Coordination modulation of iridium single-atom catalyst maximizing water oxidation activity

Single-atom catalysts (SACs) have attracted tremendous research interests in various energy-related fields because of their high activity, selectivity and 100% atom utilization. However, it is still a challenge to enhance the intrinsic and specific activity of SACs. Herein, we present an approach to fabricate a high surface distribution density of iridium (Ir) SAC on nickel-iron sulfide nanosheet arrays substrate (Ir1/NFS), which delivers a high water oxidation activity. The Ir1/NFS catalyst offers a low overpotential of ~170 mV at a current density of 10 mA cm−2 and a high turnover frequency of 9.85 s−1 at an overpotential of 300 mV in 1.0 M KOH solution. At the same time, the Ir1/NFS catalyst exhibits a high stability performance, reaching a lifespan up to 350 hours at a current density of 100 mA cm−2. First-principles calculations reveal that the electronic structures of Ir atoms are significantly regulated by the sulfide substrate, endowing an energetically favorable reaction pathway. This work represents a promising strategy to fabricate high surface distribution density single-atom catalysts with high activity and durability for electrochemical water splitting.

Filtering pore chanels distribution density in Western Siberia

It is well known that information on filter channels distribution density can be obtained based on the data of core samples capillary studies in laboratory conditions. The curve of the fractional participation of pore channels in filtration, as a rule, is obtained by numerical processing of the capillary studies results. In this study, using a generalized mathematical model of capillary curves, an analytical solution is obtained for filtration channels distribution density by size in the conditions of Western Siberia reservoirs. The work shows that the main share in the filtration is taken by pore channels, the sizes of which are close to the maximum value. The density function of the filtering channels is mainly determined by the maximum radius and heterogeneity of the pore channel size distribution. Keywords: capillary pressure curve; generalized model; distribution density; filtering channels.

On distribution densities of algebraic points under different height functions

In the article we consider the spatial distribution of points, whose coordinates are conjugate algebraic numbers of fixed degree. The distribution is introduced using a height function. We have obtained universal upper and lower bounds of the distribution density of such points using an arbitrary height function. We have shown how from a given joint density function of coefficients of a random polynomial of degree n, one can construct such a height function H that the polynomials q of degree n uniformly chosen under H[q] ≤1 have the same distribution of zeros as the former random polynomial.

The number of glandular trichomes on the peduncles of true lavender inflorescences as an additional breeding trait for essential oil

The main receptacle of essential oil in true lavender is the peltate glandular trichomes of the calyxes in the whorls of the inflorescences. Their average size is 175 ± 25 µm, in some cases – up to 250 µm. For the extraction of lavender oil, not only the calyxes are used, but the whole inflorescences including the flowering shoots. The surface of the peduncles of lavender inflorescences is also covered with peltate glandular trichomes. However, their contribution to the total volume of essential oil in the inflorescence has almost never been determined. The aim of this research was to study the distribution density of glandular trichomes within the inflorescence and to determine the proportion of the contribution of flowering trichomes to the formation of essential oil in the inflorescence. The research was carried out in 2021 on the basis of the V.S. Pustovoit All-Russian Research Institute of Oil Crops in two ecological and geographical points of the Krasnodar region. The object of the study was the true lavender varieties Voznesenskaya 34, Rannyaya, Yuzhanka and Voznesenskaya Aroma. It was found that the size of glandular trichomes on peduncles of true lavender is 90 ± 15 µm. Their number on peduncles, depending on the variety, varies from 2141 to 3003 pcs. The density of distribution of glandular trichomes on the surface of peduncles is equal to 8.60–14.93 pcs/mm3 . The total volume of essential oil in all glandular trichomes of peduncles is 0.41–0.57 cmm . The total volume of essential oil in the inflorescences varied from 2.28 to 5.15 cmm . The share of essential oil in the glandular trichomes of the peduncles in relation to the entire inflorescence ranged from 9.33 to 19.56%. It is concluded that peltate glandular trichomes on flower-bearing axes make a significant contribution to the essential oil content of lavender inflorescences. For the selection of true lavender to increase the essential oil content and the yield of essential oil, an additional selection trait is proposed – the amount of glandular trichomes on the surface of peduncles, which can be regulated by changing their distribution density on the surface of peduncles, or increasing the length of inflorescences.

Use of Probabilistic Approaches to Predict Cash Deficits

This article deals with issues related to the use of mathematical methods of cash deficit probability predictions. A number of objective and subjective factors are described that prevent the wide integration of mathematical methods in the practical activities of economists. It is justified that, due to the large number of external and internal factors affecting the economic system state, the values of indicators of an economic system state are often random. The possibility of using probability theory methods to predict the occurrence of cash deficits is proved. Using empirical data including the results of thousands of observations, the possibility of using the normal distribution density function for the purpose of predicting insufficient funds for payment is illustrated. The essence of the proposed model is that it contains a prediction of a macrotrend—i.e., the risk of a cash gap—based on high-frequency microlevel data. At the same time, a prediction of the probability of a cash deficit, and not its estimation for a specific date, was made. This is the main difference between the described model and common scoring estimates. This article proposes an approach to estimate the probability of a cash deficit based on data from a specific business entity, rather than aggregated data from other organizations.

