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Presents the use of the dual reciprocity method (DRM) for solving inverse problems described by Poisson's equation. DRM provides a technique for taking the domain integrals associated with the inhomogeneous term to the boundary. For that reason, the DRM is supposed to be ideal for solving inverse problems. Solving inverse problems, a linear system is produced which is usually predetermined and ill‐posed. To solve that kind of problem, implements the Tikhonov algorithm and compares it with the analytical solution. In the end, tests the whole algorithm on different problems with analytical solutions.

The purpose of the paper is to propose an effective approach of artificial intelligence (AI) addressing social-humanitarian reality comprising non-formalizable representation. The new task is to describe processes of integration of AI and humans in the hybrid systems framework.

Social-humanitarian dynamics contradict traditional characteristics of AI. Suggested methodology embraces formalized and non-formalized parts as a whole. Holonic and special convergent approaches are combined to ensure purposefulness and sustainability of collective decision-making. Inverse problem solving on topology spaces, control thermodynamics and non-formalizable (considering quantum and relativistic) semantics include observers of eigenforms of reality.

Collective decision-making cannot be represented only by formal means. Thus, this paper suggests the equation of hybrid reality (HyR), which integrates formalizable and non-formalizable parts conveying and coalescing holonic approaches, thermodynamic theory, cognitive modeling and inverse problem solving. The special convergent approach makes the solution of this equation purposeful and sustainable.

The suggested approach is far reaching with respect of current state-of-the-art technology; medium-term limitations are expected in the creation of cognitive semantics.

Social-humanitarian events embrace all phenomena connected with individual and collective human behavior and decision-making. The paper will impact deeply networked experts, groups of crowds, rescue teams, researchers, professional communities, society and environment.

New possibilities for advanced AI to enable purposeful and sustainable social-humanitarian subjects. The special convergent information structuring during collective decision-making creates necessary conditions toward the goals.

This paper aims to study the strategies used by ten students diagnosed with autism when solving multiplication and division problems because these operations are rarely studied in students with this condition.

This study conducted an exploratory study with ten students diagnosed with autism to explore and describe the strategies used in solving equal group problems. The authors also describe in detail the case of a student whom the authors deem to be representative because of the reasoning the student employed.

The informal strategies that they used are described, as well as the difficulties observed in the various problems, depending on the operation required to solve them. The strategies used include direct modeling with counting and others that relied on incorrect additive relationships, with strategies based on multiplication and division operations being scarce. Difficulties were observed in several problems, with measurement division being particularly challenging for the study participants.

The detailed description of the strategies used by the students revealed the meanings that they associate with the operations they are executing and brought to light potential difficulties, which can help teachers plan their instruction.

This research supplements other studies focusing on mathematical problem-solving with autistic students.

This paper aims to increase corporate social responsibility (CSR), including business acting in an ethical and transparent way, through the prism of strategic conversation with applying the author’s convergent methodology that ensures the integrity, purposefulness and sustainability of development of corporations in the external environment.

The methodology is based on the integration of following approaches and methods: international CSR standards, strategic planning, networked virtual collaboration, group cognitive (conceptual) modelling, inverse problem-solving in topological spaces, categories theory, control thermodynamics, big data analysis for cognitive models verification and quantum semantic approach.

The convergent methodology helps to visualize the strategic situation in a corporation and gives more chances to get a clear feeling for every employee that his or her social responsibility helps to achieve not only his or her own goals but the goals of the company. This approach helps to accelerate the raising of the level of CSR.

The strategic situation for raising the level of CSR has to be represented during strategic conversations. The strategic process should cover all the employees of the corporation. Groups can be hierarchically organized. The number of participants of one group can be about 35, and the duration of one conversation is up to 5 hours.

The convergent methodology was applied many times for creating a high-level CSR atmosphere by the collective building of companies’ strategies.

The convergent approach provides proactive identification of adverse effects of the external environment on the level of CSR and prevention of such impacts. The approach also provides acceleration of corporate strategic planning, processes of network democracy and group decision-making processes.

The main developing problem, which is beyond the state of the art, is that the CSR situation cannot be described in a clear, logical and formalised way, and a traditional computer model cannot be created for this case with formalised approach. The proposed convergent methodology with cognitive modelling helps to do it.

The purpose of this paper is to develop a source reconstruction technique, applied to a case study in biomagnetism, using both evolutionary optimization and regularization techniques.

The magnetic field, produced by a current dipole in a spheroidal domain modeling the head, is calculated. Although the model is very simple, the magnetic effect of a brain source is appropriately simulated. In order to solve the source identification problem, the following approaches have been implemented: a single‐objective minimization of a residual function, based on an evolutionary algorithm, is applied first; then, the L‐curve criterion for regularization is implemented by means of an iterative search.

A variable number of unknown parameters, defining direction and magnitude of the current dipole, have been considered. As a consequence, several optimization problems are solved: a technique based on the use of the lead field matrix identifies the source with the smallest error. Eventually, an iterative procedure based on Tikhonov regularization is proposed. The algorithm is tested with and without noise affecting data. The results showed an accuracy comparable to that obtained independently with the optimization approach.

A model problem in inverse biomagnetism, which is both simple and significant, has been formulated and solved. The magnetic source of brain activity is reconstructed in a fast way and with small errors by means of two techniques of field inversion.

This paper presents a method to improve inverse problem resolution. This method focuses on the measurement set and particularly on sensor position. Based on experiment, it aims at finding sensor position criteria to insure the least bad inverse problem solving.

