# krainaksiazek basic physics equations and complex phenomena 20124260

- znaleziono 26 produktów w 4 sklepach

### Nonlinear Dielectric Phenomena in Complex Liquids Springer Netherlands

**Książki / Literatura obcojęzyczna**

Complex liquids constitute a basic element in modern materials science; their significant features include self-assembly, mesoscale structures, complex dynamics, unusual phases and enormous sensitivity to perturbations. Understanding their nature and properties are a great challenge to modern materials science that demands novel approaches. This book focuses on nonlinear dielectric phenomena, particularly on nonlinear dielectric spectroscopy (NDS), which may be considered a possible successor to broadband dielectric spectroscopy (BDS). NDS phenomena directly coupled to mesoscale heterogeneity fluctuations, so information obtained in this way is basically complementary to BDS tests. The book also discusses the application of NDS in a set of complex liquid systems: glassy liquids, liquid crystals, liquids with critical point phenomena, and bio-relevant liquids. The complementary application of NDS and BDS may allow the discovery of universal patterns for the whole category of complex liquids. Written by specialists in the field of nonlinear dielectric studies, theoreticians and experimentalists, ranging from solid state physics to biophysics, the book is organized so that it can serve as a basic textbook for a non-experienced reader.

Sklep: Libristo.pl

### Physics Of Thermal Phenomena LAP Lambert Academic Publishing

**Książki / Literatura obcojęzyczna**

Thermodynamics is a macroscopic science concerned with properties such as pressure, temperature, chemical potential, and volume. Unlike quantum mechanics, thermodynamics is not based on a specific molecular model and therefore it is unexpected by our changing concepts of atoms and molecules. Indeed, the major foundations of thermodynamics were laid long before detailed atomic theories became available. On the negative side, equations derived from laws of thermodynamics do not provide us with a molecular interpretation of complex phenomena. Although thermodynamics helps us predict the direction and extent of chemical reactions, it tells us nothing about the rate of the process which is rather addressed by chemical kinetics. This book introduces the Zeroth, first, Second and Third laws of thermodynamics and discusses some examples of thermochemistry.

