Approximate computing is an attractive technique to gain substantial improvement in the area, speed, and power applications where exact computation not required. This paper proposes two improved multiplier designs based on a new 4:2 approximate compressor circuit simplify hardware at partial product reduction stage. The proposed are targeted towards error-tolerant applications. Exhaustive error...

If a function f is of bounded variation on TN (N ≥ 1) and {φn} is a positive approximate identity, we prove that the area of the graph of f ∗φn converges from below to the relaxed area of the graph of f . Moreover we give asymptotic estimates for the area of the graph of the square partial sums of multiple Fourier series of functions with suitable discontinuities.

According to Larsen [15, p. 13], a function F from a nonvoid subset DF of a commutative semigroup A into A is called a partial multiplier on A if F (D) · E = F (E) ·D for all D, E ∈ DF . Note that if in particular DF is a subsemigroup of A and F ( D · E ) = F (D) · E for all D , E ∈ DF , then F is a partial multiplier on A . A partial multiplier F on A is called total if DF = A . Clearly, the i...

We extend the standard Fourier multiplier result to square integrable functions with values in (possibly nonseparable) Hilbert spaces. As a corollary, we extend the standard Hardy class boundary trace result to H (even Nevanlinna or bounded type) functions whose values are bounded linear operators between Hilbert spaces. Both results have been well-known in the case that the Hilbert spaces are ...

It is demonstrated that the pre-dual for problems with total bounded variation regularization terms can be expressed as bilaterally constrained optimization problem. Existence of a Lagrange multiplier and an optimality system are established. This allows to utilize efficient optimization methods developed for problems with box constraints in the context of bounded variation formulations. Here, ...

Reflectivists consider reflective reasoning crucial for good judgment and action. Anti-reflectivists deny that reflection delivers what reflectivists seek. Alas, the evidence is mixed. So, does confer normative value or not? This paper argues a middle way: can value, but its ability to do this bound by factors such as we might call epistemic identity: an identity involves particular beliefs—for...