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Contents

Chapter I. Variables and Functions
§ 1. Quantities

Concept of a Quantity
Dimensions of Quantities
Constants and Variables
Number Scale. Slide Rule
Characteristics of Variables

§ 2. Approximate Values of Quantities
6. The Notion of an Approximate Value
7. Errors
8. Writing Approximate Numbers
9. Addition and Subtraction of Approximate Numbers
10. Multiplication and Division of Approximate Numbers. General Remarks

§ 3. Functions and Graphs
11. Functional Relation
12. Notation
13. Methods of Representing Functions
14. Graphs of Functions
15. The Domain of Definition of a Function
16. Characteristics of Behaviour of Functions
17. Algebraic Classification of Functions
18. Elementary Functions
19. Transforming Graphs
20. Implicit Functions
21. Inverse Functions

§ 4. Review of Basic Functions
22. Linear Function
23. Quadratic Function
24. Power Function
25. Linear-Fractional Function
26. Logarithmic Function
27. Exponential Function
28. Hyperbolic Functions
29. Trigonometric Functions
30. Empirical Formulas

Chapter II. Plane Analytic Geometry
§ 1. Plane Coordinates

Cartesian Coordinates
Some Simple Problems Concerning Cartesian Coordinates
Polar Coordinates

§ 2. Curves in Plane
4. Equation of a Curve in Cartesian Coordinates
5. Equation of a Curve in Polar Coordinates
6. Parametric Representation of Curves and Functions
7. Algebraic Curves
8. Singular Cases

§ 3. First-Order and Second-Order Algebraic Curves
9. Curves of the First Order
10. Ellipse
11. Hyperbola
12. Relationship Between Ellipse, Hyperbola and Parabola
13. General Equation of a Curve of the Second Order

Chapter III. Limit. Continuity
§ 1. Infinitesimal and Infinitely Large Variables

Infinitesimal Variables
Properties of Infinitesimals
Infinitely Large Variables

§ 2. Limits
4. Definition
5. Properties of Limits
6. Sum of a Numerical Series

§ 3. Comparison of Variables
7. Comparison of Infinitesimals
8. Properties of Equivalent Infinitesimals
9. Important Examples
10. Orders of Smallness
11. Comparison of Infinitely Large Variables

§ 4. Continuous and Discontinuous Functions
12. Definition of a Continuous Function
13. Points of Discontinuity
14. Properties of Continuous Functions
15. Some Applications

Chapter IV. Derivatives, Differentials, Investigation of the Behaviour of Functions
§ 1. Derivative

Some Problems Leading to the Concept of a Derivative
Definition of Derivative
Geometrical Meaning of Derivative
Basic Properties of Derivatives
Derivatives of Basic Elementary Functions
Determining Tangent in Polar Coordinates

§ 2. Differential
7. Physical Examples
8. Definition of Differential and Its Connection with Increment
9. Properties of Differential
10. Application of Differentials to Approximate Calculations

§ 3. Derivatives and Differentials of Higher Orders
11. Derivatives of Higher Orders
12. Higher-Order Differentials

§ 4. V. H.ospital’s Rule
13. Indeterminate Forms of the Type 0/0
14. Indeterminate Forms of the Type ∞/∞

§ 5. Taylor’s Formula and Series
15. Taylor’s Formula
16. Taylor’s Series

§ 6. Intervals of Monotonicity. Extremum
17. Sign of Derivative
18. Points of Extremum
19. The Greatest and the Least Values of a Function

§ 7. Constructing Graphs of Functions
20. Intervals of Convexity of a Graph and Points of Inflection
21. Asymptotes of a Graph
22. General Scheme for Investigating a Function and Constructing Its Graph

Chapter V. Approximating Roots of Equations. Interpolation
§ 1. Approximating Roots of Equations

Introduction
Cut-and-Try Method. Method of Chords. Method of Tangents
Iterative Method
Formula of Finite Increments
5*. Small Parameter Method

§ 2. Interpolation
6. Lagrange’s Interpolation Formula
7. Finite Differences and Their Connection with Derivatives
8. Newton’s Interpolation Formulas
9. Numerical Differentiation

Chapter VI. Determinants and Systems of Linear Algebraic Equations
§ 1. Determinants

Definition
Properties
Expanding a Determinant in Minors of Its Row or Column

§ 2. Systems of Linear Algebraic Equations
4. Basic Case
5. Numerical Solution
6. Singular Case

Chapter VII. Vectors
§ 1. Linear Operations on Vectors

Scalar and Vector Quantities
Addition of Vectors
Zero Vector and Subtraction of Vectors
Multiplying a Vector by a Scalar
Linear Combination of Vectors

§ 2. Scalar Product of Vectors
6. Projection of Vector on Axis
7. Scalar Product
8. Properties of Scalar Product

§ 3. Cartesian Coordinates in Space
9. Cartesian Coordinates in Space
10. Some Simple Problems Concerning Cartesian Coordinates

§ 4. Vector Product of Vectors
11. Orientation of Surface and Vector of Area
12. Vector Product
13. Properties of Vector Product
14*. Pseudovectors

§ 5. Products of Three Vectors
15. Triple Scalar Product
16. Triple Vector Product

§ 6. Linear Spaces
17. Concept of Linear Space
18. Examples
19. Dimension of Linear Space
20. Concept of Euclidean Space
21. Orthogonality

§ 7. Vector Functions of Scalar Argument. Curvature
22. Vector Variables
23. Vector Functions of Scalar Argument
24. Some Notions Related to the Second Derivative
25. Osculating Circle
26. Evolute and Evolvent

Chapter VIII. Complex Numbers and Functions
§ 1. Complex Numbers

Complex Plane
Algebraic Operations on Complex Numbers
Conjugate Complex Numbers
Euler’s Formula
Logarithms of Complex Numbers

§ 2. Complex Functions of a Real Argument
6. Definition and Properties
7*. Applications to Describing Oscillations

§ 3. The Concept of a Function of a Complex Variable
8. Factorization of a Polynomial
9*. Numerical Methods of Solving Algebraic Equations
10. Decomposition of a Rational Fraction into Partial Rational Fractions
11*. Some General Remarks on Functions of a Complex Variable

