APM Institute for the Advancement of Physics and Mathematics



Location of the APM Institute

The APM Institute begun its operations in its new space in March 2014 in Athens, Greece. Its premises include research space, a presentation hall and a library.


Purpose of the APM Institute is the progress and Advancement of Physics and Mathematics and the support of its members. Fundamental physics, Cosmology, Iterative systems, Chaos, Information physics, History of science, are some research areas pursued by the institute’s members. A main target of the Institute is to keep gifted Greek scientists from leaving Greece. One such promising research topic is the physical Theory of Self-variation, originated by Emmanuil Manoussos in 2007.


WCGO 2023: The 2023 World Congress on Global Optimization

Historical Library (Reading room, Exhibitions)
Athens, Greece, July 10-14, 2023


WCGO 2023: The 2023 World Congress on Global Optimization
Historical Library (Reading room, Exhibitions)
Athens, Greece, July 10-14, 2023
Conference website http://www.globaloptimization.org/conferences/wcgo-2023/
Submission link https://easychair.org/conferences/?conf=wcgo2023
Abstract registration deadline April 30, 2023
Submission deadline April 30, 2023

Topics: global optimization international society of global optimization wcgo 2023

A primary goal of the WCGO is to bring together scientists, engineers, mathematicians and practitioners from a variety of related disciplines, to exchange ideas and present original research results in the theory and applications of global optimization. One of the highlights of this biannual meeting is the announcement of Constantin Carathéodory Prize of the International Society of Global Optimization awarded in recognition of lifetime contributions to the field of global optimization.

1. Constantin Caratheodory Prize

The Constantin Caratheodory Prize of the International Society of Global Optimization is awarded bi-annually to an individual (or a group) for fundamental contributions to theory, algorithms, and applications of global optimization. The Prize named after mathematician Constantin Caratheodory is awarded for outstanding work that reflects contributions that have stood the test of time. The criteria include scientific excellence, innovation, significance, depth, and impact. The winner will receive a certificate with an award of $2,000 and deliver a plenary lecture. The Constantin Caratheodory Prize was established by the International Society of Global Optimization in 2011, and was first awarded at the Second World Congress on Global Optimization, held in Chania, Greece during July 3-7, 2011.


DOD 2023: Dynamics of Disasters 2023

Aikaterini Laskaridis Foundation
Athens, Greece, July 3-6, 2023


DOD 2023: Dynamics of Disasters 2023
Aikaterini Laskaridis Foundation
Athens, Greece, July 3-6, 2023
Conference website http://caopt.com/DOD2023/
Submission link https://easychair.org/conferences/?conf=dod2023
Abstract registration deadline May 15, 2023
Submission deadline May 15, 2023

Topics: disaster management operations research computing

We are organizing the 6th International conference on Dynamics of Disasters (DOD 2023) to be held July 3—6, 2023 in Athens, Greece. For more information about the conference and the venue, please visit the conference website at http://caopt.com/DOD2023/.

The last five years have had us realize the long-lasting impacts that disasters have in our societal welfare. The impacts of wildfires, hurricanes, tornadoes are increasing in intensity even in areas that were historically “spared” from natural hazards before. The interdependencies of our built environment and our societal structures with the occurring disasters have rendered the study of the dynamics of disasters an even more important subject. Like we have done in the past, the DOD series of conferences aims to bring together researchers, practitioners, and policy-makers to discuss and advance this interdisciplinary array of topics. Topics of interest include (but are not limited to) optimization, computing, mathematical and statistical modeling, data analytics, emergency and disaster management, among others.


Introduction to the Theory of Self-variation (TSV)

Emmanuil Manousos

Axiomatic Foundation of Theoretical Physics
The Theory of Self-variation

published 13 June 2021     Order from Amazon

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Hilbert’s Sixth Problem
Vacuum State vs Big Bang

published 16 September 2021     Order from Amazon


Theory of Self-variation

Chapter 16, The Cosmological Data as a Consequence of the Theorem of
Internal Symmetry, June 13, 2021

Chapter 16 of the book “Manousos, E. Axiomatic Foundation of Theoretical Physics. The Theory of Self-variation. (2021) APM Institute for the Advancement of Physics and Mathematics. Columbia, SC.”includes the cosmological equations of the Theory of Self-variation.The set of these equations determines the cause of the currently known cosmological data.

