Books and Theses by Georgios Papanastasiou
Εκδόσεις Α. Σιμώνη, Σ. Χ"π'αντου Ο.Ε., 1993
This book is the first part of a series of three books entitled: Stochastic Methods This series ... more This book is the first part of a series of three books entitled: Stochastic Methods This series includes the books:
Stochastic Methods. Part I. Basic Principles of Applied Statistical Analysis.
Stochastic Methods. Part II. Basic Principles of Statistical Thermodynamics.
Stochastic Methods. Part III. Basic Mathematics of Stochastic Methods.
All these books are registered in the Library of the Chemistry Department of the Aristotle University of Thessaloniki.
Several topics of basic and applied science require the use of stochastic methods, which are based on probability theory and statistics. A typical example is statistical thermodynamics. In this topic, the macroscopic behavior of a system is linked to the microscopic properties of the particules of the examined system.
This series aim to help the reader gaining a thorough understanding of such methods.
The present book outlines and details the main proposals and principles of the probability theory and statistics, which are used in various stochastic methods.
This theoretical exercise is not the sole aim of this book. Nowadays, there are several statistical software packages for data analysis using a variety of statistical methods or tests. These methods are accessible even to scientists lacking a basic knowledge of mathematics. Nevertheless, a critical question remains open; which statistical method is appropriate for the analysis of a specific dataset?
This book provides the fundamental theoretical background for the main statistical methods and tests. This knowledge is essential for both the selection of appropriate methods of analysis and the interpretation of the obtained results.
It is noted that the use of the appropriate statistical methods for the processing of the data, debunks the myth that statistics can prove whatever we want to prove! This can definitely happen when we erroneously chose (either on purpose or out of ignorance) invalid statistical tests.
Statistics is a rigorous mathematical discipline, which can generate reliable results, if properly applied. What is different from other mathematical methods is that statistics do not always answer a raised question with a definite answer; instead, statistics consider all possibilities and calculate the probabilities of each, using appropriate methods.
This book consists of 13 chapters and an Appendix providing the indispensable mathematical proposals required to comprehend the main text. A significant number of resolved exercises are also appended, aiming to assist the reader in achieving a deeper knowledge of statistical methods.
In each chapter the theorems, relationships and examples are numbered separately. This book also contains 13 Statistical Tables.
To those wishing to expand their knowledge beyond this book, available literature offers a plethora of excellent textbooks, both in Greek and English. Relevant bibliography can be found at the end of this book.
All Chapters of this Book, in pdf format, are posted online at:
http://ikee.lib.auth.gr/record/310203.
This book is the second part of a series of three books under the general title: Stochastic Metho... more This book is the second part of a series of three books under the general title: Stochastic Methods. This series includes the books:
1. Stochastic Methods. Part I. Basic Principles of Applied Statistical Analysis.
2. Stochastic Methods. Part II. Basic Principles of Statistical Thermodynamics.
3. Stochastic Methods. Part III. Basic Mathematics of Stochastic Methods.
These books are registered in the Library of the Chemistry Department of the Aristotle University of Thessaloniki.
In this book, by means of Statistical Thermodynamics, Ideal particle systems (i.e. systems without interactions between their constituent particles) are examined.
The macroscopic - phenomenological character of the so-called Basic or Classical Thermodynamics relates to the examination of the macro¬scopic behavior of the matter. But this behavior is not linked to the properties of the particles (atoms, molecules and/or ions) that compose the examined system.
Thus, classical thermodynamics cannot investigate microscopic phenomena. The Brown movement is cited as an example. In it, heavy particles are automatically lifted, contrary to the direction of the gravity field, while the necessary energy is obtained from the heat of the system. Therefore, contrary to the second thermodynamic law, we have conversion of heat into work without the existence of a second cold source.
The efforts to explain such phenomena gave birth to Statistical Thermodynamics. Its main purpose is to examine and interpret the macroscopic behavior of various systems with the help of theoretical and experimental data referring to the particles that compose these systems.
Of course, both Classical and Quantum Mechanics provide suitable techniques for describing a particulate system. However, this description can only be extended to systems consisting of a relatively small number of particles.
The use of statistical methods was considered necessary to examine systems with large numbers of particles, where only the average values of the various physical quantities, and possibly their changes, can be determined. To illustrate the necessity to use such statistical methods, one should remember that Molecules are contained in just one mol of a gaseous substance (eg 2 g H¬2).
