Algorithmic Determination of a Large Integer in the Two-Term Machin-like Formula for π

In our earlier publication we have shown how to compute by iteration a rational number u2,k in the two-term Machin-like formula for π of the kind π4=2k−1arctan1u1,k+arctan1u2,k,k∈Z,k≥1, where u1,k can be chosen as an integer u1,k=ak/2−ak−1 with nested radicals defined as ak=2+ak−1 and a0=0. In this work, we report an alternative method for determination of the integer u1,k. This approach is based on a simple iteration and does not require any irrational (surd) numbers from the set ak in computation of the integer u1,k. Mathematica programs validating these results are presented.

Iterative Block Ciphers from Tweakable Block Ciphers with Long Tweaks

We consider a problem of constructing a secure block cipher from a tweakable block cipher (TBC) with long tweaks. Given a TBC with n-bit blocks and Γn-bit tweaks for Γ ≥ 1, one of the constructions by Minematsu in DCC 2015 shows that a simple iteration of the TBC for 3d rounds yields a block cipher with dn-bit blocks that is secure up to 2dn/2 queries, where d = Γ + 1. In this paper, we show three results.1. Iteration of 3d − 2 rounds is enough for the security up to 2dn/2 queries, i.e., the security remains the same even if we reduce the number of rounds by two.2. When the number of queries is limited to 2n, d+1 rounds are enough, and with d + l rounds for 1 ≤ l ≤ d − 1, the security bound improves as l grows.3. A d-round construction gives a block cipher secure up to 2n/2 queries, i.e., it achieves the classical birthday-bound security. Our results show that a block cipher with beyond-birthday-bound (BBB) security (with respect to n) is obtained as low as d + 1 rounds, and we draw the security spectrum of d + l round version in the range of 1 ≤ l ≤ d−1 and l = 2d−2 for BBB security, and l = 0 for birthday-bound security.

Structural Optimization of Box Wing Aircraft

The box wing system is an unconventional way to connect the lifting surfaces that the designers willingly to use in prototypes of new aircrafts. The article present a way to quickly optimize the wing structure of box wing airplane that can be useful during conceptual design. At the beginning, there is presented theory and methods used to code optimization program. Structure analysis is based on FEM beam model, which is sufficient in conceptual design. Optimization is performed using hybrid method, connection of simple iteration and gradient descent methods. Finally, the program is validated by case study.

Modifying Charge Input Optimization in Arc Surfacing with the Controlling Magnetic Influence

The hydrodynamic processes modelling in the weld pool under the influence of the electromagnetic bulk force was carried out. For the approximation of the model equations the finite difference method was used. The resulting system of linear algebraic equations was solved by simple iteration. The finding served the basis for determining the optimal scheme supply of powder material adding for the modification and alloying of the weld (build-up) metal in the presence of an external magnetic field.