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A quadratic form with integer coefficients is called an integral binary quadratic form, often abbreviated to binary quadratic form. This article is entirely devoted to integral binary quadratic forms. This choice is motivated by their status as the driving force behind the development of algebraic number theory.
Physical weathering, also called mechanical weathering or disaggregation, is the class of processes that causes the disintegration of rocks without chemical change. Physical weathering involves the breakdown of rocks into smaller fragments through processes such as expansion and contraction, mainly due to temperature changes.
Chemical weathering of igneous minerals leads to the formation of secondary minerals, which constitute the weathering products of the parent minerals. Secondary weathering minerals of igneous rocks can be classified mainly as iron oxides, salts, and phyllosilicates. The chemistry of the secondary minerals is controlled in part by the chemistry ...
Denudation incorporates the mechanical, biological, and chemical processes of erosion, weathering, and mass wasting. Denudation can involve the removal of both solid particles and dissolved material. These include sub-processes of cryofracture, insolation weathering, slaking, salt weathering, bioturbation, and anthropogenic impacts. [4]
The rate of weathering is sensitive to factors that change how much land is exposed. These factors include sea level , topography , lithology , and vegetation changes. [ 4 ] Furthermore, these geomorphic and chemical changes have worked in tandem with solar forcing, whether due to orbital changes or stellar evolution, to determine the global ...
A mapping q : M → R : v ↦ b(v, v) is the associated quadratic form of b, and B : M × M → R : (u, v) ↦ q(u + v) − q(u) − q(v) is the polar form of q. A quadratic form q : M → R may be characterized in the following equivalent ways: There exists an R-bilinear form b : M × M → R such that q(v) is the associated quadratic form.
Structural changes are the result of hydration, oxidation, and reduction. Chemical weathering mainly results from the excretion of organic acids and chelating compounds by bacteria [24] and fungi, [25] thought to increase under greenhouse effect. [26] Physical disintegration is the first stage in the transformation of parent material into soil.
Over F 2, the Arf invariant is 0 if the quadratic form is equivalent to a direct sum of copies of the binary form , and it is 1 if the form is a direct sum of + + with a number of copies of . William Browder has called the Arf invariant the democratic invariant [ 3 ] because it is the value which is assumed most often by the quadratic form. [ 4 ]