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The pine pitch canker fungus, Fusarium circinatum, has caused large-scale mortality of Pinus patula crops in South African nurseries and high in-field post-planting mortality. Tree breeders have identified selection and breeding of tolerant material as the likely long-term solution to this disease. In this study, the greenhouse artificial inoculation screening method was employed to investigate the genetic control of F. circinatum tolerance in a factorial mating design of Pinus patula × P. tecunumanii low elevation (PPTL) and high elevation (PPTH) hybrid families and their parental species. Results indicated that F. circinatum tolerance is under moderate genetic control (h2 between 0.13 and 0.36) as assessed in a hybrid factorial mating design with a large number of PPTL and PPTH families. The PPTL hybrid displayed the highest level of tolerance, followed by pure P. tecunumanii LE, then the PPTH hybrid, pure P. tecunumanii HE and lastly pure P. patula. A general hybridising ability (GHA) and specific hybridising ability (SHA) analysis was also conducted to rank parent families as well as hybrid families. These breeding values can be used to identify superior families for commercial production and further breeding. A poor correlation between frost tolerance and F. circinatum tolerance was also found when compared to a previous frost tolerance study utilising the same hybrid families. The results from this study indicated that it is possible for breeders to cross selected P. patula seed parents with selected P. tecunumanii pollen parents to develop F. circinatum tolerant hybrid families for commercial production. [ABSTRACT FROM AUTHOR]

The results of determining the stability and variability of the main characteristic of glass capillary reference viscometers — conversion coefficient — by analyzing a set of data on viscometers having different diameters of the measuring capillary are presented. It is shown that the mean values of the sample differ from the mean values of the symmetric normal distribution curves within (2–4) %, as well as the correspondence of statistics to the normal distribution law by means of the inverse standard function and histograms showing the degree of correspondence of the sample distribution to the theoretical one.

The transition from Riemann integrals to other real integrals has been discussed previously in mathematics education literature. In this transition, the interpretation of integrals as averages of the integrated functions generalises smoothly to measure and probability theory. In this paper, I address the transition to complex path integrals. Based on the premise that using core ideas throughout mathematics curricula may facilitate the transition from earlier to more advanced courses, I analyse epistemologically to what extent the idea of averaging may be transferred to complex path integrals. In this case, the transition poses special epistemological challenges. Using an example from an expert interview, in which the expert aims to apply the interpretation of integrals as averages to complex path integrals, I illustrate the aforementioned challenges empirically. [ABSTRACT FROM AUTHOR]

For B ∈ F q [ T ] of degree 2 n ≥ 2 , consider the number of ways of writing B = E 2 + γ F 2 , where γ ∈ F q ⁎ is fixed, and E , F ∈ F q [ T ] with deg E = n and deg F = m < n. We denote this restricted sum-of-squares function by S γ ; m (B). We obtain an exact formula for the variance of S γ ; m (B) over short intervals in F q [ T ] where q is an odd prime power. Interestingly, when m + 1 ≤ n ≤ 2 m , the variance vanishes on some (not all) short intervals, which is in contrast to the standard function that counts representations as a sum of two squares. We use the method of additive characters and Hankel matrices that we previously used for the variance and correlations of the divisor function. In Section 2, we give a short overview of our approach. Section 3 gives new results relating to values of quadratic forms, over F q , that are defined from Hankel matrices. [ABSTRACT FROM AUTHOR]

We develop the L-functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of quadratic Hecke L-functions in the Gaussian field using multiple Dirichlet series under the generalized Riemann hypothesis. We also obtain an asymptotical formula for the first moment of central values of the same family of L-functions, obtaining an error term of size O (X 1 / 2 + ε) . [ABSTRACT FROM AUTHOR]

In this paper, we introduce new notions of mean values based on ideas of multicriteria optimization. The distances between the current point to all points in the sample are regarded as elements of a vector estimate. Such vector estimates are usually scalarized, for example, by taking the sum of all components. In contrast, we introduce preference relations on the set of all such vectors, based on the information about the preferences of the decision maker who could be a statistician, analyst or researcher. Such preference relations reflect the distances between points, including the case in which all distances are equally important. We define the mean values as the points whose corresponding vector estimates are nondominated with respect to the defined preference relation, and investigate their properties. Such mean values turn out to be multi‐valued. We further explore the relationship between the new notions of mean values with their conventional definitions and suggest computational approaches to the calculation of the suggested new means. We also outline generalisations of the suggested approach to the case of multidimensional data. [ABSTRACT FROM AUTHOR]

