We assume that the current mathematical knowledge K is a finite set of statements from both formal and constructive mathematics, which is time-dependent and publicly available. Any theorem of any mathematician from past or present belongs to K. The set K exists only theoretically. Ignoring K and its subsets, sets exist formally in ZFC theory although their properties can be time-dependent (when they depend on K) or informal. In every branch of mathematics, the set of all knowable truths is the set of all theorems. This set exists independently of K. Algorithms always terminate. We explain the distinction between algorithms whose existence is provable in ZFC and constructively defined algorithms which are currently known. By using this distinction, we obtain non-trivial statements on decidable sets X⊆N that belong to constructive and informal mathematics and refer to the current mathematical knowledge on X. This and the next sentence justify the article title. For any empirical science, we can identify the current knowledge with that science because truths from the empirical sciences are not necessary truths but working models of truth about particular real phenomena.

This article articulates the significance of conceptual analysis (CA) methods for the postgraduate philosophy scholar at the G-CAR institution. In order to clarify the significance, first the concepts were defined, their context examined and the problems posed by the concepts looked at. The activity of scholars who are bent on researching for concepts meaning, was highlighted and the methods scholars use in determining meaning were carefully examined. Three major methods discussed by philosophers, namely, constructive, reductive and detective were explained as well as their significance in helping philosophy scholars do qualitative research in meaning determination. Meaning was found to be a discovery of the observer’s relationship to the objective reality as depicted by concepts. The common factor in these three methods was the dominant role both the observer and the human subjects played in determining meaning – a constructive engagement. It was clarified too, that the ability to explicate concepts’ meaning is the tool kit or skill sets that all scholars need to navigate the semantic jungle in the 21^st Century.

Modularity in the construction of industrial robots is becoming increasingly popular, as the modules can be assembled in different ways so as to obtain various architectures of industrial robots determined by the requirements of specific applications. Such a robot with modular structure is considered in this paper. The tracked mobile robot, with translation – rotation – translation – translation – rotation (TRTTR) modular serial structure, is the subject of national invention patent number RO132301 B1/2021, granted by the State Office for Inventions and Trademarks of Bucharest, to “Nicolae Bălcescu” Land Forces Academy of Sibiu, Romania [1]. The tracked mobile robot has been designed to perform the task of humanitarian demining operations and the mechanical structure, respectively the kinematic analysis were described in detail in papers [1,2]. A first general objective of this paper is to highlight a dynamic-organological method to achieve an architectural structure of mobile robot on tracks, able to replace the human element in areas with high risk for health and life, for detection and demining anti-personnel and anti-armor minefields in countries where military conflicts have taken place. For this scope it was performed the dynamic modeling using the Lagrange’s formalism and to achieve the constructive optimization of the TRTTR mechanical structure, in order to obtain a minimum energy consumption through an optimal arrangement of the modules in its structure. A second objective is to improve the action flexibility of the technological product in humanitarian detection and demining operations, as well as for educational purposes, by training highly educated and specialized human resources in the field of advanced military technologies. The differential equations of motion of the robot has obtained and respectively the mechanical design equations, which lead to the optimal choice of the drive motors of the modules in the robot structure. Also, it is presented the mathematical model for obtaining the driving motor of base translation modulus (MTB SIL) of the modular serial tracked robot and the constructive solution of the MTB SIL module.

The definition of a Smart-complex of educational discipline and its technology is given. Attention is focused on the form of the Smart-complex and constructive elements: the creative educational environment, the author's environment, the non-verbal environment, the encyclopedia, the creative / self-realization environment, the monitoring / self-evaluation environment.A feature of the Smart-complex of the academic discipline is the integration into it of the structural equalization block. Constructive alignment (alignment) is based on the design of the student's own learning participation in educational projects. Alignment refers to creating an appropriate learning environment and involves selecting the most appropriate training activities and evaluating each learning outcome. If the result of the training is to develop analytical skills, then for the assessment it is necessary to build questions and scenarios for their development.Two main components of the structural alignment are considered: 1) the first component is based on cognitive psychology and constructivist theory, recognizes the importance of linking new material with the concepts and experiences of students and extrapolation to possible future scenarios in the process of mission activity - they comprehend what they are doing during training; 2) the second component is based on the declaration by the teacher of the correspondence between the planned educational activities and the results of the training of students. This makes planning of educational activities and development of self-assessment criteria for organizing feedback. It is necessary to take into account the impact of Smart-complexes of educational disciplines on three think-tank training networks: 1) effective networks (why learn) - several ways of presenting to give students different ways of obtaining information and knowledge; 2) recognition networks (learning outcomes) - several ways of expressing them to provide them with an alternative for demonstrating what they know; 3) strategic exercises (how to learn) - several ways to increase the motivation for learning to attract their attention to both their own learning project and its technical and historical decision. Smart-complexes of educational disciplines should be: 1) scientific; 2) with user-friendly interface; 3) have a connection with LMS; 4) structured; 5) with visual material; 6) working in Off-line mode; 7) used on various devices in an educational institution, as well as at home.

The recent Google’s claim on breakthrough in quantum computing is a gong signal for further analysis of foundational roots of (possible) superiority of some quantum algorithms over the corresponding classical algorithms. This note is a step in this direction. We start with critical analysis of rather common reference to entanglement and quantum nonlocality as the basic sources of quantum superiority. We elevate the role of the Bohr’s principle of complementarity¹ (PCOM) by interpreting the Bell-experiments as statistical tests of this principle. (Our analysis also includes comparison of classical vs genuine quantum entanglements.) After a brief presentation of PCOM and endowing it with the information interpretation, we analyze its computational counterpart. The main implication of PCOM is that by using the quantum representation of probability, one need not compute the joint probability distribution (jpd) for observables involved in the process of computation. Jpd’s calculation is exponentially time consuming. Consequently, classical probabilistic algorithms involving calculation of jpd for n random variables can be over-performed by quantum algorithms (for big values of n). Quantum algorithms are based on quantum probability calculus. It is crucial that the latter modifies the classical formula of total probability (FTP). Probability inference based on the quantum version of FTP leads to constructive interference of probabilities increasing probabilities of some events. We also stress the role the basic feature of the genuine quantum superposition comparing with the classical wave superposition: generation of discrete events in measurements on superposition states. Finally, the problem of superiority of quantum computations is coupled with the quantum measurement problem and linearity of dynamics of the quantum state update.