The class number problem of quadratic fields is one of the oldest problems in number theory. Now a days researchers expanding this problem in different directions not only for quadratic fields but also for other number fields. This monograph offers a clear, efficient and recent expositions of some aspects of class number problem of quadratic fields as well as cyclotomic fields. Topics include: fundamental concepts of number fields with special reference to quadratic and cyclotomic fields; class numbers of real, imaginary quadratic fields and cyclotomic; discriminant of quadratic fields. Some new topic: generalized Mersenne primes and their application in class number of quadratic fields; conjugate quadratic fields and their class numbers; equivalent quadratic fields and their class numbers. The monograph is suitable for graduate students and researchers.
The book is devoted to the approximation and periodic representation of algebraic numbers, like quadratic and cubic irrationalities. Continued fractions surely provide rational approximations and periodic representation for quadratic irrationals. Here, new kinds of representation for square roots are exploited with the aid of linear recurrent sequences. A beautiful connection with the solution of the Pell equation is highlighted, finding an original way to solve it through a group structure over the Pell hyperbola. Moreover, similar results are obtained and illustrated for cubic irrationals, approaching the Hermite problem, i.e., the problem of finding a way to write algebraic numbers (irrational numbers that are solution of some algebraic equation with rational coefficients) as a periodic sequence of integers.
This book is a collection of my lecture notes, exercise, homework and real-world projects. Foundations Mathematics is the first step in Mathematics for science and engineering students and it is a pre-requisite for ALL coming Math courses. The topics are: Fundamental operations with numbers,Some products, Factoring, Percentage, Ration and Proportion, Operations with polynomials, Linear equations, Linear inequalities, Quadratic equations, Analytic Geometry, Functions, Linear functions, Quadratic Functions, System of linear equations.
The subject of the research in this book algebraic geometry. Quadratic equality Z2=X2+Y2 and U2=X2+Y2+Z2 well known from the time of Pythagoras. However, the history of their research continues. The aim of this work is the analysis of the symmetry groups of solutions of quadratic equations on the basis of Periodical System of Natural Numbers. The book is the first to use the language of symmetry groups integers inhearent to physical phenomena and States: from the fine structure of crystals to arrangement of the periodic system of chemical elements and the solution of applied problems. Given in the book form of the calculation of the symmetry groups of quadratic identities Z2=X2+Y2 exhausts infinitely many solutions “Pythagorean” equalities and allows you to subdivide them according to the symmetry groups of numbers on 32 species - number equal to the number of point of crystallographic groups. Full package of solutions of quadratic equality U2=X2+Y2+Z2 has 230 options - known amount of all space groups of crystal symmetry.
Learn the Chinese numbers from 1 to 100 with this amusing and innovative game.Play at home or in class with useful and interesting cards, designed to help you memorise the numbers.A comprehensive Instruction Booklet complete with suggestions for exercises, games and activities, and interesting facts about numbers, makes Playing with Numbers an essential part of the Chinese lesson.• 2 packs of 50 cards• 36 individual cards• Instruction Booklet.Instruction Booklet available in:EnglishFrancaisDeutschEspanolItaliano.
Learn the Chinese numbers from 1 to 100 with this amusing and innovative game.Play at home or in class with useful and interesting cards, designed to help you memorise the numbers.A comprehensive Instruction Booklet complete with suggestions for exercises, games and activities, and interesting facts about numbers, makes Playing with Numbers an essential part of the Chinese lesson.• 2 packs of 50 cards• 36 individual cards• Instruction Booklet.Instruction Booklet available in:EnglishFrancaisDeutschEspanolItaliano
In this book, first of all i give simple introduction about integer programming(e.g. history, defination, types, methods, applications etc.). Next i give introduction about quadratic programming, bounded decision variables etc. In last to get integer solution, i use simplex method and branch and bound method for quadratic programming problems with bounded decision variables and fractional programming problems.
In this publication a new class of Hybrid/Mixed Finite Elements (HM-FE) is developed for heat conductivity problems and thermoelasticity in solids. These elements are based on the independent approximation of secondary fields (strains and temperature gradient field) and on the collocation of these fields in some cleverly chosen points with the secondary fields derived from primal variables (mechanical displacements and temperature field). After that the HM-FEM is utilized to investigate the influence of material porous micro-structure to the overall material parameters using the multiscale approach.
To succeed in Algebra II, start practicing now Algebra II builds on your Algebra I skills to prepare you for trigonometry, calculus, and a of myriad STEM topics. Working through practice problems helps students better ingest and retain lesson content, creating a solid foundation to build on for future success. Algebra II Workbook For Dummies, 2nd Edition helps you learn Algebra II by doing Algebra II. Author and math professor Mary Jane Sterling walks you through the entire course, showing you how to approach and solve the problems you encounter in class. You'll begin by refreshing your Algebra I skills, because you'll need a strong foundation to build upon. From there, you'll work through practice problems to clarify concepts and improve understanding and retention. Revisit quadratic equations, inequalities, radicals, and basic graphs Master quadratic, exponential, and logarithmic functions Tackle conic sections, as well as linear and nonlinear systems Grasp the concepts of matrices, sequences, and imaginary numbers Algebra II Workbook For Dummies, 2nd Edition includes sections on graphing and special sequences to familiarize you with the key concepts that will follow you to trigonometry and beyond. Don't waste any time getting started. Algebra II Workbook For Dummies, 2nd Edition is your complete guide to success.
A quadratic form is a homogeneous polynomial of degree two in a number of variables. Quadratic forms occupy a central place in various branches of mathematics, including Number Theory, Linear Algebra, Group Theory, Differential Topology and Lie Theory. In this book we study the quadratic forms from side of Analytic Number Theory. In particular we look for the small zeros of quadratic forms modulus p prime to the power positive integer m.
Мыльница tatkraft quadratic выполнена из акрила, имеет удобную прямоугольную форму и ребристую поверхность дна, что позволяет удобно расположить мыло и не даст ему скользить. плавность линий и прозрачный цвет мыльницы позволяют мыльнице вписаться в любой интерьер, а прочный небьющийся материал, очень приятный на ощупь, сделают ее еще более удобной в использовании. может использоваться как самостоятельно, так и с другими элементами коллекции quadratic.