# Ismail AbbasCairo University | CU · Department of Physics

Ismail Abbas

PhD lecturer at MTC Cairo Univ-Ex Professor at ULP Strasbourg-Ex Research director at CNRS France

## About

89

Publications

27,960

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

119

Citations

Introduction

Mathematical Physics.

## Publications

Publications (89)

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...

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 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...

The present 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 density vector. Numerical results of the required solution are pres...

The two basic hypotheses of Markov chains and the four basic hypotheses of B-Matrix chains proposed are carefully examined and compared to find a way to improve Markov chains in certain specific situations .Our objective is to allow Markov chains to handle boundary conditions and / or source / sink term in addition to ensuring the stability and con...

The search for perpetual motion and invaluable energy dream machines dates back centuries and the question is still appealing.
Theoretical attempts to describe such "inventions" on Earth are now transferred to far vacuum space, considered frictionless and at a temperature close to zero Kelvin to validate or approach perpetual motion. Therefore, att...

Using matrix algebra, how to show that the infinite power series [(1+2 x)/3]^N is equal to (1+2 x)/(2-2 x), ∀x∈[0,1] Abstract. The physical statistical matrix is not a random set of numbers, there is a lot of informational data inherent in it. In accordance with this fact, we propose an axiom or mathematical principle: [For positive symmetric physi...

Abstract
Current work on the numerical solution of Laplace partial differential equation LPDE and of the Poisson partial differential equation PPDE is based on the replacement of the LPDE by an approximately equivalent system of n linear algebraic equations. The solution of this system has two distinct main approaches, namely direct methods and ind...

We propose an axiom or mathematical principle: [For positive symmetric physical power matrices, the sum of their eigenvalues is equal to the eigenvalue of their sum of power series] To this end, we present a stochastic transition matrix B explained previously in the numerical statistical solution of the heat equation among other spatiotemporal PDEs...

The Poynting vector theorem P = ExH is one of the universal laws of physics which apply to both AC and DC circuits electromagnetic fields.
The rigorous analysis of DC circuits EM fields prove that the Poynting universal law of physics P=ExH applies to DC circuits as well. We presented the simplest case of DC circuits, a uniform cylindrical wire car...

Assuming the photon has a moving mass, why current quantum mechanics is unable to prove or deny it. Abstract photon particles have, in addition to their energy, a certain momentum which has been measured experimentally and which has proven its existence. While the current theory of QM described by the Schrodinger equation with the Bohr-Heisenberg i...

We investigate some of the shortcomings of the separation of variables method when applied to many different physical situations. This analysis extends to the discussion of the ad hoc definition of thermal conductivity It is shown that the 4 D stochastic transition matrix is able to replace the linear spatiotemporal PDE and offers more powerful sol...

In the heat diffusion equation, how to relate thermal diffusion to the properties of the 4D matrix. Abstract-We live in a 4D world.In fact, all physical phenomena and nature itself are in 4D, which means that we interact with 4D objects in a large part of our daily life like heat flow and electrostatic voltage distribution ... etc.. Thus, the linea...

In fact, all physical phenomena and nature itself are in 4D, which means that we interact with 4D objects in a large part of our daily life like heat flow and electrical voltage distribution ... etc. For example, it is true that temperature derives its existence from statistical mechanics, no relativity is involved, but in fact it derives its exist...

In the Laplace problem of boundary value and initial conditions, to what extent is the 4D numerical method more powerful than 3 D.-Abstract-In fact, all physical phenomena and nature itself are in 4D, which means that we interact with 4D objects in a large part of our daily life like heat flow and electrical voltage distribution ... etc. For exampl...

Russians have their own unique way of teaching mathematics and physics, from school teaching to university under and post graduate studies. Russian professors and researchers in mathematics and physics have a different way of thinking or analyzing theories and proofs.

• Abstract
In general, the linear spatiotemporal PDE can be replaced by an appropriate or adequate stochastic matrix which is the aim of this work.
this new technique is a small step in a long way, when it is developed and generalized through the use of supercomputers, many of the existing classic PDE numerical solutions can only become a thing of...

In the numerical solution of the heat equation, how to simultaneously solve the boundary conditions and the initial conditions. Abstract We present a statistical transition matrix capable of processing the heat equation with Dirichlet conditions BC and arbitrary initial conditions IC simultaneously. It can solve, in addition to the temperature dist...

In the numerical solution of the heat equation, how to simultaneously solve the boundary conditions and the initial conditions. Abstract We present a statistical transition matrix capable of processing the heat equation with Dirichlet conditions BC and arbitrary initial conditions IC simultaneously. It can solve, in addition to the temperature dist...