Therefore, it becomes obvious that the description of such a system using only the Classical Mechanics requires the solution of a system of an equally large number (order of ) of differential equations of motion. Such a system is currently impossible to solve using the most powerful computers available. But, even if a solution was feasible, it would be practically impossible to determine the initial system conditions, i.e. the physical positions and momenta of all these molecules.
Of course, neither Quantum Mechanics can be effectively used in describing such a system, since Schrődinger's equation can only be solved in systems with a limited number of particles.
Briefly, we could say that Statistical Thermodynamics is based on a combination of the laws of Mechanics, Thermodynamics and Probability Theory.
To those wishing to expand their knowledge beyond this book, available literature offers a plethora of excellent textbooks, both in Greek and English. Relevant bibliography can be found at the end of this book.
This book consists of 22 chapters and an Appendix providing the indispensable mathematical proposals required to comprehend the main text.
The first two chapters briefly provide the basic concepts and principles of Classical Thermodynamics
In each chapter, paragraphs and relationships are numbered separately.
All Chapters of this Book, in pdf format, are posted online at:
http://ikee.lib.auth.gr/record/310205.
This book is the third part of a series of three books under the general title: Stochastic Method... more This book is the third part of a series of three books under the general title: Stochastic Methods. This series includes the books:
Stochastic Methods. Part I. Basic Principles of Applied Statistical Analysis.
Stochastic Methods. Part II. Statistical Thermodynamics.
Stochastic Methods. Part III. Basic Mathematics of Stochastic Methods.
These books are registered in the Library of the Chemistry Department of the Aristotle University of Thessaloniki.
The development of atomic and molecular theory at the beginning of the 20th century and the attempt to correlate, on the basis of this theory, macroscopic with microscopic behavior of various systems inevitably led to the use of stochastic methods.
In particular, the application of such methods to the¬ thermodynamic behaviour of various systems resulted in¬ the creation of a new discipline: Statistical Thermody¬namics. This branch consists of the examination, by means of stochastic¬ methods, of the macroscopic behaviour of a system, taking into account the mechanical properties of the particles contained in the considered system.
This series aims to contribute to a fuller understanding of such methods, which increasingly find applications in various fields of both natural and applied sciences.
This present book details and analyzes the main mathematical propositions and principles used in the various Stochastic Methods. Notable, the content of the first two books of this series can still be understood by those with limited knowledges of mathematics.
This book consists of 22 Chapters and an Appendix, where the basic principles of Algebraic Structures are mentioned. In each chapter the theorems, relationships and examples are numbered separately.
Chapter 7 provides a very brief overview of the basic principles of the probability theory. A more detailed description of these principles is given in the first chapter¬ ¬of the first book (Part I. Basic Principles of Applied Statistical Analysis) of this series.
To those wishing to expand their knowledge beyond this book, available literature offers a plethora of excellent textbooks, both in Greek and English. Relevant bibliography can be found at the end of this book.
All Chapters of this Book, in pdf format, are posted online at:
http://ikee.lib.auth.gr/record/310210.
This book examines the thermodynamic and electrochemical behavior of weak acids and bases with r... more This book examines the thermodynamic and electrochemical behavior of weak acids and bases with regards to their acid-base equilibria in various solution systems.
The study of the dissociation equilibria of weak acids in aqueous or in various binary water - organic solvent systems is of a considerable theoretical interest as conclusions regarding the structure and the solvation of these acids can be reached. In addition, a detailed examination of such balances could elucidate the interpretation of the behavior of various electrochemical systems.
In particular, the dissociation equilibria of weak bases, monoprotic-, polyprotic- and amino- acids are examined in aqueous as well in mixed solvent systems.
Chapters 1, 2 and 3 provide the necessary theoretical background (thermodynamics and electrostatics) to understand the dissociation of weak acids in dilute solutions.
The examination of the dissociation equilibria of weak electrolytes in mixed water - organic solvent systems leads to conclusions about the structure ¬of the electrolytes tested, as well as the extent of the solvation of ions participating in the corresponding dissociation equilibrium.
This book details methods for¬ the determination of thermo¬dynamic dissociation constants of weak electrolytes in aqueous or mixed solvent systems.
These methods, based on the analysis of pHmetric titration curves of weak acids or bases with a strong base or strong acid respectively, allow the determination of their accurate thermodynamic .
In general, precise analytical concentrations of weak acids or bases are required for the accurate determination of their thermodynamic dissociation constants. These concentrations are obtained experimentally mainly by means of potentiometric titration.