Chapter IX. Functions of Several Variables
§ 1. Functions of Two Variables

Methods of Representing
Domain of Definition
Linear Function
Continuity and Discontinuity
Implicit Functions

§ 2. Functions of Arbitrary Number of Variables
6. Methods of Representing
7. Functions of Three Arguments
8. General Case
9. Concept of Field

§ 3. Partial Derivatives and Differentials of the First Order
10. Basic Definitions
11. Total Differential
12. Derivative of Composite Function
13. Derivative of Implicit Function

§ 4. Partial Derivatives and Differentials of Higher Orders
14. Definitions
15. Equality of Mixed Derivatives
16. Total Differentials of Higher Order

Chapter X. Solid Analytic Geometry
§ 1. Space Coordinates

Coordinate Systems in Space
2*. Degrees of Freedom

§ 2. Surfaces and Curves in Space
3. Surfaces in Space
4. Cylinders, Cones and Surfaces of Evolution
5. Curves in Space
6. Parametric Representation of Surfaces in Space. Parametric Representation of Functions of Several Variables

§ 3. Algebraic Surfaces of the First and the Second Orders
7. Algebraic Surfaces of the First Order
8. Ellipsoid
9. Hyperboloids
10. Paraboloids
11. General Review of Algebraic Surfaces of the Second Order

Chapter XI. Matrices and Their Applications
§ 1. Matrices

Definitions
Operations on Matrices
Inverse Matrix
Eigenvectors and Eigenvalues of a Matrix
The Rank of a Matrix

§ 2. Linear Mappings
6. Linear Mapping and Its Matrix
7. Transformation of the Matrix of a Linear Mapping When the Basis Is Changed
8. The Matrix of a Mapping Relative to the Basis Consisting of Its Eigenvectors
9. Transforming Cartesian Basis
10. Symmetric Matrices

§ 3. Quadratic Forms
11. Quadratic Forms
12. Simplification of Equations of Second-Order Curves and Surfaces

§ 4. Non-Linear Mappings
13*. General Notions
14*. Non-Linear Mapping in the Small
15*. Functional Relation Between Functions

Chapter XII. Applications of Partial Derivatives
§ 1. Scalar Field

Directional Derivative. Gradient
Level Surfaces
Implicit Functions of Two Independent Variables
Plane Fields
Envelope of One-Parameter Family of Curves

§ 2. Extremum of a Function of Several Variables
6. Taylor’s Formula for a Function of Several Variables
7. Extremum
8. The Method of Least Squares
9*. Curvature of Surfaces
10. Conditional Extremum
11. Extremum with Unilateral Constraints
12*. Numerical Solution of Systems of Equations

Chapter XIII. Indefinite Integral
§ 1. Elementary Methods of Integration

Basic Definitions
The Simplest Integrals
The Simplest Properties of an Indefinite Integral
Integration by Parts
Integration by Change of Variable (by Substitution)

§ 2. Standard Methods of Integration
6. Integration of Rational Functions
7. Integration of Irrational Functions Involving Linear and Linear-Fractional Expressions
8. Integration of Irrational Expressions Containing Quadratic Trinomials
9. Integrals of Binomial Differentials
10. Integration of Functions Rationally Involving Trigonometric Functions
11. General Remarks

Chapter XIV. Definite Integral
§ 1. Definition and Basic Properties

Examples Leading to the Concept of Definite Integral
Basic Definition
Relationship Between Definite Integral and Indefinite Integral
Basic Properties of Definite Integral
Integrating Inequalities

§ 2. Applications of Definite Integral
6. Two Schemes of Application
7. Differential Equations with Variables Separable
8. Computing Areas of Plane Geometric Figures
9. The Arc Length of a Curve
10. Computing Volumes of Solids
11. Computing Area of Surface of Revolution

§ 3. Numerical Integration
12. General Remarks
13. Formulas of Numerical Integration

§ 4. Improper Integrals
14. Integrals with Infinite Limits of Integration
15. Basic Properties of Integrals with Infinite Limits of Integration
16. Other Types of Improper Integral
17*. Gamma Function
18*. Beta Function
19*. Principal Value of Divergent Integral

§ 5. Integrals Dependent on Parameters
20*. Proper Integrals
21*. Improper Integrals

§ 6. Line Integrals
22. Line Integrals of the First Type
23. Line Integrals of the Second Type
24. Conditions for a Line Integral of the Second Type to Be Independent of the Path of Integration

§ 7. The Concept of Generalized Function
25*. Delta Function
26*. Application to Constructing Influence Function
27*. Other Generalized Functions

Chapter XV. Differential Equations
§ 1. General Notions

Examples
Basic Definitions

§ 2. First-Order Differential Equations
3. Geometric Meaning
4. Integrable Types of Equations
5*. Equation for Exponential Function
6. Integrating Exact Differential Equations
7*. Singular Points and Singular Solutions
8*. Equations Not Solved for the Derivative
9*. Method of Integration by Means of Differentiation

§ 3. Higher-Order Equations and Systems of Differential Equations
10. Higher-Order Differential Equations
11*. Connection Between Higher-Order Equations and Systems of First-Order Equations
12*. Geometric Interpretation of System of First-Order Equations
13*. First Integrals

§ 4. Linear Equations of General Form
14. Homogeneous Linear Equations
15. Non-Homogeneous Equations
16*. Boundary-Value Problems

§ 5. Linear Equations with Constant Coefficients
17. Homogeneous Equations
18. Non-Homogeneous Equations with Right-Hand Sides of Special Form
19*. Euler’s Equations
20*. Operators and the Operator Method of Solving Differential Equations

§ 6. Systems of Linear Equations
21. Systems of Linear Equations
22*. Applications to Testing Lyapunov Stability of Equilibrium State

§ 7. Approximate and Numerical Methods of Solving Differential Equations
23. Iterative Method
24*. Application of Taylor’s Series
25. Application of Power Series with Undetermined Coefficients
26*. Bessel’s Functions
27*. Small Parameter Method
28*. General Remarks on Dependence of Solutions on Parameters
29*. Methods of Minimizing Discrepancy
30*. Simplification Method
31. Euler’s Method
32. Runge-Kutta Method
33. Adams Method
34. Milne’s Method

