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The purpose of this paper is to solve both eigenvalue and boundary value problems coming from the field of quantum mechanics through the application of meshless methods, particularly the one known as meshless local Petrov‐Galerkin (MLPG).

Regarding eigenvalue problems, the authors show how to apply MLPG to the time‐independent Schrödinger equation stated in three dimensions. Through a special procedure, the numerical integration of weak forms is carried out only for internal nodes. The boundary conditions are enforced through a collocation method. The final result is a generalized eigenvalue problem, which is readily solved for the energy levels. An example of boundary value problem is described by the time‐dependent nonlinear Schrödinger equation. The weak forms are again stated only for internal nodes, whereas the same collocation scheme is employed to enforce the boundary conditions. The nonlinearity is dealt with by a predictor‐corrector scheme.

Results show that the combination of MLPG and a collocation scheme works very well. The numerical results are compared to those provided by analytical solutions, exhibiting good agreement.

The flexibility of MLPG is made explicit. There are different ways to obtain the weak forms, and the boundary conditions can be enforced through a number of ways, the collocation scheme being just one of them. The shape functions used to approximate the solution can incorporate modifications that reflect some feature of the problem, like periodic boundary conditions. The value of this work resides in the fact that problems from other areas of electromagnetism can be attacked by the very same ideas herein described.

The purpose of this paper is to introduce new non‐classical implementations of neural networks (NNs). The developed implementations are performed in the quantum, nano, and optical domains to perform the required neural computing. The various implementations of the new NNs utilizing the introduced architectures are presented, and their extensions for the utilization in the non‐classical neural‐systolic networks are also introduced.

The introduced neural circuits utilize recent findings in the quantum, nano, and optical fields to implement the functionality of the basic NN. This includes the techniques of many‐valued quantum computing (MVQC), carbon nanotubes (CNT), and linear optics. The extensions of implementations to non‐classical neural‐systolic networks using the introduced neural‐systolic architectures are also presented.

Novel NN implementations are introduced in this paper. NN implementation using the general scheme of MVQC is presented. The proposed method uses the many‐valued quantum orthonormal computational basis states to implement such computations. Physical implementation of quantum computing (QC) is performed by controlling the potential to yield specific wavefunction as a result of solving the Schrödinger equation that governs the dynamics in the quantum domain. The CNT‐based implementation of logic NNs is also introduced. New implementations of logic NNs are also introduced that utilize new linear optical circuits which use coherent light beams to perform the functionality of the basic logic multiplexer by utilizing the properties of frequency, polarization, and incident angle. The implementations of non‐classical neural‐systolic networks using the introduced quantum, nano, and optical neural architectures are also presented.

The introduced NN implementations form new important directions in the NN realizations using the newly emerging technologies. Since the new quantum and optical implementations have the advantages of very high‐speed and low‐power consumption, and the nano implementation exists in very compact space where CNT‐based field effect transistor switches reliably using much less power than a silicon‐based device, the introduced implementations for non‐classical neural computation are new and interesting for the design in future technologies that require the optimal design specifications of super‐high speed, minimum power consumption, and minimum size, such as in low‐power control of autonomous robots, adiabatic low‐power very‐large‐scale integration circuit design for signal processing applications, QC, and nanotechnology.

As any attempts at explaining quantum theory in terms of simple, local “cause‐and‐effect” models have remained unsatisfactory, approaches from the perspectives of systems theory seem called for, which is rich in a variety of more complex understandings of causality.

This paper presents one option for such approaches, which the author has introduced previously as “quantum cybernetics”: considering waves (but not “wave functions”!) and “particles” as mutually dependent system components, and thus defining “organizationally closed systems” characterized by a fundamental circular causality. Using such an approach, a new look can be achieved on both classical and quantum physics.

It was found that quantum theory's most fundamental equation, the Schrödinger equation, can actually be derived from classical physics, once the latter is considered anew, i.e. under said approach involving both particles and (Huygens) waves. In fact, the only difference to existing views is that Huygens waves are here considered to be real, physically effective waves in some hypothesized sub‐quantum medium, rather than mere formal tools.

What is particularly new in the present paper is that quantum systems can be described by what Heinz von Foerster has called “nontrivial machines”, whereas the corresponding classical counterparts turn out to behave as “trivial machines”. This should provide enough stimulus for discussing system theoretical issues also in the context of the foundations of quantum theory.

Recent advances in the fabrication technology of heterojunction semiconductor nanostructures have made possible the realization of systems with extremely small sizes. In these devices, electrons are confined along some directions and are free to move in others. Semiconductor nanostructures have become so small that we have to take into account quantum effects. The two dimensional physical model consists of Poisson’s equation for the electrostatic potential φ, coupled with an eigenvalue problem for Schrödinger’s equation. Proposes

The purpose of this paper is to concern with a reliable treatment of the (2+1)-dimensional and the (3+1)-dimensional logarithmic Boussinesq equations (BEs). The author uses the sense of the Gaussian solitary waves to determine these gaussons. The study confirms that models characterized by logarithmic nonlinearity give gaussons solitons of distinct physical structures.

