the vertical bundle and the horizontal bundle are vector bundles associated to a smooth fiber bundle. More precisely, given a smooth fiber bundle π :...

customers with specialized needs Vertical and horizontal bundles, mathematical fiber bundles Horizontal and vertical writing in East Asian scripts – many...

vertical bundle V along H (so that H = ker Φ). This is determined by the above direct sum decomposition of TE into horizontal and vertical parts and is...

with tensors now being geometric objects in the vertical and horizontal bundles of a fiber bundle, instead of being indexed algebraic objects defined...

sections of that bundle along tangent directions in the base manifold. Principal connections generalize to arbitrary principal bundles the concept of a...

discrimination Refusal to deal and exclusive dealing Tying (commerce) and product bundling Despite wide agreement that the above constitute abusive practices...

vector bundle, and to some principal fiber bundles. This metric is often called a bundle metric, or fibre metric. If M is a topological manifold and π :...

sequence of vector bundles over Y: where TY and TX are the tangent bundles of Y, respectively, VY is the vertical tangent bundle of Y, and Y ×X TX is the...

bundles π Y Σ : Y → Σ , π Σ X : Σ → X . {\displaystyle \pi _{Y\Sigma }:Y\to \Sigma ,\qquad \pi _{\Sigma X}:\Sigma \to X.} It is provided with bundle coordinates...

addition to a bundle metric ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } on E leads to Kaluza–Klein theory. Vertical and horizontal bundles Jost, Jürgen...

high-rise vertical durability. The first building to apply the tube-frame construction was the DeWitt-Chestnut Apartment Building which Khan designed and which...

cheaper, horizontal microcode came to dominate the design of CPUs using microcode, with vertical microcode being used less often. When both vertical and horizontal...

and especially differential geometry and mathematical physics, gauge theory is the general study of connections on vector bundles, principal bundles,...

arrangements). Vertical agreements are often exempted from regulatory controls as they give rise to fewer competition concerns than horizontal agreements...

G} forming what's known as a fiber of the fiber bundle. These fiber bundles are called principal bundles. Locally the resulting space looks like R d × G...

space into the horizontal and vertical subspaces. Let h : T u P → H u {\displaystyle h:T_{u}P\to H_{u}} be the projection to the horizontal subspace. If...

for calculation in ancient East Asia. They are placed either horizontally or vertically to represent any integer or rational number. The written forms...

pedicle or an inferior-lateral pedicle, and features no vertical incision (like the anchor pattern). The horizontal-scar technique best applies to the patient...

noise reducer, emboss horizontal only/in all directions/(laplacian)/vertical only/with variable depth/horizontal and vertical, small tiles, round corners...

Dicot stems with primary growth have pith in the center, with vascular bundles forming a distinct ring visible when the stem is viewed in cross section...

(the vertical gaze center). The paramedian pontine reticular formation (PMPRF) is involved in coordinating horizontal conjugate eye movements and saccades...

involves a unit time vector field on the base space, a horizontal lift to the bundle space, and a spacelike surface "normal" (in the Minkowski metric)...

horizontal component of Z, on the right we identified a vertical vector field and a Lie algebra element generating it (fundamental vector field), and...

elimination: Problem 8-1: Suppose we have 3 bundles of top quality cereals, 2 bundles of medium quality cereals, and a bundle of low quality cereal with accumulative...

of a fiber bundle in an invariant form. Jets may also be seen as the coordinate free versions of Taylor expansions. Historically, jet bundles are attributed...

complementary, and even integrated. Application software can also be seen as being either horizontal or vertical. Horizontal applications are more popular and widespread...

attached at the ends and in the middle. Lattice tower structures have two common forms. One has a pyramidal base, then a vertical section, where three...

for horizontal mounting (often referred to as "dead ends") therefore incorporate flanges to shed water, and strain insulators intended for vertical mounting...

firebrick or ceramic refractory vertical secondary combustion chamber, the exhaust from which then passes along horizontal metal ducting embedded within...

right (Fig 2), the left horizontal canal gets stimulated (and thus predominantly signals) by head rotations to the left. Vertical canals are coupled in...