The studied device is a magnetized steel sheet measured by four sensors. Three optimization techniques are compared: condition number, solid angle and signature optimization.

An efficient criterion to compare the inverse problem resolution quality is presented. The comparison of optimization techniques shows that only signature optimization gives accurate results.

A relative simple case is studied in this paper: only four sensors are used to measure a steel sheet. Moreover magnetostatic low‐field case is supposed. Nevertheless techniques presented could be applied to more complex studies. Condition number and solid angle optimizations techniques should be tested with more sensors to confirm or infirm their inefficiency.

This paper presents the first step of a larger study concerning ships for naval application. The aim is to predict magnetic anomaly created by ship to compensate it. This anomaly could be computed through the resolution of an inverse problem based on internal measurements. The signature optimization technique could be used to find the optimal sensor location onboard.

Traditional regularization techniques are focusing on adding mathematical or physical information to the system in order to improve it. This paper provides another approach to improve inverse problem resolution through measurement set. It shows that sensor position optimization should be efficient.

This paper aims to discuss the inverse problems that arise in various practical heat transfer processes. The purpose of this paper is to provide an identification method for predicting the internal boundary conditions for thermal analysis of mechanical structure. A few examples of heat transfer systems are given to illustrate the applicability of the method and the challenges that must be addressed in solving the inverse problem.

In this paper, the thermal network method and the finite difference method are used to model the two-dimensional heat conduction inverse problem of the tube structure, and the heat balance equation is arranged into an explicit form for heat load prediction. To solve the matrix ill-conditioned problem in the process of solving the inverse problem, a Tikhonov regularization parameter selection method based on the inverse computation-contrast-adjustment-approach was proposed.

The applicability of the proposed method is illustrated by numerical examples for different dynamically varying heat source functions. It is proved that the method can predict dynamic heat source with different complexity.

The modeling calculation method described in this paper can be used to predict the boundary conditions for the inner wall of the heat transfer tube, where the temperature sensor cannot be placed.

This paper presents a general method for the direct prediction of heat sources or boundary conditions in mechanical structure. It can directly obtain the time-varying heat flux load and thtemperature field of the machine structure.

The purpose of this study is to optimize multilayer vacuum thermal insulation (MLI) of modern high-weight spacecrafts. An adequate mathematical simulation of heat transfer in the MLI is impossible if there is no available information on the main insulation properties.

The results of experiments in thermo-vacuum facilities are used to re-estimate some radiative properties of metallic foil/metalized polymer foil and spacer on the basis of the inverse problem solution. The experiments were carried out for the sample of real MLI used for the BP-Colombo satellite (ESA). The recently developed theoretical model based on neglecting possible near-field effects in radiative heat transfer between closely spaced aluminum foils was used in theoretical predictions of heat transfer through the MLI.

A comparison of the computational results and the experimental data confirms that there are no significant near-field effects between the neighboring MLI layers. It means that there is no considerable contradiction between the far-field model of radiative transfer in MLI and the experimental estimates.

An identification procedure for mathematical model of the multilayer thermal insulation showed that a modified theoretical model developed recently can be used to estimate thermal properties of the insulation at conditions of space vacuum.

Inverse problems in electromagnetism, namely, the recovery of sources (currents or charges) or system data from measured effects, are usually ill-posed or, in the numerical formulation, ill-conditioned and require suitable regularization to provide meaningful results. To test new regularization methods, there is the need of benchmark problems, which numerical properties and solutions should be well known. Hence, this study aims to define a benchmark problem, suitable to test new regularization approaches and solves with different methods.

To assess reliability and performance of different solving strategies for inverse source problems, a benchmark problem of current synthesis is defined and solved by means of several regularization methods in a comparative way; subsequently, an approach in terms of an artificial neural network (ANN) is considered as a viable alternative to classical regularization schemes. The solution of the underlying forward problem is based on a finite element analysis.

The paper provides a very detailed analysis of the proposed inverse problem in terms of numerical properties of the lead field matrix. The solutions found by different regularization approaches and an ANN method are provided, showing the performance of the applied methods and the numerical issues of the benchmark problem.

The value of the paper is to provide the numerical characteristics and issues of the proposed benchmark problem in a comprehensive way, by means of a wide variety of regularization methods and an ANN approach.

The principle of microwave characterization of dielectric materials using open-ended coaxial line probe is to link the dielectric properties of the sample under test to the measurements of the probe admittance (Y(f) = G(f)+ jB(f )). The purpose of this paper is to develop an alternative inversion tool able to predict the evolution of the complex permittivity (ε = ε′ – jε″) on a broad band frequency (f from 1 MHz to 1.8 GHz).

The inverse problem is solved using adaptive network based fuzzy inference system (ANFIS) which needs the creation of a database for its learning. Unfortunately, train ANFIS using f, G and B as inputs has given unsatisfying results. Therefore, an inputs selection procedure is used to select the three optimal inputs from new inputs, created mathematically from original ones, using the Jang method.

Inversion results of measurements give, after training, in real time the complex permittivity of solid and liquid samples with a very good accuracy which prove the applicability of ANFIS to solve inverse problems in microwave characterization.

The originality of this paper consists on the use of ANFIS with input selection procedure based on the Jang method to solve the inverse problem where the three optimal inputs are selected from 26 new inputs created mathematically from original ones (f, G and B).