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If t=1 the Macdonald polynomials become the sums over W orbits, which are the monomial symmetric functions when the root system has type A. If we put t = q α and let q tend to 1 the Macdonald polynomials become Jack polynomials when the root system is of type A , and Heckman–Opdam polynomials for more general root systems.
A bone is a rigid organ [1] that constitutes part of the skeleton in most vertebrate animals. Bones protect the various other organs of the body, produce red and white blood cells, store minerals, provide structure and support for the body, and enable mobility. Bones come in a variety of shapes and sizes and have complex internal and external ...
There is controversy whether bone grows through Lrp5 through bone or the intestine. [25] The majority of the current data supports the concept that bone mass is controlled by LRP5 through the osteocytes. [26] Mice with the same Lrp5 gain-of-function mutations as also have high bone mass. [27]
In the development of vertebrate animals, the functional matrix hypothesis is a phenomenological description of bone growth. It proposes that "the origin, development and maintenance of all skeletal units are secondary, compensatory and mechanically obligatory responses to temporally and operationally prior demands of related functional matrices."
Bone tissue is a dynamic system with active metabolism. [24] Bone tissue remodelling or bone remodeling is a successive chain of old bone matrix removal and its replacement with a new one. [25] These processes make a child’s skeleton grow and extend, while childhood is characterized by bone tissue growth rather than its resorption.
The functional part of bone, the bone matrix, is entirely extracellular. The bone matrix consists of protein and mineral. The protein forms the organic matrix. It is synthesized and then the mineral is added. The vast majority of the organic matrix is collagen, which provides tensile strength. The matrix is mineralized by deposition of ...
In mathematics, the Macdonald identities are some infinite product identities associated to affine root systems, introduced by Ian Macdonald . They include as special cases the Jacobi triple product identity , Watson's quintuple product identity , several identities found by Dyson (1972) , and a 10-fold product identity found by Winquist (1969) .
A subdiscipline of anatomy, anthropology, and paleontology, osteology is the detailed study of the structure of bones, skeletal elements, teeth, microbone morphology, function, disease, pathology, the process of ossification from cartilaginous molds, and the resistance and hardness of bones . [1]