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The two sides have the same value, expressed differently, since equality is symmetric. [1] More generally, these terms may apply to an inequation or inequality; the right-hand side is everything on the right side of a test operator in an expression, with LHS defined similarly.
A Clifford algebra is a unital associative algebra that contains and is generated by a vector space V over a field K, where V is equipped with a quadratic form Q : V → K.The Clifford algebra Cl(V, Q) is the "freest" unital associative algebra generated by V subject to the condition [c] = , where the product on the left is that of the algebra, and the 1 on the right is the algebra's ...
In the particular case p = 1, this shows that L 1 is a Banach algebra under the convolution (and equality of the two sides holds if f and g are non-negative almost everywhere). More generally, Young's inequality implies that the convolution is a continuous bilinear map between suitable L p spaces.
Edge, a 1-dimensional element; Face, a 2-dimensional element; Cell, a 3-dimensional element; Hypercell or Teron, a 4-dimensional element; Facet, an (n-1)-dimensional element; Ridge, an (n-2)-dimensional element; Peak, an (n-3)-dimensional element; For example, in a polyhedron (3-dimensional polytope), a face is a facet, an edge is a ridge, and ...
The boundary homomorphism is given by ∂D = 2C 1 and ∂C 1 = ∂C 2 = 0, yielding the homology groups of the Klein bottle K to be H 0 (K, Z) = Z, H 1 (K, Z) = Z×(Z/2Z) and H n (K, Z) = 0 for n > 1. There is a 2-1 covering map from the torus to the Klein bottle, because two copies of the fundamental region of the Klein bottle, one being ...
For curves on surfaces, a curve is 2-sided if and only if it preserves orientation, and 1-sided if and only if it reverses orientation: a tubular neighborhood is then a Möbius strip. This can be determined from the class of the curve in the fundamental group of the surface and the orientation character on the fundamental group, which ...
A thin paper strip with its ends joined to form a Möbius strip can bend smoothly as a developable surface or be folded flat; the flattened Möbius strips include the trihexaflexagon. The Sudanese Möbius strip is a minimal surface in a hypersphere , and the Meeks Möbius strip is a self-intersecting minimal surface in ordinary Euclidean space.
For the leptons, the gauge group can be written SU(2) l × U(1) L × U(1) R. The two U(1) factors can be combined into U(1) Y × U(1) l, where l is the lepton number. Gauging of the lepton number is ruled out by experiment, leaving only the possible gauge group SU(2) L × U(1) Y. A similar argument in the quark sector also gives the same result ...