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A smooth embedding is an injective immersion f : M → N that is also a topological embedding, so that M is diffeomorphic to its image in N. An immersion is precisely a local embedding – that is, for any point x ∈ M there is a neighbourhood, U ⊆ M, of x such that f : U → N is an embedding, and conversely a local embedding is an ...
On-the-job training (widely known as OJT) is an important topic of human resource management. It helps develop the career of the individual and the prosperous growth of the organization. On-the-job training is a form of training provided at the workplace. During the training, employees are familiarized with the working environment they will ...
For example, the real projective space of dimension , where is a power of two, requires = for an embedding. However, this does not apply to immersions; for instance, R P 2 {\displaystyle \mathbb {R} \mathrm {P} ^{2}} can be immersed in R 3 {\displaystyle \mathbb {R} ^{3}} as is explicitly shown by Boy's surface —which has self-intersections.
Let M and N be differentiable manifolds and : be a differentiable map between them. The map f is a submersion at a point if its differential: is a surjective linear map. [1] In this case p is called a regular point of the map f, otherwise, p is a critical point.
The multiplicity of terms used to refer to instructional approaches for the integration of content and language learning (immersion, CBI, CBLT, CLIL, EMI) can be a source of confusion in EIL studies, although they all commonly share the purpose of additive bilingualism via a dual focus on content and language learning.
Instructor-led training, [1] or ILT, is the practice of training and learning material between an instructor and learners, either individuals or groups. Instructors can also be referred to as a facilitator, who may be knowledgeable and experienced in the learning material, but can also be used more for their facilitation skills and ability to deliver material to learners.
The model may not reflect the changes in the market instigated by online technologies. For example, it does not reflect the recent focus on informal learning. [5] The 70:20:10 model is not prescriptive. Author and learning and development professional Andy Jefferson asserts it "is neither a scientific fact nor a recipe for how best to develop ...
The technical statement appearing in Nash's original paper is as follows: if M is a given m-dimensional Riemannian manifold (analytic or of class C k, 3 ≤ k ≤ ∞), then there exists a number n (with n ≤ m(3m+11)/2 if M is a compact manifold, and with n ≤ m(m+1)(3m+11)/2 if M is a non-compact manifold) and an isometric embedding ƒ: M → R n (also analytic or of class C k). [15]