However, in some cases, i.e. very weak acids or certain mixed solvent systems, the corresponding potentiometric titration curves do not have a vertical portion at the end of the ¬neutralization of the titrated substance. In other cases, the¬ differential titration curve present multiple peaks in the vicinity of the equivalent point, resulting in an uncertain determination of the analytical concentration of the titrated substance.
In such cases, the application of iterative methods allows the simultaneous determination of both accurate thermodynamics and the precise analytical concentrate¬ of the corresponding substances, even when the titration is stoped before the titrated substance has been completely neutralized. Such methods are described in Chapter 4 of this book.
Chapter 5 describes the role of weak acids when used as growth inhibitors in plating solution in order to improove certain physical and/or mechanical properties of various metals electrodeposits. In particular, the contribution of tartaric and citric acid to the preparation of compact and smooth silver plates from solutions is examined.
Chapters 6, 7, 8 and 9 examine the ionic behaviour of α-amino acids. Methods for the determination of the thermodynamic constants of the groups and .are described
This book consists of 9 Chapters and four Appendices. In each Chapter the numbering of relationships is done separately.
The various methods for determining the thermodynamic dissociation constants of the various equilibria presented in this book are mainly based on the analysis of linear relationships. For this reason, Annex 1 presents ¬the basic principles of the stochastic method of Linear Regression.
Annex 2 details the various phenomena that occur during the electrolytic deposition of metals and examines the crystal structure of the produced polycrystalline deposits. In particular, the so-called fibrous texture (texture de fibre) of certain polycrystalline deposits is analyzed. (e.g. the crystal structure of deposits that¬ have one or more crystallographic axes perpendicularly oriented to the surface of the deposit). Fibrous texture is usually achieved in deposits prepared from electrolytic solutions containing additives, mainly organic, such as tartar¬or citric acid.
Annex 3 details the solution of the main ordinary differential equations. The basic principles and properties of the “Laplace Τransforms” method and its use in solving linear differential equations are developed.
Appendix 4 provides elements of linear algebra (matrix algebra) and discusses the solution of systems of algebraic linear equations.
To those wishing to expand their knowledge beyond this book, available literature offers a plethora of excellent textbooks, both in Greek and English. Relevant bibliography can be found at the end of this book.
All Chapters of this Book, in pdf format, are posted online at:
http://ikee.lib.auth.gr/record/325486.
Διδακτορική Διατριβή, 1969
Πραγματεία για Υφηγεσία, 1981
Iterative Methods by Georgios Papanastasiou
Th eory an d iterative m eth od s for an alysis of p oten tiom etric titration d ata are p resen ... more Th eory an d iterative m eth od s for an alysis of p oten tiom etric titration d ata are p resen ted in th is p ap er. Th e m eth od s con cern titration s of (i) weak m on op rotic acid s, (ii) m ixtu res of weak acid s with th eir con ju gate bases (bu ffer solu tion s), (iii) m ixtu res of two m on op rotic acid s, (iv) solu tion s of p olyp rotic (d i-an d trip rotic) acid s with overlap p in g ion isation step s,
Th eory an d iterative m eth od s for an alysis of p oten tiom etric titration d ata are p resen ... more Th eory an d iterative m eth od s for an alysis of p oten tiom etric titration d ata are p resen ted in th is p ap er. Th e m eth od s con cern titration s of (i) weak m on op rotic acid s, (ii) m ixtu res of weak acid s with th eir con ju gate bases (bu ffer solu tion s), (iii) m ixtu res of two m on op rotic acid s, (iv) solu tion s of p olyp rotic (d i-an d trip rotic) acid s with overlap p in g ion isation step s,
Collect. Czech. Chem. Commun., 2003
Theory and iterative methods for analysis of potentiometric titration data are presented in this ... more Theory and iterative methods for analysis of potentiometric titration data are presented in this paper. The methods concern titrations of (i) weak monoprotic acids, (ii) mixtures of weak acids with their conjugate bases (buffer solutions), (iii) mixtures of two monoprotic acids, (iv) solutions of polyprotic (di-and triprotic) acids with overlapping ionisation steps,
Analytica Chimica Acta, 1993
New iterative methods for the analysis of potentiometric titration data of weak monoprotic acids ... more New iterative methods for the analysis of potentiometric titration data of weak monoprotic acids or of mixtures of two monoprotic acids are presented. These methods, using equations without approximations and data exclusively resulting from the acidic region of the titration curve, seem to be valid throughout the acidic strength range. In the titration of weak monoprotic acids, the proposed procedures are able to extract accurate values of the equivalence volume and also the thermodynamic dissociation constant. On the other hand, in the titration of mixtures of two monoprotic acids, the proposed approach is able to extract accurate values of the concentrations and the thermodynamic dissociation constants of the component acids even when their acidity strengths are similar. The test of the proposed procedures by means of ideal simulated data (free from any extraneous "noise") and Monte Carlo simulated data revealed that these methods are fairly applicable even when the titration data are considerably obscured by "noise". Further, for acids having pK > 4 the proposed procedures lead to accurate results even when the pH data contain an important systematic error. The proposed procedures were also successfully applied to experimental titration data for weak acids. A procedure for the analysis of titration data carried out in binary water-dhnethylformamide solvent systems is also presented.
