We develop an expression for the Li-Keiper coefficients λn in terms of k-blocks partitions, to begin with, for low values of n. The k-blocks partitions are given in terms of our cluster functions φn ...and the main point of this work lies in the emergence of an alternating sequence of values converging toward values of λn near the true values, i.e., increasing the index k of the blocks one obtains an increasing range of positivity of the Li-Keiper coefficients. With the contribution of k = 1 and k = 2 blocks, positivity of the λn is reached already until n = 26-27. The treatment is given here until k = 4 blocks up to n = 30. λn are all found to be positive.
For definition of cost of works on the engineering technical investigation we need to apply some correcting coefficients presented in the article. These coefficients are recommended and show the ...difficulty of real investigation. We have found some other coefficients, that reflect the conditions of investigation more exactly, based on real works in certain investigation organization, that are not recommended in standards. For each coefficient we bring the frequency of its use, based on the data of certain organization. If the coefficient is used rather often but not always, we think it possible to obtain the right value of the coefficient. The obtained results for the coefficients are compared to the new regulatory documents. The comparison lets us say, that coefficients, brought in different documents vary. Moreover, for certain cases, met rather often in the practice of investigation, there are no coefficient in the recommended sourcebook. So we propose to create the common system of coefficients, based on statistics of several investigative organizations.
Conventional Savonius or modified forms of the conventional Savonius rotors are being investigated in an effort to improve the coefficient of power and to obtain uniform coefficient of static torque. ...To achieve these objectives, the rotors are being studied with and without central shaft between the end plates. Tests in a closed jet wind tunnel on modified form of the conventional Savonius rotor with the central shaft is reported to have a coefficient of power of 0.32. In this study, modified Savonius rotor without central shaft between the two end plates is tested in an open jet wind tunnel. Investigation is undertaken to study the effect of geometrical parameters on the performance of the rotors in terms of coefficient of static torque, coefficient of torque and coefficient of power. The parameters studied are overlap ratio, blade arc angle, aspect ratio and Reynolds number. The modified Savonius rotor with an overlap ratio of 0.0, blade arc angle of 124° and an aspect ratio of 0.7 has a maximum coefficient of power of 0.21 at a Reynolds number of 1,50,000, which is higher than that of conventional Savonius rotor (0.19). Correlation is developed for a single stage modified Savonius rotor for a range of Reynolds numbers studied.
With the help of the improved tanh-function method, some exact variable separation solutions for a (2+1)-dimensional variable coefficient BroeraKaup system in water waves are found. The detailed ...investigation indicates that these seemly independent variable separation solutions actually depend on each other. Based on the exact variable separation solution, completely and noncompletely elastic interactions between multi-valued foldons and anti-foldons are studied analytically and graphically.
•The μs' of strawberry generally decreased with increased maturity.•The best correlations between μa and SSC and moisture content were found at 1411 nm.•The models based on μa performed best in ...determining SSC and moisture content.•Absorption property has great potential in determining internal quality of strawberry.
To understand the relationship of optical properties with soluble solids content (SSC) and moisture content of strawberry during ripening, a single integrating sphere system was built to estimate the absorption coefficient (μa) and reduced scattering coefficient (μs') of strawberry in white, color turning and red ripening stages over the wavelength range of 550−850 nm and 950−1650 nm. The relationship between optical properties and SSC and moisture content was analyzed, and the determination models for SSC and moisture content were established by using partial least squares regression and support vector machine methods based on the spectra of μa, μs', and μa together with μs'. The results showed that the absorption peaks of strawberry were at 675, 975, 1197 and 1411 nm, and the μs' generally decreased with increased maturity of strawberry. The μa was positively correlated with SSC and negatively correlated with moisture content, while the μs'was positively correlated with moisture content and negatively with SSC. The best correlations of μa with SSC and moisture content were found at 1411 nm with the correlation coefficients of 0.72 and -0.74, respectively. The established support vector machine models based on the μa spectra in 950−1650 nm and 550−850 nm had the smallest root-mean-squares error of calibration set of 0.98 % and 0.89 % for SSC and moisture content, respectively. This study indicates that SSC and moisture content mainly affect the absorption property of strawberry, and μa has greater potential than μs' and μa together with μs' in determining the internal quality of strawberry.