Chapter XVI. Multiple Integrals
§ 1. Definition and Basic Properties of Multiple Integrals

Some Examples Leading to the Notion of a Multiple Integral
Definition of a Multiple Integral
Basic Properties of Multiple Integrals
Methods of Applying Multiple Integrals
Geometric Meaning of an Integral over a Plane Region

§ 2. Two Types of Physical Quantities
6*. Basic Example. Mass and Its Density
7*. Quantities Distributed in Space

§ 3. Computing Multiple Integrals in Cartesian Coordinates
8. Integral over Rectangle
9. Integral over an Arbitrary Plane Region
10. Integral over an Arbitrary Surface
11. Integral over a Three-Dimensional Region

§ 4. Change of Variables in Multiple Integrals
12. Passing to Polar Coordinates in Plane
13. Passing to Cylindrical and Spherical Coordinates
14*. Curvilinear Coordinates in Plane

Chapter XVII. [Heading not present in the supplied contents]

§ 5. Fourier Transformation
32*. Fourier Transform
33*. Properties of Fourier Transforms
34*. Application to Oscillations of Infinite String

Chapter XVIII. Elements of the Theory of Probability
§ 1. Random Events and Their Probabilities

Random Events
Probability
Basic Properties of Probabilities
Theorem of Multiplication of Probabilities
Theorem of Total Probability
6*. Formulas for the Probability of Hypotheses
Disregarding Low-Probability Events

§ 2. Random Variables
8. Definitions
9. Examples of Discrete Random Variables
10. Examples of Continuous Random Variables
11. Joint Distribution of Several Random Variables
12. Functions of Random Variables

§ 3. Numerical Characteristics of Random Variables
13. The Mean Value
14. Properties of the Mean Value
15. Variance
16*. Correlation
17. Characteristic Functions

§ 4. Applications of the Normal Law
18. The Normal Law as the Limiting One
19. Confidence Interval
20. Data Processing

Chapter XIX. Computers
§ 1. Two Classes of Computers

Analogue Computers
Digital Computers

§ 2. Programming
3. Number Systems
4. Representing Numbers in a Computer
5. Instructions
6. Examples of Programming

Appendix. Equations of Mathematical Physics
1*. Derivation of Some Equations
2*. Some Other Equations
3*. Initial and Boundary Conditions

§ 2. Method of Separation of Variables
4*. Basic Example
5*. Some Other Problems

Bibliography

Name Index

Subject Index

List of Symbols

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Engineering Thermodynamics by V.A. Kirillin; V.V. Sychev; A.E. Sheindlin

Posted on September 20, 2026 by The Mitr

Although many Soviet and foreign textbooks in engineering thermodynamics already exist, the authors have decided to write a new textbook for university students in power engineering, heat physics, and applied physics departments. We have done so for the following reasons.

With improved instruction in thermodynamics in most higher educational institutions, the authors feel a more thorough presentation of basic problems is necessary. Of primary importance is an understanding of the fundamental concepts and methods of thermodynamics for analysing various physical phenomena.

Clearly, a modern course in engineering thermodynamics must reflect today’s and even tomorrow’s level of technology. Therefore, it is difficult to conceive of a modern textbook in thermodynamics which does not present the different methods of converting heat directly into electric power, modern methods of analysing the efficiency of the cycles of heating plants, the thermodynamics of dissociated and ionised gases, and other problems.

Since the authors consider it unjustified to include in courses of engineering thermodynamics problems relating to statistical physics and the molecular-kinetic theories of gases, we will limit ourselves to a short discussion of the statistical aspects of the second law of thermodynamics.

Although, as a rule, institutes of power engineering do not offer a special course in chemical thermodynamics, modern heat engineering involves many processes accompanied by chemical reactions, dissociation, and ionisation. The authors consider it necessary, therefore, to devote a special chapter to a short presentation of chemical thermodynamics to give the reader an idea of the methods applied in a thermodynamic description of chemical processes.

All numerical examples are given in the SI system (the unit to measure energy is the joule, and the unit to measure pressure is the pascal). As a general rule, along with their values in the SI system, the values of energy have also been indicated in calories (and pressure, in kgf/cm²).

The authors will be grateful for criticism and will take it into consideration in future work on the book.

Translated from the Russian by S. Semyonov

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Contents

Preface
Preface to the English edition

Introduction
Thermodynamics and its method
Properties of state
Concept of a thermodynamic process
Ideal gas Ideal gas laws
Concept of mixtures Mixtures of ideal gases
Concept of heat capacity

The first law of thermodynamics
Heat Joule’s experiment Equivalence of heat and work
Law of conservation and conversion of energy
Internal energy and external work
Mathematical statement of the first law of thermodynamics
Enthalpy
Mathematical statement of the first law of thermodynamics for processes of flow

The second law of thermodynamics
Cycles Concept of thermal efficiency Heat sources
Reversible and irreversible processes
Statements of the second law of thermodynamics
The Carnot cycle Carnot’s theorem
The thermodynamic temperature scale

Entropy
Change of entropy in irreversible processes
Combined mathematical statement of the first and second laws of thermodynamics
Entropy and thermodynamic probability
Reversibility and work

Differential equations of thermodynamics
Basic methods
Maxwell’s relations
Partial derivatives of internal energy and enthalpy
Heat capacities

Equilibrium in thermodynamic systems and phase changes
Homogeneous and heterogeneous thermodynamic systems
Thermodynamic equilibrium
Conditions of stability and equilibrium for an isolated homogeneous system
Conditions for phase equilibrium
Phase changes
The Clausius-Clapeyron equation
Phase stability
Phase changes at unequal phase pressures
Phase changes under curved surfaces

Thermodynamic properties of substances
Thermal and caloric properties of solids
Thermal and caloric properties of liquids
Andrews’ experiment The critical point Van der Waals’ equation
Thermal and caloric properties of real gases Equation of state for real gases
Thermodynamic properties of substances on the change-of-phase line Two-phase systems
Properties of substance at the critical point
Methods of calculating the entropy of substance
Thermodynamic diagrams of state for substances
Thermodynamic properties of substance in a metastable state

