Note that titles may be used in information retrieval; therefore every word counts.

Include relevant important names into the title.

Do not use formulae in the title.)

Do not refer to the reference list of the paper in the abstract, because

the abstract should be self-contained and appropriate to be used in data bases.)

In this paper, we are concerned with the following question:

At the outset, it is important to realize ...

My delightful task here will be to survey the startlingly wide range of applications of ... and to sketch the many varied and interesting proofs of ...

(Even if you are a

... in the sequel, we shall work with this formulation.

We shall now state two theorems on ...

These theorems are minor restatements of results obtained in ...

Let the function

It should be noted that although this result covers a very wide range of problems, there are some standard, simple examples for which uniqueness fails.

If we imposed two conditions, Theorem 1 would imply that we would have a unique solution.

Let

Part 1 is merely a rephrasing of the definition.

The reader is encouraged to prove this using Cauchy's integral formula.

(It is poor style to use =, ∈, ⇒, →, &, or ∀, ∃ etc. in the text unless they are absolutely essential.)

The set X endowed with this topology ...

Without loss of generality ...

Upon multiplying both sides with ...

Straightforward calculation shows ...

Idiom | Meaning |

By and large. | Taking everything into account. |

End up. | Reach a state eventually. |

In that. | In so far as. |

It goes without saying. | Something so obvious that it needn't be said. |

On the other hand. | From the other point of view. |

On the whole. | In general, ignoring minor details. |

Over and above. | In addition to. |

Rule of thumb. | A rule based on experience and estimation rather than precise calculation. |

Start from scratch. | To start from the beginning with no help. |

To be replaced | By this |

by means of | by |

conduct an investigation | investigate |

due to the fact that | since/because |

in a position to | can |

in order to | to |

in the case that | if |

in the course of | during |

in the event that | if |

in the first place | first |

it is apparent that | apparently |

it may happen that | there may/might |

most unique | unique |

take into consideration | consider |

that is to say | in other words, that is |

to begin with | to begin |

closed set

fundamental theorem of calculus

initial value problem

inverse function theorem

neighborhood

open set

system of equations

annihilator

column vector

composition

direct sum

divisor of zero

eigenvalue

eigenvector

isomorphism

linear combination

linearly independent

linear operator

quotient space

row vector

selfadjoint operator

semigroup

similarity transformation

absolutely continuous

Borel field

conditional expectation

(Lebesgue) dominated convergence theorem

elementary event

measurable space

probability density function

probability distribution function (previously: cumulative distribution function)

probability measure

probability space

random variable

Papers:

Lyle, K. M.:

Steenrod, N. E. (ed.):

Steenrod, N. E.; Halmos, P. R.; Schiffer, M. M.; Dieudonné, J. A.:

This manuscript has not been previously published in any language anywhere and it is not under simultaneous consideration by another journal. This paper is in final form and no version of it will be submitted for publication elsewhere.