Basic convergence theory for the network element method

A recent paper introduced the network element method (NEM) where the usual mesh was replaced by a discretization network. Using the associated network geometric coefficients and following the virtual element framework, a consistent and stable numerical scheme was proposed. The aim of the present paper is to derive a convergence theory for the NEM under mild assumptions on the exact problem. We also derive basic error estimates, which are sub-optimal in the sense that we have to assume more regularity than usual.

CALCULATION OF THE BASIC AND ADDITIONAL ERRORS OF THE MOISTURE METER OF GRAIN AND GRAIN PRODUCTS

Calculation of the basic error of the moisture meter is determined by the error in measuring the frequency. The latter, in turn, consists of the error of the timer-counter when counting the frequency (quantization), the error in determining the coefficients a1and a2of the mathematical model of the measuring transducer during calibration, and the error due to the noise of the comparator-amplifier.Keywords:error, error calculation, measurements, result.

Armenia in Ptolemy’s Geography (ca. AD 150): A “Parody” of His Work? Some Corrections and Suggestions

Ptolemyʾs Geographike Hyphegesis (Introduction to Geography) (ca. AD 150) consists of a huge and invaluable stock of topographical information. More than 6,000 toponyms are even defined by coordinates. Nevertheless, Ptolemyʾs cities are often misplaced or pop up more than once in his maps. This is especially true with his confusing description of Armenia (geogr. 5.13), which caused a modern scholar to call it a ‘parody’ of his work and method. This paper aims at clarifying the basic error in all of Ptolemyʾs coordinates and proposes some explanations and corrections for his Armenian toponyms.

PROBLEMATIC ISSUES OF THE USE OF FIBER-OPTIC PRESSURE SENSORS IN MEDICAL PRACTICE

The problematic issues that arise when measuring low pressures in medical practice, and the associated difficulties in designing measuring instruments, first of all, the low sensitivity of signal conversion, leading to an increase in the components of the basic error, the overall dimensions of the devices, the use of indirect measurement methods that entail large methodo-logical measurement errors, are considered. It is proposed to switch to advanced fiber-optic pressure sensors and new ways to measure low pressures with them.

A New Kinematic Error Modelling and Identification Method of the Parallel Manipulator

Parallel manipulators have broad application prospects on hybrid machine tools. Kinematic error modelling and identification are two key processes to improve the accuracy of parallel manipulators. The traditional kinematic error modelling method adopts the partial differentiation of the ideal kinematic model. However, the partial differentiation method is pure mathematical calculation, which ignores physical meaning of error terms corresponding to each link. In the process of error identification, the Jacobian matrix obtained from the partial differentiation method is usually ill-conditioned, which leads to non-convergence of the identification process. In order to solve the above problems, this paper proposes a new kinematic error modelling method and an error identification model. Firstly, the basic error terms for single link are analyzed. Based on basic error terms, the kinematic error model is established by using the practical connection point of two adjacent links. Then, a new error identification model is derived from the kinematic error model. Finally, as a study case, a 3-DOF parallel tool head is used to verify the correctness of the proposed method. The numerical results show that the proposed method is effective and the accuracy of the 3-DOF parallel tool head improves significantly after compensation of error terms.

HOTA: A Higher Order Metric for Evaluating Multi-object Tracking

Multi-object tracking (MOT) has been notoriously difficult to evaluate. Previous metrics overemphasize the importance of either detection or association. To address this, we present a novel MOT evaluation metric, higher order tracking accuracy (HOTA), which explicitly balances the effect of performing accurate detection, association and localization into a single unified metric for comparing trackers. HOTA decomposes into a family of sub-metrics which are able to evaluate each of five basic error types separately, which enables clear analysis of tracking performance. We evaluate the effectiveness of HOTA on the MOTChallenge benchmark, and show that it is able to capture important aspects of MOT performance not previously taken into account by established metrics. Furthermore, we show HOTA scores better align with human visual evaluation of tracking performance.

The Problem of the Meaning of Life: Philosophical and Psychological Content and Research Perspectives

The paper analyzes the problem of the meaning of life in a single conceptual framework grounded in philosophical/religious and psychological knowledge. It reveals the philosophical/religious and psychological con¬tent of the problem: the former is defined in terms of the meaning of life as a sign/symbolic unit of initial experience, while the latter — in terms of the ideal form of an event in personality development, which is considered an existential structure of personality represented in the form of affective and meaning constructs and initial symbols. The paper criticizes existing psychological studies on meanings of life for their basic error of conceptual substitution of the ideal object of research: the meaning of life as the ideal form is replaced with eudemonic attitude and regarded as the real form. The paper concludes that perspectives of psychological research into the meaning of life which would take into account its philosophical/religious content lie at the junction of explorations of the meaning of life and explorations of reflective activity of the subject of consciousness solving the task of finding the meaning.

Geometric and thermal error compensation for CNC milling machines based on Newton interpolation method

The fast and accurate modeling for machine errors is an important step for the implementation of error compensation. In this article, a new approach for real-time compensation of geometric and thermal errors is presented, including an accurate error model and a real-time error compensation system. An experiment is carried out on a three-axis milling center to obtain machine positioning errors under different temperatures. A serial of error data collected under normal temperature is regarded as the basic error and modeled with the machine position coordinates based on Newton interpolation method which is also used for modeling the other error curves under different working temperatures in order to get their coefficients of fitting formulas. According to the relationship among these formulas, all the coefficients and the corresponding temperature variations are modeled using the Newton interpolation method again. The final compensation model can be obtained by substituting the coefficients of basic error formula. In addition, an external real-time error compensation system is developed based on the function of external machine zero point shift in Fanuc CNC systems. Experimental results show that the proposed geometric and thermal error compensation system can be utilized as an effective manner to improve the accuracy of CNC milling machines.