Sr doped BaZn sub(2)Sb sub(2) polycrystalline materials with nominal compositions of Ba sub(1-x)Sr sub(x)Zn sub(2)Sb sub(2) (x = 0.0, 0.25, 0.5) were prepared by synthesizing single crystals using a ...Sn-flux method followed by vacuum melting. The materials were characterized by powder X-ray diffraction and scanning electron microscopy equipped with electron energy dispersive spectroscopy, respectively. The electrical conductivity and Seebeck coefficient of the materials from room temperature to 773 K were measured. The electrical conductivity of all the materials decreased with increasing temperature and turned to increase with increasing temperature when temperature is above ~600 K, while the Seebeck coefficient increased with increasing temperature and turned to decrease with increasing temperature when temperature is above ~580 K. The electrical conductivity and Seebeck coefficient both increased after doping Sr into BaZn sub(2)Sb sub(2). The maximum power factor for the sample with nominal composition of Ba sub(0.5)Sr sub(0.5)Zn sub(2)Sb sub(2) reached 10.67 mu W cm super(-1) K super(-2), which was about five times as high as that of the pure BaZn sub(2)Sb sub(2).
To evaluate binary classifications and their confusion matrices, scientific researchers can employ several statistical rates, accordingly to the goal of the experiment they are investigating. Despite ...being a crucial issue in machine learning, no widespread consensus has been reached on a unified elective chosen measure yet. Accuracy and F
score computed on confusion matrices have been (and still are) among the most popular adopted metrics in binary classification tasks. However, these statistical measures can dangerously show overoptimistic inflated results, especially on imbalanced datasets.
The Matthews correlation coefficient (MCC), instead, is a more reliable statistical rate which produces a high score only if the prediction obtained good results in all of the four confusion matrix categories (true positives, false negatives, true negatives, and false positives), proportionally both to the size of positive elements and the size of negative elements in the dataset.
In this article, we show how MCC produces a more informative and truthful score in evaluating binary classifications than accuracy and F
score, by first explaining the mathematical properties, and then the asset of MCC in six synthetic use cases and in a real genomics scenario. We believe that the Matthews correlation coefficient should be preferred to accuracy and F
score in evaluating binary classification tasks by all scientific communities.
A theory of quasilinear diffusion for obliquely propagating electromagnetic waves was developed in the 1960's and applied in the 1970's to model scattering of relativistic electrons by a prescribed ...distribution of waves. In the latter work, a transformation of variables, from wavevector space to the temporal frequency and tangent of the wave normal angle, was used so that simple Gaussian functions of frequency and tangent of the wave normal angle could be multiplied together to define the distribution of wave power, although arbitrary distributions of power in these two variables is also permitted. Finally, in 2005, previous work was consolidated and has been widely used in heliophysics studies that require computation of quasilinear diffusion coefficients. Here it is shown that this transformation is inppropriate when the precise wave vector distribution is known. The correct transformation is derived and used to produce diffusion coefficients that can differ by orders of magnitude from those computed using the inappropriate transformation. The differences are largest when the distribution of wave power extends to wave normal angles near the resonance cone. When the ratio of the plasma frequency to the gyrofrequency is large, only low energies (keV) are affected, but as the ratio decreases higher energies (MeV) also show differences. It is also shown that the derivation from the 1960's uses a notation that results in the diffusion coefficients depending on the distribution of wave power with respect to the wave azimuthal angle whereas there should be no such dependence.
Plain Language Summary
Electrons can become trapped in the near‐Earth space environment and stay trapped for days to years, damaging sensitive electronics on space assets. The flux of relativistic electrons varies over time due to source and loss processes, some of which are due to interactions with electromagnetic waves. When the wave amplitudes are small, the effect of the waves on electrons can be modeled as a diffusion equation, with the diffusion coefficients proportional to the wave power. The theory currently used to compute diffusion coefficients was developed in the 1960s using a coordinate system based on all three components of the wave propagation direction. The theory was adapted to a coordinate system that uses the wave frequency and wave normal angle, and has been used for 50 years in a variety of heliophysics models. It is shown for the first time here that the transformation of the coordinate system is inappropriate when the precise distribution of wave k‐vectors is available, and the correct transformation is derived. The newly computed diffusion coefficients can be orders of magnitude different than the old coefficients, potentially implying large differences in the predicted time scales over which the source and loss processes will occur for some situations.
Key Points
Quasilinear theory from the 1960s unphysically allows diffusion coefficients to depend on wave azimuthal angle due to a notation problem
When the precise k‐vector distribution is known, the transformation of variables in 1970s theory is incorrect, limiting its applicability
Correcting the two problems produces diffusion coefficients that can differ from the old values by orders of magnitude in some cases
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