Topic

# Remainder

About: Remainder is a(n) research topic. Over the lifetime, 3443 publication(s) have been published within this topic receiving 35379 citation(s). The topic is also known as: dividend mod divisor.

##### Papers

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Abstract: We present further evidence for a dual conformal symmetry in the four-gluon planar scattering amplitude in N=4 SYM. We show that all the momentum integrals appearing in the perturbative on-shell calculations up to four loops are dual to true conformal integrals, well defined off shell. Assuming that the complete off-shell amplitude has this dual conformal symmetry and using the basic properties of factorization of infrared divergences, we derive the special form of the finite remainder previously found at weak coupling and recently reproduced at strong coupling by AdS/CFT. We show that the same finite term appears in a weak coupling calculation of a Wilson loop whose contour consists of four light-like segments associated with the gluon momenta. We also demonstrate that, due to the special form of the finite remainder, the asymptotic Regge limit of the four-gluon amplitude coincides with the exact expression evaluated for arbitrary values of the Mandelstam variables.

722 citations

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Abstract: This work is devoted to the description of bounded energy sequences of solutions to the equation (1) □ u + | u |4 = 0 in [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /], up to remainder terms small in energy norm and in every Strichartz norm. The proof relies on scattering theory for (1) and on a structure theorem for bounded energy sequences of solutions to the linear wave equation. In particular, we infer the existence of an a priori estimate of Strichartz norms of solutions to (1) in terms of their energy.

539 citations

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Abstract: Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomial plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces.

411 citations

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01 Oct 1996-

TL;DR: Introduction and philosophy Chinese remainder algorithm in modular computations in algorithmics in bridging computation in coding theory in cryptography tutorial in information theory tutorial in algebra list of mathematical symbols.

Abstract: Introduction and philosophy Chinese remainder algorithm in modular computations in algorithmics in bridging computations in coding theory in cryptography tutorial in information theory tutorial in algebra list of mathematical symbols.

348 citations

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Abstract: In this paper, we shall propose a new image steganographic technique capable of producing a secret-embedded image that is totally indistinguishable from the original image by the human eye. In addition, our new method avoids the falling-off-boundary problem by using pixel-value differencing and the modulus function. First, we derive a difference value from two consecutive pixels by utilizing the pixel-value differencing technique (PVD). The hiding capacity of the two consecutive pixels depends on the difference value. In other words, the smoother area is, the less secret data can be hidden; on the contrary, the more edges an area has, the more secret data can be embedded. This way, the stego-image quality degradation is more imperceptible to the human eye. Second, the remainder of the two consecutive pixels can be computed by using the modulus operation, and then secret data can be embedded into the two pixels by modifying their remainder. In our scheme, there is an optimal approach to alter the remainder so as to greatly reduce the image distortion caused by the hiding of the secret data. The values of the two consecutive pixels are scarcely changed after the embedding of the secret message by the proposed optimal alteration algorithm. Experimental results have also demonstrated that the proposed scheme is secure against the RS detection attack.

279 citations