Journal de Chimie Physique, 1977
C. R. Acad. de Paris, 1977
Journal of Solution Chemistry, 1996
The kinetics of the reaction between sodium ethoxide and methyl iodide has been studied at 25°C i... more The kinetics of the reaction between sodium ethoxide and methyl iodide has been studied at 25°C in various cyclohexane-ethanol solvent mixtures with a cyclohexane content of 10 to 50% per volume. The determination of the rate constants att=0 were carried out by a new iterative method proposed in this investigation. The obtained results show that the reaction rate decreases with the increasing cyclohexane content. This behavior can be attributed to various solute-solvent interactions of electrostatic nature. On the other hand, the variation of ion and ion pairs rate constants with solvent composition permits the various solvation effects to be taken into account.
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Books and Theses by Georgios Papanastasiou
Stochastic Methods. Part I. Basic Principles of Applied Statistical Analysis.
Stochastic Methods. Part II. Basic Principles of Statistical Thermodynamics.
Stochastic Methods. Part III. Basic Mathematics of Stochastic Methods.
All these books are registered in the Library of the Chemistry Department of the Aristotle University of Thessaloniki.
Several topics of basic and applied science require the use of stochastic methods, which are based on probability theory and statistics. A typical example is statistical thermodynamics. In this topic, the macroscopic behavior of a system is linked to the microscopic properties of the particules of the examined system.
This series aim to help the reader gaining a thorough understanding of such methods.
The present book outlines and details the main proposals and principles of the probability theory and statistics, which are used in various stochastic methods.
This theoretical exercise is not the sole aim of this book. Nowadays, there are several statistical software packages for data analysis using a variety of statistical methods or tests. These methods are accessible even to scientists lacking a basic knowledge of mathematics. Nevertheless, a critical question remains open; which statistical method is appropriate for the analysis of a specific dataset?
This book provides the fundamental theoretical background for the main statistical methods and tests. This knowledge is essential for both the selection of appropriate methods of analysis and the interpretation of the obtained results.
It is noted that the use of the appropriate statistical methods for the processing of the data, debunks the myth that statistics can prove whatever we want to prove! This can definitely happen when we erroneously chose (either on purpose or out of ignorance) invalid statistical tests.
Statistics is a rigorous mathematical discipline, which can generate reliable results, if properly applied. What is different from other mathematical methods is that statistics do not always answer a raised question with a definite answer; instead, statistics consider all possibilities and calculate the probabilities of each, using appropriate methods.
This book consists of 13 chapters and an Appendix providing the indispensable mathematical proposals required to comprehend the main text. A significant number of resolved exercises are also appended, aiming to assist the reader in achieving a deeper knowledge of statistical methods.
In each chapter the theorems, relationships and examples are numbered separately. This book also contains 13 Statistical Tables.
To those wishing to expand their knowledge beyond this book, available literature offers a plethora of excellent textbooks, both in Greek and English. Relevant bibliography can be found at the end of this book.
All Chapters of this Book, in pdf format, are posted online at:
http://ikee.lib.auth.gr/record/310203.
1. Stochastic Methods. Part I. Basic Principles of Applied Statistical Analysis.
2. Stochastic Methods. Part II. Basic Principles of Statistical Thermodynamics.
3. Stochastic Methods. Part III. Basic Mathematics of Stochastic Methods.
These books are registered in the Library of the Chemistry Department of the Aristotle University of Thessaloniki.
In this book, by means of Statistical Thermodynamics, Ideal particle systems (i.e. systems without interactions between their constituent particles) are examined.
The macroscopic - phenomenological character of the so-called Basic or Classical Thermodynamics relates to the examination of the macro¬scopic behavior of the matter. But this behavior is not linked to the properties of the particles (atoms, molecules and/or ions) that compose the examined system.
