Ismail Abbas

• PhD lecturer at MTC Cairo Univ-Ex Professor at ULP Strasbourg-Ex Research director at CNRS France
• Senior LecturerAuthor of the original numerical theory called the Cairo technique. at Cairo University

Theory and Practice of Artificial Intelligence Abstract If you don't understand artificial intelligence, ask yourself if Iam right because others don't understand it either. There is no generally applicable definition of artificial intelligence. The field is so vast that its actors will always have to develop a more precise definition of their own...

Artificial Intelligence AI can be simply defined as solving problems through automated algorithms. In this article, we explain the basic prerequisite skills of a future AI programmer and how he can improve his abilities in the field of artificial intelligence programming. Finally, we use AI to test the correctness of the well-known theories of rela...

Artificial Intelligence AI can be simply defined as solving problems through automated algorithms. In this article, we define and explain the basic prerequisite skills of a future AI programmer and show how he can improve his abilities in the field of artificial intelligence programming. Finally, we use AI to test the correctness of the well-known...

If you don't understand the theories of physics and mathematics, ask yourself if I'm right, because others don't understand these theories either. These theories cannot be made understandable in the current, incomplete R^4 space. Einstein, Schrödinger, Heisenberg, Minkowski, Hilbert, Rieman, among others, overcomplicated the theory of mathematics a...

If you don't understand the theories of physics and mathematics, ask yourself if I'm right, because others don't understand these theories either. These theories cannot be made understandable in the current, incomplete R^4 space. Einstein, Schrödinger, Heisenberg, Minkowski, Hilbert, Rieman, among others, overcomplicated the theory of mathematics a...

The one-dimensional intelligence quotient (IQ), commonly used as a measure of human intelligence from special tests, is incomplete. We assume that IQ tests alone are not sufficient to classify people and that we can find more comprehensive tests. These tests should allow us to classify humans in a more comprehensive way, applicable to job assignmen...

If you don't understand the theories of physics and mathematics, ask yourself if I'm right, because others don't understand these theories either. These theories cannot be made understandable in the current, incomplete R^4 space. Einstein, Schrödinger, Heisenberg, Minkowski, Hilbert, Rieman, among others, overcomplicated the theory of mathematics a...

If you don't understand Einstein's theory of relativity, Schrödinger's theory of quantum mechanics, or integral mathematical equations, ask yourself if I'm right, because others don't understand these theories either. These theories cannot be made understandable in the current, incomplete R^4 space.

If you don't understand Einstein's theory of relativity, Schrödinger's theory of quantum mechanics or integral mathematical equations, ask yourself if I'm right, because others don't understand these theories either.

Einstein, Schrödinger, Heisenberg, Minkowski, Hilbert, Rieman, among others, overcomplicated the theory of relativity and the theory of quantum mechanics simply because they did not define time correctly. The theory of relativity and the Schrödinger partial differential equation are the newest science and therefore should be the most accurate, but...

If you don't understand special and general relativity, ask yourself if I'm right, because others don't understand Einstein's relativity either. In 1905, A. Einstein published his theory of special relativity for two inertial frames and in 1915 he published his theory of general relativity for two frames moving with arbitrary acceleration relative...

If you don't understand special and general relativity, ask yourself if I'm right, because others don't understand Einstein's relativity either. In 1905, A. Einstein published his theory of special relativity for two inertial frames and in 1915 he published his theory of general relativity for two frames moving with arbitrary acceleration relative...

If you don't understand special and general relativity, ask yourself if I'm right, because others don't understand Einstein's relativity either. In 1905, A. Einstein published his theory of special relativity for two inertial frames and in 1915 he published his theory of general relativity for two frames moving with arbitrary acceleration relative...

If you don't understand quantum mechanics, ask yourself if I'm right, because others don't understand quantum mechanics either. Quantum mechanics and the Schrödinger partial differential equation are the newest science and therefore should be the most accurate, but unfortunately it is the opposite. In a previous article we show that the proper refo...

Abstract:- If you don't understand quantum mechanics, ask yourself if I'm right, because others don't understand quantum mechanics either. Quantum mechanics is the newest science and therefore should be the most accurate, but unfortunately the opposite is true. By unnecessary quantum mechanics we mean incomplete/inexact parts of quantum mechanics i...

If you don't understand quantum mechanics, ask yourself if I'm right, because others don't understand quantum mechanics either. Quantum mechanics is the newest science and therefore should be the most accurate, but unfortunately the opposite is true. By unnecessary quantum mechanics we mean incomplete/inexact parts of quantum mechanics in the class...

