# 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 ?
Distribution of the pathological conditions according to gender Condition Osteomeatal complex Concha bullosa Nasal septal disease deviation Gender Present Absent Present Absent Present Female 22 (84.6%) 79 (45.4%) 45 (45%) 56 (56%) 69 (57.9%) Male 4 (15.4%) 95 (54.6%) 55 (55%) 44 (44%) 50 (42%) Total 26 (13%) 174 (87%) 100 (50%) 100 (50%) 119 (59%) Condition Nasal septal Odontogenic lesion Mucosal thickening deviation Gender Absent Present Absent Present Absent Female 31 (38.2%) 23 (58.9%) 78 (48.4%) 64 (57.1%) 37 (42%) Male 50 (61.7%) 16 (41%) 83 (51.6%) 48 (42.9%) 51 (58%) Total 81 (41%) 39 (19.5%) 161 (80.5%) 112 (56%) 88 (44%) Table 2.
CT is the modality of choice for imaging inflammatory disease of the sinuses and the osteomeatal complex. High resolution CT is used routinely before functional endoscopic sinus surgery13,14 to evaluate the extent of the inflammatory disease and to assess important anatomic landmarks and their variations.
Limiting the focus of functional endoscopic sinus surgery to the osteomeatal complex in a patient with a pneumatized superior turbinate may theoretically contribute to a failure of adequate drainage of the posterior sinuses along their natural pathways and the persistence of sinus-related complaints.
Pathological findings noted were Septal deviation (67.3%), Osteomeatal complex block (96.1%), Maxillary sinusitis (96.1%), Anterior ethmoidal sinusitis (86.5%), Posterior ethmoidal sinusitis (67.3%), Sphenoid sinusitis (34.6%), Frontal sinusitis (42.3%), Polyps which included sinonasal polyposis (22.7%), Antrochoanal polyps (45.4%) and Allergic Fungal Polyposis (31.8%) are present in 42.3% of patients.
Neither polyp involved the osteomeatal complex. Only the left maxillary sinus ostium was occluded by polypoid mucosa.
It is inadequate to identify other structural abnormalities like Concha bullosa, Paradoxical middle turbinate, Haller cells, Onodi cells, Osteomeatal complex and Agger nasi cells.
(7) In a case report published in 2001, Hasbini et al wrote that the proximity of the third molar to the medial wall of the maxillary sinus and its height at the level of the osteomeatal complex facilitated endoscopic exploration and extraction.
CT also showed that the mass had widened and obstructed the osteomeatal complex; fluid levels were seen in the left frontal and maxillary sinuses.
FUNCTIONAL ANATOMY2: The antero lateral nasal wall, has functionally important structures that make up the drainage system for the frontal, maxillary, ethmoid, sphenoid sinuses and is designated as the osteomeatal unit (OMU) also known as osteomeatal complex or osteomeatal channels.
We report a rare case of an ectopic third molar at the level of the osteomeatal complex. A 21-year-old man came to us with a left-sided nasal obstruction of 2 years' duration.
PREDISPOSING FACTORS: Massive fungal exposure, Local tissue hypoxia, Dental treatment, Usage of positive airway pressure apparatus, deviated nasal septum, Osteomeatal complex occlusion.
Mucosal opacity in right maxillary, frontal, ethmoidal sinus with occlusion of osteomeatal complex.

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