We evaluate the smoothed first moment of central values of a family of quadratic Hecke L -functions in the Gaussian field using the method of double Dirichlet series. The asymptotic formula we obtain has an error term of size O (X 1 / 4 + ) under the generalized Riemann hypothesis. The same approach also allows us to obtain asymptotic formulas for all X , Y for a smoothed double character sum involving ∑ N (m) ≤ X , N (n) ≤ Y (m n) , where (⋅ n) denotes the quadratic symbol in the Gaussian field. [ABSTRACT FROM AUTHOR]

Background: An increased tibial slope (TS) has been identified as a risk factor for anterior cruciate ligament (ACL) injury and graft failure after ACL reconstruction. However, different imaging modalities are used to determine the TS, resulting in divergent values. Consequently, no reference values and no consensus on thresholds can be reached, which in turn is mandatory for indicating correction osteotomies when facing outlier TS. Purpose: To determine the mean values of the TS and the incidence of their outliers in large cohorts of patients with ACL-injured and noninjured knees and to determine the feasibility of measuring TS on conventional lateral radiographs (CLRs). Study Design: Cross-sectional study; Level of evidence 3. Methods: TS of ACL-injured knees (n = 1000, group A) and ACL-intact knees (n = 1000, group B) was measured by 3 experienced examiners. Medial TS was measured on CLRs using the technique of Dejour and Bonnin. Patients with radiographs with poor image quality, osteoarthritis, previous osteotomies, or nondigital radiographs were excluded. The intra- and interrater reliability was calculated using the intraclass correlation coefficient. Results: The mean TS was significantly higher in group A than in group B (10.04°± 3° [range, 2°-22°] vs 9.02°± 2.9° [range, 1°-18°], respectively; P <.001). Significantly more participants in group A had TS larger than 12° (≥12°, 32.2% vs 19.8%, P <.001; ≥13°, 20.9% vs 11.1%, P <.001; ≥14°, 13.5% vs 5.7%, P <.001; ≥15°, 8% vs 2.7%, P <.001; ≥16°, 3.7% vs 1.4%, P =.0005), respectively. In contrast, significantly more participatns in group B had TS 8° or less (≤8°, 32.1% vs 42.7%, P <.001; ≤7°, 20% vs 30.9%, P <.001; ≤6°, 12.4% vs 19.8%, P <.001; ≤5°, 6.6% vs 12%, P =.0003; ≤4°, 2.8% vs 5.3%, P =.0045). The intraclass correlation coefficient revealed a good to excellent reliability throughout measurements. Conclusion: Median values for the TS were 9° for uninjured and 10° for ACL-injured knees on CLRs. Notwithstanding its statistical significance, this finding might be negligible in clinical practice. However, a significantly larger number of outliers were found in the ACL-injured group exceeding a TS of 12° and demonstrating an incremental proportion with increasing TS, serving as a potential threshold for correction osteotomy. Furthermore, CLRs in the largest cohort to date exhibited high reproducibility, proving the feasibility of CLRs as a routine measurement for TS. [ABSTRACT FROM AUTHOR]

Homogeneous random fractals form a probabilistic extension of self-similar sets with more dependencies than in random recursive constructions. For such random fractals we consider mean values of the Lipschitz–Killing curvatures of their parallel sets for small parallel radii. Under the uniform strong open set condition and some further geometric assumptions, we show that rescaled limits of these mean values exist as the parallel radius tends to 0. Moreover, integral representations are derived for these limits which extend those known in the deterministic case. [ABSTRACT FROM AUTHOR]

Copyright of Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio Computatorica is the property of Eotvos Lorand University, Faculty of Informatics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We give a characterization of continuous functions in a complex plane domain satisfying a weighted polygonal mean value property. [ABSTRACT FROM AUTHOR]