If you don't understand quantum mechanics, ask yourself if I'm right, because others don't understand quantum mechanics either. Quantum mechanics is the newest science and therefore should be the most accurate, but unfortunately the opposite is true. By useless quantum mechanics we mean incomplete/inexact parts of quantum mechanics in the classical...

If you don't understand quantum mechanics, ask yourself if I'm right, because others don't understand quantum mechanics either. Quantum mechanics is the newest science and therefore should be the most accurate, but unfortunately the opposite is true. By useless quantum mechanics we mean incomplete parts of quantum mechanics in the classical R^4 or...

If you don't understand mathematics, ask yourself if I'm right, because others don't understand mathematics either. By effective alternative to current mathematics, we mean working in a more complete mathematical space than the classical 3D+t variety which is inadequate for generating well-defined definitions and hypotheses as well as its limited a...

If you don't understand mathematics, ask yourself if I'm right, because others don't understand mathematics either. By useless mathematics we mean incomplete mathematical spaces of a classical 3D+t variety that are inadequate for generating well-defined definitions and hypotheses as well as time-dependent partial differential equations. The current...

If you don't understand mathematics, ask yourself if I'm right, because others don't understand mathematics either. By useless mathematics we mean incomplete mathematical spaces of a classical 3D+t variety that are inadequate for generating well-defined definitions and hypotheses as well as time-dependent partial differential equations. The Cairo n...

If you don't understand mathematics, ask yourself if I'm right, because others don't understand mathematics either. The Cairo numerical theory of techniques and the Laplacian theorem constitute an advanced and exhaustive form of the energy continuity equation and thus they can create new logical mathematics. This is also the case of the famous Schr...

If you don't like mathematics, ask yourself if I'm right, because others don't like mathematics either. The mathematics of classical physics and quantum physics are not understandable in their current format. Laplacian's theorem, is an advanced and exhaustive form of the energy continuity equation, can create new logical mathematics. In previous ar...

If you don't understand mathematics, ask yourself if I'm right, because others don't understand mathematics either. By useless mathematics we mean incomplete mathematical spaces of a classical 3D+t variety that are inadequate for generating well-defined definitions and hypotheses as well as time-dependent partial differential equations. The current...

If you don't understand mathematics, ask yourself if I'm right, because others don't understand mathematics either. By useless mathematics we mean incomplete mathematical spaces of a classical 3D+t variety that are inadequate for generating well-defined definitions and hypotheses as well as time-dependent partial differential equations. The current...

If you don't understand mathematics, ask yourself if I'm right, because others don't understand mathematics either. By worst or ugliest mathematics and mathematical spaces we mean some classical 3D+t spaces inadequate for generating well-defined definitions and hypotheses as well as for the numerical solution of partial differential equations. The...

The time-dependent statistical chains of transition matrix B are successfully used to calculate the reverberation time TR and sound energy density field in audio rooms. This is a real breakthrough in the search for a statistical derivation of Sabines' imperial theory which has never been rigorously proven since 1898. Additionally, we provide proper...

Current mathematics in 3D geometric space plus real time t as an external control is incomplete and misleading. The dream of theoretical physicists and mathematicians to demolish all current mathematics and replace it with a single universal numerical statistical law in 4D is now within reach. In this paper, we first focus on the introduction and d...

This article aims to describe the inherent connection between three seemingly unrelated topics: 4D unit space, Laplacian's theorem in 4D unit space and finally the speed of light c in relation to thermal conductivity k. We first define the discrete 4D unit space from the numerical statistical theory of B matrix chains of Cairo techniques. Next, we...

The time-dependent statistical chains of transition matrix B are successfully used to calculate the reverberation time TR and sound energy density field in audio rooms. This is a real breakthrough in the search for a statistical derivation of Sabines' imperial theory which has never been rigorously proven since 1898. Additionally, we provide proper...

In this paper, the time-dependent statistical chains of transition matrix B are successfully used to calculate the reverberation time TR and sound energy density field in audio rooms. This is a real breakthrough in the search for a statistical derivation of Sabines' imperial theory which has never been rigorously proven since 1898. Additionally, we...

It is easy to show that unified field theory belongs to the square of the Schrödinger wave equation rather than to the classical Schrödinger wave equation itself. One first transform the Schrödinger PDE describing the wave function Ψ into another describing its square Ψ^2=Ψ. Ψ*. Strikingly, the modified Schrödinger PDE describing Ψ^2, when suppleme...

