In the structure of the title compound, C(12)H(11)N(3)O(3)·H(2)O, the dihedral angle formed by the benzene and isoxazole rings is 2.03 (8)°. The mol-ecular conformation is stabilized by an intra-molecular O-H⋯N hydrogen bond. In the crystal structure, mol-ecules are linked into a three-dimesional network by inter-molecular N-H⋯O, O-H⋯N and O-H⋯O hydrogen bonds, and by π-π stacking inter-actions...

2 Knapsack Problem (continued) 2.1 Algorithm Recap Definition: We define states (sub-problems) as the following: the maximum value for a knapsack with capacity j and we are given the first i items. Then, we have ∀i, j, the corresponding state, a[i, j] is max(a[i−1, j−wi] + vi, a[i−1, j]), where the first option is the value if item i is in the knapsack and the second option is the value if item...

The 0/1 knapsack problem is a well known problem occurring in many real world problems. The problem is NP-Complete. The multiobjective 0/1 knapsack problem is a generalization of the 0/1 knapsack problem in which multiple knapsacks are considered. A new evolutionary algorithm for solving multiobjective 0/1 knapsack problem is proposed in this paper. This algorithm used a ε-dominance relation fo...

It is well known that the knapsack cryptosystem is a type of public key cryptosystems. It is based on the well known mathematical concept, i.e., the choosing of one way function. Many Knapsack cryptosystems were invented in the last 20 years, and many attacking methods were invented as a counterattack against the developed knapsack cryptosystems. All the attacking methods aim towards breaking t...

Ralph Gomory has recently aroused interest in a special type of knapsack problem in which the constraint coefficients and constant term are elements of a finite additive group. The significance of this problem lies in the fact that it is closely related to the general integer linear programming problem, resulting by removing the nonnegativity restrictions on those variables in the general probl...

We consider the polyhedral structure of the precedence constrained knapsack (PCK) problem, also known as the partially ordered knapsack problem. A set of items N is given, along with a partial order, or set of precedence relationships, on the items, denoted by S ⊆ N × N. A precedence relationship (i, j) ∈ S exists if item i can be placed in the knapsack only if item j is in the knapsack. Each i...

This paper presents and analyzes cryptanalytic attacks on knapsack public key cryptosystems that are based on ideas from Diophantine approximation. Shamir’s attack on the basic Merkle-Hellman knapsack cryptosystem is shown to depend on the existence of ‘‘unusually good’’ simultaneous Diophantine approximations to a vector constructed from the public key. This aspect of Shamir’s attack carries o...

& is called a knapsack constraint. The special case of the MKP01 with %*!) is the classical knapsack problem (KP01), whose usual statement is the following. Given a knapsack of capacity and objects, each being associated a profit (gain) and a volume occupation, one wants to select + ( +, and + not fixed) objects such that the total profit is maximized and the capacity of the knapsack is not exc...