We consider the augmented Lagrangian dual for integer programming, and provide a primal characterization of the resulting bound. As a corollary, we obtain proof that the augmented Lagrangian is a strong dual for integer programming. We are able to show that the penalty parameter applied to the augmented Lagrangian term may be placed at a fixed, large value and still obtain strong duality for pu...

We consider the class of linear programs with infinitely many variables and constraints having the property that every constraint contains at most finitely many variables while every variable appears in at most finitely many constraints. Examples include production planning and equipment replacement over an infinite horizon. We form the natural dual linear programming problem and prove strong d...

Substitution boxes with thorough cryptographic strengths are essential for the development of strong encryption systems. They are the only portions capable of inducing nonlinearity in symmetric encryption systems. Bijective substitution boxes having both high nonlinearities and high algebraic complexities are the most desirable to thwart linear, differential and algebraic attacks. In this paper...

1.1 Complementary Slackness: Full and Approximate Recall our canonical linear programs, where x ∈ R, y ∈ R, A ∈ R, b ∈ R, c ∈ R. Primal (P) min cx Ax ≥ b x ≥ 0 Dual (D) max by A y ≤ c y ≥ 0 Also recall that Strong Duality ensures that if both (P) and (D) have finite optima, they are equal. Assume this is the case. Then, for the optima x and y of the primal and dual programs respectively, we hav...

We prove the weak consistency of the posterior distribution and that of the Bayes estimator for a two-phase piecewise linear regression mdoel where the break-point is unknown. The non-differentiability of the likelihood of the model with regard to the break-point parameter induces technical difficulties that we overcome by creating a regularised version of the problem at hand. We first recover ...

This study presents a new efficient password-based strong key derivation algorithm using the key based random permutation the KBRP method. The algorithm consists of five steps, the first three steps are similar to those formed the KBRP method. The last two steps are added to derive a key and to ensure that the derived key has all the characteristics of a strong key. In order to demonstrate the ...

We consider Continuous Linear Programs over a continuous finite time horizon T , with linear cost coefficient functions and linear right hand side functions and a constant coefficient matrix, where we search for optimal solutions in the space of measures or of functions of bounded variation. These models generalize the Separated Continuous Linear Programming models and their various duals, as f...

We derive generalized Lüscher formulas for finite size corrections in a theory with a general dispersion relation. For the AdS5 × S5 superstring these formulas encode leading wrapping interaction effects. We apply the generalized μ-term formula to calculate finite size corrections to the dispersion relation of the giant magnon at strong coupling. The result exactly agrees with the classical str...

A sufficient condition for graphs with circular flow index less than 4 is found in this paper. In particular, we give a simple proof of a result obtained by Galluccio and Goddyn (Combinatorica, 2002), and obtain a larger family of such graphs. We refer readers to [1], [2] and [7] for the standard terminology and notations in this paper. The following theorem was proved by Galluccio and Goddyn. ...

Abstract: This paper considers a special class of wiretap networks with a single source node and K sink nodes. The source message is encoded into a binary digital sequence of length N, divided into K subsequences, and sent to the K sink nodes respectively through noiseless channels. The legitimate receivers are able to obtain subsequences from arbitrary μ1 = Kα1 sink nodes. Meanwhile, there exi...