We follow a particular approach to show that unified field theory belongs to the square of the Schrödinger wave equation rather than to the classical Schrödinger wave equation itself. We first transform the Schrödinger PDE describing the wave function Ψ into another describing its square Ψ^2=Ψ. Ψ*. Strikingly, the modified Schrödinger PDE describin...

This Article Aims to Describe the Inherent Connection between Three Seemingly Unrelated Topics: The quantum buzz, vacuum dynamics and the Big Bang. First, we introduce what are called quantum buzzles. Next, we explain what is called vacuum dynamics, which refers to the space where the quantum particle lives and functions in unexpected ways. Finally...

This article aims to describe three main topics: the quantum buzzle, vacuum dynamics and the Big Bang. First, we introduce what are called quantum buzzles. Next, we explain what is called vacuum dynamics, which refers to the space where the quantum particle lives and functions. Finally, we use matrix mechanics to show how to combine the first and s...

The Schrödinger wave equation, in its current form, is confusing and misleading in many cases. Furthermore, an endless debate emerges over whether Schrödinger's partial differential equation is a wave equation or a diffusion equation. In this article we propose to replace the ambiguous wave function Ψ in the Schrödinger PDE, i h dΨ/dt)partial=-h 2....

The Schrödinger wave equation, in its current form, is confusing and misleading in many cases. Furthermore, an endless debate emerges over whether Schrödinger's partial differential equation is a wave equation or a diffusion equation. In this article we propose to replace the ambiguous wave function Ψ in the Schrödinger PDE, i h dΨ/dt)partial=h 2....

The modern theory of quantum mechanics is incomplete. It is capable of describing the quantum energy field on the microscopic scale via the Schrödinger equation and its derivatives but is not capable of describing the energy field on the macroscopic scale such as the domain of thermal diffusion and sound intensity in audio rooms.. etc. On the other...

The aim of this article is to compare two different approaches for the description of time-dependent physical phenomena (both in classical macroscopic physics and in modern microscopic quantum mechanics), namely classical partial differential equations and statistical theories state-of-the-art digital technology. We assume that nature can only be d...

The aim of this article is to compare two different approaches for the description of time-dependent physical phenomena (both in classical macroscopic physics and in modern microscopic quantum mechanics), namely classical partial differential equations and statistical theories state-of-the-art digital technology. We assume that nature can only be d...

The aim of this article is to compare two different approaches for the description of time-dependent physical phenomena (both in classical macroscopic physics and in modern microscopic quantum mechanics), namely classical partial differential equations and statistical theories state-of-the-art digital technology. We present a detailed theoretical a...

Abstract:- The classical finite difference method for solving time-dependent partial differential equations has become quite tedious and requires the use of off-the-shelf algorithms such as those in MATLAB. The treatment by finite difference method then solution of the n resulting first order algebraic equations is quite difficult since the underly...

The modern theory of quantum mechanics is incomplete. It is capable of describing the quantum energy field on the microscopic scale via the Schrödinger equation and its derivatives but is not capable of describing the energy field on the macroscopic scale such as the domain of thermal diffusion and sound intensity in audio rooms.. etc. On the other...

The modern theory of quantum mechanics is incomplete. It is capable of describing the quantum energy field on the microscopic scale via the Schrödinger equation and its derivatives but is not capable of describing the energy field on the macroscopic scale such as the domain of thermal diffusion and sound intensity in audio rooms.. etc. On the other...

The classical finite difference method for solving time-dependent partial differential equations has become quite tedious and requires the use of off-the-shelf algorithms such as those in MATLAB. The treatment by finite difference method then solution of the n resulting first order algebraic equations is quite difficult since the underlying matrix...

The normal procedure for numerically solving the PDEs is to advance via the following three consecutive step procedure: Discretization into n free nodes, treatment by finite difference method then the solution of the n resulting first order algebraic equations which is quite difficult since the underlying matrix is singular. An alternative revoluti...

There is a serious flaw in current numerical methods used to solve time-dependent partial differential equations. In order to establish a new effective digital technique, we apply the rules or principles inherent in the universal laws of nature such as the principles of stability, least action, symmetry, etc. to construct an efficient statistical t...

We propose a modern three-dimensional classification valid for humans on all seven continents. The proposed classification is based on three elements, human intelligence, activity and knowledge. The importance of the proposed classification is that: it is not based on color, race or origin; ii-it can be effectively applied to the current seven eart...

