Complex

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complex

1. Maths of or involving one or more complex numbers
2. Psychoanal a group of emotional ideas or impulses that have been banished from the conscious mind but that continue to influence a person's behaviour
3. Informal an obsession or excessive fear
4. a chemical compound in which molecules, groups, or ions are attached to a central metal atom, esp a transition metal atom, by coordinate bonds
5. any chemical compound in which one molecule is linked to another by a coordinate bond

Complex

(in mathematics), one of the fundamental concepts of combinatorial topology. It is essential to the aims of this science to regard geometric figures as being subdivided into more elementary figures. It is easiest to construct geometric figures out of simplexes, that is, in the case of three-dimensional space, out of points, lines, triangles, and tetrahedra. Thus, we are most often dealing with simplicial complexes.

A simplicial complex is a finite set of simplexes situated in a certain Euclidean (or Hilbert) space and possessing the following property: the intersection of two simplexes of this set is either empty or is a face of each of them. If a complex contains a γ-dimensional simplex and no simplexes of higher dimension, then the complex is termed γ-dimensional. This very simple concept has undergone many generalizations, proceeding in different directions. Together with the just-defined finite complexes it is possible to define countable complexes. It is further possible to proceed from simplicial complexes to analogously defined cell complexes, whose elements are not necessarily simplexes but any convex polyhedrons or even any figures homeomorphic to them; in the latter case, we speak of “curvilinear” complexes. Ordinarily, only those complexes are considered that satisfy the following closure condition: each face of a simplex belonging to a given complex must also belong to that complex. A set that can be represented as a union of simplexes forming an n-dimensional complex is termed an n-dimensional polyhedron.

REFERENCES

Aleksandrov, P. S. Kombinatornaia topologiia. Moscow-Leningrad, 1947.
Pontriagin, L. S. Osnovy kombinatornoi topologii. Moscow-Leningrad, 1947.

Complex

in psychology, in the most general sense, a particular combination of psychological processes into some sort of whole; in a narrower sense, the word is taken to mean a group of heterogeneous psychic elements connected by a single affect.

Complex, in the latter sense, has become one of the basic concepts of various schools of depth psychology. According to psychoanalysis (S. Freud, Austria), complexes form around tendencies that are displaced to the subconscious (for example, the Oedipus complex arises as a result of the displacement in early childhood of hostile impulses toward the father). Complexes produce deviations in human behavior that are manifested in the form of improper actions, neuroses, and obsessions. In individual psychology (A. Adler, Austria), an exceptional role is attributed to the inferiority complex—an individual’s feeling of his own organic or mental inadequacy. Overcoming this complex by means of compensation is regarded by Adler to be the principal factor in man’s mental development, character formation, and behavior.

D. N. LIALIKOV

complex

[′käm‚pleks]
(geology)
An assemblage of rocks that has been folded together, intricately mixed, involved, or otherwise complicated.
(mathematics)
A space which is represented as a union of simplices which intersect only on their faces.
(medicine)
(mineralogy)
Composed of many ingredients.
(psychology)
A group of associated ideas with strong emotional tones, which have been transferred from the conscious mind into the unconscious and which influence the personality.
References in periodicals archive ?
Scientists no longer believe that there are simple genetic or physiological switches or indicators that distinguish the rapist from the gentleman; biology almost always interacts complexly with social and familial environments.
It is rendered via lush sketches and pencilled notations--lists, diary entries, queries, assertions, meditations and laments--that complexly traverse the turbulent arc of coming into oneself in a new city.
That she does so realistically and complexly is a testament to the author's experience in dealing with the same issue and the many unexpected feelings that come into play.
Even when lifted out of one's immediate locale, language complexly intersects other ways of living and relating to others.
We hope the articles provide you with practical ideas and inspire you to think broadly and complexly about students.
But it's often hard for researchers to visualize and thus study these complexly folded proteins.
A third narrator, Peter Wormwood, a British expatriate who becomes Johnny's best friend--and who ultimately participates in the worst sort of betrayal--views him even more complexly, as a "native" with an intensely inquiring mind, in fact, "the only person in Singapore [where he first encounters him in a cafe] who reads Shelley.
Taylor set out on a solo in Up Too Late that summed up perfectly why he is so special: double-handed, complexly knotted constructions at the centre of the keyboard, harmonically and rhythmically free of clichA, maintaining an easily heard form to his improvisations even though the lines are long and winding.
This complexly flavored black truffle, a tuber that lies hidden in the ground beneath oak trees and must be sniffed out by dogs and pigs, is the prime ingredient in the finest foie gras.
Admirably avoiding these pitfalls, Rheinheimer renders all characters complexly, providing them with qualities they as realistic personalities deserve.
It is this complexly contradictory spin that, I posit, conservatives love to love.

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