Sklep: Libristo.pl

### Selected problems in physics with examples and exercises Politechnika Gdańska

**FIZYKA**

What is physics? The answer to this question has been changing, because physics also changes with time. But physics has always dealt with the basic rules governing the world: the macro-world as well as the world of atoms, electrons and nucleons. Physicists are concerned with various kinds of matter and radiation and their interactions. Their main purpose is to find, understand and use the basic laws that govern the natural world. The foundation of physics is experiment. Experimental observation of the phenomena of nature allows physicists to find the rules and principles that relate these phenomena. This leads to formulation of models and theories, which form our perceptions of the investigated phenomena. Any physical model or theory must always be confronted with experiment. Essential contradictions between a particular model or theory and experimental data are a signal that the model or theory should be corrected or replaced by a new one. This confrontation is a source of development of physics and its continuous approaching a truth of nature. Contemporary physics is a highly developed basic science with many fields, which are the foundation of all engineering and technology. Especially strong relations exist between physics and chemistry. Ever since chemistry ceased to be a purely phenomenological science, chemists not only employ certain laws of physics, but even include some complex and subtle physical phenomena and physics' arcane methods of measurement in their own research. This results in a gradual obliteration of the border line between some branches of chemistry and physics. Spis treści: 1. INTRODUCTION 1.1. The nature of physics 1.2. The language and units. of physics 1.3. How to study physics? Questions and problems 2. FUNDAMENTAL LAWS AND LAWS OF CONSERVATION IN PHYSICS 2.1. The meaning of fundamental laws 2.2. On the laws of conservation in physics 2.2.1. Newton's laws of motion 2.2.2. Conservation of momentum 2.2.3. Conservation of angular momentum 2.3. Work and energy 2.3.1. Definition of work in physics 2.3.2. Energy 2.3.3. The law of conservation of energy 2..3.3.1. Conservation of mechanical energy 2.3.3.2. Conservation of total energy Questions and problems 3. KINETIC THEORY AND LAWS OF THERMODYNAMICS 3.1. The microscopic interpretation of temperature 3.2. Measuring temperature 3.3. Internal energy and equipartition of energy 3.4. Laws of thermodynamics 3.4.1. The first law of thermodynamics 3.4.2. The second law of thermodynamics Questions and problems 4. ELECTROMAGNETIC INTERACTIONS 4.1. Static electric force 4.1.1. Electric charges 4.1.2. Quantization and conservation of charge 4.1.3. Electrical interaction between two charged particles - Coulomb's law 4.1.4. Electrical interactions in a system of several charges 4.2. Electric field 4.2.1. Graphic representation of electric fields 4.3. Gauss's law 4.3.1. Flux of electric field 4.3.2. Gauss's law 4.4. Electric potential and voltage 4.4.1. Electric potential energy 4.4.2. Electric potential 4.5. Capacitance and electric energy storage 4.5.1. Capacitors and capacitance 4.5.2. Energy storage 4.6. Electric current and magnetic force 4.6.1. Electric current 4.6.2. Ohm's law 4.6.3. Magnetic force and magnetic field 4.6.4. Magnetic field of linear current. Ampere's law 4.6.5. Gauss's law for magnetic field 4.7. Electromagnetic induction 4.7.1. Faraday's law of induction 4.7.2. Self-induced emf (? s) 4.8. Maxwell's equations Questions and problems 5. SELECTED PROBLEMS OF MODERN PHYSICS 5.1. The photoelectric effect 5.1.1. Photoelectrons 5.1.2. Fundamental features of the photoelectric effect 5.1.3. Einstein's theory of the photoelectric effect 5.2. Photons and electrons 5.2.1. X-ray photons 5.2.2. The Compton effect 5.3. The Bohr model of the atom of hydrogen 5.3. 1. Bohr's assumptions and postulates 5.3.2. Quantization of electron's total energy5.3.3. Electron jumps 5.3.4. Advantages and limitations of the Bohr model 5.4. Wave-particle duality 5.4.1. De Broglie's hypothesis 5.4.2. Experimental verification of de Broglie's hypothesis Questions and problems 6. NUCLEAR PHYSICS 6.1. Nuclear size and structure 6.1.1. Constituents of the nucleus 6.1.2. Nuclear size 6.1.3. Nuclear forces 6.2. Radioactivity 6.2.1. Kinetics of radioactive decay 6.2.2. Beta decay 6.2.3. Alpha decay 6.2.4. Gamma decay 6.3. Nuclear reactions 6.3.1. General remarks 6.3.2. The fission reaction 6.3.3. Nuclear fusion Questions and problems EXERCISES APPENDIX A. Mathematics A.1. Vector algebra A.2. Derivatives A.3. Integrals APPENDIX B. ENGLISH-POLISH PHYSICS DICTIONARY.

Sklep: ksiegarnia.edu.pl

### Introduction to Partial Differential Equations Dover Publications

**Książki / Literatura obcojęzyczna**

Chapter 1. Fourier series 1.1 Basic concepts 1.2 Fourier series and Fourier coefficients 1.3 A mimimizing property of the Fourier coefficients. The Riemann-Lebesgue theorem 1.4 Convergence of Fourier series 1.5 The Parseval formula 1.6 Determination of the sum of certain trigonemetric series Chapter 2. Orthogonal systems 2.1 Integration of complex-valued functions of a real variable 2.2 Orthogonal systems 2.3 Complete orthogonal systems 2.4 Integration of Fourier series 2.5 The Gram-Schmidt orthogonalization process 2.6 Sturm-Liouville problems Chapter 3. Orthogonal polynomials 3.1 The Legendre polynomials 3.2 Legendre series 3.3 The Legendre differential equation. The generating function of the Legendre polynomials 3.4 The Tchebycheff polynomials 3.5 Tchebycheff series 3.6 The Hermite polynomials. The Laguerre polynomials Chapter 4. Fourier transforms 4.1 Infinite interval of integration 4.2 The Fourier integral formula: a heuristic introduction 4.3 Auxiliary theorems 4.4 Proof of the Fourier integral formula. Fourier transforms 4.5 The convention theorem. The Parseval formula Chapter 5. Laplace transforms 5.1 Definition of the Laplace transform. Domain. Analyticity 5.2 Inversion formula 5.3 Further properties of Laplace transforms. The convolution theorem 5.4 Applications to ordinary differential equations Chapter 6. Bessel functions 6.1 The gamma function 6.2 The Bessel differential equation. Bessel functions 6.3 Some particular Bessel functions 6.4 Recursion formulas for the Bessel functions 6.5 Estimation of Bessel functions for large values of x. The zeros of the Bessel functions 6.6 Bessel series 6.7 The generating function of the Bessel functions of integral order 6.8 Neumann functions Chapter 7. Partial differential equations of first order 7.1 Introduction 7.2 The differential equation of a family of surfaces 7.3 Homogeneous differential equations 7.4 Linear and quasilinear differential equations Chapter 8. Partial differential equations of second order 8.1 Problems in physics leading to partial differential equations 8.2 Definitions 8.3 The wave equation 8.4 The heat equation 8.5 The Laplace equation Answers to exercises; Bibliography; Conventions; Symbols; Index