Thus, classical thermodynamics cannot investigate microscopic phenomena. The Brown movement is cited as an example. In it, heavy particles are automatically lifted, contrary to the direction of the gravity field, while the necessary energy is obtained from the heat of the system. Therefore, contrary to the second thermodynamic law, we have conversion of heat into work without the existence of a second cold source.
The efforts to explain such phenomena gave birth to Statistical Thermodynamics. Its main purpose is to examine and interpret the macroscopic behavior of various systems with the help of theoretical and experimental data referring to the particles that compose these systems.
Of course, both Classical and Quantum Mechanics provide suitable techniques for describing a particulate system. However, this description can only be extended to systems consisting of a relatively small number of particles.
The use of statistical methods was considered necessary to examine systems with large numbers of particles, where only the average values of the various physical quantities, and possibly their changes, can be determined. To illustrate the necessity to use such statistical methods, one should remember that Molecules are contained in just one mol of a gaseous substance (eg 2 g H¬2).
Therefore, it becomes obvious that the description of such a system using only the Classical Mechanics requires the solution of a system of an equally large number (order of ) of differential equations of motion. Such a system is currently impossible to solve using the most powerful computers available. But, even if a solution was feasible, it would be practically impossible to determine the initial system conditions, i.e. the physical positions and momenta of all these molecules.
Of course, neither Quantum Mechanics can be effectively used in describing such a system, since Schrődinger's equation can only be solved in systems with a limited number of particles.
Briefly, we could say that Statistical Thermodynamics is based on a combination of the laws of Mechanics, Thermodynamics and Probability Theory.
To those wishing to expand their knowledge beyond this book, available literature offers a plethora of excellent textbooks, both in Greek and English. Relevant bibliography can be found at the end of this book.
This book consists of 22 chapters and an Appendix providing the indispensable mathematical proposals required to comprehend the main text.
The first two chapters briefly provide the basic concepts and principles of Classical Thermodynamics
In each chapter, paragraphs and relationships are numbered separately.
All Chapters of this Book, in pdf format, are posted online at:
http://ikee.lib.auth.gr/record/310205.
Stochastic Methods. Part I. Basic Principles of Applied Statistical Analysis.
Stochastic Methods. Part II. Statistical Thermodynamics.
Stochastic Methods. Part III. Basic Mathematics of Stochastic Methods.
These books are registered in the Library of the Chemistry Department of the Aristotle University of Thessaloniki.
The development of atomic and molecular theory at the beginning of the 20th century and the attempt to correlate, on the basis of this theory, macroscopic with microscopic behavior of various systems inevitably led to the use of stochastic methods.
In particular, the application of such methods to the¬ thermodynamic behaviour of various systems resulted in¬ the creation of a new discipline: Statistical Thermody¬namics. This branch consists of the examination, by means of stochastic¬ methods, of the macroscopic behaviour of a system, taking into account the mechanical properties of the particles contained in the considered system.
This series aims to contribute to a fuller understanding of such methods, which increasingly find applications in various fields of both natural and applied sciences.
This present book details and analyzes the main mathematical propositions and principles used in the various Stochastic Methods. Notable, the content of the first two books of this series can still be understood by those with limited knowledges of mathematics.
This book consists of 22 Chapters and an Appendix, where the basic principles of Algebraic Structures are mentioned. In each chapter the theorems, relationships and examples are numbered separately.
Chapter 7 provides a very brief overview of the basic principles of the probability theory. A more detailed description of these principles is given in the first chapter¬ ¬of the first book (Part I. Basic Principles of Applied Statistical Analysis) of this series.
To those wishing to expand their knowledge beyond this book, available literature offers a plethora of excellent textbooks, both in Greek and English. Relevant bibliography can be found at the end of this book.
All Chapters of this Book, in pdf format, are posted online at:
http://ikee.lib.auth.gr/record/310210.
The study of the dissociation equilibria of weak acids in aqueous or in various binary water - organic solvent systems is of a considerable theoretical interest as conclusions regarding the structure and the solvation of these acids can be reached. In addition, a detailed examination of such balances could elucidate the interpretation of the behavior of various electrochemical systems.
In particular, the dissociation equilibria of weak bases, monoprotic-, polyprotic- and amino- acids are examined in aqueous as well in mixed solvent systems.
Chapters 1, 2 and 3 provide the necessary theoretical background (thermodynamics and electrostatics) to understand the dissociation of weak acids in dilute solutions.