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Predating General Relativity

The Einstein-Besso manuscript

The auction houses Aguttes and Christies (Paris) have jointly auctioned on 22 Nov 2021, one of the most important manuscripts shedding light into how Albert Einstein arrived to the formulation of his General Relativity theory, published on 2 Dec 2015, almost 106 years before the auction. The manuscript consists of 54 pages full of equations, half of them handwritten by Einstein and the other half written by Michele Besso, a close friend of Einstein from the days of the Federal Polytechnic Institute in Zurich (today ETH). The manuscript was a collaboration of the two friends  and contains an early version of the field equations. It was written in 1913/ early 1914 and its target was to account for the perihelion shift of Mercury. In the manuscript no firm conclusion about the Mercury anomaly was reached and it was eventually abandoned by Einstein. However it offers invaluable insight into the minds of both men and on the stages of development of what was to become the famous theory of general relativity. Its estimate was already a record €2-3 Million. However after fierce competition is was sold for €13,383,000.


Optimization of Pharmaceutical Processes

Editors: Antonios Fytopoulos, Rohit Ramachandran, Panos M. Pardalos

Optimization of Pharmaceutical Processes presents contributions from leading authorities in the fields of optimization and pharmaceutical manufacturing. Formulated within structured frameworks, practical examples and applications are given as guidance to apply optimization techniques to most aspects of pharmaceutical processes from design, to lab and pilot scale, and finally to manufacturing. The increasing demand for better quality, higher yield, more efficient-optimized and green pharmaceutical processes, indicates that optimal conditions for production must be applied to achieve simplicity, lower costs and superior yield. The application of such methods in the pharmaceutical industry is not trivial. Quality of the final product is of major importance to human health and the need for deep knowledge of the process parameters and the optimization of the processes are imperative.

The volume, which includes new methods as well as review contributions will benefit a wide readership including engineers in pharmaceuticals, chemical, biological, to name just a few.

Record Factorization of Chebyshev Integers

Maintained by Kyriakos Kefalas

Record factorizations are well known for some famous integer sequences like Fermat numbers and Fibonacci numbers. At the APM Institute’s site we present tables of record factorizations of integer sequences which may be less known to the general public, but are well known to mathematicians. In particular we maintain tables of record factorizations for the following sequences

  • Chebyshev integers (i.e. integer values of Chebyshev polynomials)

A completely factorized integer is placed in our tables according to its 2nd largest principal prime factor (explained in the text), which is exactly the prime factor which is most difficult to find. However, under some conditions, we include in our tables also incompletely factorized integers with large principal prime factors. The most difficult factorization included in our tables (as of 10.4.2019) is the Chebyshev integer:

7 • 1880678238403581484491261600488335063 {37, P} • 12131078272029453254528593283997361448667051367 {47, P}

contributed by Ilias Kotsireas

Anyone is welcome to contribute to our factorization tables. For this please contact Kyriakos Kefalas through the contact page of the Institute, but make sure that the material you send us deserves to be included in the tables.


 The Antikythera Mechanism

Prof. Xenophon Moussas*

The origin of all technical achievements is the divine curiosity [of Socrates/Plato] and the play instinct of the working and thinking researcher as well as the constructive fantasy of the inventor… Albert Einstein, speech on the radio at the opening of the 7 Deutsche Funkausstellung in Berlin, 1930.

APM Institute, Antik-Mech-radiography-2005

Astronomy is the oldest science developed as humans that have been watching the sky for centuries and millennia started attempting to understand all celestial motions, of the stars, the Sun, the Moon and finally the planets. This eventually led them to try to understand their existence in the Cosmos. This was the birth of Philosophy and Humanity. Humans develop calendars form prehistoric times and for this they develop mathematics and astronomy…

The Antikythera Mechanism is the oldest known astronomical instrument and astronomical computer that we have in hands, probably made between 150 and 100 BC, by a Greek mechanic and astronomer with excellent knowledge of mathematics.
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* Professor of Space Physics, University of Athens, Greece


