We present a new approach to the distributed vi-sualization of geometric algorithms that emphasizes the position of the end user. Concepts are introduced that enable a more exible usage of visualized geometric algorithms, while keeping the task of adapting existing algorithms to the new scheme as simple as possible. A main proposition is that interactivity should not be built into the visualize...

Geometric distortion may occur in the data acquisition phase in information systems, and it can be characterized by some geometric transformation models. Once the distorted image is approximated by a certain geometric transformation model, we can apply its inverse transformation for the geometric restoration to remove the distortion. Harmonic model is a very important one, which can cover other...

the concept of geometric-arithmetic indices (ga) was put forward in chemical graph theoryvery recently. in spite of this, several works have already appeared dealing with these indices.in this paper we present lower and upper bounds on the second geometric-arithmetic index(ga2) and characterize the extremal graphs. moreover, we establish nordhaus-gaddum-typeresults for ga2.

continuing the work k. c. das, i. gutman, b. furtula, on second geometric-arithmetic indexof graphs, iran. j. math chem., 1(2) (2010) 17-28, in this paper we present lower and upperbounds on the third geometric-arithmetic index ga3 and characterize the extremal graphs.moreover, we give nordhaus-gaddum-type result for ga3.

We show that every [n, k, d]3 code with diversity (Φ0, Φ1), 3 ≤ k ≤ 5, gcd(d, 3) = 1, is (2, 1)-extendable except for the case (Φ0, Φ1) = (40, 36) for k = 5, and that an [n, 5, d]3 code with diversity (40, 36), gcd(d, 3) = 1, is (2, 1)-extendable if Ad ≤ 50. Geometric conditions for the (2, 1)-extendability of not necessarily extendable [n, k, d]3 codes for k = 5, 6 are also given.

We survey some encoding methods for AG codes, focusing primarily on one approach utilizing code automorphisms. If a linear code C over Fq has a finite abelian group H as a group of automorphisms, then C has the structure of a module over a polynomial ring P. This structure can be used to develop systematic encoding algorithms using Gröbner bases for modules. We illustrate these observations wit...

Let β be the middle-(1−2β) Cantor set with β ∈ (1/3, 1/2). We give all real numbers t with unique {−1, 0, 1}-code such that the intersections β ∩ ( β + t) are self-similar sets. For a given β ∈ (1/3, 1/2), a criterion is obtained to check whether or not a t ∈ [−1, 1] has the unique {−1, 0, 1}-code from both geometric and algebraic views. Mathematics Subject Classification: 28A80, 28A78

A. two-step sub-optimal algorithm for decoding binary product codes is discussed. This algorithm realizes at least half the minimum Euclidean distance of the code. The fundamental geometric properties associated with the algorithm are investigated, and bounds on the number of nearest neighbors are derived. This investigation also results with an improved algorithm which achieves the minimum eff...

‎in this paper first we define the morphism between geometric spaces in two different types‎. ‎we construct two categories of $uu$ and $l$ from geometric spaces then investigate some properties of the two categories‎, ‎for instance $uu$ is topological‎. ‎the relation between hypergroups and geometric spaces is studied‎. ‎by constructing the category $qh$ of $h_{v}$-groups we answer the question...