Sklep: Libristo.pl

### Complex Dynamics and Morphogenesis Springer Netherlands

**Książki / Literatura obcojęzyczna**

This book offers an introduction to the physics of nonlinear phenomena through two complementary approaches: bifurcation theory and catastrophe theory. Readers will be gradually introduced to the language and formalisms of nonlinear sciences, which constitute the framework to describe complex systems. The difficulty with complex systems is that their evolution cannot be fully predicted because of the interdependence and interactions between their different components. Starting with simple examples and working toward an increasing level of universalization, the work explores diverse scenarios of bifurcations and elementary catastrophes which characterize the qualitative behavior of nonlinear systems. The study of temporal evolution is undertaken using the equations that characterize stationary or oscillatory solutions, while spatial analysis introduces the fascinating problem of morphogenesis. Accessible to undergraduate university students in any discipline concerned with nonlinear phenomena (physics, mathematics, chemistry, geology, economy, etc.), this work provides a wealth of information for teachers and researchers in these various fields. Chaouqi Misbah is a senior researcher at the CNRS (National Centre of Scientific Research in France). His work spans from pattern formation in nonlinear science to complex fluids and biophysics. In 2002 he received a major award from the French Academy of Science for his achievements and in 2003 Grenoble University honoured him with a gold medal. Leader of a group of around 40 scientists, he is a member of the editorial board of the French Academy of Science since 2013 and also holds numerous national and international responsibilities.

Sklep: Libristo.pl

### Finite Volumes for Complex Applications VI Problems & Perspectives Springer, Berlin

**Książki / Literatura obcojęzyczna**

Finite volume methods are used for various applications in fluid dynamics, magnetohydrodynamics, structural analysis or nuclear physics. A closer look reveals many interesting phenomena and mathematical or numerical difficulties, such as true error analysis and adaptivity, modelling of multi-phase phenomena or fitting problems, stiff terms in convection/diffusion equations and sources. To overcome existing problems and to find solution methods for future applications requires many efforts and always new developments. The goal of The International Symposium on Finite Volumes for Complex Applications 6 is to bring together mathematicians, physicists and engineers dealing with Finite Volume Techniques in a wide context. This book, divided in two volumes, brings a critical look at the subject (new ideas, limits or drawbacks of methods, theoretical as well as applied topics).