Basic thermodynamic processes
The isochoric process
The isobaric process
The isothermal process
The adiabatic process
Polytropic processes
Throttling The Joule-Thomson effect
Joule expansion (expansion into a vacuum)
Mixing
Compression processes

Fluid flow processes
Basic flow equations
Velocity of sound
Flow through convergent nozzles
Transonic range The Laval nozzle
Adiabatic flow with friction
General regularities of flow The influence inversion law
Adiabatic stagnation temperature

Methods to analyse the efficiency of thermopower plants
Cycle efficiency
Comparison methods for thermal efficiencies of reversible cycles
Method of efficiencies in the analysis of irreversible cycles
Entropy calculation method for the loss of availability in irreversible cycles
Exergy calculation method for availability losses

Gas power cycles
Cycles of reciprocating internal combustion engines
Gas-turbine cycles
Reaction-engine cycles

Vapour power cycles
The Carnot cycle
The Rankine cycle
Rankine cycle analysis allowing for irreversibilities

Reheat cycle

Regenerative cycle

Binary cycles

Thermification cycles

Cycles of direct-energy conversion systems

Thermoelectric generator cycle

The cycle of a thermionic converter

MHD-generator cycle

Refrigeration cycles

Reverse heat cycles and processes
Refrigeration installations

Air-compression refrigeration cycle

Vapour-compression refrigeration cycle

Steam-jet refrigeration cycle

Absorption refrigeration cycle

Thermoelectric refrigeration cycle

Heat pump
Principle of operation

Liquefaction of gases

Humid air

Basic concepts

I-d diagram for humid air

Fundamentals of chemical thermodynamics

Thermochemistry
Hess’s law
Kirchhoff’s equation

Chemical equilibrium and the second law of thermodynamics

Equilibrium constant and degree of dissociation

The Nernst heat theorem

Conclusion

Bibliography

Name index

Subject index

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Quimica Orgánica by V. M. Potapov; S. N. Tatarinchik

Posted on September 19, 2026 by The Mitr

La química orgánica atraviesa un período de notable desarrollo caracterizado por el descubrimiento de nuevas sustancias con propiedades excepcionales y la creación de compuestos innovadores de aplicación práctica en diversas áreas. Este progreso se apoya en el uso de métodos modernos de investigación fundamentados en la física y en una profundización de las nociones teóricas. Sin embargo, esto plantea retos educativos, ya que es necesario condensar una gran cantidad de material en los planes de estudio. Los autores abogan por priorizar las leyes generales de la química orgánica, dejando en segundo plano el contenido puramente descriptivo, y basan su enfoque en la teoría de la estructura química de Bútlerov, complementada con una mejor comprensión de los enlaces químicos y las reacciones orgánicas. Este enfoque permite clasificar las reacciones de manera sistemática y facilitar su aprendizaje.

El libro sigue una clasificación basada en los grupos funcionales, que determinan el comportamiento químico de los compuestos orgánicos. Se abordan primero los hidrocarburos y luego sus derivados, incluyendo halogenados e hidroxílicos, destacando aquellos compuestos de relevancia práctica en la industria, agricultura y medicina. Para esta nueva edición, los autores han incorporado recomendaciones de instituciones académicas como las escuelas politécnicas de Moscú y Leningrado, ajustando el contenido al programa aprobado en 1974 para especialidades como química analítica y química de explotaciones petrolíferas. Finalmente, los autores invitan a los lectores a proporcionar observaciones críticas para mejorar la obra en futuras ediciones.

Traducido del ruso por Neiml Sosa

Todos los créditos a los cargadores originales.

Nota: La calidad del escaneo es promedio

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The Stranger by Titus Popovici

Posted on September 18, 2026 by The Mitr

A Soviet era novel of the political awakening of a young Romanian intellectual in 1944.

Translated from the Romanian by Lazar Marinescu

Illustrations: P. Nazarie

Jacket: P. Vulcanescu

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Examples And Problems To The Course Of Unit Operations Of Chemical Engineering by K. F. Pavlov; P. G. Romankou; A. A. Noskov

Posted on September 17, 2026 by The Mitr

The gaining of skill in solving practical engineering problems is very important for students of the course in unit operations. The Department of Unit Operations of Chemical Engineering at the Leningrad Technological Institute places great emphasis on this aspect, and the present book contains many examples and problems in the course that are the result of many years of instructional experience.

Great attention is devoted to the independent work of students, and problems are provided on all sections of the course:

Fundamentals of applied hydraulics
Pumps, fans, compressors
Hydromechanical separation methods
Hydrodynamics of a fluidised bed
Agitation in a liquid medium
Heat transfer in chemical apparatus
Evaporation, crystallisation
Mass transfer, absorption
Distillation and rectification
Extraction and leaching
Adsorption
Drying
Moderate and deep refrigeration
The basic formulas and equations needed for solving the problems are given at the beginning of each chapter. The appendices contain numerous reference tables and diagrams.

The present book, edited by Associate Member of the USSR Academy of Sciences, P. G. Romankov, is intended as a training aid for students of chemical engineering and related specialities in day, evening, and correspondence faculties. It will also be a useful aid in course and diploma designing.

About the Authors

Konstantin F. Pavlov (1895–1944)
Konstantin F. Pavlov was an outstanding specialist in the separation of natural and industrial gases. In 1934, he received his doctorate and the rank of professor. He headed the departments of Chemical Engineering of Inorganic Substances and General Chemical Engineering at the Leningrad Technological Institute, where, in 1936, he founded the first training laboratory in unit operations of chemical engineering in the country (now named after him).

He is the author of several training aids in chemical engineering and original research works (e.g., the rule of linearity of chemical engineering functions). During his final years, he worked in Moscow at the Institute of Physical Problems of the USSR Academy of Sciences.

Pyotr G. Romankov, D.Sc.
Professor Pyotr G. Romankov worked for many years as a chemical engineer and instructor at various chemical institutes. Since 1941, he has been the head of the Department of Unit Operations of Chemical Engineering at the Leningrad Technological Institute. Together with his pupils and collaborators, he has published over 250 scientific works, including several monographs on the theory and application of hydromechanical, heat, and mass-exchange processes of chemical engineering.

