Discrete and continuous methods in applied mathematics

379

Book reviews

next paper by J. Wolfowitz

The

The paper on Sperling’s Tompkins.

An analysis

Brouwer’s

is a short introduction

lemma aud some extensions

is made of Sperling’s

fundamental

As an example

theorem of algebra

singularities

of vector

fields

of crystallography

topology

and probability

the crystallographic diffraction,

and its generalization,

the finda-

of the use of these topological

is proved and an analysis

facts

the

is made of the

is by K. N. Trueblood.

are connected theory.

state,

of it is due to C. B.

on a Zsphere.

Chapter 16 on crystallography aspects

theory.

lemma from which follows

famous theorem on the fixed point,

mental index theorem.

to information

The topics

the principles

methods of solving

The mathematical

with group theory, considered

combinational

analysis,

here are the nature of

of crystal structure

analysis

the phase problem and some problems

by X-ray of the

arrangement of atoms in molecules. Chapter 17 on combinatorial It considers acids

principles

in genetics

the problem of the transmission

of genetic

was written by G. Gamow. information

from nucleic

to proteins.

The book finishes collection

of general problems

biology.

widely

methods

of content,

applied

and level

will by published

applied

to demonstrate

to different

fields

to express

(by ‘Mir”)

The paper is a

to physics,

chemistry

the unity and effectiveness of knowledge.

and skill of presenta

used and it only remains

translation

written by H. Weyl.

of combinatorices

The whole book attempts

combinatorial richness

with appendices

Because

that the Russian

and S. S. Lavrov

Translated

upplied mathematics. nepretynye

of economics,

and continuous

by J. Berry

methods

in

i

matematiki).

This book is a two or three semester professtions

Discrete

John Wiley, 1966, XIII + 525 pp. (Discretnye

metody prikladnoi

to be

in 1968.

L. S. Chistyakov

J. C. MATHEWS and C. E. LANGENSOP.

of its

ion the book deserves

our satisfaction

genetics,

and of

course

psychology,

of applied control,

mathematics

for the

for the engineering

Book reviews

380

professions theory; V.

etc.

The book consists

II. Linear

Transport

linear

algebra;

differential

stability;

IX.

given.

VIII.

equations;

The fundamental

intuitive

Finite

Ordinary

I. Discrete

Markov chains; differential

Non-linear

IV.

Linear

equations;

differential

probability programming;

VII.

Systems

equations

etc.

concepts

are illustrated

In addition,

for independent

level,

in almost

by examples

The presentation

solution.

and modem

usually

begins

On the whole the book is of interest

(for example,

notation

engineer-

there is a large number

proofs of the fundamental

We also note that in a number of chapters terminology

from physics,

every paragraph

and then as a rule, strict

modern mathematical

at the

theorems

in Chapter

to specialists

in economics,

criteria: for linear cfynumicd

II)

genetics

Oliver

systems.

etc.

V. Feroryuk by J. Berry

Translated

Stability

are

are used.

M.

B. PORTER.

of

and

Random processes.

ing, economics of problems

III.

VI.

networks;

of 9 chapters:

& Boyd,

1%7,

x + 195 pp., 50s. B. PORTER. This

Kriterii

ystoichivosti

book is devoted

author indicates,

to the stability

of such

professions,

and at the same

form the basis

analysis

systems

method;

examples,

some

some examples

of eight

with constant

In Chapter

2 the principle

devoted

only for the case and Nyquist

to the criteria

the rootloci

chosen

specially

function)

are considered. equations

characteristics transformation.

(for simplicity

and then

Chapters

of Routh and Hurwitz.

the proof

the stability

criteria

4 and 5, respectively,

In Chapter are studied.

number

of real devices.

by the Laplace

is introduced

facts

of non-linear

a considerable

1 the frequency

are investigated

of a rational

mathematical

some mathematical

of models

In Chapter

chapters.

of the argument

of the characteristic

to illustrate

As the

of investigating

in technical

The problems

the analysis

parameters

to people

The book contains

siatem.

systems.

the methods

the fundamental

presented.

omitted.

describe

of systems

of Leonhard

of linear

in a form accessible

of the methods

The book consists

is given

problems

time to indicate

are here deliberately

of concrete

dinamicheskikh

the aim of the book is to explain

the stability which

dlya lineinykh

6 methods In Chapter

are

of constructing 7 methods

of