Lattice-based cryptography, which is based on Learning with Errors (LWE) problems, used matrix multiplication and

vector addition operations for key generation, encryption, and decryption.

The gradual shifting of PFRC is achieved by means of rotating input samples through an additional angle in their

vector addition. Besides, the gradual shifting of PFRC is achieved by the additional rotation of output signal vector.

Then, we apply the

vector addition theorem [10,11] to translate the wave functions from the secondary loop to the coordinate of the primary loop, and vice versa to derive a set of equations that satisfy the boundary conditions of the loops.

ALGORITHM 2: CUDA kernel for constant vector multiplication and vector

vector addition. input: colOut, colln, [a.sub.2], U output: U (1) for all threads in each thread block do in parallel (2) local variable gid, [xi] (3) gid [left arrow] threadld.x + blockld.x x blockDim.x (4) [xi] [left arrow] [a.sub.2] x U[M x colln + gid] (5) U[M x colOut + gid] [left arrow] U[M x colOut + gid] + [xi] 3.1.

use such a representation to perform fast

vector addition and subtraction needing six binary operations for each ternary operation.

with

vector addition [direct sum] and scalar multiplication [cross product], such that for all r [member of] R and a, b [member of] G,

Dilation is the morphological transformation that combines two sets by

vector addition of set elements.

At or around the time the student learns about the vector nature of forces in physics, she is involved in a thorough-going examination of

vector addition and right-angle trig in her math class.

k [is less than or equal to] 1) A [symmetry] B =

vector addition of A and B

The FDR principle involves the

vector addition of the source's output signal with reflected signals from faults and other reflective characteristics within the tested transmission line.

(iii) an operation, called

vector addition, which associates with each pair of vectors a; b in V a vector a + b in V, called the sum of a and b, in such a way that

Depending on the relative phase, the

vector addition of the two signal paths recombines destructively or constructively to yield phase and amplitude ripple as a signal is swept across the measurement band of the channel passband.