In 1964, Pyotr Romankov was elected an associate member of the USSR Academy of Sciences. He is an Honoured Scientist of the RSFSR and has received numerous government awards. He is also a Doctor honoris causa of several foreign higher educational establishments.

Anatoli A. Noskov (1904–1977)
Anatoli A. Noskov worked for many years as an engineer in gas separation under the guidance of Prof. Konstantin Pavlov. He was later invited to work at the Department of Unit Operations of Chemical Engineering at the Leningrad Technological Institute, where he advanced from lecturer to professor.

Anatoli Noskov is well known for his contributions to improving rectification processes and methods for calculating standard operations of chemical engineering.

Edited by P. G. Romankov
Associate Member, USSR Academy of Sciences

Translated from the Russian by G. Leib

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Contents

CONTENTS
Preface
Introductory Methodical Instructions
Chapter 1. FUNDAMENTALS OF APPLIED HYDRAULICS
Fundamental Relationships and Formulas for Calculations
Examples
Problems
Symbols
Chapter 2. PUMPS, FANS, COMPRESSORS
Fundamental Relationships and Formulas for Calculations
Examples
Problems
Symbols
Chapter 3. HYDROMECHANICAL SEPARATION METHODS. HYDRODYNAMICS OF A FLUIDIZED BED. AGITATION IN A LIQUID MEDIUM
Fundamental Relationships and Formulas for Calculations
Settling
Filtration
Centrifugal Separation
Hydrodynamics of a Fluidized Bed
Agitation in a Liquid Medium
Examples
Settling
Filtration
Centrifugal Filtration
Fluidized Bed
Agitation in a Liquid Medium
Problems
Example of Calculating and Selecting a Multi-Tube Cyclone Separator
Example of Calculating and Selecting a Foam Gas Washer for Purifying a Gas of Dust
Example of Calculating and Selecting a Rotary Vacuum Filter
Symbols
Chapter 4. HEAT TRANSFER IN A CHEMICAL APPARATUS
Fundamental Relationships and Formulas for Calculations
Heat Conduction
Heat Transfer
Overall Heat Transfer in Surface Heat Exchangers
Overall Heat Transfer in Direct Contact of Streams
Approximate Values of Individual and Overall Heat Transfer Coefficients
Examples
Problems
Examples of Calculating and Selecting Heat Exchangers
Symbols
Chapter 5. EVAPORATION. CRYSTALLIZATION
Fundamental Relationships and Formulas for Calculations
Examples
Problems
Example of Calculating and Selecting a Triple-Effect Evaporator
Symbols
Chapter 6. MASS TRANSFER. ABSORPTION
Fundamental Relationships and Formulas for Calculations
Examples
Problems
Symbols
Chapter 7. DISTILLATION AND RECTIFICATION
Fundamental Relationships and Formulas for Calculations
Examples
Problems
Example of Calculating and Selecting a Plate Rectification Column
Symbols
Chapter 8. EXTRACTION AND LEACHING
Fundamental Relationships and Formulas for Calculations
Examples
Problems
Symbols
Chapter 9. ADSORPTION
Fundamental Relationships and Formulas for Calculations
Examples
Problems
Symbols
Chapter 10. DRYING
Fundamental Relationships and Formulas for Calculations
Examples
Problems
Example of Calculating and Selecting a Fluidized-Bed Dryer for Drying Potassium Chloride
Example of Calculating and Selecting a Drum Dryer
Symbols
Chapter 11. MODERATE AND DEEP REFRIGERATION
Fundamental Relationships and Formulas for Calculations
Examples
Problems
Symbols
Answers to Problems
Bibliography
Appendices
Guide to Tables and Diagrams in Appendices

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Binary Automatic Control Systems ( Advances In Science And Technology In The USSR Technology Series) by S.V. Emelyanov

Posted on September 16, 2026 by The Mitr

The book outlines a new approach to the synthesis of nonlinear dynamic systems, a key problem in control engineering.

The suggested design formalism is based on the “binary” principle, which is essentially a dual treatment of signals in the dynamic system – as a phase variable in one circumstance and as a transformation operator in another. This principle opens up the possibility of handling control laws as ordinary phase variables and invokes feedback to generate such laws. The feedback mechanism, in this case, is exploited in a non-orthodox manner, leading to the occurrence of new types of feedback.

The efficiency of the new approach is demonstrated by constructing control systems that stabilize the motion of nonlinear dynamic plants with ill-defined dynamics. Stabilization is attained with continuous control and bounded gains.

Apart from solving the problems of ill-defined plant control, the binary principle is used advantageously for the development of nonlinear filters that separate close frequencies, for multiple differentiating noisy signals, and for the control of multi-connected systems.

The value of the binary principle is not confined to the control field; it may also be employed in studies of complicated dynamic systems in biology, biomechanics, social sciences, robotics, and biotechnology engineering, to name a few of the most promising applications.

About the Author
S.V. Emelyanov, Fellow of the Academy of Sciences of the USSR, has been engaged in solving many diverse problems of control. He is renowned for his pioneering efforts in the development of variable structure systems. The idea of incorporating unstable structures and sliding modes into the closed-loop control system for the purpose of system stabilization was also devised by the author of this book.

Translated from the Russian by Michael G. Edelev

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Introduction 7
1 BINARY SYSTEMS OF AUTOMATIC CONTROL. MOTIVATION, DEFINITIONS AND CONCEPTUALIZATION 10
1 Basic Principles and Definitions 10
1.1 Functional Diagrams of Control Systems in Classical Control Theory Setting 10
1.2 Block Diagrams of Adaptive Control Systems 12
1.3 The Concept of Operator-Variable and the Binary Principle 14
1.4 Generalized Elements of Binary Dynamic Systems 16
1.5 New Types of Feedback 17

2 The Principles of Control Under Uncertainty 18
2.1 Three Principles of Control for Solving Control Problems 18
2.2 Methods of Control for Ill-Defined Dynamic Systems 23

3 Generalized Block Diagrams of Binary Control Systems 28
3.1 Constructing Binary Control Systems 28
3.2 Structures of Binary Control Systems with Coordinate-Operator Feedback 29
3.3 Structures of Binary Control Systems with Coordinate-Operator and Operator Feedback 32
3.4 Structures of Binary Control Systems with Coordinate-Operator, Operator, and Operator-Coordinate Feedback 34