Sklep: Libristo.pl

### The Mathematics of Classical and Quantum Physics Dover Publications

**Książki / Literatura obcojęzyczna**

VOLUME ONE 1 Vectors in Classical Physics Introduction 1.1 Geometric and Algebraic Definitions of a Vector 1.2 The Resolution of a Vector into Components 1.3 The Scalar Product 1.4 Rotation of the Coordinate System: Orthogonal Transformations 1.5 The Vector Product 1.6 A Vector Treatment of Classical Orbit Theory 1.7 Differential Operations on Scalar and Vector Fields *1.8 Cartesian-Tensors 2 Calculus of Variations Introduction 2.1 Some Famous Problems 2.2 The Euler-Lagrange Equation 2.3 Some Famous Solutions 2.4 Isoperimetric Problems - Constraints 2.5 Application to Classical Mechanics 2.6 Extremization of Multiple Integrals 2.7 Invariance Principles and Noether's Theorem 3 Vectors and Matrics Introduction 3.1 "Groups, Fields, and Vector Spaces" 3.2 Linear Independence 3.3 Bases and Dimensionality 3.4 Ismorphisms 3.5 Linear Transformations 3.6 The Inverse of a Linear Transformation 3.7 Matrices 3.8 Determinants 3.9 Similarity Transformations 3.10 Eigenvalues and Eigenvectors *3.11 The Kronecker Product 4. Vector Spaces in Physics Introduction 4.1 The Inner Product 4.2 Orthogonality and Completeness 4.3 Complete Ortonormal Sets 4.4 Self-Adjoint (Hermitian and Symmetric) Transformations 4.5 Isometries-Unitary and Orthogonal Transformations 4.6 The Eigenvalues and Eigenvectors of Self-Adjoint and Isometric Transformations 4.7 Diagonalization 4.8 On The Solvability of Linear Equations 4.9 Minimum Principles 4.10 Normal Modes 4.11 Peturbation Theory-Nondegenerate Case 4.12 Peturbation Theory-Degenerate Case 5. Hilbert Space-Complete Orthonormal Sets of Functions Introduction 5.1 Function Space and Hilbert Space 5.2 Complete Orthonormal Sets of Functions 5.3 The Dirac d-Function 5.4 Weirstrass's Theorem: Approximation by Polynomials 5.5 Legendre Polynomials 5.6 Fourier Series 5.7 Fourier Integrals 5.8 Sphereical Harmonics and Associated Legendre Functions 5.9 Hermite Polynomials 5.10 Sturm-Liouville Systems-Orthogaonal Polynomials 5.11 A Mathematical Formulation of Quantum Mechanics VOLUME TWO 6 Elements and Applications of the Theory of Analytic Functions Introduction 6.1 Analytic Functions-The Cauchy-Riemann Conditions 6.2 Some Basic Analytic Functions 6.3 Complex Integration-The Cauchy-Goursat Theorem 6.4 Consequences of Cauchy's Theorem 6.5 Hilbert Transforms and the Cauchy Principal Value 6.6 An Introduction to Dispersion Relations 6.7 The Expansion of an Analytic Function in a Power Series 6.8 Residue Theory-Evaluation of Real Definite Integrals and Summation of Series 6.9 Applications to Special Functions and Integral Representations 7 Green's Function Introduction 7.1 A New Way to Solve Differential Equations 7.2 Green's Functions and Delta Functions 7.3 Green's Functions in One Dimension 7.4 Green's Functions in Three Dimensions 7.5 Radial Green's Functions 7.6 An Application to the Theory of Diffraction 7.7 Time-dependent Green's Functions: First Order 7.8 The Wave Equation 8 Introduction to Integral Equations Introduction 8.1 Iterative Techniques-Linear Integral Operators 8.2 Norms of Operators 8.3 Iterative Techniques in a Banach Space 8.4 Iterative Techniques for Nonlinear Equations 8.5 Separable Kernels 8.6 General Kernels of Finite Rank 8.7 Completely Continuous Operators 9 Integral Equations in Hilbert Space Introduction 9.1 Completely Continuous Hermitian Operators 9.2 Linear Equations and Peturbation Theory 9.3 Finite-Rank Techniques for Eigenvalue Problems 9.4 the Fredholm Alternative for Completely Continuous Operators 9.5 The Numerical Solutions of Linear Equations 9.6 Unitary Transformations 10 Introduction to Group Theory Introduction 10.1 An Inductive Approach 10.2 The Symmetric Groups 10.3 "Cosets, Classes, and Invariant Subgroups" 10.4 Symmetry and Group Representations 10.5 Irreducible Representations 10.6 "Unitary Representations, Schur's Lemmas, and Orthogonality Relations" 10.7 The Determination of Group Representations 10.8 Group Theory in Physical Problems General Bibliography Index to Volume One Index to Volume Two

Sklep: Libristo.pl

### Observation, Prediction and Simulation of Phase Transitions in Complex Fluids, 1 Springer Netherlands

**Książki / Literatura obcojęzyczna**

Observation, Prediction and Simulation of Phase Transitions in Complex Fluids presents an overview of the phase transitions that occur in a variety of soft-matter systems: colloidal suspensions of spherical or rod-like particles and their mixtures, directed polymers and polymer blends, colloid--polymer mixtures, and liquid-forming mesogens. This modern and fascinating branch of condensed matter physics is presented from three complementary viewpoints. The first section, written by experimentalists, emphasises the observation of basic phenomena (by light scattering, for example). The second section, written by theoreticians, focuses on the necessary theoretical tools (density functional theory, path integrals, free energy expansions). The third section is devoted to the results of modern simulation techniques (Gibbs ensemble, free energy calculations, configurational bias Monte Carlo). The interplay between the disciplines is clearly illustrated. §For all those interested in modern research in equilibrium statistical mechanics. §

