Solar System Wave Function and its Achievements

Pluto, Ceres and all planets of solar system except Neptune, with a high approximation, follow a rule called Titius-Bode rule or Bode rule, which can by no means be considered as a stochastic event. This rule shows that the distance of the planets from the sun in Solar system is regulated. Here, we prove that the existence of a standing and cosine wave packet in solar system, with the wavelength λ = 0.6 AU (AU represents the distance of earth from the sun) and the phase constant ∅_0=π/6, is the reason for Bode rule. Moreover, we prove that this huge wave packet belongs to the sun. In the following of the article, based on the solar system wave function, we will enter into the atomic field and arrive to a new atomic model that helps us to describe many phenomena such as the normal Zeeman effect.

Secondary Iron Overload in Pediatric Hematology: the Priority of Free-Breathing Liver Study at 3.0 T Magnetic Resonance Scanner in Children with Severe Iron Overload

The aim of the study was to compare the effectiveness and scanning features of iron detection in the liver based on 3T MR scanner data using a breath holding and free breathing sequences in children with iron overload. 108 patients aged of 3 to 17 years with secondary iron overload associated with the regular blood transfusions underwent an MRI study on a 3.0 T MR scanner using specialized sequences for obtaining relaxometric maps: 3T-mGRE and 3T-uTE. The quality of the images received by the 3T-mGRE and 3T-uTE sequences was assessed by determining the signal-to-noise ratio (SNR). The SNR of 3T-uTE was found to be 8 times higher than the SNR of 3T-mGRE. In addition, it was found that for patients with an iron overload less than 25 mg/g the 3T-mGRE and 3T-uTE sequences showed the same efficacy in iron detection in the liver (r = 0.99, p = 0.54). The concentration of iron in the liver in patients with extremely severe iron overload could be calculated only using 3T-uTE relaxometric maps due to the high approximation error of the results obtaining by 3T-mGRE maps. These data demonstrate the possibility of using the 3T-mGRE sequence to determine the concentration of iron in the liver below 25 mg/g. However, with extremely severe iron overload, it is better to use the 3T-uTE sequence.

Solar System Wave Function and its Achievements

Pluto, Ceres and all planets of solar system except Neptune, with a high approximation, follow a rule called Titius-Bode rule or Bode rule, which can by no means be considered as a stochastic event. This rule shows that the distance of the planets from the sun in Solar system is regulated. Here, we prove that the existence of a standing and cosine wave packet in solar system, with the wavelength λ = 0.6 AU (AU represents the distance of earth from the sun) and the phase constant ∅_0=π/6, is the reason for Bode rule. Moreover, we prove that this huge wave packet belongs to the sun. In the following of the article, based on the solar system wave function, we will enter into the atomic field and arrive to a new atomic model that helps us to describe many phenomena such as the normal Zeeman effect.

Solar System Wave Function and its Achievements

Pluto, Ceres and all planets of solar system except Neptune, with a high approximation, follow a rule called Titius-Bode rule or Bode rule, which can by no means be considered as a stochastic event. This rule shows that the distance of the planets from the sun in Solar system is regulated. Here, we prove that the existence of a standing and cosine wave packet in solar system, with the wavelength λ = 0.6 AU (AU represents the distance of earth from the sun) and the phase constant ∅_0=π/6, is the reason for Bode rule. Moreover, we prove that this huge wave packet belongs to the sun. In the following of the article, based on the solar system wave function, we will enter into the atomic field and arrive to a new atomic model that helps us to describe many phenomena such as the normal Zeeman effect.

Solar System Wave Function and its Achievements

Pluto, Ceres and all planets of solar system except Neptune, with a high approximation, follow a rule called Titius-Bode rule or Bode rule, which can by no means be considered as a stochastic event. This rule shows that the distance of the planets from the sun in Solar system is regulated. Here, we prove that the existence of a standing and cosine wave packet in solar system, with the wavelength λ = 0.6 AU (AU represents the distance of earth from the sun) and the phase constant ∅_0=π/6, is the reason for Bode rule. Moreover, we prove that this huge wave packet belongs to the sun. In the following of the article, based on the solar system wave function, we will enter into the atomic field and arrive to a new atomic model that helps us to describe many phenomena such as the normal Zeeman effect.