We have shown in previous papers that B-matrix string mechanics, which is the product of a numerical statistical method called the Cairo technique, can be successfully applied to solve the most general form of the diffusion equation of heat as well as the time-independent equation. Schrödinger equation. In this paper we examine the extension of mat...

Abstract We propose a modern three-dimensional classification of humans on all seven continents. The proposed classification is based on three elements, human intelligence, activity and knowledge. The importance of the proposed classification is twofold: i-it is not based on color, race or origin; ii-it can be effectively applied to the current sev...

In previous articles we have shown that the solution of the heat diffusion equation is stimulated and forced by the boundary conditions and the material tested, while the solution of the Schrödinger SE equation or quantum mechanics problems in general is generated spontaneously in the space of the isolated object. object. called a quantum system. W...

B-transition matrix chains resulting from the Cairo technique numerical statistical solution method have been successfully applied to statistically solve time-dependent partial differential equations in classical physics. This paper studies the extension of transition matrix chains B to the numerical statistical solution of the time-independent Sch...

In 1925, W. Heisenberg, Max Born and Pascual Jordan introduced the first so-called matrix mechanics (HMJ theory) to study the fine structure of the Bohr hydrogen atom. However, in the early 1930s, the equivalence between the HMJ theory and the Schrödinger equation was denied and the HMJ theory fell. In 2020, a new theory of matrix mechanics emerged...

In 1925, W. Heisenberg, Max Born and Pascual Jordan introduced the first so-called matrix mechanics (HMJ theory) to study the fine structure of the Bohr hydrogen atom. However, in the early 1930s, the equivalence between the HMJ theory and the Schrödinger equation was denied and the HMJ theory fell. In 2020, a new theory of matrix mechanics emerged...

In 1925, W. Heisenberg, Max Born and Pascual Jordan introduced the first so-called matrix mechanics (HMJ theory) to study the fine structure of the Bohr hydrogen atom. However, in the early 1930s, the equivalence between the HMJ theory and the Schrödinger equation was denied and the HMJ theory fell. In 2020, a new theory of matrix mechanics emerged...

In previous papers we have studied the extension of transition matrix chains B to the numerical statistical solution of the time-independent Schrödinger equation in one and two dimensions x,y. In this paper we examine the extension of B-transition matrix chains to the numerical statistical solution of the time-independent Schrödinger equation in th...

In a previous paper we studied the extension of transition matrix chains B from the heat diffusion equation to the numerical statistical solution of the time-independent Schrödinger equation in a spatial dimension x. In this paper, we propose the extension of transition matrix chains B to the numerical statistical solution of the time-independent S...

In a previous article we studied the extension of transition matrix chains B to the numerical statistical solution of the time-independent Schrödinger equation in one dimension x. In this paper we examine the extension of B-transition matrix chains to the numerical statistical solution of the time-independent Schrödinger equation in the two x,y dim...

In a previous paper we studied the extension of transition matrix chains B from the heat diffusion equation to the numerical statistical solution of the time-independent Schrödinger equation in a spatial dimension x. In this paper, we propose the extension of transition matrix chains B to the numerical statistical solution of the time-independent S...

In previous papers we have studied the extension of transition matrix chains B to the numerical statistical solution of the time-independent Schrödinger equation in one two dimensions x,y. In this paper we examine the extension of B-transition matrix chains to the numerical statistical solution of the time-independent Schrödinger equation in the th...

B-transition matrix chains resulting from the Cairo technique numerical statistical solution method have been successfully applied to statistically solve time-dependent partial differential equations in classical physics. This paper studies the extension of transition matrix chains B to the numerical statistical solution of the time-independent Sch...

B-transition matrix chains resulting from the Cairo technique numerical statistical solution method have been successfully applied to statistically solve time-dependent partial differential equations in classical physics. This paper studies the extension of transition matrix chains B to the numerical statistical solution of the time-independent Sch...

Theory and Design of audio rooms - A Statistical View Abstract In this paper, the numerical solution of the statistical chains of matrix B is successfully used to calculate the sound intensity field in audio rooms. Here we use B-chain techniques as a real breakthrough with the time-dependent sound field problem in 3D geometric space. We offer the a...

Abstract In this paper, the numerical solution of the statistical chains of matrix B is successfully used to calculate the sound intensity field in audio rooms. Here we use B-chain techniques as a real breakthrough with the time-dependent sound field problem in 3D geometric space. We offer the appropriate design of audio rooms via an example of a c...