Sklep: Libristo.pl

### Mathematical Methods for Physics Perseus Books

**Książki / Literatura obcojęzyczna**

This classic book helps students learn the basics in physics by bridging the gap between mathematics and the basic fundamental laws of physics. With supplemental material such as graphs and equations, Mathematical Methods for Physics creates a strong, solid anchor of learning. The text has three parts: Part I focuses on the use of special functions in solving the homogeneous partial differential equations of physics, and emphasizes applications to topics such as electrostatics, wave guides, and resonant cavities, vibrations of membranes, heat flow, potential flow in fluids, plane and spherical waves. Part II deals with the solution of inhomogeneous differential equations with particular emphasis on problems in electromagnetism, Green's functions for Poisson's equation, the wave equation and the diffusion equation, and the solution of integral equations by iteration, eigenfunction expansion and the Fredholm series. Finally, Part II explores complex variable techniques, including evalution of itegrals, dispersion relations, special functions in the complex plane, one-sided Fourier transforms, and Laplace transforms.

Sklep: Libristo.pl

### Physics of Semiconductor Devices Springer, Berlin

**Książki / Literatura obcojęzyczna**

Physics of Semiconductor Devices covers both basic classic topics such as energy band theory and the gradual-channel model of the MOSFET as well as advanced concepts and devices such as MOSFET short-channel effects, low-dimensional devices and single-electron transistors. Concepts are introduced to the reader in a simple way, often using comparisons to everyday-life experiences such as simple fluid mechanics. They are then explained in depth and mathematical developments are fully described. §Physics of Semiconductor Devices contains a list of problems that can be used as homework assignments or can be solved in class to exemplify the theory. Many of these problems make use of Matlab and are aimed at illustrating theoretical concepts in a graphical manner.Physics of Semiconductor Devices is a textbook aimed at college undergraduate and graduate teaching. It covers both basic classic topics such as energy band theory and the gradual-channel model of the MOSFET as well as advanced concepts and devices such as MOSFET short-channel effects, low-dimensional devices and single-electron transistors. As a prerequisite, this text requires mathematics through differential equations and modern physics where students are introduced to quantum mechanics. Concepts are introduced to the reader in a simple way, often using comparisons to everyday-life experiences such as simple fluid mechanics. They are then explained in depth and mathematical developments are fully described. §Physics of Semiconductor Devices contains a list of problems that can be used as homework assignments or can be solved in class to exemplify the theory. Many of these problems make use of Matlab and are aimed at illustrating theoretical concepts in a graphical manner. A series of these Matlab problems is based on a simple finite-element solution of semiconductor equations. These yield the exact solution to equations that have no analytical solutions and are usually solved using approximations, such as the depletion approximation. The exact numerical solution can then be graphically compared to the solution using the approximation. §The different chapters of Physics of Semiconductor Devices cover the following material: Energy Band Theory. Theory of Electrical Conduction. Generation/Recombination Phenomena. The PN Junction Diode. Metal-semiconductor contacts. JFET and MESFET. The MOS Transistor. The Bipolar Transistor. Heterojunction Devices. Quantum-Effect Devices. Semiconductor Processing.

Sklep: Libristo.pl

### Mathematical Tools for Physics Dover Publications

**Książki / Literatura obcojęzyczna**

Preface to the Dover Edition Introduction Bibliography 1. Basic Stuff 2. Infinite Series 3. Complex Algebra 4. Differential Equations 5. Fourier Series 6. Vector Spaces 7. Operators and Matrices 8. Multivariable Calculus 9. Vector Calculus 1 10. Partial Differential Equations 11. Numerical Analysis 12. Tensors 13. Vector Calculus 2 14. Complex Variables 15. Fourier Analysis 16. Calculus of Variations 17. Densities and Distributions Index

