In [section]2 we explain the interpretation of the Hecke operators on [M.sub.3m]([GAMMA]) and the Petersson
inner product on [S.sub.3]([GAMMA]) in terms of the pluricanonical forms.
The
inner product of incident wave [r.sub.s]'s unit vector and subreflector's unit normal vector is
By a number of authors [1-4], it has been recommended to enhance the flexibility of the formalism by making use of an ad hoc, quantum-system-adapted physical
inner product in H, that is, by an introduction of a nontrivial, stationary metric operator [THETA] [not equal to] [THETA](t).
In this section, we define a new
inner product to determine the solution which satisfies the initial boundary value problem.
These polynomials coincide with the orthogonal polynomials associated with the
inner product defined in (6) and verify
Obviously, the Fock-Sobolev type space [F.sup.p.sub.[alpha]] equipped with the natural
inner product defined by
Functional Encryption for
Inner Product. Although FE supports the computation of general circuits relying on a wide spectrum of assumptions, there are two major problems with the state-of-the-art general FE constructions.
Then for each block, a dissimilar dictionary is learned by using the
inner product approach.
In Section 2, we introduce the concept of a matrix-valued
inner product [<<x,x>>.sub.S] for block vectors with values in a *-algebra S [subset] [C.sup.s x s].
Since cochains are column vectors, we use an
inner product between two column vectors to represent the volume integration of their wedge product.
We will be able to use some specific mathematical tools as
inner product.
A solution for this problem is provided by conformal geometric algebra (CGA), which can represent the geometries of Euclidean space effectively by the outer product,
inner product, and geometric product.