We study the first moments of central values of Hecke L-functions associated with quadratic, cubic and quartic symbols to prime moduli. This also enables us to obtain results on first moments of central values of certain families of cubic and quartic Dirichlet L-functions of prime moduli. [ABSTRACT FROM AUTHOR]

We examine some ordinal measures of inequality that are familiar from the literature. These measures have a quite simple structure in that their values are determined by combinations of specific summary statistics such as the extreme values and the arithmetic mean of a distribution. In spite of their common appearance, there seem to be no axiomatizations available so far, and this paper is intended to fill that gap. In particular, we consider the absolute and relative variants of the range, the max‐mean and the mean‐min orderings, and quantile‐based measures. In addition, we provide some empirical observations that are intended to illustrate that, although these orderings are straightforward to define, some of them display a surprisingly high correlation with alternative (more complex) measures. [ABSTRACT FROM AUTHOR]

This article presents a new approach to processing data in identifying and evaluating defects of structures with deformation measurement signals. By using sensitive characteristics observed in the old statistical parameters such as mean values, variances, and standard deviations, we propose three new parameters including kurtosis, skewness of signals, and statistical density function. In addition, we apply cumulative function in statistical and data analysis. High reliability and accuracy of the present approach has been verified through 38 bridges with over 300 span structures in Ho Chi Minh City (HCMC). Furthermore, we have conducted experiments with a small-scale model at the Laboratory of Applied Mechanics (LAM) to compare computational results with ones derived from practical data. Obtained results show promising applicability of sensitive parameters extracted from statistical features in identifying and evaluating defects in structures. [ABSTRACT FROM AUTHOR]

Let χ be a nonprincipal Dirichlet character modulo a prime number p ⩾ 3 of order k ⩾ 2. Define A p (χ) : = 1 p − 1 ∑ 1 ⩽ N ⩽ p − 1 ∑ 1 ⩽ n 1 , n 2 ⩽ N χ (n 1) = χ (n 2) 1. We prove that A p (χ) = p (2 p − 1) 6 k + (k − 1) (p + 1) 12 k + a χ p 2 π 2 k (p − 1) ∑ j = 1 k / 2 | L (1 , χ 2 j − 1) | 2 where a χ : = (1 − χ (− 1)) / 2. [ABSTRACT FROM AUTHOR]

Copyright of Rechtsmedizin is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

G = G(x, y) = √xy, L = L(x,y) = x-y/log(x)-log(y)' I=I(x,y)= 1/e(xx-yy) 1/(x-y) be the geometric, logarithmic, identric, and arithmetic means of x and y. We prove that the inequalities L(G²,A²) < G(L²,I²) < A(L²,I²) < I(G²,A²) are valid for all x, y > 0 with x ≠ y. This refines a result of Seiffert. [ABSTRACT FROM AUTHOR]

Using internally consistent albedo, aerosol, cloud, and surface data from the Multiangle Imaging Spectroradiometer (MISR) instrument onboard the Terra satellite, top-of-atmosphere (TOA) spectral albedo change (dα) in the presence of aerosols over land is estimated and its dependence on aerosol and surface properties is analyzed. Linear regressions between spectral TOA albedo and aerosol optical depth (AOD) for different surface types are examined to derive the aerosol-free TOA albedo. MISR surface BiHemispherical Reflectance (BHR) values are used to differentiate surface types. We find relatively high correlations between spectral TOA albedo and AOD for BHR-stratified data in 2° × 2° grid cells. The global mean values of cloud-free dα over land for June–September 2007 are estimated to be 0.018 ± 0.003 (blue), 0.010 ± 0.003 (green), 0.007 ± 0.003 (red), and 0.008 ± 0.006 (near-infrared). Individual regions show large variations from these values. Global patterns of dα are determined mainly by AOD and aerosol radiative efficiency. Large positive values of dα are observed over regions with high aerosol loading and large single-scattering albedo, where the aerosol scattering effect is dominant. The presence of light-absorbing aerosols reduces aerosol radiative efficiency and dα. Surface reflectance influences both aerosol scattering and absorbing effects. Generally, the aerosol radiative efficiency decreases with increasing BHR. We also examined dα-AOD correlations over different vegetation types. We find the smallest dα values are over needleleaf forests and shrublands, whereas the largest values are over cropland and barren regions. The aerosol radiative efficiencies are lowest over needleleaf forests and barren regions and highest over grasslands and croplands.

