# 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 ?
Sequence based differentiation of strains in the Mycobacterium avium complex.
Distribution by sex of patients with positive nontuberculous mycobacteria (NTM) cultures, NTM disease, and disease of the respiratory tract caused by Mycobacterium avium complex (MAC), New York-Presbyterian Hospital, Columbia University Medical Center, 2000-2003, compared with age-adjusted base population from 2000 US Census data.
Food and Drug Administrati on (FDA), seeking marketing approval for the use of clarithromycin (Biaxin) for the prevention of disseminated Mycobacterium avium complex (MAC) disease in patients with advanced HIV infection.
Hot tub lung is believed to be a hypersensitivity pneumonitis caused by exposure to aerosolized Mycobacterium avium complex (MAC) and other nontuberculous mycobacteria (NTM) predisposed to grow in indoor hot tubs, enclosed swimming pools, spas, and therapy pools.
Prophylaxis against Mycobacterium avium complex recommendations were followed by 83% and 75% of those in the risk behavior and ver tical-transmission groups, respectively.
Species identification of Mycobacterium avium complex isolates by a variety of molecular techniques.
Abstract: Hot tub lung is a form of hypersensitivity pneumonitis (HP) reported to be associated with exposure to large aerosolized inocula of Mycobacterium avium complex (MAC).
I have an opportunistic infection called mycobacterium avium complex that is slowly killing me, and I don't have any new AIDS drugs with any efficacy.
Mycobacterium avium complex infection in the acquired immunodeficiency syndrome.
Vaccinations, such as those against pneumococcal pneumonia and influenza, as well as prophylaxis against Pneumocystis pneumonia and Mycobacterium avium complex, are intended to prevent specific clinical diseases.
Approved June 14, 1996 for the prevention of Mycobacterium avium complex in persons with advanced HIV infection.

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