The examination of the dissociation equilibria of weak electrolytes in mixed water - organic solvent systems leads to conclusions about the structure ¬of the electrolytes tested, as well as the extent of the solvation of ions participating in the corresponding dissociation equilibrium.
This book details methods for¬ the determination of thermo¬dynamic dissociation constants of weak electrolytes in aqueous or mixed solvent systems.
These methods, based on the analysis of pHmetric titration curves of weak acids or bases with a strong base or strong acid respectively, allow the determination of their accurate thermodynamic .
In general, precise analytical concentrations of weak acids or bases are required for the accurate determination of their thermodynamic dissociation constants. These concentrations are obtained experimentally mainly by means of potentiometric titration.
However, in some cases, i.e. very weak acids or certain mixed solvent systems, the corresponding potentiometric titration curves do not have a vertical portion at the end of the ¬neutralization of the titrated substance. In other cases, the¬ differential titration curve present multiple peaks in the vicinity of the equivalent point, resulting in an uncertain determination of the analytical concentration of the titrated substance.
In such cases, the application of iterative methods allows the simultaneous determination of both accurate thermodynamics and the precise analytical concentrate¬ of the corresponding substances, even when the titration is stoped before the titrated substance has been completely neutralized. Such methods are described in Chapter 4 of this book.
Chapter 5 describes the role of weak acids when used as growth inhibitors in plating solution in order to improove certain physical and/or mechanical properties of various metals electrodeposits. In particular, the contribution of tartaric and citric acid to the preparation of compact and smooth silver plates from solutions is examined.
Chapters 6, 7, 8 and 9 examine the ionic behaviour of α-amino acids. Methods for the determination of the thermodynamic constants of the groups and .are described
This book consists of 9 Chapters and four Appendices. In each Chapter the numbering of relationships is done separately.
The various methods for determining the thermodynamic dissociation constants of the various equilibria presented in this book are mainly based on the analysis of linear relationships. For this reason, Annex 1 presents ¬the basic principles of the stochastic method of Linear Regression.
Annex 2 details the various phenomena that occur during the electrolytic deposition of metals and examines the crystal structure of the produced polycrystalline deposits. In particular, the so-called fibrous texture (texture de fibre) of certain polycrystalline deposits is analyzed. (e.g. the crystal structure of deposits that¬ have one or more crystallographic axes perpendicularly oriented to the surface of the deposit). Fibrous texture is usually achieved in deposits prepared from electrolytic solutions containing additives, mainly organic, such as tartar¬or citric acid.
Annex 3 details the solution of the main ordinary differential equations. The basic principles and properties of the “Laplace Τransforms” method and its use in solving linear differential equations are developed.
Appendix 4 provides elements of linear algebra (matrix algebra) and discusses the solution of systems of algebraic linear equations.
To those wishing to expand their knowledge beyond this book, available literature offers a plethora of excellent textbooks, both in Greek and English. Relevant bibliography can be found at the end of this book.
All Chapters of this Book, in pdf format, are posted online at:
http://ikee.lib.auth.gr/record/325486.
Iterative Methods by Georgios Papanastasiou
Stochastic Methods. Part I. Basic Principles of Applied Statistical Analysis.
Stochastic Methods. Part II. Basic Principles of Statistical Thermodynamics.
Stochastic Methods. Part III. Basic Mathematics of Stochastic Methods.
All these books are registered in the Library of the Chemistry Department of the Aristotle University of Thessaloniki.
Several topics of basic and applied science require the use of stochastic methods, which are based on probability theory and statistics. A typical example is statistical thermodynamics. In this topic, the macroscopic behavior of a system is linked to the microscopic properties of the particules of the examined system.
This series aim to help the reader gaining a thorough understanding of such methods.
The present book outlines and details the main proposals and principles of the probability theory and statistics, which are used in various stochastic methods.
This theoretical exercise is not the sole aim of this book. Nowadays, there are several statistical software packages for data analysis using a variety of statistical methods or tests. These methods are accessible even to scientists lacking a basic knowledge of mathematics. Nevertheless, a critical question remains open; which statistical method is appropriate for the analysis of a specific dataset?
This book provides the fundamental theoretical background for the main statistical methods and tests. This knowledge is essential for both the selection of appropriate methods of analysis and the interpretation of the obtained results.
It is noted that the use of the appropriate statistical methods for the processing of the data, debunks the myth that statistics can prove whatever we want to prove! This can definitely happen when we erroneously chose (either on purpose or out of ignorance) invalid statistical tests.