We study the mean square of the error term of the mean value for binary Egyptian fractions. We get an asymptotic formula under the Riemann Hypothesis. [ABSTRACT FROM AUTHOR]

Let b ∈ ℝ, let c > 0, let x > 0, and let Gb,c(x) = e-x / xb Pc(x) with Pc(x) = ∞Σ k=0 xk / Γ(c + k) . We prove that Gb,c is completely monotonic on (0,∞) if and only if b ≥ 0 and b+c ≥ 1. Moreover, we present various functional inequalities for Pc. Among others, we show that if c ∈ (0, 1), then, for x, y > 0 we have e < Pc(1/x)x Pc(1/y)y / Pc(1/(x + y))x+y . If c > 1, then the reverse inequality holds for x, y > 0. In both cases, the constant bound e is best possible. [ABSTRACT FROM AUTHOR]

We investigate the distribution of the function ω ( n ) , the number of distinct prime divisors of n , in residue classes modulo q for natural numbers q greater than 2. In particular we ask ‘prime number races’ style questions, as suggested by Coons and Dahmen in their paper ‘On the residue class distribution of the number of prime divisors of an integer’. [ABSTRACT FROM AUTHOR]

In this paper, we examine unpublished notes of a course on thermodynamics delivered by Eugenio Beltrami. This course is clearly influenced by Clausius's work and aims to present thermodynamics along the lines of rational mechanics, viewed as both a sound foundation and a methodological model, where use of mathematical tools can help to understand delicate points. The course contains also some lessons on the kinetic theory of gases where Beltrami never mentions probability explicitly. [ABSTRACT FROM AUTHOR]

Using super-efficiency, with regard to ranking efficient units, is increasing in DEA. However, this model has some problems such as the infeasibility. Thus, this article studies infeasibility of the input-based super-efficiency model (because of the zero inputs and outputs), and presents a solution by adding two virtual DMUs with mean values (one for inputs and one for outputs). Adding virtual DMUs to Production Possibility Set (PPS) changed the basic super-efficiency model, so a new model is proposed for solving this problem. Finally, the newly developed model is illustrated with a real-world data set. [ABSTRACT FROM AUTHOR]

Given c , a positive integer, we give an asymptotic formula for ∑ χ ≠ χ 0 χ ( c ) | L ( 1 , χ ) | 2 , where χ is the non-trivial Dirichlet character mod f with f coprime to c . [ABSTRACT FROM AUTHOR]

Recently (Nagel and Weiss, 2005), the class of homogeneous random tessellations that are stable under the operation of iteration (STIT) was introduced. In the present paper this model is reviewed and new results for the mean values of essential geometric features of STIT tessellations in two and three dimensions are provided and proved. For the isotropic model, these mean values are compared with those ones of the Poisson-Voronoi and of the Poisson plane tessellations, respectively.

Homogeneous random tessellations in the 3-dimensional Euclidean space are considered that are stable under iteration – STIT tessellations. A classification of vertices, segments and flats is introduced and a couple of new metric and topological mean values for them and for the typical cell are calculated. They are illustrated by two examples, the isotropic and the cuboid case. Several extremum problems for these mean values are solved with the help of techniques from convex geometry by introducing an associated zonoid for STIT tessellations.

Let B(x, y) be Euler's beta function. We prove that the inequalities 0 < B(√xy, x + y/2)/ B(x, y) < 1 hold for all x, y > 0 with x 6≠ y. The given constant bounds are best possible. This result is extended to the case when the beta function in the numerator has arguments given by the weighted geometric and arithmetic means. [ABSTRACT FROM AUTHOR]

Mean values of Witten L-functions in the 'character' aspect are investigated. After giving a general formula for mean values with the first and the second power, we explicitly calculate the cubic moment for SU(2). [ABSTRACT FROM AUTHOR]