The proposed technique, as presented in this work has been shown to be very efficient for solving nonlinear equations with logarithmic nonlinearity.

The (2+1) and the (3+1)-dimensional BEs were examined as well. The examined models feature interesting results in propagation of waves and fluid flow.

The paper presents a new efficient algorithm for the higher dimensional logarithmic BEs.

The work shows the effect of logarithmic nonlinearity compared to other nonlinearities where standard solitons appear in the last case.

The work will benefit audience who are willing to examine the effect of logarithmic nonlinearity.

The paper presents a new efficient algorithm for the higher dimensional logarithmic BEs.

This paper applies a volume-price probability wave differential equation to propose a conceptual theory and has innovative behavioral interpretations of intraday dynamic market equilibrium price, in which traders' momentum, reversal and interactive behaviors play roles.

The authors select intraday cumulative trading volume distribution over price as revealed preferences. An equilibrium price is a price at which the corresponding cumulative trading volume achieves the maximum value. Based on the existence of the equilibrium in social finance, the authors propose a testable interacting traders' preference hypothesis without imposing the invariance criterion of rational choices. Interactively coherent preferences signify the choices subject to interactive invariance over price.

The authors find that interactive trading choices generate a constant frequency over price and intraday dynamic market equilibrium in a tug-of-war between momentum and reversal traders. The authors explain the market equilibrium through interactive, momentum and reversal traders. The intelligent interactive trading preferences are coherent and account for local dynamic market equilibrium, holistic dynamic market disequilibrium and the nonlinear and non-monotone V-shaped probability of selling over profit (BH curves).

The authors will understand investors' behaviors and dynamic markets through more empirical execution in the future, suggesting a unified theory available in social finance.

The authors can apply the subjects' intelligent behaviors to artificial intelligence (AI), deep learning and financial technology.

Understanding the behavior of interacting individuals or units will help social risk management beyond the frontiers of the financial market, such as governance in an organization, social violence in a country and COVID-19 pandemics worldwide.

It uncovers subjects' intelligent interactively trading behaviors.

A new quantum effect device which is capable of highly coherent electron emission is theoretically proposed and analysed. The new device works by using the potential induced accumulation layer at a heterointerface to produce dimensionally reduced electrons. These electrons tunnel through a heterobarrier ensuring that their energy is quantised in the direction of propagation. To avoid the problem of unquantised three dimensional electrons dominating the current the two dimensional electrons that tunnel through the barrier are replenished by electrons from two side contacts. A self‐consistent model is used to analyse the performance of the device and it is found that the new device performs very well, producing electrons with a very narrow energy spread in the direction of propagation. The current density/coherency combination is easily controlled by the applied bias and the device also offers the potential for ultra fast switching through the transition between coherent and incoherent states.

The decomposition model has demon‐strated accurate and physically realistic solutions of systems modelled by non‐linear equations. Linear or determin‐istic equations become simple special cases and the result is a general method of solution connecting the fields of ordinary and partial differential equations. No linearisation or resort to numerically intensive discretised methods is involved. The avoidance of these limiting and restrictive methods offers physically correct solutions as well as insights into the behaviour of real systems where non‐linear effects play a crucial role. In difficult applications, such as those now approached by computational fluid dynamics, the potential saving in computation will be substantial. The method clearly offers the potential of a significant step forward in the rapid solution of complex applications in a time and memory‐saving manner with important implications for computa‐tional analysis and modelling.

The purpose of this paper is to propose a numerical technique based on polynomial differential quadrature method (PDQM) to find the numerical solutions of two-space-dimensional quasilinear hyperbolic partial differential equations subject to appropriate Dirichlet and Neumann boundary conditions.

The PDQM reduced the equations into a system of second order linear differential equation. The obtained system is solved by RK4 method by converting into a system of first ordinary differential equations.

The accuracy of the proposed method is demonstrated by several test examples. The numerical results are found to be in good agreement with the exact solutions. The proposed technique can be applied easily for multidimensional problems.

The main advantage of the present scheme is that the scheme gives very accurate and similar results to the exact solutions by choosing less number of grid points and the problem can be solved up to big time. The good thing of the present technique is that it is easy to apply and gives us better accuracy in less numbers of grid points as comparison to the other numerical techniques.

The purpose of this paper is to present the computational modeling of second-order two-dimensional nonlinear hyperbolic equations by using cosine expansion-based differential quadrature method (CDQM).

The CDQM reduced the equations into a system of second-order differential equations. The obtained system is solved by RK4 method by converting into a system of first ordinary differential equations.

The computed numerical results are compared with the results presented by other workers (Mohanty et al., 1996; Mohanty, 2004) and it is found that the present numerical technique gives better results than the others. Second, the proposed algorithm gives good accuracy by using very less grid point and less computation cost as comparison to other numerical methods such as finite difference methods, finite elements methods, etc.

The author extends CDQM proposed in (Korkmaz and Dağ, 2009b) for two-dimensional nonlinear hyperbolic partial differential equations. This work is new for two-dimensional nonlinear hyperbolic partial differential equations.