Statistics is a rigorous mathematical discipline, which can generate reliable results, if properly applied. What is different from other mathematical methods is that statistics do not always answer a raised question with a definite answer; instead, statistics consider all possibilities and calculate the probabilities of each, using appropriate methods.
This book consists of 13 chapters and an Appendix providing the indispensable mathematical proposals required to comprehend the main text. A significant number of resolved exercises are also appended, aiming to assist the reader in achieving a deeper knowledge of statistical methods.
In each chapter the theorems, relationships and examples are numbered separately. This book also contains 13 Statistical Tables.
To those wishing to expand their knowledge beyond this book, available literature offers a plethora of excellent textbooks, both in Greek and English. Relevant bibliography can be found at the end of this book.
All Chapters of this Book, in pdf format, are posted online at:
http://ikee.lib.auth.gr/record/310203.
1. Stochastic Methods. Part I. Basic Principles of Applied Statistical Analysis.
2. Stochastic Methods. Part II. Basic Principles of Statistical Thermodynamics.
3. Stochastic Methods. Part III. Basic Mathematics of Stochastic Methods.
These books are registered in the Library of the Chemistry Department of the Aristotle University of Thessaloniki.
In this book, by means of Statistical Thermodynamics, Ideal particle systems (i.e. systems without interactions between their constituent particles) are examined.
The macroscopic - phenomenological character of the so-called Basic or Classical Thermodynamics relates to the examination of the macro¬scopic behavior of the matter. But this behavior is not linked to the properties of the particles (atoms, molecules and/or ions) that compose the examined system.
Thus, classical thermodynamics cannot investigate microscopic phenomena. The Brown movement is cited as an example. In it, heavy particles are automatically lifted, contrary to the direction of the gravity field, while the necessary energy is obtained from the heat of the system. Therefore, contrary to the second thermodynamic law, we have conversion of heat into work without the existence of a second cold source.
The efforts to explain such phenomena gave birth to Statistical Thermodynamics. Its main purpose is to examine and interpret the macroscopic behavior of various systems with the help of theoretical and experimental data referring to the particles that compose these systems.
Of course, both Classical and Quantum Mechanics provide suitable techniques for describing a particulate system. However, this description can only be extended to systems consisting of a relatively small number of particles.
The use of statistical methods was considered necessary to examine systems with large numbers of particles, where only the average values of the various physical quantities, and possibly their changes, can be determined. To illustrate the necessity to use such statistical methods, one should remember that Molecules are contained in just one mol of a gaseous substance (eg 2 g H¬2).
Therefore, it becomes obvious that the description of such a system using only the Classical Mechanics requires the solution of a system of an equally large number (order of ) of differential equations of motion. Such a system is currently impossible to solve using the most powerful computers available. But, even if a solution was feasible, it would be practically impossible to determine the initial system conditions, i.e. the physical positions and momenta of all these molecules.
Of course, neither Quantum Mechanics can be effectively used in describing such a system, since Schrődinger's equation can only be solved in systems with a limited number of particles.
Briefly, we could say that Statistical Thermodynamics is based on a combination of the laws of Mechanics, Thermodynamics and Probability Theory.
To those wishing to expand their knowledge beyond this book, available literature offers a plethora of excellent textbooks, both in Greek and English. Relevant bibliography can be found at the end of this book.
This book consists of 22 chapters and an Appendix providing the indispensable mathematical proposals required to comprehend the main text.
The first two chapters briefly provide the basic concepts and principles of Classical Thermodynamics
In each chapter, paragraphs and relationships are numbered separately.
All Chapters of this Book, in pdf format, are posted online at:
http://ikee.lib.auth.gr/record/310205.
Stochastic Methods. Part I. Basic Principles of Applied Statistical Analysis.
Stochastic Methods. Part II. Statistical Thermodynamics.
Stochastic Methods. Part III. Basic Mathematics of Stochastic Methods.
These books are registered in the Library of the Chemistry Department of the Aristotle University of Thessaloniki.
The development of atomic and molecular theory at the beginning of the 20th century and the attempt to correlate, on the basis of this theory, macroscopic with microscopic behavior of various systems inevitably led to the use of stochastic methods.
In particular, the application of such methods to the¬ thermodynamic behaviour of various systems resulted in¬ the creation of a new discipline: Statistical Thermody¬namics. This branch consists of the examination, by means of stochastic¬ methods, of the macroscopic behaviour of a system, taking into account the mechanical properties of the particles contained in the considered system.
This series aims to contribute to a fuller understanding of such methods, which increasingly find applications in various fields of both natural and applied sciences.