The question of whether it is time to reformulate the time-independent partial differential equations of Poisson and Laplace is no longer a matter of debate but rather an urgency and a principle of decision. The Poisson partial differential equation PPDE subject to Dirichlet boundary conditions which is currently expressed as, L.U=s Should it be re...

In this article we propose specific answers to three of the most persistent questions: i-Do probabilities and statistics belong to physics or mathematics? ii-Followed by the related question, does nature operate in 3D geometry plus time as an external controller or more specifically, does it operate in the inseparable 4D unit space where time is wo...

The "walking mechanism" of bacterial cells and the role of their legs and falagellae in their transfer or walking is the subject of this article. Additionally, the structure of bacterial cells and the role of their own thermal diffusion field, electric and magnetic fields constructed by the geometric Dirichlet boundary conditions in their transfer...

In particular, probability and statistics are a missing part of mathematics and classical theoretical physics. The introduction of the stochastic transition matrix B proposed by the Cairo Physical Technique suggests that probability and statistics should belong to physics rather than mathematics. We first study the comparison between chains of stoc...

In particular, probability and statistics are a missing part of mathematics and classical theoretical physics. The introduction of the stochastic transition matrix B proposed by the Cairo Physical Technique suggests that probability and statistics should belong to physics rather than mathematics. We first study the comparison between chains of stoc...

Abstract We propose a semi-statistical technique to calculate the value of the Gamma function G(x) in the whole space of positive x, i.e. 0<x=<infinity. The proposed method is simple and applies a second-order polynomial fit to find accurate values for Gamma(x) in the interval 0<x<=2. The precision of the numerical results of the new method is s...

In general, probability and statistics are a missing part of mathematics and belong to physics rather than mathematics. In previous papers we have shown that the solution of partial differential equations such as Laplace's and Poisson's PDE with Dirichlet boundary conditions and the time-dependent heat equation in its most general form can be solve...

It is true that statistical differentiation and statistical integration is a missing part in mathematics. Moreover, it is important to understand that mathematics is only a tool to quantitatively describe physical phenomena, it cannot replace physical understanding. There is an assertion that mathematics is the language of physics but the converse...

This present work is a continuation and validation of the results explained in a previous paper titled A Rigorous Experimental Technique for Measuring the Thermal Diffusivity of Metals and goes further to describe the notion of dimensionless time t D practical for solving the energy-density field distribution in 4D space. Moreover, the notion of di...

In this paper, we present a basis for rigorous experimental measurements of the thermal diffusivity α of metals and hence their thermal conductivity K in 3D geometric material objects rather than the 1D objects used in current literature. The proposed experimental technique is based on the numerical method known as the Cairo technique. The key poin...

In the heat diffusion/conduction equation, how to extend the validity of the Dirichlet boundary conditions to more than one dimensional geometric space II. By Ismail Abbas, PhD Lecturer at MTC, Cairo University. Abstract In fact, the heat equation with Dirichlet boundary conditions has analytical solutions for a number of geometries that involve su...

In fact, the heat equation has analytical solutions for a number of geometries that involve sufficient symmetry. You might say it's "cheating" since you're using symmetry to reduce the 2D or 3D equation to a simpler 1D problem. It can be thought that more broadly, any arbitrary heat equation can be solved with any desired accuracy using finite dif...

In fact, the heat equation has analytical solutions for a number of geometries that involve sufficient symmetry. You might say it's "cheating" since you're using symmetry to reduce the 2D or 3D equation to a simpler 1D problem. It can be thought that more broadly, any arbitrary heat equation can be solved with any desired accuracy using finite dif...

Abstract In fact, the heat equation has analytical solutions for a number of geometries that involve sufficient symmetry. You might say it's "cheating" since you're using symmetry to reduce the 2D or 3D equation to a simpler 1D problem. It can be thought that more broadly, any arbitrary heat equation can be solved with any desired accuracy using fi...

Abstract In fact, the heat equation has analytical solutions for a number of geometries that involve sufficient symmetry. You might say it's "cheating" since you're using symmetry to reduce the 2D or 3D equation to a simpler 1D problem. It can be thought that more broadly, any arbitrary heat equation can be solved with any desired accuracy using...