Background: Cranial base is used as reference structure to determine the skeletal type in cephalometric analysis. The purpose was to assess the cranial base length on lateral cephalic radiographs of children between 8 and 12 and compare these measurements with baseline studies in order to evaluate the relationship between the length and the cranial base angle, articular angle, gonial angle and skeletal type. Methods: A Cross-sectional study in 149 children aged 8-12 years, originally from Aburrá Valley, who had lateral cephalic radiographs and consented to participate in this study. The variables studied included: age, sex, sella-nasion, sella-nasion-articular, sella-nasion-basion, articular-gonion-menton, gonion-menton, sella-nasion-point B, sella- nasion-point A y point A-nasion-point B. These variables were digitally measured through i-dixel 2 digital software. One-way ANOVA was used to determine mean values and mean value differences. The values obtained were compared with previous studies. A p value <0.05 was considered significant. Results: Cranial base lengths are smaller in each age and sex group, with differences exceeding 10 mm for measurement, compared both with the study by Riolo (Michigan) and the study carried out in Damasco (Antioquia). No relation was found between the skeletal type and the anterior cranial base length, the sella angle and the cranial base angle. Also, no relation was found between the gonial angle and sella angle or the cranial base angle. Conclusion: The cranial base varies from one population to another. Accordingly, compared to other studies it is shorter for the assessed sample. [ABSTRACT FROM AUTHOR]

We present various inequalities for means in two variables. One of our results states that the inequalities 0 ≤ 1/Mr - 1/Ms ≤ 1/G - 1/A (r, s ≥ 0) hold for all x, y > 0 if and only if 0 ≤ s - r ≤ 1. Here, A = A(x, y) = (x + y)/2, G = G(x, y) = √ xy and Mt = Mt(x, y) = [(xt + yt)/2]1/t denote the arithmetic, geometric and power mean of x and y, respectively. [ABSTRACT FROM AUTHOR]

This paper proposes an energy flow model and an optimal energy management strategy based on mean values for maximizing driving mileage of a fuel cell bus (FCB), which is powered by a polymer electrolyte membrane (PEM) fuel cell system and a lithium battery. Firstly, an energy flow model describing the relations between vehicle performance and power flow parameters is quantitatively established. An optimization problem for maximizing driving mileage on a predetermined route is defined, and an analytical solution with clear physical meanings is derived. Next, a practical real-time supervisory Energy Management strategy basing on Mean Values (EMMV) is proposed. The strategy, which doesn't require a priori knowledge of the driving trip, is then compared with several well-known strategies, e.g. charge depleting and charge-sustaining (CDCS), Blended, dynamic programming (DP), and Pontryagin's Minimum Principle (PMP). Simulation results show that, the proposed strategy achieves a near-optimal effect, and converges after one driving cycle on a predetermined bus route. Finally, on-road testing is carried out. The proposed strategy achieves an average endurance mileage on a real bus route of 162 km with a usable battery state of charge (SOC) of 90% and 20 kg hydrogen gas for a fully loaded fuel cell city bus. [ABSTRACT FROM AUTHOR]

We present several new Young-type inequalities for positive real numbers and we apply our results to obtain the matrix analogues. Among others, for real numbers,and, withand, we prove the inequalitieswhereandare, respectively, the (weighted) arithmetic and geometric means of the positive real numbersandwith. In addition, we show that both bounds are sharp. An example of a matrix analogue for the caseis the double-inequalityfor positive definite matrices. Our results extend some fresh inequalities established by Kittaneh, Manasrah, Hirzallah and Feng. Estimates for the quotientand its matrix analogues given by Furuichi and Minculete are also improved. [ABSTRACT FROM AUTHOR]

This letter presents a new method to derive the image feature descriptor for vehicle verification. The effectiveness of the proposed feature descriptor is based on the nature of the Gabor filter magnitude that tends to obey the Gamma distribution. The statistical parameters of the Gabor magnitude are computed using the Maximum Likelihood Estimation (MLE), which is later utilized to construct the feature descriptor. Conventionally, the Gabor magnitude is simply modeled by using Gaussian distribution, and thus the image descriptor consists of mean, standard deviation, and skewness values of the Gabor filter magnitude. However, recent investigations found that the skewness parameter is not contributing towards class separation. Based on our observation, the Gamma distribution provides a better statistical fitting to represent the Gabor filter magnitude when compared to the Gaussian distribution. As documented in the experimental results, the proposed feature descriptor yields higher accuracy for vehicle verification when compared to the conventional schemes. [ABSTRACT FROM AUTHOR]