This present book details and analyzes the main mathematical propositions and principles used in the various Stochastic Methods. Notable, the content of the first two books of this series can still be understood by those with limited knowledges of mathematics.
This book consists of 22 Chapters and an Appendix, where the basic principles of Algebraic Structures are mentioned. In each chapter the theorems, relationships and examples are numbered separately.
Chapter 7 provides a very brief overview of the basic principles of the probability theory. A more detailed description of these principles is given in the first chapter¬ ¬of the first book (Part I. Basic Principles of Applied Statistical Analysis) of this series.
To those wishing to expand their knowledge beyond this book, available literature offers a plethora of excellent textbooks, both in Greek and English. Relevant bibliography can be found at the end of this book.
All Chapters of this Book, in pdf format, are posted online at:
http://ikee.lib.auth.gr/record/310210.
The study of the dissociation equilibria of weak acids in aqueous or in various binary water - organic solvent systems is of a considerable theoretical interest as conclusions regarding the structure and the solvation of these acids can be reached. In addition, a detailed examination of such balances could elucidate the interpretation of the behavior of various electrochemical systems.
In particular, the dissociation equilibria of weak bases, monoprotic-, polyprotic- and amino- acids are examined in aqueous as well in mixed solvent systems.
Chapters 1, 2 and 3 provide the necessary theoretical background (thermodynamics and electrostatics) to understand the dissociation of weak acids in dilute solutions.
The examination of the dissociation equilibria of weak electrolytes in mixed water - organic solvent systems leads to conclusions about the structure ¬of the electrolytes tested, as well as the extent of the solvation of ions participating in the corresponding dissociation equilibrium.
This book details methods for¬ the determination of thermo¬dynamic dissociation constants of weak electrolytes in aqueous or mixed solvent systems.
These methods, based on the analysis of pHmetric titration curves of weak acids or bases with a strong base or strong acid respectively, allow the determination of their accurate thermodynamic .
In general, precise analytical concentrations of weak acids or bases are required for the accurate determination of their thermodynamic dissociation constants. These concentrations are obtained experimentally mainly by means of potentiometric titration.
However, in some cases, i.e. very weak acids or certain mixed solvent systems, the corresponding potentiometric titration curves do not have a vertical portion at the end of the ¬neutralization of the titrated substance. In other cases, the¬ differential titration curve present multiple peaks in the vicinity of the equivalent point, resulting in an uncertain determination of the analytical concentration of the titrated substance.
In such cases, the application of iterative methods allows the simultaneous determination of both accurate thermodynamics and the precise analytical concentrate¬ of the corresponding substances, even when the titration is stoped before the titrated substance has been completely neutralized. Such methods are described in Chapter 4 of this book.
Chapter 5 describes the role of weak acids when used as growth inhibitors in plating solution in order to improove certain physical and/or mechanical properties of various metals electrodeposits. In particular, the contribution of tartaric and citric acid to the preparation of compact and smooth silver plates from solutions is examined.
Chapters 6, 7, 8 and 9 examine the ionic behaviour of α-amino acids. Methods for the determination of the thermodynamic constants of the groups and .are described
This book consists of 9 Chapters and four Appendices. In each Chapter the numbering of relationships is done separately.
The various methods for determining the thermodynamic dissociation constants of the various equilibria presented in this book are mainly based on the analysis of linear relationships. For this reason, Annex 1 presents ¬the basic principles of the stochastic method of Linear Regression.
Annex 2 details the various phenomena that occur during the electrolytic deposition of metals and examines the crystal structure of the produced polycrystalline deposits. In particular, the so-called fibrous texture (texture de fibre) of certain polycrystalline deposits is analyzed. (e.g. the crystal structure of deposits that¬ have one or more crystallographic axes perpendicularly oriented to the surface of the deposit). Fibrous texture is usually achieved in deposits prepared from electrolytic solutions containing additives, mainly organic, such as tartar¬or citric acid.
Annex 3 details the solution of the main ordinary differential equations. The basic principles and properties of the “Laplace Τransforms” method and its use in solving linear differential equations are developed.
Appendix 4 provides elements of linear algebra (matrix algebra) and discusses the solution of systems of algebraic linear equations.
To those wishing to expand their knowledge beyond this book, available literature offers a plethora of excellent textbooks, both in Greek and English. Relevant bibliography can be found at the end of this book.
All Chapters of this Book, in pdf format, are posted online at:
http://ikee.lib.auth.gr/record/325486.