II FREE MOTION CONTROL 36
4 Definitions and Nomenclature 36
5 Time-Invariant Linear Coordinate Feedback 41
5.1 Finite Gain 41
5.2 High Feedback Gain 42
5.3 Constrained Control Signal 44
5.4 Imperfections 46
5.5 Linear Zone 49
5.6 Coordinate Feedback Under Inaccurate Information 51
5.7 Inaccuracies in Model Approximation 53

6 Coordinate-Operator Feedback 55
6.1 Proportional Coordinate-Operator Feedback 59
6.2 Proportional Coordinate-Operator Feedback with Magnitude Bounded Output 61
6.3 Nonlinear Time-Invariant Coordinate-Operator Feedback 67
6.4 Bang-Bang Coordinate-Operator Feedback 75
6.5 Bang-Bang Coordinate-Operator Feedback with Constraints and Dynamic Nonlinearities 79
6.6 Integral Coordinate-Operator Feedback 89
6.7 Integral Coordinate-Operator Feedback with a Constant Integration Rate 92
6.8 Inertial Coordinate-Operator Feedback 110
6.9 Integral Coordinate-Operator Feedback with Variable Integration Rate 118
6.10 Continuous Inertial Coordinate-Operator Feedback 124
6.11 Sur (2) Systems Under Integral Coordinate-Operator Feedback Law 128
6.12 Application of Algorithms with Inertial Coordinate-Operator Feedback to S System Control 136

7 Operator Feedback 154
7.1 (1) Systems with Integral Coordinate-Operator Feedback 160
7.2 Sp and Systems Under Imperfect Information 168
7.3 Spp (1) Systems with Inertial Coordinate-Operator Feedback 189
7.4 Quasicontinuous Control Algorithm 192
7.5 Spp (2) Systems with Integral Coordinate-Operator Feedback 206
7.6 S System Control with Algorithms 214

8 Operator-Coordinate Feedback 221
8.1 OCFB Generation Concepts 224
8.2 Suv (1) Systems with Proportional and Integral Coordinate-Operator Feedback 236
8.3 iS’ppv (1) Systems with Proportional Operator-Coordinate and Integral Coordinate-Operator Feedback 247
8.4 iSpV (1) Systems with Integral Laws of Coordinate-Operator and Operator-Coordinate Feedback 253
8.5 SppV (1) Systems with Integral Laws of Coordinate-Operator and Operator-Coordinate Feedback 258
8.6 Sppv (1) Systems with Inertial Laws of Coordinate-Operator and Operator-Coordinate Feedback 264

References
Index

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Fundamentals Of Crystal Physics by Yu.I. Sirotin; M.P. Shaskolskaya

Posted on September 15, 2026 by The Mitr

Over the past 15-20 years, experimental crystal physics has expanded beyond research laboratories and into practical applications in fields like quantum electronics, optics, semiconductor production, and piezotechnology. These advancements have highlighted the need for comprehensive textbooks on crystal physics. This book aims to fill that gap, offering a more detailed work to complement Nye’s 1967 textbook. It focuses on combining general physical principles with the symmetry approach characteristic of the Soviet crystal physics school founded by A.V. Shubnikov. The content is based on lectures and courses delivered at the Moscow Institute of Steel and Alloys and Moscow State University.

The book focuses on the anisotropy of crystal properties, particularly in areas such as diffusion, dielectric permittivity, magnetostriction, and piezooptical effects. It includes illustrations like representation surfaces and stereographic projections to explain the anisotropy of physical properties. The authors also provide a novel description of phase transitions with a double change of symmetry, illustrating how crystal properties change during phase transitions. The appendices include reference data, enhancing the book’s practical utility.

Translated from the Russian by Valentina Snigirevskaya.
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Contents

Preface to the Second Russian Edition 9
Excerpts from the Preface to the First Russian Edition 10
List of Notation 13

Chapter I. Basic Information on Crystallography 17

Crystal Structure and Space Lattice 17

Crystallographic Projections 23

Simple Finite Elements of the Symmetry of Crystals 27

Crystallographic Categories and Systems 42

Point Groups of Crystal Symmetry (Symmetry Classes) 47

Derivation and Description of 32 Classes of Crystal Symmetry (32 Point Groups of Symmetry) 55

Limit Groups of Symmetry (Curie Groups) 68

Symmetry of Crystal Structure 71

Combinations of the Symmetry Elements of Structures. Bravais Lattices. Generation of New Symmetry Elements 74

230 Space Groups of Symmetry 84

Mutual Vectors Basis and Reciprocal Lattice 88

Indexing of Directions and Planes in Crystals 92

Transformation of Indices with a Change of the System of Coordinates 101

Symmetrically Equivalent Sets of Planes and Directions. Simple Crystal Forms 114

Some Problems of Geometric Crystallography 125

Chapter II. Coordinate Systems, Vectors and Tensors 134

16. Cartesian Coordinate Systems 134
17. Orthogonal Transformations 137
18. Second-Rank Tensors 144
19. Eigenvectors and Eigenvalues of a Symmetric Second-Rank Tensors 147
20. Small Changes of a Symmetric Second-Rank Tensor 152
21. Normal and Tangential Components of a Second-Rank Symmetric Tensor 155
22. External Symmetry and Representation of Vectors and Second-Rank Symmetric Tensors 159
23. Axial Vectors 165

Chapter III. Introduction to Crystal Physics. Electrical and Thermal Properties of Crystals 174
24. Anisotropic Continuous Media 174
25. The Symmetry Principle in Crystal Physics 182
26. Fundamental Equations of Electrostatics of Crystals 188
27. Symmetry of the Dielectric Properties of Crystals 191
28. Crystals in a Uniform Electric Field 196
29. The Field in a Spherical Gap in an Anisotropic Medium 201
30. Fields of a Point Charge and a Dipole in an Anisotropic Medium 204
31. Pyroelectrics 207
32. Direct Electric Current in Crystals 210
33. Thermal Conductivity of Crystals 212