Poynting's vector theorem P=ExH is one of the universal laws of physics that applies to electromagnetic fields in AC and DC circuits. A rigorous analysis of two arbitrary cases of DC and AC circuit electromagnetic fields shows that Poynting's law P=ExH applies to both stationary and time-varying electromagnetic fields. Keeping the generality, we an...

Abstract It is true that the conclusions of Einstein SR in 1905 are perfect and incontestable but on the other hand it is also real that his derivation is doubtful and fundamentally fluid or not rigorous on certain physical points. However, while each of his 5 assumptions is impossible to dispute or prove wrong, we assume that not all of them are e...

This is an in-depth theoretical and experimental study explaining the formation of colonial patterns in the macroscopic growth of bacterial colonies under its own E&H electric and magnetic fields. Recently there has been more and more work on the formation of bacterial colony patterns but they only consider the case where E and H are external to th...

This is probably the first theoretical and experimental study explaining the formation of colonial patterns in the macroscopic growth of colonies of bacteria under its own E&H electric and magnetic fields. Recently there has been more and more work on the formation of colony batterns but they only consider the case where E and H are external to the...

Since the time of Archimedes 200 BC and up to the present day, it is still generally accepted that the Greek letter (Pi) is Pi) is a mathematical constant approximately π (Pi) equal to 3.142 and is defined as the ratio of the circumference of a circle to its diameter. But it is quite mysterious how it appears in many formulas in most fields of math...

We provide an experimental proof showing that the macroscopic exponential growth of bacteria on a delimited 2D planar surface follows precisely the same solution of the heat diffusion equation with the source / sink term. The B-chains previously used successfully in solving the heat equation can be applied to solve the complicated PDE resulting fro...

Sabine's semi-imperial formula, sometimes referred to as Sabine's theory, proposed a century ago, remains the main formula for calculating RT reverberation time in audio rooms, in addition to a rough estimate of sound volume in audio rooms. We prove that Sabine's formula for the reverberation time TR is fairly accurate but fails in the computation...

Abstract In addition to visible light and soft X-ray cameras, there is a third type of cameras known as infrared IR cameras. All three types are used for security reasons. However, the infrared camera can display photos of male and female passengers without clothing in black and white or light colors. A quick tip for shy or conservative women and g...

ABSTRACT We present a statistical numerical solution for the time-dependent 2D and 3D heat diffusion problem based on the ergodic principle without the need for the partial differential equation of heat diffusion or any of its FDM techniques.. The ergodic stochastic chains of matrix B combine the diffusion of heat, the time increment dt and the L...

ABSTRACT We present a statistical numerical solution for the time-dependent 3D heat diffusion problem without the need for the PDE heat equation or any of its FDM techniques. The ad hoc one-dimensional definition of the scalar thermal diffusion coefficient D defined as K / Roh C is short and inadequate to deal with the resolution of the 2D and 3D...

ABSTRACT The ad hoc one-dimensional definition of the scalar thermal diffusion coefficient D defined as K / Roh C is short and inadequate to deal with the resolution of the 2D and 3D thermal diffusion equation. We have alternatively applied the chains of matrix B to the solution of the 2D and 3D heat diffusion equation for stationary solutions and...

the role of 3D thermal diffusivity in the numerical resolution of the heat equation is carefully studied. The ad hoc one-dimensional definition of the thermal diffusion coefficient D is short to deal with the resolution therefore we have alternatively applied the solution of the heat diffusion equation for different RO elements of [0,1]. In matrix...

We introduce and define a B-stochastic transition matrix other than the stochastic Markov transition matrix and explain the main features of both. We show that the matrices B and M can be real or imaginary and their chains work in both real and imaginary spaces. Matrix B is easy to formulate and handle for a 2D and 3D spatiotemporal scattering pro...

How to find a stochastic transition matrix other than Markov ?. The answer is the offered B-Matrix and B-Matrix chains. B-Matrix chains have the advantage over Markov chains since they are able to solve boundary value and initial value problems in Poisson and Laplace PDEs as well as the heat diffusion equation while the Markov chain solutions are l...

In part 1, we propose a statistical tecnique to the solution of the steady-state eigenvectors of Markov chains that is more efficient and more precise than the classical algebraic method. However, it only fails when the Markov matrix is not invertible, which is the same for the classical solution as well. In part 2, we propose a principle valid for...

This article is an extension of the previous article based on the statistical transition matrix B which aimed to study the steady-state solution of the IC-BC distribution in the diffusion PDE. We extend here the same theory to find the spatio-temporal evolution of the energy vector. Numerical results of the required solution are presented for 2D an...