Solving the Abel Difference Equation

Kyriakos Kefalas

In simple cases, dynamical systems are described by the 1st order autonomous difference equation of the form:


which we call the Abel Difference Equation (ADE)*, where u, is an arbitrary function defining the system. Despite its simplicity, it is difficult (or impossible) to find smooth functions f (i.e. smooth flows) which are solutions of the ADE, for arbitrary non-linear smooth functions u. An elegant solution to this problem is presented by Kyriakos Kefalas ( On smooth solutions of non linear dynamical systems, fn+1 = u(fn), part I, Phys. Int., 5: 112-127, 2014) for wide classes of increasing functions u. There it is shown that sufficiently smooth solutions of (1) , are given by:


where, , is the kth iterate of u. The solutions depend on a modulator function, , which introduces a (usually remarkably tiny) oscillation into f. Central inside the parenthesis is an infinite composition of functions called a continued form, defined as:


where, {uj }, is a sequence of functions and the variable s, on top indicates the composition variable. The symbolism stems from the analogy with  , with the binary operation replaced by (non-commutative) composition. The conditions for the existence of the overall limit in (2) are investigated as well as the conditions for the convergence of the infinite continued form inside, where the two limits have to be independent from each other. It is also proved that (2) converges to the desired function f, , for a wide class of defining functions u. It is also remarkable that in many cases  (for ex., ), the speed of convergence is amazing.
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*To avoid confusion with the related Abel Functional Equation (AFE),   .


 Dark Matter Cosmology and Astrophysics

Vladimir S. Netchitailo*

Hypersphere World-Universe Model (WUM) envisions Matter carried from Universe into World from fourth spatial dimension by Dark Matter Particles (DMPs). Luminous Matter is byproduct of Dark Matter (DM) annihilation. WUM introduces Dark Epoch (spanning from Beginning of World for 0.4 billion years) when only DMPs existed, and Luminous Epoch (ever since for 13.8 billion years). Big Bang discussed in standard cosmological model is, in our view, transition from Dark Epoch to Luminous Epoch due to Rotational Fission of Overspinning DM Supercluster’s Cores and annihilation of DMPs. WUM solves a number of physical problems in contemporary Cosmology and Astrophysics through DMPs and their interactions: Angular Momentum problem in birth and subsequent evolution of Galaxies and Extrasolar systems—how do they obtain it; Fermi Bubbles—two large structures in gamma-rays and X-rays above and below Galactic center; Mysterious Star KIC 8462852 with irregular dimmings; Coronal Heating problem in solar physics—temperature of Sun’s corona exceeding that of photosphere by millions of degrees; Cores of Sun and Earth rotating faster than their surfaces; Diversity of Gravitationally-Rounded Objects in Solar system and their Internal Heat; Lightning Initiation problem—electric fields observed inside thunderstorms are not sufficient to initiate sparks; Terrestrial Gamma-Ray Flashes—bursts of high energy X-rays and gamma rays emanating from Earth. Model makes predictions pertaining to Masses of DMPs, proposes New Types of their Interactions. WUM reveals Inter-Connectivity of Primary Cosmological Parameters and calculates their values, which are in good agreement with the latest results of their measurements.
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5-Dim General Relativity

Late Prof. Paul S. Wesson*

APM InstituteOur group is using an extension of general relativity from four to five dimensions where the extra dimension is interpreted as giving rise to matter. Hence the name, Space-Time-Matter theory. Mathematically, STM theory is based on an old embedding theorem of Campbell, which ensures that the 5D Ricci-flat field equations contain the 4D Einstein field equations with matter. Physically, the forms of 4D matter are determined by the dependence of the 5D metric on the extra coordinate. Vacuum is especially simple, being the result of a 5D metric whose 4D part is quadratically factorized by the extra coordinate.
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* Late Professor in Astrophysics and Theoretical Physics, University of Waterloo, Canada

Shannon’s idea of information in biological respiratory sedimentation

Dr. Ioannis Haranas*, Dr. Ioannis Gkigkitzis**

The concept of “information” is widely used in modern science and means “data” or “message”. In spite its use by various scientists no physical essence can be still attached to it. The first appearance of the original concept of information theory took place during the development of various communications systems, which had to ensure information transfer or exchange. The operational principles of various systems obey strictly the laws of physics, where optimization of the same systems operation requires the dealing with the amount of information, which can be transmitted through communication channels. H. Nyquist, R. Hartlee and C. Shannon, and Landauer all employees of Bell Laboratories were pioneers in the field. Their works resulted to Shannon’s theory of information which further resulted in the optimization of the operation of the technical systems. Furthermore, a collection of these notions, called by Shannon himself “Mathematical Theory of Communication”, became the basis of classic Information Theory (Shannon, 1948).
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*Adjunct Professor, Department of Physics and Computer Science, Wilfrid Laurier University, Canada
**Ass. Professor, Department of Mathematics, East Carolina University, USA


More Topics

For more scientific topics see the Physics and Mathematics categories or choose from the selection below:


We kindly thank our Donators who have contributed to the Research Departments and the Scientific Library of the APM Institute.

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