Chapter IV. Optical Properties of Crystals 216
34. Electromagnetic Waves in Transparent Crystals 216
35. Optical Indicatrix 220
36. Waves and Rays. Principle of Duality. Fresnel’s Ellipsoid 227
37. Solution of the Problem of Light Propagation in a Crystal in an Arbitrary System of Coordinates 232
38. Fresnel’s Equation. Wave and Ray Surfaces 236
39. Interconnection Between the Optical Surfaces in Crystals. Conical Refraction 240
40. Observation of the Optical Anisotropy of Crystals in Polarized Light 245

Chapter V. Symmetry of Higher-Rank Tensors 253
41. Tensors and Pseudotensors of Higher Ranks 253
42. Internal Symmetry of Tensors and Duality Relations 257
43. Non-Coordinate Notation of Tensors. Invariant Differential Operations on Tensors 263
44. External Symmetry and Representation of Tensors and Pseudotensors 266
45. Method of Direct Verification 275
46. Cyclic Coordinates. Hermann’s Theorem 281
47. Application of the Theory of Group Representation to the Problems of Tensor Symmetry 287
48. The Isotropic and Gyrotropic Tensors 301

Chapter VI. Elasticity of Crystals 308
49. Small Strains of a Continuous Medium 308
50. Stress Tensor 314
51. Generalized Hooke’s Law 319
52. Symmetry of the Elastic Properties of Crystals 324
53. Simple States of Stress 330
54. Bending and Twisting of Crystals 339
55. Temperature Stresses in Crystals 350
56. Elastic Waves in Crystals 358

Chapter VII. Thermodynamics of Crystals
57. Internal Energy and Thermodynamic Potential of a Crystal 380
58. Piezoelectric Effect and Its Symmetry 386
59. Simultaneous Solution of the Equations of the Electro- and Elastostatics of Crystals 396
60. Invariant and Non-Invariant Thermodynamic Potentials and Their Matrices 406
61. Dependence of Thermodynamic Coefficients on Conditions of Measurement 411
62. Elastic Waves in Piezoelectric Crystals 416
63. Thermodynamic Inequalities 419
64. Alterations of Crystal Symmetry in Phase Transitions of the Second Kind 423
65. Changes of the Physical Properties of Crystals Under Phase Transitions of the Second Kind 430
66. Mathematical Methods of the Theory of Phase Transitions 445

Chapter VIII. Magnetic Symmetry in Crystal Physics
67. Time Reversal and Antisymmetry 456
68. Point Groups of Magnetic Symmetry 460
69. Space Groups of Magnetic Symmetry—Shubnikov’s Groups 466
70. Magnetic Symmetry of Crystals 470
71. Geometric Realization of the Expanded Orthogonal Group 476
72. Tensors Defined on an Expanded Orthogonal Group 479
73. Piezomagnetic and Magnetoelectric Effects 485

Chapter IX. Effects of the Higher Orders
74. Thermodynamic Consideration of Non-Linear Effects 488
75. Piezoresistive Effect 491
76. Onsager Reciprocal Relations and Thermogalvanomagnetic Effects 493
77. Electrooptical and Piezooptical Effects 503
78. Artificial Optical Anisotropy of Crystals 508
79. Non-Linear Polarization in Case of Propagation of Electromagnetic Intense Waves 515
80. Generation of Light Harmonics. Directions of Synchronism 519
81. Optical Activity of Crystals 525
82. Artificial Optical Activity 540
83. Acoustic Activity of Crystals 545

Chapter X. Some General Problems of Crystal Physics
84. Extreme-Value Problems of Crystal Physics 551
85. The Problem of Comparing Tensor Properties of Crystals 535
86. The Problem of Choosing Standard Crystallographic and Crystal-Physical Systems of Coordinates 561
87. Functional Relations in Crystal Physics 556

Appendices
A. Crystallographic and Crystal-Physical Systems of Coordinates 581
B. Bravais Lattices and Crystallographic Matrices 581
C. Properties of Directions in Crystals 590
D. Analytical Proof of Theorems on the Multiplication of Symmetry Operations 597
E. Tensors Invariant with Respect to Crystallographic and Limit Groups 627
F. Contracted Notation of Tensors 627

References 637
Index 646

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Steam Power Plant Piping Design by B. Rudomino; Yu. Remzhin

Posted on September 14, 2026 by The Mitr

In the last decade, Soviet heat-power engineering has made significant advancements, including increased power plant capacities and improvements in thermodynamic cycles through intermediate superheating and higher steam parameters. These changes have simplified piping layouts in some aspects, but also made them more complex due to the need for superheating. The use of higher steam parameters has necessitated the use of stronger steels and thicker-walled pipes, which in turn requires better piping design methods. Current strength calculations for pipelines are governed by standards like “The Standard Procedures to Calculate Steam Boiler Elements for Strength” and industry-specific standards, ensuring mass production of piping elements while focusing on general strength principles.

The advent of digital computers has greatly enhanced piping design, enabling complex calculations for self-compensating pipelines and systems with movable inflection points and multiple anchor points. This book outlines the general theory of computer-aided pipeline design and presents a simpler calculation procedure with adequate accuracy. It emphasizes the importance of considering the deformation of bent ovalled elbows under internal pressure. It also introduces methods for calculating thermal expansion compensation using bellows-type expansion joints, as well as hydrodynamic calculations for pipelines with large pressure drops. The book is primarily aimed at engineers designing thermal power stations and can serve as a textbook for students in the field.

