General Mathematics

2309 Submissions

[3] viXra:2309.0070 [pdf] submitted on 2023-09-14 20:11:32

Fundamental Theorem of Algebra

Authors: Edgar Valdebenito
Comments: 4 Pages.

One of the immediate consequences of Cauchy's integral formula is Liouville's theorem, which states that an entire ( that is, holomorphic in the whole complex plane C ) function cannot be bounded if it is not constant. This profound result leads to arguably the most natural proof of Fundamental Theorem of Algebra.
Category: General Mathematics

[2] viXra:2309.0039 [pdf] submitted on 2023-09-06 23:56:43

Thermostatic Control of Mems Imu Using a Peltier Plate

Authors: Sok Hun Kim, Thae Ju Ri, Ung Cha
Comments: 7 Pages.

In recent years, the micro-electro- mechanical-system(MEMS) IMUs (Inertial Measurement Units) have been widely used in UAVs(Unmanned Aerial Vehicles), UGVs(Unmanned Ground Vehicles) and Robotics due to their small size, light weight, low power consumption and low cost.MEMS IMU contains 3-axis accelerometer, 3-axis gyroscope, 3-axis magnetometer, thermometer, etc. in a single microchip, but MEMS gyroscope’s accuracy tends to be low, especially by temperature influence, and they generally require error compensation in practical applications.Especially, the zero-bias is greatly changed by temperature variations.Considering the simplification and real-time requirement, we present the hardware and software design methods for thermostatic control of MEMS IMU using a peltier plate.Then the Neural Adaptive PID (Proportion Integration Differentiation) controller is used to stabilize the inner temperature of MEMS IMU enclosure by controlling the amount of heating and cooling of a peltier plate.As shown in the experiment, the transient time is less than 3 min , the rising time is less than 5s/℃ and the falling time is less than 10 s/℃ so the property of the dynamic response in the thermostatic control system is improved much better than in other methods.The overall cost is lower than 100$ and it is easy to implement hardware and software.Thus this can be widely used in UAVs, UGVs and Robotics
Category: General Mathematics

[1] viXra:2309.0026 [pdf] submitted on 2023-09-04 19:56:34

Numerical Calculation of Roots of Real Polynomial Functions, Convergent Method

Authors: Juan Jorge Isaac Lopez
Comments: 5 Pages.

The Newton-Raphson method is the most widely used numerical calculation method to determine the roots of Real polynomial functions, but it has the drawback that it does not always converge. The method proposed in this work establishes the convergence condition and the development of its application, and therefore will always converge towards the roots of the function. This will mean a conclusive advance for the determination of roots of Real polynomial functions. According to interpretation of the Abel-Ruffini theorem, the roots of polynomial functions of degree greater than 4 can only be determined by numerical calculation.
Category: General Mathematics