polyunsaturated fatty acids (PUFA) were predominant compared with the monounsaturated fatty acids (MUFA) at stations E 0 and E 4a (surface and interface), indicating freshly biosynthesized planktonic material. The terrigenous fatty acids (FA > C 24) were totally absent at this period. The microbially derived fatty acid contribution is still low, except at station E 4a interface (9.2% of total FA). In May 1988, FA and pigment taxonomic information was qualitatively in good agreement, and in some cases a significant linear correlation was observed, e.g. the ratio of sum C 16/sum C 18, known to be very much higher in diatoms than in other algae, was correlated with the fucoxanthin percentage of chlorophyll a. The concentration of 18:4ω3 was also positively correlated with the alloxanthin concentration and 18:3ω3 with chlorophyll b. These results are in good agreement with a phytoplanktonic production generally dominated by diatoms, with ubiquitous Cryptophyceae and Chlorophyceae present to a smaller extent throughout the estuary. In contrast, in winter conditions (March 1987) FA and pigments do not follow the same general trends.

Asymptotics of the distribution of the ratio of sums of random variables

We present results of the asymptotics of the mean and variance of the ratio of sums of random variables.

Testing for No Effect When Estimating a Smooth Function by Nonparametric Regression: A Randomization Approach

Abstract When a linear regression function is estimated by ordinary least squares, the null hypothesis of no relationship between the response and the design variable can be tested by the normal theory F test. This article describes a new test for use in the case in which a smooth regression function is estimated by a nonparametric procedure such as kernel estimation or local regression. The test is constructed as an approximation to an exact permutation test. The test statistic is the ratio of sums of squares that are defined by analogy to the analysis of variance. The null permutation distribution of the test statistic is approximated by matching its exact mean and variance to the moments of a gamma distribution. A simulation study shows that the approximation is excellent for several regression procedures and for normal, heavy-tailed, and skewed error distributions. Simulation results are also used to investigate the power of the test as a function of the smoothing parameter. The test is applied to dat...

On sums of independent gamma eandom yariames

This paper gives the exact probability density function of a sum of independent gamma random variables in terms of infinite series. This representation is obtained by means of the technique of the inverse MELLIN transform and is used to derive the distri¬bution function of a ratio of sums of independent gamma random variables whose numera¬tor and denominator may have variables in common.

Water Vapor and ice Mass Transported into the Anvils Of CCOPE Thunderstorms: Comparison with Storm Influx and Rainout

Abstract The transport of water substance (ice and vapor) into the anvils of midlatitude continental thunderstorms is examined. Doppler radar reflectivity fields and horizontal and vertical windfields, in situ anvil measurements, and environmental soundings were used to estimate the anvil water mass flux for approximately five-minute intervals over one hour periods in six moderate to severe storms. Vapor and ice mass fluxes into the anvil time-averaged for the study periods are about equal. Ratios of the time-averaged sums of these fluxes (A¯) to aircraft-derived cloud base influx (from Fankhauser) range from 18% to greater than 100%. Estimated accuracies are ±30 to 40%. Anvil fluxes exceed rainout at cloud base level as derived from radar reflectivity data by Fankhauser for half the storms. It is shown that influx values alone are not reliable predictors of total storm condensation rates. The water mass storage term is evaluated and is found to be unimportant in relation to influx for all but one storm s...

Comparison of single and double balloon valvuloplasty in children with aortic stenosis

To compare the effectiveness of the single and double balloon techniques, the short-term results of percutaneous balloon valvuloplasty were assessed in two consecutive groups of children with valvular aortic stenosis. In 16 children (aged 3 months to 17 years) the single balloon technique was utilized; the ratio of balloon diameter to valve anulus diameter was 0.96 ± 0.03 (mean ± SEM). In 11 children (aged 3 months to 21 years) the double balloon technique was utilized in which two balloons are positioned across the valve and inflated simultaneously; the ratio of the balloon diameter sum to valve anulus diameter was 1.32 ± 0.05. The groups were similar in age, weight, cardiac output, prevalvuloplasty gradient and valve anulus diameter.Overall, valvuloplasty reduced the peak systolic gradient by 53% from 80 ± 4 to 38 ± 3 mm Hg (p < 0.0001). In the single balloon group the gradient decreased from 82 ± 6 to 46 ± 4 mm Hg (p < 0.0001), whereas in the double balloon group the gradient decreased from 76 ± 5 to 26 ± 4 mm Hg (p < 0.0001). The peak systolic gradient after valvuloplasty was 43% lower in the double balloon group (p < 0.01). Furthermore, the single balloon technique reduced the gradient by an average of 43% compared with a 67% reduction with the double balloon technique (p < 0.001). The short-term complications of valvuloplasty were similar, with an increase in aortic insufficiency occurring in three children in each group. Although not a randomized trial, the present study suggests that the double balloon approach may be superior to single balloon valvuloplasty for children with aortic stenosis.