Translated from the Russian by Prem Kumar Dang
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Foreword 7
Chapter One
Piping Layout and Design 9
1.1. Piping Project Design 9
1.2. Layout and Design 12
1.3. Drainage of Pipelines 20
1.4. Pipeline Supports 24
1.5. Application of Pipe Fittings 35
Chapter Two
Hydrodynamic Calculations and Selection of Pipe Diameter 40
2.1. General Information and Formulas 40
2.2. Resistance Coefficients 51
2.3. Hydrodynamic Calculations of Pipelines for Small Specific Volume Changes 59
2.4. Hydrodynamic Calculations of Pipes with Large Steam Specific Volume Variations 66
2.5. Hydrodynamic Calculations of Boiling Water and High-Pressure Saturated Steam Pipelines 88
2.6. Selection of the Most Rational Pipe Size 106
Chapter Three
Pipeline Structural Calculations 117
3.1. General 117
3.2. Basic Properties of Steels Used for Power Station Pipelines 121
3.3. Wall Thickness Calculations 128
3.4. Calculation for Combined Action of Internal Pressure and Additional External Loads 132
3.5. Self-Elongation of Pipelines 138
3.6. Check Calculation of Stresses Caused by Compensating for Thermal Elongations 143
3.7. Flexure in Curved Pipes and Equivalent Stress Ranges 149
3.8. Check Calculation of Elbows for Cyclic Stress Ranges 161
3.9. Hydrodynamic Forces in Pipelines 172
Chapter Four
Pipeline Thermal Elongation Compensation and Its Calculation 176
4.1. Methods of Compensating Thermal Elongations 176
4.2. Self-Compensation Problem and Methods of Its Solution 177
4.3. Coordinate System and Determination of Displacements to Be Compensated 180
4.4. General Theory of Pipeline Calculation for Self-Compensation 186
4.5. Determination of Bending Moments Due to Weight Load 196
4.6. Methods of Calculating Pipelines for Self-Compensation 200
4.7. Bellows-Type Expansion Joints and Their Use as Axial Expansion Joints 215
4.8. Compensation of Pipelines Through the Use of Bellows-Type Expansion Joints as Elastic Hinges 222
4.9. Use of Electronic Digital Computing Machines for Calculating Self-Compensation of Pipelines 230
4.10. Criterion for Calculating the Compensating Capacity of Pipelines 234
Appendices 237
Index 269

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Examples And Problems In Chemical Thermodynamics by M.Kh. Karapetyants

Posted on September 13, 2026 by The Mitr

The present textbook is a study aid to the course in chemical thermodynamics.

The examples and problems contained in it cover the most essential and characteristic sections of the course, which should assist students in mastering the elementary methods of both general thermodynamic calculations and special calculations connected with separate processes of chemical technology.

The topics of the examples and problems mainly reflect questions concerning the technology of inorganic production processes and the chemical processing and refining of fuel. In this connection, the main attention has been devoted to gaseous systems.

Each chapter of the book begins with a brief theoretical introduction containing the equations and formulas needed for calculations. This is followed by examples with detailed solutions and problems.

The examples contain all the data necessary for calculations and can be used for independent solution. In compiling the book, the author tried to avoid identical examples and problems (using the same formulas and quantities, but describing different objects).

For a greater approximation to practical calculations, the book acquaints students with approximate methods of computation, graphical methods of calculation, and with some semi-empirical and empirical laws. The results of the calculations, when possible, are compared with experimental data or with calculations by other methods, which makes it possible to assess the accuracy of different methods and the limits of their application.

A considerable part of the examples and problems have been drawn up according to the published works of Soviet investigators. The experimental data are also taken from reference books and monographs. Some problems have been taken from different textbooks.

Translated from the Russian by G. Leib

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Preface 5
List of Symbols 9
Chapter One. The First Law of Thermodynamics 11
Chapter Two. Heats, Heat Capacity and Enthalpy 19
2.1. Hess’s Law 19
2.2. Thermochemical Laws 26
2.3. Heat Capacity and Enthalpy 31
2.4. Theoretical Temperature of Combustion 45
2.5. Influence of Temperature on Heat Reaction 49
Chapter Three. The Second Law of Thermodynamics 58
3.1. Entropy 58
3.2. Thermodynamic Potentials 76
Chapter Four. Real Gases 82
4.1. Pressure-Volume-Temperature-Composition Relationships 82
4.2. Fugacity 94
4.3. Heat Capacity 100
4.4. Enthalpy 104
4.5. Joule-Thomson Effect 109
Chapter Five. One-Component Heterogeneous Systems 114
5.1. Clapeyron-Clausius Equation 114
5.2. Methods for Comparative Calculation of the Temperature Dependence of Saturated Vapour Pressure 127
5.3. Critical Parameters 132
5.4. Heat Capacities of Coexisting Phases and Heats of Phase Transitions 137
Chapter Six. Generalized Methods of Calculation 145
6.1. Gases 145
6.2. Liquid-Vapour Equilibrium 156
Chapter Seven. Solubility 160
7.1. Influence of Temperature 160
7.2. Influence of Pressure 173
7.3. Mutual Solubility of Liquids 183
Chapter Eight. Vapour Pressure of Solutions 191
8.1. Completely Miscible Liquids 191
8.2. Incompletely Miscible and Immiscible Liquids 200
Chapter Nine. Equilibrium Constant and Change in Standard Gibbs Energy 209
9.1. Calculation of K and AG° According to Equilibrium Data 209
9.2. Calculation of K and AG° According to Thermal Data 225
Chapter Ten. Equilibrium Transition 243
10.1. Calculation of Equilibrium Transition 243
10.2. Influence of Various Factors on the Extent of a Reaction 252
10.3. Calculating the Equilibrium of Complex Processes 261
Answers to Problems 271
Chapter One 271
Chapter Two 271
Chapter Three 273
Chapter Four 275
Chapter Five 276
Chapter Six 279
Chapter Seven 280
Chapter Eight 282
Chapter Nine 283
Chapter Ten 285
Appendices 288

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Chemical Thermodynamics by M.Kh. Karapetyants

Posted on September 12, 2026 by The Mitr

The book is primarily aimed at students in higher education specialising in chemistry, particularly future engineers. The author has avoided unnecessary abstraction and overly complex mathematics to ensure the material remains practical and accessible, while still providing a solid theoretical foundation. The content includes approximate laws that allow for quick, practical problem-solving, even when precise values are unavailable. The author integrates empirical thermodynamics with the periodic table to make thermodynamic concepts more comprehensible, particularly entropy, which students often find difficult to grasp.

The book also addresses the importance of connecting thermodynamics with other branches of chemistry, such as general and inorganic chemistry, to enhance students’ understanding for later courses. The primary focus is on the thermodynamics of gaseous systems, with less emphasis on solutions and electrolytes. Numerous examples, mainly related to inorganic substances and chemical processing, help students apply theory to practical problems, with calculations that can be compared to experimental data. The book also includes many tables and figures derived from various sources to support these applications.

Translated from the Russian by G. Leib

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