Ancient civilizations took into account the mixture and the various properties it produced, such as hardness, toughness and melting point, under various conditions of temperature and work hardening, developing much of the information contained in modern alloy constitution diagrams.

Relations among morphisms ( such as ) are often depicted using commutative diagrams, with " points " ( corners ) representing objects and " arrows " representing morphisms.

Many of his other novels, such as The Andromeda Strain and Jurassic Park, also incorporated large quantities of fabricated scientific documents in the form of diagrams, DNA sequences, footnotes and bibliography.

Further examples of such medieval diagrams can be found in medieval manuscripts of the Dream of Scipio.

As David Kaiser writes, " since the middle of the 20th century, theoretical physicists have increasingly turned to this tool to help them undertake critical calculations ," and as such " Feynman diagrams have revolutionized nearly every aspect of theoretical physics ".

While the diagrams are applied primarily to quantum field theory, they can also be used in other fields, such as solid-state theory.

The naïve application of such calculations often produces diagrams whose amplitudes are infinite, because the short-distance particle interactions require a careful limiting procedure, to include particle self-interactions.

Diagrams such as schematic diagrams and Gantt charts and treemaps display logical relationships between items, and do not display spatial relationships at all.

The most popular computers such as the Apple II and IBM PC had published schematic diagrams and other documentation which permitted rapid reverse-engineering and third-party replacement motherboards.

The results of such experiments can be plotted in phase diagrams.

Modern PLCs can be programmed in a variety of ways, from the relay-derived ladder logic to programming languages such as specially adapted dialects of BASIC and C. Another method is State Logic, a very high-level programming language designed to program PLCs based on state transition diagrams.

In mathematics education, elementary topics such as Venn diagrams are taught at a young age, while more advanced concepts are taught as part of a university degree.

This approach is similar to that of electrical circuit diagrams ; while these were not the inspiration for Beck's maps, his colleagues pointed out the similarities and he once produced a joke map with the stations replaced by electrical circuit symbols and names, with terminology such as " bakelite " for the Bakerloo line.

Mathematical details can be found in the tachyonic antitelephone article, and an illustration of such a scenario using spacetime diagrams can be found here.

The model also contains documentation that drives the model elements and diagrams ( such as written use cases ).

There are also many 2D graphics editors specialized for certain types of drawings such as electrical, electronic and VLSI diagrams, topographic maps, computer fonts, etc.

Logic is done inside a system while reason is done outside the system by such methods as skipping steps, working backward, drawing diagrams, looking at examples, or seeing what happens if you change the rules of the system.

such as Fitch-style calculus ( or Fitch's diagrams ) or Suppes ' method of which e. g. Lemmon gave a variant called system L.

The RDF data model is similar to classic conceptual modeling approaches such as entity-relationship or class diagrams, as it is based upon the idea of making statements about resources ( in particular Web resources ) in the form of subject-predicate-object expressions.

According to Lewis ( 1918 ), the " principle of these diagrams is that classes set ( mathematics ) | set s be represented by regions in such relation to one another that all the possible logical relations of these classes can be indicated in the same diagram.

He also showed that such symmetric Venn diagrams exist when n is 5 or 7.

As microprocessors have become more powerful, notations such as sequential function charts and function block diagrams can replace ladder logic for some limited applications.

With such date markings, diagrams of the analemma can be put to good use in calculating such things as the times of sunrise and sunset.

I am not making a clinical judgment here, for such personal tragedies are real and are commonplace in the analyst's consulting room, but literature makes a different claim upon our sympathies than tragedy in life.

It must be recognized that countries at different stages of development have very different capabilities of meeting such conditions.

Some of them are obvious, such as the fact that we associate recorded and live music with our responses and behavior in different types of environments and social settings.

One such disagreement, which will receive attention in this next chapter, concerns the question whether rates for different kinds of service, in order to avoid the attribute of discrimination, must be made directly proportional to marginal costs, or whether they should be based instead on differences in marginal costs.

By seeing such varied places, both interesting and beautiful, you will become aware of the many different civilizations Rome has lived through, and in particular, get a feel of Renaissance Rome.

The secretary's greatest achievement is perhaps the rekindling of NATO realization that East-West friction, wherever it take place around the globe, is in essence the general conflict between two entirely different societies, and must be treated as such without regard to geographical distance or lack of apparent connection.

Yet are not we of the mid-twentieth century, who rightly do not believe there is any such `` thing '' as the devil, just as bad off as they -- only in a different way??

The outcome of such an experiment has been in due time the acceptance of the Bible as the Word of God inspired in a sense utterly different from any merely human book, and with it the acceptance of our Lord Jesus Christ as the only begotten Son of God, Son of Man by the Virgin Mary, the Saviour of the world.

Here Keys and others, such as Dr. A. E. Ahrens of the Rockefeller Institute, took over to demonstrate the chemical difference between vegetable and animal fats -- and even between different varieties of each.

While cyanobacteria have been traditionally considered algae, recent works usually exclude them due to large differences such as the lack of membrane-bound organelles, the presence of a single circular chromosome, the presence of peptidoglycan in the cell walls, and ribosomes different in size and content from those of the Eukaryotes .< ref >

The basic ordering of the Latin alphabet ( ABCDEFGHIJKLMNOPQRSTUVWXYZ ) is well established, although languages using this alphabet have different conventions for their treatment of modified letters ( such as the French é, à, and ô ) and of certain combinations of letters ( multigraphs ).

* A language may use different sets of symbols or different rules for distinct sets of vocabulary items, such as the Japanese hiragana and katakana syllabaries, or the various rules in English for spelling words from Latin and Greek, or the original Germanic vocabulary.

" His system, however, is based primarily on such terminology as the different " orders of abstraction ," and formulations such as " consciousness of abstracting.

Note that " completeness " has a different meaning here than it does in the context of Gödel's first incompleteness theorem, which states that no recursive, consistent set of non-logical axioms of the Theory of Arithmetic is complete, in the sense that there will always exist an arithmetic statement such that neither nor can be proved from the given set of axioms.

Abbreviations can also be used to give a different context to the word itself, such as " PIN Number " ( wherein if the abbreviation were removed the context would be invalid ).

The physical properties, such as density, reactivity, Young's modulus, and electrical and thermal conductivity, of an alloy may not differ greatly from those of its elements, but engineering properties such as tensile strength and shear strength may be substantially different from those of the constituent materials.

However, this did not explain similarities between different atoms, as expressed by the periodic table, such as the fact that helium ( 2 electrons ), neon ( 10 electrons ), and argon ( 18 electrons ) exhibit similar chemical behavior.

Since complex scalar fields admit two different kinds of annihilation operators, which are related by conjugation, such fields describe charged bosons.

Moody and Sankey began publishing their compositions in 1875, and " Amazing Grace " appeared three times with three different melodies, but they were the first to give it its title ; hymns were typically published using the first line of the lyrics, or the name of the tune such as " New Britain ".

An entirely different class of ideas, also termed animistic, is the belief in the world soul anima mundi, held by philosophers such as Schelling and others.

The names of foods are different as well, such as Manapua, from Hawaiian meaning " chewed up pork " for dim sum bao, though the meat is not necessarily pork.