The importance of finding a powerful solution for the Laplacian matrix in the partial differential equation of Poisson PPDE, the partial differential equation of Laplace LPDE and the thermal conduction equation is obvious.
We present a numerical model that goes beyond all conventional mathematical methods prescribed to solve the problems of LPDE, P...

Abstract
photon particles have, in addition to their energy, a certain momentum which has been measured experimentally and which has proven its existence.
there is an apparent paradox on how "massless" particles like photons have a momentum which is correlated to their wavelengths. This paradox can be rigorously resolved.

Abstract
Recent work on the numerical solution of the partial differential equation of Laplace LPDE and the partial differential equation of Poisson PPDE is based on the replacement of LPDE by an approximately equivalent system of n linear algebraic equations.The solution to this system has two main distinct approaches, namely direct methods and in...

This article introduces statistical hypotheses, defines a statistical transformation matrix B. It also explains how to construct a so-called E- matrix. Chains of Matrix B or Matrix E are able to address the Laplace and Poisson equations in boundary value problems.
Consequently, the stochastic chains of the matrix B were examined (explicitly or imp...

The designer of a clinical trial needs to make many assumptions about real-life practice based on prior knowledge. Simulation allows us to learn from experience by using the information obtained from a trial to improve the original estimators of population parameters. We propose using data from a previous trial to formulate assumptions that can be...

Introduction
The objective is to show how disease and clinical trial modeling can be applied to estimate the success probability, duration and cost that resulting from a certain trial design or from similar decisions.
Methods
Multidisplinar team has participated in the construction of the general simulation model of clinical trials. This model is...

The patient recruitment process of clinical trials is an essential element which needs to be designed properly.
In this paper we describe different simulation models under continuous and discrete time assumptions for the design of recruitment in clinical trials.
The results of hypothetical examples of clinical trial recruitments are presented. The...

To develop and validate a model of a clinical trial that evaluates the changes in cholesterol level as a surrogate marker for lipodystrophy in HIV subjects under alternative antiretroviral regimes, i.e., treatment with Protease Inhibitors vs. a combination of nevirapine and other antiretroviral drugs.
Five simulation models were developed based on...

Clinical trials can be looked at as an economic optimization problem. They are often costly and take a great deal of time. Inappropriate design and management of a clinical trial can lead to inefficient and wasteful use of resources. The objective of our research programme is to develop simulation models for the economic optimization of clinical tr...

Clinical trials can be looked at as an economic optimization problem. They are often costly and take a great deal of time. Inappropriate design and management of a clinical trial can lead to inefficient and wasteful use of resources. The objective of our research programme is to develop simulation models for the economic optimization of clinical tr...

The possibility of performing complete simulations of
clinical trials, based on pharmacological action models,
has been considered since the advent of the computer era,
as a tool to optimise their practical realisation. Thanks to
the advances in computation technology and in discrete
event simulation tools, today it is possible to perform
realistic...

OBJECTIVE
Cost-effectiveness analysis of combined enalapril-nitrendipine therapy (E/N), as second-line therapy for light or moderate hypertension.
DESIGN
Theoretical model of cost-effectiveness, based on the norms of hypertension treatment in primary care, the considered view of a panel of experts and the direct costs of health resources and purch...

Objective
Cost-effectiveness analysis of combined enalapril-nitrendipine therapy (E/N), as second-line therapy for light or moderate hypertension.
Design
Theoretical model of costeffectiveness, based on the norms of hypertension treatment in primary care, the considered view of a panel of experts and the direct costs of health resources and purcha...

Aquest volum constitueix el primer fruit que s'ofereix als lectors com a resultat de la col·laboració entre l'editorial DOCUMENTA UNIVERSITARIA i l'INSTITUT BORJA DE BIOÈTICA per tractar temes específics de bioètica que constituiran la col·lecció. Així doncs, aquesta primera aportació és el resultat d'un treball col·lectiu i multidisciplinari prota...

The formation and propagation of ionising waves in impulsive overvolted gas discharges for parallel plane electrode geometry is studied. The spatio-temporal evolution of the electronic and ionic densities together with the space-charge distorted field was thoroughly examined for different initial electron distributions. The study elucidates the imp...

For pt.I see ibid., vol.14, p.649 (1981). The authors present here the results of the numerical solution to the macroscopic model of a gas discharge described in part I (preceding paper). This model considers the non-equilibrium between the electron energy and field in the electron shock leading the ionising wave in the discharge. It is possible to...

The authors propose a macroscopic model for gas breakdown ionising waves based on a consistent hydrodynamic system of equations describing the spatio-temporal evolution of particle density, momentum and energy. They apply this model to investigate the properties of the electron shock zone situated at the head of a discharge channel, so that it can...