Another Proof of Born’s Rule on Arbitrary Cauchy Surfaces

In 2017, Lienert and Tumulka proved Born’s rule on arbitrary Cauchy surfaces in Minkowski space-time assuming Born’s rule and a corresponding collapse rule on horizontal surfaces relative to a fixed Lorentz frame, as well as a given unitary time evolution between any two Cauchy surfaces, satisfying that there is no interaction faster than light and no propagation faster than light. Here, we prove Born’s rule on arbitrary Cauchy surfaces from a different, but equally reasonable, set of assumptions. The conclusion is that if detectors are placed along any Cauchy surface $$\Sigma $$ Σ , then the observed particle configuration on $$\Sigma $$ Σ is a random variable with distribution density $$|\Psi _\Sigma |^2$$ | Ψ Σ | 2 , suitably understood. The main different assumption is that the Born and collapse rules hold on any spacelike hyperplane, i.e., at any time coordinate in any Lorentz frame. Heuristically, this follows if the dynamics of the detectors is Lorentz invariant.

Degree estimates of one class cut-offs for improper integrals

The paper considers a normalized non-integral integral of the first kind with a variable lower bound. In this case the integrand is a generalization of the standard Gaussian distribution density. Such integrals are often called cutoffs or incomplete functions. The purpose of this paper is to obtain power inequalities for this kind of integrals. The necessity of obtaining this type of estimations is due to the fact that incomplete functions have become widespread in applications and theoretical studies. The peculiarity of the results established in the article consists in the fact that arbitrary degrees of a given integral for any value of an argument are evaluated from above not by means, of the value of integrable functions at a certain point, but by the value of the integral in question at some point proportional to this argument. The coefficient of proportionality, a parameter, can take any value from some closed interval. The main difficulty in obtaining these inequalities is that the integrand is a logarithmically concave function, that is, its logarithm is a concave function. The paper also proves that both limits of the closed interval for the parameter cannot be extended. This shows that the obtained estimates are unimprovable.

A New Goodness of Fit Test for Multivariate Normality and Comparative Simulation Study

The testing of multivariate normality remains a significant scientific problem. Although it is being extensively researched, it is still unclear how to choose the best test based on the sample size, variance, covariance matrix and others. In order to contribute to this field, a new goodness of fit test for multivariate normality is introduced. This test is based on the mean absolute deviation of the empirical distribution density from the theoretical distribution density. A new test was compared with the most popular tests in terms of empirical power. The power of the tests was estimated for the selected alternative distributions and examined by the Monte Carlo modeling method for the chosen sample sizes and dimensions. Based on the modeling results, it can be concluded that a new test is one of the most powerful tests for checking multivariate normality, especially for smaller samples. In addition, the assumption of normality of two real data sets was checked.

Physically realizable algorithms for the localization of random pulse-point sources

In this paper, we describe algorithms for the optimal search for pulsed-point sources, and the information on their distribution is limited to single-mode functions with a stepped probability distribution density, which makes it possible to physically implement the algorithms.

Analysis of the error distribution density convergence with its orthogonal decomposition in navigation measurements

Modern trends towards the expansion of online services lead to the need to determine the location of customers, who may also be on a moving object (vessel or aircraft, others vehicle – hereinafter the “Vehicle”). This task is of particular relevance in the fields of medicine – when organizing video conferencing for diagnosis and/or remote rehabilitation, e.g., for post-infarction and post-stroke patients using wireless devices, in education – when organizing distance learning and when taking exams online, etc. For the analysis of statistical materials of the accuracy of determining the location of a moving object, the Gaussian normal distribution is usually used. However, if the histogram of the sample has “heavier tails”, the determination of latitude and longitude’s error according to Gaussian function is not correct and requires an alternative approach. To describe the random errors of navigation measurements, mixed laws of a probability distribution of two types can be used: the first type is the generalized Cauchy distribution, the second type is the Pearson distribution, type VII. This paper has shown that it’s possible obtaining the decomposition of the error distribution density using orthogonal Hermite polynomials, without having its analytical expression. Our numerical results show that the approximation of the distribution function using the Gram-Charlier series of type A makes it possible to apply the orthogonal decomposition to describe the density of errors in navigation measurements. To compare the curves of density and its orthogonal decomposition, the density values were calculated. The research results showed that the normalized density and its orthogonal decomposition practically coincide.