Universal spectrum for short period (days) variability in atmospheric total ozone

Long-range spatio-temporal correlations manifested as the self-similar fractal geometry to the spatial pattern concomitant with inverse power law form for the power spectrum of temporal fluctuations are ubiquitous to real world dynamical systems and are recently identified as signatures of self-organized criticality Self-organised criticality in atmospheric flows is exhibited as the fractal geometry 10 the global cloud cover pattern and the inverse power law form for the atmospheric eddy energy spectrum, In this paper, a recently developed cell dynamical system model for atmospheric flows is summarized. The model predicts inverse power law form of the statistical normal distribution for atmospheric eddy energy spectrum as a natural consequence of quantum-like mechanics governing atmospheric flows extending up to stratospheric levels and above, Model Predictions are in agreement with continuous periodogram analyses of atmospheric total ozone. Atmospheric total ozone variability (in days) exhibits the temporal signature of self-organized criticality, namely, inverse power law form for the power spectrum. Further, the long-range temporal correlations implicit to self-organized criticality can be quantified in terms of the universal characteristics of the normal distribution. Therefore the total pattern of fluctuations of total ozone over a period of time is predictable.

Existence of stable standing waves for the nonlinear Schrödinger equation with attractive inverse-power potentials

<abstract><p>In this paper, we consider the following nonlinear Schrödinger equation with attractive inverse-power potentials</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ i\partial_t\psi+\Delta\psi+\gamma|x|^{-\sigma}\psi+|\psi|^\alpha\psi = 0, \; \; \; (t, x)\in\mathbb{R}\times\mathbb{R}^N, $\end{document} </tex-math></disp-formula></p> <p>where $ N\geq3 $, $ 0 &lt; \gamma &lt; \infty $, $ 0 &lt; \sigma &lt; 2 $ and $ \frac{4}{N} &lt; \alpha &lt; \frac{4}{N-2} $. By using the concentration compactness principle and considering a local minimization problem, we prove that there exists a $ \gamma_0 &gt; 0 $ sufficiently small such that $ 0 &lt; \gamma &lt; \gamma_0 $ and for any $ a\in(0, a_0) $, there exist stable standing waves for the problem in the $ L^2 $-supercritical case. Our results are complement to the result of Li-Zhao in ^{[<xref ref-type="bibr" rid="b23">23</xref>]}.</p></abstract>

Odd Inverse Power Generalized Weibull Generated Family of Distributions: Properties and Applications

A novel family of produced distributions, odd inverse power generalized Weibull generated distributions, is introduced. Various mathematics structural properties for the odd inverse power generalized Weibull generated family are computed. Numerical analysis for mean, variance, skewness, and kurtosis is performed. The new family contains many new models, and the densities of the new models can be right skewed and symmetric with “unimodal” and “bimodal” shapes. Also, its hazard rate function can be “constant,” “decreasing,” “increasing,” “increasing-constant,” “upside-down-constant,” and “decreasing-constant.” Different types of entropies are calculated. Some numerical values of various entropies for some selected values of parameters for the odd inverse power generalized Weibull exponential model are computed. The maximum likelihood estimation, least square estimation, and weighted least square estimation approaches are used to estimate the OIPGW-G parameters. Many bivariate and multivariate type models have been also derived. Two real-world data sets are used to demonstrate the new family’s use and versatility.

On the Characteristics and Application of Inverse Power Pranav Distribution

In this article, we study the mathematical characteristics of the inverse power Pranav distribution. The proposed distribution has three special cases namely Pranav, inverse Pranav and inverse power Pranav distributions. In addition with the basic properties of the distribution, the maximum likelihood method was employed in computing the parameters of the distribution. The 95% confidence interval was estimated for each of the parameters and finally, the distribution was applied to 128 bladder cancer patients to illustrate its applicability, and compared to Pranav distribution, inverse power Lindley distribution and inverse Ishita distribution. However, the inverse power Pranav distribution proved superiority over the competing models.

Inference for Inverse Power Lomax Distribution with Progressive First-Failure Censoring

This paper investigates the statistical inference of inverse power Lomax distribution parameters under progressive first-failure censored samples. The maximum likelihood estimates (MLEs) and the asymptotic confidence intervals are derived based on the iterative procedure and asymptotic normality theory of MLEs, respectively. Bayesian estimates of the parameters under squared error loss and generalized entropy loss function are obtained using independent gamma priors. For Bayesian computation, Tierney–Kadane’s approximation method is used. In addition, the highest posterior credible intervals of the parameters are constructed based on the importance sampling procedure. A Monte Carlo simulation study is carried out to compare the behavior of various estimates developed in this paper. Finally, a real data set is analyzed for illustration purposes.

Lattice ground states for embedded-atom models in 2D and 3D

The Embedded-Atom Model (EAM) provides a phenomenological description of atomic arrangements in metallic systems. It consists of a configurational energy depending on atomic positions and featuring the interplay of two-body atomic interactions and nonlocal effects due to the corresponding electronic clouds. The purpose of this paper is to mathematically investigate the minimization of the EAM energy among lattices in two and three dimensions. We present a suite of analytical and numerical results under different reference choices for the underlying interaction potentials. In particular, Gaussian, inverse-power, and Lennard-Jones-type interactions are addressed.

A Broadband High-Efficiency Hybrid Continuous Inverse Power Amplifier Based on Extended Admittance Space

A novel hybrid continuous inverse power amplifier (PA) that is constituted by a continuum of PA modes from the continuous inverse class-F to the continuous inverse class-B/J is proposed, and a detailed mathematical analysis is presented. The fundamental and second harmonic admittance spaces of the hybrid PA proposed in this article are analyzed mathematically. By introducing the phase shift parameter into the current waveform formula of the hybrid continuous inverse PA, the design space of the fundamental and second harmonic admittance is expanded, further increasing the operating bandwidth. The efficiency of the amplifier under different parameter conditions is calculated. In order to verify this method, a broadband high-efficiency PA is designed and fabricated. The drain voltage and current waveforms of the amplifier are extracted for analysis. The experimental measured results show a 60.7–71.5% drain efficiency across the frequency band of 0.5–2.5 GHz (133% bandwidth), and the designed PA can obtain an 11.8–13.9 dB gain in the interesting frequency range. The measured results are confirmed to be in good agreement with theory and simulations.