Numerical Solution of Radioactive Core Decay Activity Rate of Actinium Series Using Matrix Algebra Method

The Actinium 235 series is one of the radioactive series which is widely used as a raw material for reactors and nuclear activities. The existence of this series is found in several countries such as West USA, Canada, Australia, South Africa, Russia, and Zaire. The purpose of this study was to determine the activity value and the number of radioactive nucleus decay atoms on the actinium 235 rendered in a very long decay time of 4.3 x 109 years. The decay count in this study uses an algebraic matrix method to simplify the chain decay solution, which generally uses the concept of differential equations. The solution using this method can be computationally simulated using the Matlab program. This study indicates that the value of the decay activity experienced by each element in this series is the same, which is equal to 2,636 x 1011 Bq. This condition causes the actinium 235 series to experience secular equilibrium because the half-life of the parent nuclide is greater than the nuclide derivatives. The decay activity of the radioactive nucleus under the actinium 235 series is strongly influenced by the half-life of the nuclides, the decay constants, and the number of atoms after decay

Transfer Modeling for 1T1R Crossbar Arrays with Line Resistances

Progress of neuromorphic computing and next-generation information storage technologies hinges on the development of emerging nonvolatile memory (eNVM) devices, which are typically organized employing the crossbar array architecture. To facilitate quantitative performance analysis of eNVM crossbar array architecture, this paper proposes a way to study the one-transistor-one-resistor (1T1R, R: eNVM devices) crossbar arrays based on matrix algebra method. The comparative analysis of 1T1R crossbar array modeling based on matrix algebra method and compact-model SPICE simulations verifies the accuracy of the proposed method, which can be directly used for static quantitative analysis and evaluation of 1T1R crossbar array performance. With the proposed method, the optimization of array operation schemes and current backflow issue are discussed. Our analysis indicates that the proposed method is capable of flexibly adjusting array parameters and consider the influence of line resistance on array operation, and can provide guidance for improving the sensing margin of the array through multi-parameter co-simulation. The proposed matrix algebra-based 1T1R crossbar array modeling method can bridge the gap between the accuracy and flexibility of the available methods.

A gantry robot system for cutting single Y-shaped welding grooves on plane workpieces

To guarantee the strength and precision of the final welding assemblies, it is necessary to cut welding grooves before welding thick workpieces. General methods to cut welding grooves on plane workpieces need much manual assistance, and some even need manual operation purely. Therefore, this paper proposed a robot system for cutting Y-shaped welding grooves with full automation. Flame cutting technology has been adopted, requiring no jig to fix workpieces, which also causes no direct vibration to robot structure. Vision-based sub-system firstly captures the edges to be cut, which are composed of continuous points, and a laser range finder (LRF) starts to obtain the thickness of the edges precisely. To convert these edges into the trajectory of flamer, Least Square Method and Hermite Interpolation are respectively utilized to fit lines and curves. Robot system subsequently computes the motion-related parameters according to the position of the edges and geometric parameters of the desired welding grooves. The inverse kinematics of this robot is solved by geometry methods, which decreases computation burden and saves much time compared with traditional algebra method. Another core novelty is that a velocity planning method combining optimization algorithm has been put forward, which, we think, is not only useful in this gantry robot but also benefits other motion axes with heavy load. This further reduces vibration. Finally, the simulation and experimental results both prove the feasibility of this system. To date, no available robots or machines tool can finish this process with full automation (to the best of our knowledge).

The maximum number of triangles in a graph of given maximum degree

Maximizing or minimizing the number of copies of a fixed graph in a large host graph is one of the most classical topics in extremal graph theory. Indeed, one of the most famous problems in extremal graph theory, the Erdős-Rademacher problem, which can be traced back to the 1940s, asks to determine the minimum number of triangles in a graph with a given number of vertices and edges. It was conjectured that the mnimum is attained by complete multipartite graphs with all parts but one of the same size whilst the remaining part may be smaller. The problem was widely open in the regime of four or more parts until Razborov resolved the problem asymptotically in 2008 as one of the first applications of his newly developed flag algebra method. This catalyzed a line of research on the structure of extremal graphs and extensions. In particular, Reiher asymptotically solved in 2016 the conjecture of Lovász and Simonovits from the 1970s that the same graphs are also minimizers for cliques of arbitrary size. This paper deals with a problem concerning the opposite direction: _What is the maximum number of triangles in a graph with a given number $n$ of vertices and a given maximum degree $D$?_ Gan, Loh and Sudakov in 2015 conjectured that the graph maximizing the number of triangles is always a union of disjoint cliques of size $D+1$ and another clique that may be smaller, and showed that if such a graph maximizes the number of triangles, it also maximizes the number of cliques of any size $r\ge 4$. The author presents a remarkably simple and elegant argument that proves the conjecture exactly for all $n$ and $D$.

An active contour model for medical image segmentation using a quaternion framework

This paper presents a new method for segmenting medical images is based on Hamiltonian quaternions and the associative algebra, method of the active contour model and LPA-ICI (local polynomial approximation - the intersection of confidence intervals) anisotropic gradient. Since for segmentation tasks, the image is usually converted to grayscale, this leads to the loss of important information about color, saturation, and other important information associated color. To solve this problem, we use the quaternion framework to represent a color image to consider all three channels simultaneously when segmenting the RGB image. As a method of noise reduction, adaptive filtering based on local polynomial estimates using the ICI rule is used. The presented new approach allows obtaining clearer and more detailed boundaries of objects of interest. The experiments performed on real medical images (Z-line detection) show that our segmentation method of more efficient compared with the current state-of-art methods.

Dynamics of a System of Two Connected Bodies Moving along a Circular Orbit around the Earth

Symbolic–numeric methods are used to investigate the dynamics of a system of two bodies connected by a spherical hinge. The system is assumed to move along a circular orbit under the action of gravitational torque. The equilibrium orientations of the two-body system are determined by the real roots of a system of 12 algebraic equations of the stationary motions. Attention is paid to the study of the conditions of existence of the equilibrium orientations of the system of two bodies refers to special cases when one of the principal axes of inertia of each of the two bodies coincides with either the normal of the orbital plane, the radius vector or the tangent to the orbit. Nine distinct solutions are found within an approach which uses the computer algebra method based on the algorithm for the construction of a Gröbner basis.