Sophisticated gradient design can greatly improve the versatility and performance of triply periodic minimal surface (TPMS). However, intricate process TPMS structures with has restricted their widespread adoption across various research fields. Currently, existing software is limited to providing complex designs in structures. In this study, a new MATLAB software, MD-TPMS, developed generate s...

Finding solutions to minimal problems for estimating epipolar geometry and camera motion leads to solving systems of algebraic equations. Often, these systems are not trivial and therefore special algorithms have to be designed to achieve numerical robustness and computational efficiency. The state of the art approach for constructing such algorithms is the Gröbner basis method for solving syst...

Convolutional codes over rings have been motivated by phase-modulated signals. Some structural properties of the generator matrices of such codes are presented. Successively stronger notions of invertibility of generator matrices are studied, and a new condition for a convolutional code over a ring to be systematic is given and shown to be equivalent to a condition given by Massey and Mittelhol...

In this paper, we deal with the convex generators 1 of a graph G = (V(G),E(G)). A convex generator being a minimal set whose convex hull is V(G), we show that it is included in the "boundary" of G. Then we show that the "boundary" of a polymino's graph, or more precisely the seaweed's "boundary", enjoys some nice properties which permit us to prove that for such a graph G, the minimal size of a...

We give an arithmetic criterion which is sufficient to imply the discreteness of various two-generator subgroups of PSL(2,C). We then examine certain two-generator groups which arise as extremals in various geometric problems in the theory of Kleinian groups, in particular those encountered in efforts to determine the smallest co-volume, the Margulis constant and the minimal distance between el...

We present an eecient algorithm for computing the minimal trellis for a group code over a nite Abelian group, given a generator matrix for the code. We also show how to compute a succinct representation of the minimal trellis for such a code, and present algorithms that use this information to eeciently compute local descriptions of the minimal trellis. This extends the work of Kschischang and ...

Pseudorandom sequences with certain properties are widely used in simulation, software testing, ranging systems, global positioning systems, code-division multiple-access systems, radar systems, spread-spectrum communication systems, and especially in stream ciphers. The cyclotomic sequences [1] have a number of attractive randomness properties. In this letter we first describe generalized cycl...