Variability of the radiative index of dryness in an Appalachian watershed

The radiative index of dryness, β (i.e., the ratio of seasonal sums of net radiation to those of the latent heat of precipitation) was used to characterize spatial and temporal variability of moisture conditions in a central Appalachian watershed during 35 growing seasons (1948–1982). The mean seasonal value of the index for the watershed and the whole study period was 1.2: year-to-year seasonal values fluctuated from 0.72 for the wet growing season of 1956 to 1.80 for the dry growing season of 1959. The highest values of the index were observed on south-west facing upper slopes at the northern boundary of the watershed, and the lowest values at the bottom of the watershed. The seasonal coefficient of variation of the index in the watershed was 36%. The highest monthly values of the index, reaching up to 2.94, were observed on the upper south-west facing slopes in June 1966. The correlation between β and corresponding basal area increment was poor. However, the average basal area increment during years with seasonal β > 1.5 was up to 29% less than the 35-year average.

Addendum to "Summation in the chimpanzee (Pan troglodytes)."

Rumbaugh, Savage-Rumbaugh, and Hegel (1987) reported that two chimpanzees (Pan troglodytes) could select, with better than 90% accuracy, the greater of two paired quantities of chocolate chips. In that study, no one quantity of chocolates (from 0 through 5) was used in both pairs on a given trial. We investigated the effect of having one quantity in common (CQ) in both pairs. Whether the other quantities (OQs) of chocolates were both less than or greater than the CQ, summation still occurred. Accuracy was primarily a function of the ratios of sums to be differentiated. This finding substantiated the earlier conclusion that summation was based on both quantities of each pair and not on some simpler process such as the avoidance of the tray with the smallest single amount or selection of the tray with the single largest amount.

An Invariance in the Isoheptanes of Petroleum

Four isoheptanes in petroleum display a remarkable invariance in a ratio of sums of concentrations. The isoheptanes are not at thermodynamic equilibrium, nor are they fixed to some constant composition. The four isomers display coherent change in relative amounts but maintain invariance in the ratio of sums. Within sets of genetically related petroleum samples, invariance reaches levels that approach the limits of our analytical precision. The invariance is inconsistent with a chemical origin that involves the thermal fragmentation of natural products or their derivatives. It suggests a reaction process at steady state, in which relative rates of product formation are constant. A mechanism is proposed in which the four isoheptanes are formed pairwise and sequentially through two intermediates in a catalytic process that operates at steady state.

Preliminary Evidence of Reduced Combined Output of Dopamine and Its Metabolites in Chronic Schizophrenia

The mean combined total body excretion of dopamine (DA) and its metabolites, measured by summing the molar excretion of DA and its metabolites in 24-hour urine samples (Sum DA), was reduced in 20 patients with schizophrenia who had not been receiving medication for at least two weeks. These patients were relatively resistant to treatment, as they were unable to live independently outside institutional settings despite conventional neuroleptic therapy. In contrast, sum norepinephrine (Sum NE), measured by summing the molar excretion of NE and its metabolites, was not reduced. These results are highlighted by expressing the data in terms of the ratio of Sum DA/Sum NE. Patients with schizophrenia had a significantly lower ratio. Treatment with haloperidol normalized the low ratio. Urinary excretion of 5-hydroxyindoleacetic acid was normal in the schizophrenic patients. These results suggest that chronic schizophrenia is more likely to be associated with a low rather than a high state of DA activity.

Analysis of Cultivar X Environment Interactions for Kansas Growing Wheat Using Regression, Variance Component, and Clustering Methods

Analysis of Cultivar X Environment Interactions for Kansas Growing Wheat Using Regression, Variance Component, and Clustering Methods

Distributions of sums and of ratios of sums of intensities

If intensities of reflexion have one or other of the ideal distributions [Wilson (1949). Acta Cryst. 2, 318- 320], the sum of n such intensities has a gamma (γ) distribution with parameter n (acentric) or n/2 (centric), and the ratio of two such sums has a beta (β) distribution. These distributions are applied to (i) intensities normalized to the ideal average Σ; (ii) intensities normalized to the local average (I); (iii) ratios used for scaling. Bias in scaling is discussed, and certain results are obtained for non-ideal distributions. Expressions are obtained for the variance of the traditional reliability index R for both ideal distributions; these have applications in certain methods of structure determination [Rabinovich & Shakked (1984). Acta Cryst. A40, 195-200].

Patterns of within-tree variation in a population of Pinus ponderosa

The amount and structure of within-individual variation in different aged and sized individuals in a population of Pinus ponderosa were compared using multivariate analytical techniques. We wished to determine if the increase in variation and progressive between-plant differentiation that occur with ontogeny of part of a plant are also manifested by entire plants as they age or increase in size. We detected some evidence of increasing differentiation with age or size. The impact on multivariate descriptors of within-tree variation, age and size of trees, microsite differences where the trees grew, and indicators of the climate at the time the trees became established was estimated using ratios of sums of squares. The error term accounted for most of the variation in the data. No single term (age, size, or site) accounted for more than 5% of the variation in the data. Terms that accounted for more than 10% of the variation in the data were either past climate (an extrinsic factor), or interaction terms assessing past climate, site (an extrinsic factor), size (a combination of extrinsic and intrinsic factors), and age. An impact of extrinsic factors on within-tree variation is not surprising since such factors determine which specific trees survive. Furthermore, since natural selection is the result of extrinsic factors, natural selection may have its major impact on within-tree variation. That interaction terms account for within-tree variation may be taken as evidence that selection is the result of many interacting, as opposed to single, factors.