A Calculation Method of Magnetic Anomaly Field Distribution of Ellipsoid with Arbitrary Posture

The ellipsoidal magnetization model has a wide range of application scenarios. For example, in aviation magnetic field prospecting, mineral prospecting, seabed prospecting, and UXO (unexploded ordnance) detection. However, because the existing ellipsoid magnetization formula is relatively complicated, the detection model is usually replaced by a dipole. Such a model increases the error probability and poses a significant challenge for subsequent imaging and pattern recognition. Based on the distribution of ellipsoid gravity potential and magnetic potential, the magnetic anomaly field distribution equation generated by the ellipsoid is deduced by changing the aspect ratio, making the ellipsoid equivalent to a sphere. The result of formula derivation shows that the two magnetic anomaly fields are consistent. This paper uses COMSOL finite element software to model UXO, ellipsoids, and spheres and analyzes magnetic anomalies. The conclusion shows that the ellipsoid model can completely replace the UXO model when the error range of 1nT is satisfied. Finally, we established two sets of ellipsoids and calculated the magnetic anomalous field distributions on different planes using deduction formulas and finite element software. We compared the experimental results and found that the relative error of the two sets of data was within [Formula: see text]‰. Error analysis found that the error distribution is standardized and conforms to the normal distribution. The above mathematical analysis and finite element simulation prove that the calculation method is simple and reliable and provides a magnetic field distribution equation for subsequent UXO inversion.

Prime numbers demystified

The paper is the ultimate prime numbers algorithm that gets rid of the unneccessary mystery about prime numbers. All the numerous arithmetic series patterns observed between various prime numbers are clearly explained with an elegant "pattern of remainders". With this algorithm we prove that odd numbers too can make an Ulam spiral contrary to current ""proofs". At the end of the paper this author proves the relationship between a simple arithmetic series pattern and the Riehmann's prime numbers distribution equation. This paper would be important for encryption too. As an example, prime integer 1979 is expressed as 1.2.4.5.10.3.7.3.1.7.26.18.11.1. This makes even smaller primes useful for encryption as well.

The Planckian Distribution Equation As A Novel Method To Predict The Efficacy Of Breast Cancer Pharmacotherapy

Chemotherapy-related deaths, the result of treatment with faulty medications, account for nearly 10% of all breast cancer deaths (Rashbass, 2016). Patient-specific, personalized medicine is evidently required to administer optimized therapeutics and prevent treatment-related mortality. In order to develop a predictive model for breast cancer therapy, the following study analyzed the mRNA data of 4,704 genes derived from 20 breast cancer patients before and after doxorubicin treatment for 16 weeks (O’brien et al., 2006; Perou et al., 2000). The genomic data of each patient was first stratified into 9 groups (corresponding to the 9 Mechanisms defined in Figure 4) based on mRNA expression in response to the tumor and to the doxorubicin treatment. The study then employed the Planckian Distribution Equation (PDE) discovered at Rutgers University to model the stratified samples by transforming each mechanism into a single long-tailed histogram fitted by the PDE. Our PDE model is based on 3 parameters - A, B, and C - of which 2 were extracted from each model to generate the plots seen in figures 5e and 5f. The drug-induced slopes of the A vs C plots were then determined for all 9 mechanisms of each patient. The study observed an increase in post-treatment mRNA levels for longer surviving patients in 6 mechanisms. Further analysis displayed how the drug treatment uniquely altered each of the mechanisms based on the length of patient survival. These results indicate that the PDE-based procedures described herein may provide a novel tool for discovering potential anti-breast cancer pharmaceuticals.

Static Mantle Density Distribution 3 Dimpling and Bucking of Spherical Crust

This paper is the third step of project “Static mantle distribution, Equation, Solution and Application”. It consists of < Static Mantle Distribution 1 Equation>, <Static Mantle Density Distribution 2 Improved Equation and Solution>, and this paper. Our result on shape of core is a “X type”, which differs from the traditional view that core is a sphere. Which one is correct? or, both are not correct? The aim of thispaper is to study dimpling and bucking of the spherical crust under mantle loading. Dimpling analysis depends on the outer solution of non-homogeneous non-linear D.E., while bucking analysis depends on non-linear Eigen value of the homogeneous D. E The results based on two models and governing equations show that crust dimpled at poles is proved theoretically and numerical result well consists with pole radius, while the non-linear bucking Eigen value boundary problem is solved by decomposition method. The results show that bucking can occur, and the un-continuity of internal force per unit length causes un-continuity of masses by mantle material emitting to crust at turning point of “X”. The growing of Tibet high-land might be viewed as an evidence of the mass ms(θ0)increasing due to mantle emission. Both poles radius and equatorial radius have been used to support our analysis. Question: how the nature makes cold at poles?

THE MODEL OF THE DISTRIBUTION OF AIR FLOW IN THE MINE SHAFT

Under some assumptions of a general nature, a partial differential equation of the second strand is compiled with respect to the air concentration in the mine shaft for a direct-flow ventilation circuit. Boundary conditions are formulated and on their basis an analytical solution to the leakage air distribution equation is obtained. Received three-dimensional visualization of air distribution.

Non-Linear Model for a Spiral Porous Fin Subjected to Darcy Flow

In this study, the temperature distribution equation for a spiral porous fin is presented. Based on Darcy’s model, a mathematical equation of the energy is derived and a suitable dimensionless form is outlined to highlight some characteristic parameters, namely, the spiral fin pitch, the porosity, and the modified Rayleigh number. The behavior of the solution is analyzed for two cases of interest, taking into account the temperature-dependent thermal conductivity of the fin encountered in a hostile environment. A Numerical method is applied to solve this non-linear problem. It is found that the thermal transfer is not affected by the change of the spiral fin pitch, whereas increasing the porosity or the parameter β* makes higher fin temperature and improve the fin efficiency.

Sine–cosine wavelets operational matrix method for fractional nonlinear differential equation

In this paper, we present a solution method for fractional nonlinear ordinary differential equations. We propose a method by utilizing the sine–cosine wavelets (SCWs) in conjunction with quasilinearization technique. The fractional nonlinear differential equations are transformed into a system of discrete fractional differential equations by quasilinearization technique. The operational matrices of fractional order integration for SCW are derived and utilized to transform the obtained discrete system into systems of algebraic equations and the solutions of algebraic systems lead to the solution of fractional nonlinear differential equations. Convergence analysis and procedure of implementation for the proposed method are also considered. To illustrate the reliability and accuracy of the method, we tested the method on fractional nonlinear Lane–Emden type equation and temperature distribution equation.

Investigation of Indentation Fracture Toughness (KIC) and Weibull Parameters of 0.25Li2O.2SiO2-0.75BaO.2SiO2 Glass-Ceramic

In the present study, mechanical properties of 0.25Li2O.2SiO2-0.75BaO.2SiO2glass-ceramic were investigated. The trans-formations‘ temperatures were determined by DTA instrument. The optimum nucleation temperature was found to be 540°C. This suggested the crystallization temperatures as 675, 720 and 800°C. After carrying out crystallization heat treatments, Vickers indentation test was applied. In order to determine the indentation fracture toughness (KIC), crack half-length ‚c‘ of the samples was measured. To calculateKIC, Young’s modulus,Eand the measured hardness,Hvwere used. UsingKICand probability of fracture ‚P‘, ln ln[1/(1 −P)] – lnKICgraph was drawn based on the Weibull distribution equation. Consequently, Weibull modulus, ‚m‘ and scale parameter, ‚K0‘ were determined and compared with each other.