Objectives
To make and validate a data base that allows to collect information about clinical characteristics and use of health care services by HIV-infected patients. An additional purpose is to obtain some data about costs of health care services utilization.
Methods
We have designed an informatic data base that includes: demographic data, clini...

To make and validate a data base that allows to collect information about clinical characteristics and use of health care services by HIV-infected patients. An additional purpose is to obtain some data about costs of health care services utilization.
We have designed an informatic data base that includes: demographic data, clinical data and health...

A hybrid hydrodynamic-like formalism is presented for the study of
the inception of breakdown and development of plasma bubble in the
hollow cathode phase of a pseudospark switch discharge. It allows one to
obtain the spatio-temporal evolution of the electronic and ionic
densities, velocities, and energies in fast transient situations in low
pressu...

The formation and propagation of ionizing waves in a gas discharge under pulsed electric field is essentially governed by the space charge field that super imposes the applied field Eo.

Saturday, October 6, 1973
At 10:00 a.m., huge Egyptian forces of all the weapons of the Egyptian armed forces entered the West Bank of the Suez Canal and lined up in heavy and successive offensive crossing formations. .
Here, Israel realized that the great crossing and the heavy war were coming, so it hastened the multiple and successive contacts...

## Questions

Questions (138)

This is most likely a paradox[1].

We assume that the fundamental reason is that they both treat the boundary conditions BC, the source term S and the thermal conductivity/diffusion k and D as scalar quantities when in fact they are tensors or matrices of second rank having spatial components x, y, z. [2]

for example, S=Sx+Sy+Sz and BC=BCx+BCy+BCz.

1- Spiros Konstantogiannis, Eur J 0f Ph, From the state space of quantum mechanics to position and momentum spaces through a simple relation, September 2020.

2- Abbas, Researchgate, A statistical solution to the Schrödinger equation, IJISRT journal, November 2023.

I- If the total energy is a scalar then it has no x,y,z components.

II-If the total energy is a vector then it must have a Phythagorean addition formula for its components x,y,z.

III- To our knowledge there is no mathematical proof or even a descriptive discussion of the previous statement.

We assume that this is probably a paradox, but we believe that physical analysis can prove that, in some way, it is true.

The variable separation method used in the solution of time-dependent PDEs,

d U / d t) partial = D. Nabla 2 U + S (x, t). . .(1)

with Dirichlet boundary conditions

is based on the hypothesis,

U(x,y,z,t)=X(x).Y(y),Z(z).f(t)

present an existing and precise solution.

We assume that this method constitutes a permanent difficulty bothering the two mathematicians

and physicists.

You never know if the solution will be precise enough or even if it exists, especially with the complexity of S and BC, before trying to hope for luck.

However, the statistical chains of matrix B present a successful solution [1] for equation 1 without resorting to the variable separation method or FDM techniques.

The question now is whether the proposed technique is actually becoming more and more dominant?

1- What is missing in mathematics and theoretical physics, Researchgate, IJISRT journal, March 2023.

We assume that the chains of matrix B can introduce a numerical statistical solution for ψ(r)^2 (total quantum energy) in the same way that they present a numerical statistical solution for the heat diffusion energy density without go through the PDE heat itself. .

The question arises whether this solution exists, how important is it, and whether it is as accurate as the SE solution?

We assume that this is true nowadays, because two mathematicians from two different mathematical fields can hardly find a common language to communicate.

The question arises: is it possible to reorganize at least the mathematical language?

We assume that the Nabla^2 expression in 3D geometry is quite old and its lifespan is almost expired.

B-matrix chains suggest adding a fourth dimension (mainly time t) woven into the 3D geometric space to form a 4D unit space for two fundamental reasons:

i- The classic expression in 1D,

Nabla^2 Y(x)={Y(x+ h)-2 Y(x)+Y(x-h)}/2 h^2

and similar for 2D and 3D,

is a rough approximation because it only uses 3 geometric points and requires a small interval h.

On the other hand, the same expression suggested by the statistical matrix-B chains is much more precise and uses as many geometric points “free nodes” as necessary with small or large intervals h.

ii- What is quite surprising is that the physical expression of Nabla^2 also turns out to be a differential and integral operator.

Single, double and triple finite integrals can be realized via a modern 4D expression[1].

1-Effective unconventional approach to statistical differentiation and statistical integration, Researchgate, IJISRT journal, Nov 2022.

The strings in matrix B predict this statement.

As a numerical example, the sum of the entire series 0.99 + 0.99^2 + 0.99^3 + . . . . +0.99^N increases to 190 as N goes to infinity.

Additionally, B-matrix chains provide rigorous physical proof.

The question arises whether a pure mathematical proof can also be found?