A Dimension Splitting-Interpolating Moving Least Squares (DS-IMLS) Method with Nonsingular Weight Functions

By introducing the dimension splitting method (DSM) into the improved interpolating moving least-squares (IMLS) method with nonsingular weight function, a dimension splitting–interpolating moving least squares (DS-IMLS) method is first proposed. Since the DSM can decompose the problem into a series of lower-dimensional problems, the DS-IMLS method can reduce the matrix dimension in calculating the shape function and reduce the computational complexity of the derivatives of the approximation function. The approximation function of the DS-IMLS method and its derivatives have high approximation accuracy. Then an improved interpolating element-free Galerkin (IEFG) method for the two-dimensional potential problems is established based on the DS-IMLS method. In the improved IEFG method, the DS-IMLS method and Galerkin weak form are used to obtain the discrete equations of the problem. Numerical examples show that the DS-IMLS and the improved IEFG methods have high accuracy.

Evidence-Theory-Based Reliability Analysis Through Kriging Surrogate Model

It is generally understood that intractable computational intensity stemming from repeatedly calling performance function when evaluating the contribution of joint focal elements hinders the application of evidence theory in practical engineering. In order to promote the practicability of evidence theory for the reliability evaluation of engineering structures, an efficient reliability analysis method based on the active learning Kriging model is proposed in this study. To start with, a basic variable is selected according to basic probability assignment (BPA) of evidence variables to divide the evidence space into sub-evidence spaces. Intersection points between the performance function and the sub-evidence spaces are then determined by solving the univariate root-finding problem. Sample points are randomly identified to enhance the accuracy of the subsequently established surrogate model. Initial Kriging model with high approximation accuracy is subsequently established through these intersection points and additional sample points generated by Latin hypercube sampling. An active learning function is employed to sequentially refine the Kriging model with minimal sample points. As a result, belief (Bel) measure and plausibility (Pl) measure are derived efficiently via the surrogate model in the evidence-theory-based reliability analysis. The currently proposed analysis method is exemplified with three numerical examples to demonstrate the efficiency and is applied to reliability analysis of positioning accuracy for an industrial robot.

Fast and faithful scale-aware image filters

This paper proposes a fast and accurate computational framework for scale-aware image filters. Our framework is based on accurately approximating $$L^{1}$$ L 1 Gaussian convolution with respect to a transformed pixel domain representing geodesic distance on a guidance image manifold in order to recover salient edges in a manner faithful to scale-space theory while removing small image structures. Our framework possesses linear computational complexity with high approximation precision. We examined it numerically in terms of speed, accuracy, and quality compared with conventional methods.

Application of Levenberg-Marguardt Algorithm for Prime Radio Propagation Wave Attenuation Modelling in Typical Urban, Suburban and Rural Terrains

The desire to achieve an adaptive prognostics regression learning processes of physical and empirical phenomenon is a complex task and open problem in radio frequency telecommunication engineering. One key method to solving such complex task or problems is by means of numerical based optimisation algorithms. The Levenberg–Marquardt algorithm (LMA) is an efficient nonlinear parametric machine learning based modelling algorithm with optimal, fast, and accurate convergence speed. This paper proposes and demonstrates the real-time application of the LMA in developing a log-distance like propagation loss model based on received radio strength measurements conducted over deployed long term evolution (LTE) eNodeBs antennas in three different propagation areas. The LTE eNodeB signal propagation areas were selected to reflect typical urban, suburban and rural terrains which represent urban, suburban and rural terrains. The heights of the three eNodeBs are 30, 28 and 32m respectively and each operate at 2.6GHz carrier frequency with 10MHz channel bandwidths. The resultant outcome of the proposed propagation loss modelling using LMA indicates a high approximation efficacy over the popular Gauss-Newton algorithm (GNA) modelling method, which has been used to benchmark the process. Precisely, the developed propagation loss model using LMA method attained lower maximum absolute error (MABE) of 7.73, 14.57and 10.53 for urban, suburban and rural terrains compared to the ones developed by GNA which yielded 15.19, 16.59 and 13.05 MABE values. The improved approximation performance of the LMA over the GNA can be ascribed to its capacity handle multiple free parameters and attain optimum solution irrespective of the selected values of initial guess parameters.

Correlation between the continuous-time quantum walk and cliques in graphs and its application

The continuous-time quantum walk (CTQW) provides a new approach to problems in graph theory. In this paper, the correlation between the CTQW and cliques in graphs is studied, and an approximate algorithm for the maximum clique problem (MCP) based on the CTQW is given. Via both numerical and theoretical analyses, it is found that the maximum clique is related to the transmission characteristics of the CTQW on some special graphs. For general graphs, the correlation is difficult to describe analytically. Therefore, the transmission characteristics of the CTQW are applied as a vertex selection criterion to a classical MCP algorithm and it is compared with the original algorithm. Numerous simulation on general graphs shows that the new algorithm is more efficient. Furthermore, an approximate MCP algorithm based on the CTQW is introduced, which only requires a very small number of searches with a high approximation ratio.