Sklep: Libristo.pl

### Introduction to Mathematical Physics Oxford University Press

**Książki / Literatura obcojęzyczna**

Mathematical physics provides physical theories with their logical basis and the tools for drawing conclusions from hypotheses. Introduction to Mathematical Physics explains to the reader why and how mathematics is needed in the description of physical events in space. For undergraduates in physics, it is a classroom-tested textbook on vector analysis, linear operators, Fourier series and integrals, differential equations, special functions and functions of a complex variable. Strongly correlated with core undergraduate courses on classical and quantum mechanics and electromagnetism, it helps the student master these necessary mathematical skills. It contains advanced topics of interest to graduate students on relativistic square-root spaces and nonlinear systems. It contains many tables of mathematical formulas and references to useful materials on the Internet. It includes short tutorials on basic mathematical topics to help readers refresh their mathematical knowledge. An appendix on Mathematica encourages the reader to use computer-aided algebra to solve problems in mathematical physics. A free Instructor's Solutions Manual is available to instructors who order the book for course adoption.

Sklep: Libristo.pl

### Wave Propagation and Time Reversal in Randomly Layered Media Springer, Berlin

**Książki / Literatura obcojęzyczna**

The content of this book is multidisciplinary by nature. It uses mathematical tools from the theories of probability and stochastic processes, partial differential equations, and asymptotic analysis, combined with the physics of wave propagation and modeling of time reversal experiments. It is addressed to a wide audience of graduate students and researchers interested in the intriguing phenomena related to waves propagating in random media. The book can also be used as support for various advanced topics courses where random media and related homogenization and diffusion approximation results are involved. At the end of each chapter there is a section of notes where the authors give references and additional comments on the various results presented in the chapter.Wave propagation in random media is an interdisciplinary field that has emerged from the need in physics and engineering to model and analyze wave energy transport in complex environments.§This book gives a systematic and self-contained presentation of wave propagation in randomly layered media using the asymptotic theory of ordinary differential equations with random coefficients.§The first half of the book gives a detailed treatment of wave reflection and transmission in one-dimensional random media, after introducing gradually the tools from partial differential equations and probability theory that are needed for the analysis. The second half of the book presents wave propagation in three-dimensional randomly layered media along with several applications, primarily involving time reversal. Many new results are presented here for the first time.

Sklep: Libristo.pl

### Fundamentals of Cosmic Electrodynamics Springer Netherlands

**Książki / Literatura obcojęzyczna**

Cosmic electrodynamics is the specific branch of plasma physics which studies electromagnetic phenomena -- mostly the role of electromagnetic forces in dynamics of highly-conducting compressible medium in the solar interior and atmosphere, solar wind, in the Earth's magnetosphere and magnetospheres of other planets as well as pulsars and other astrophysical objects. This textbook is written to be used at several different levels. It is aimed primarily at beginning graduate students who are assumed to have a knowledge of basic physics. Starting from the language of plasma physics, from Maxwell's equations, the author guides the reader into the more specialized concepts of cosmic electrodynamics. The main attention in the book is paid to physics rather than maths. However, the clear mathematical image of physical processes in space plasma is presented and spelled out in the surrounding text. There is not another way to work in modern astrophysics at the quantitative level. The book will also be useful for professional astronomers and for specialists, who investigate cosmic plasmas from space, as well as for everybody who is interested in modern astrophysics.

Sklep: Libristo.pl

### Special Functions Oxford University Press

**Książki / Literatura obcojęzyczna**

The subject of this book is the theory of special functions, not considered as a list of functions exhibiting a certain range of properties, but based on the unified study of singularities of second-order ordinary differential equations in the complex domain. The number and characteristics of the singularities serve as a basis for classification of each individual special function. Links between linear special functions (as solutions of linear second-order equations), and non-linear special functions (as solutions of Painleve equations) are presented as a basic and new result. Many applications to different areas of physics are shown and discussed. The book is written from a practical point of view and will address all those scientists whose work involves applications of mathematical methods. Lecturers, graduate students and researchers will find this a valuable text and reference work.

Sklep: Libristo.pl

## szukaj w Kangoo krainaksiazek basic physics equations and complex phenomena 20124260

Sklepy zlokalizowane w miastach: Warszawa, Kraków, Łódź, Wrocław, Poznań, Gdańsk, Szczecin, Bydgoszcz, Lublin, Katowice

# Szukaj w sklepach lub całym serwisie

## 1. Sklepy z krainaksiazek pl basic physics equations and complex phenomena 20124260

2. Szukaj na wszystkich stronach serwisu

t1=0.077, t2=0, t3=0, t4=0.029, t=0.078