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A mixed tensor of type or valence , also written "type (M, N)", with both M > 0 and N > 0, is a tensor which has M contravariant indices and N covariant indices. Such a tensor can be defined as a linear function which maps an (M + N)-tuple of M one-forms and N vectors to a scalar.
The Saxon Math 1 to Algebra 1/2 (the equivalent of a Pre-Algebra book) curriculum [3] is designed so that students complete assorted mental math problems, learn a new mathematical concept, practice problems relating to that lesson, and solve a variety of problems. Daily practice problems include relevant questions from the current day's lesson ...
v. t. e. In mathematics, tensor calculus, tensor analysis, or Ricci calculus is an extension of vector calculus to tensor fields (tensors that may vary over a manifold, e.g. in spacetime). Developed by Gregorio Ricci-Curbastro and his student Tullio Levi-Civita, [1] it was used by Albert Einstein to develop his general theory of relativity.
A massive open online course (MOOC / muːk /) or an open online course is an online course aimed at unlimited participation and open access via the Web. [1] In addition to traditional course materials, such as filmed lectures, readings, and problem sets, many MOOCs provide interactive courses with user forums or social media discussions to ...
The first of these sentences is a basic zero conditional with both clauses in the present tense. The fourth is an example of the use of will in a condition clause [4] (for more such cases, see below). The use of verb tenses, moods and aspects in the parts of such sentences follows general principles, as described in Uses of English verb forms.
A walk in a mixed graph is a sequence of vertices and edges/arcs such that for every index , either is an edge of the graph or is an arc of the graph. This walk is a path if it does not repeat any edges, arcs, or vertices, except possibly the first and last vertices. A walk is closed if its first and last vertices are the same, and a closed ...
In Latin, the sequence of tenses rule affects dependent verbs in the subjunctive mood, mainly in indirect questions, indirect commands, and purpose clauses. [4] If the main verb is in one of the non-past tenses, the subordinate verb is usually in the present or perfect subjunctive (primary sequence); if the main verb is in one of the past tenses, the subordinate verb is usually in the ...
A mixed model, mixed-effects model or mixed error-component model is a statistical model containing both fixed effects and random effects. [1][2] These models are useful in a wide variety of disciplines in the physical, biological and social sciences. They are particularly useful in settings where repeated measurements are made on the same ...