Search results for "designs"
showing 10 items of 38 documents
1-(v,3,r) designs and the equation x+y+z=0 in finite abelian groups
2009
Let (G, +) be a finite abelian group with more than three elements and let B_3 be the family of all the unordered triples {x,y,z} of distinct elements of G such that x+y+z=0. We show that (G, B_3) is a 1-(v,3,r) design if and only if G is either an elementary abelian 3-group or the direct sum of Z/2Z with an elementary abelian 3-group. We also characterize the groups containing at least an element that does not belong to any triple in B_3
Additivity of affine designs
2020
We show that any affine block design $$\mathcal{D}=(\mathcal{P},\mathcal{B})$$ is a subset of a suitable commutative group $${\mathfrak {G}}_\mathcal{D},$$ with the property that a k-subset of $$\mathcal{P}$$ is a block of $$\mathcal{D}$$ if and only if its k elements sum up to zero. As a consequence, the group of automorphisms of any affine design $$\mathcal{D}$$ is the group of automorphisms of $${\mathfrak {G}}_\mathcal{D}$$ that leave $$\mathcal P$$ invariant. Whenever k is a prime p, $${\mathfrak {G}}_\mathcal{D}$$ is an elementary abelian p-group.
Binary Hamming codes and Boolean designs
2021
AbstractIn this paper we consider a finite-dimensional vector space $${\mathcal {P}}$$ P over the Galois field $${\text {GF}}(2),$$ GF ( 2 ) , and the family $${\mathcal {B}}_k$$ B k (respectively, $${\mathcal {B}}_k^*$$ B k ∗ ) of all the k-sets of elements of $$\mathcal {P}$$ P (respectively, of $${\mathcal {P}}^*= {\mathcal {P}} \setminus \{0\}$$ P ∗ = P \ { 0 } ) summing up to zero. We compute the parameters of the 3-design $$({\mathcal {P}},{\mathcal {B}}_k)$$ ( P , B k ) for any (necessarily even) k, and of the 2-design $$({\mathcal {P}}^{*},{\mathcal {B}}_k^{*})$$ ( P ∗ , B k ∗ ) for any k. Also, we find a new proof for the weight distribution of the binary Hamming code. Moreover, we…
Towards the Preservation and Dissemination of Historical Silk Weaving Techniques in the Digital Era
2019
Historical weaving techniques have evolved in time and space giving as result more or less fabrics with different aesthetical characteristics. These techniques were transferred along the main silk production centers, thanks to the European Silk Road and creating a common European Frame on themes and techniques. These had made it complicated to determine whether a fabric corresponds to one century or another. Moreover, in order to understand their creation, it is necessary to determine the number of weaves and interlacements that each textile has, therefore, mathematical models can be extracted from these layers. In this sense, three dimensional (3D) virtual representations of the internal s…
Examples of additive designs
2012
In this paper we present some additive designs.
On the representations in GF(3)^4 of the Hadamard design H_11
2020
In this paper we study the representations of the 2-(11,5,2) Hadamard design H_11 = (P,B) as a set of eleven points in the 4-dimensional vector space GF(3)^4, under the conditions that the five points in each block sum up to zero, and dim ‹P› = 4. We show that, up to linear automorphism, there exist precisely two distinct, linearly nonisomorphic representations, and, in either case, we characterize the family S of all the 5-subsets of P whose elements sum up to zero. In both cases, S properly contains the family of blocks B, thereby showing that a previous result on the representations of H_11 in GF(3)^5 cannot be improved.
De Montaigne a Lope: distintos resultados de una misma decisión
2009
This essay presents the initial hypothesis of the diversity of cases shown by Lope de Vega’s theatre, that multiply perspectives and different endings from the same basic types of conflicts and designs, and tries to verify them with contemporary thought. This diversity is related with a certain type of discourse that has begun to spread out in the very beginning of the Renaissance and was gradually displacing the pre-eminence of universal principles (neo-platonic, or neoaristotelic and scholastic) for an invitation to casuistic analysis, an ethical modality applied that chose the concrete analysis of the concrete situation in front of the universally required dogmas. A type of discourse tha…
Differences in Immaterial Details: Dimensional Conversion and Its Implications for Protecting Digital Designs Under EU Design Law
2021
AbstractThe paper considers three main questions: the legal status of digital designs from the perspective of EU design law, whether the protection is tied to the reproduction of physical products, and whether the scope of protection covers dimensional conversion such as using a 3D design in 2D form or vice versa. There are two sets of views regarding dimensional conversion: the “abstract” and the “concrete” view. These two different attitudes towards the scope of protection influence the manner in which the protectability of digital designs is assessed. In the “abstract” protection, it would not matter whether a product only exists as a digital image and not as a physical shape. In the “co…
Perceivability of Map Information for Disaster Situations for People with Low Vision
2019
Digital maps have become increasingly popular in disaster situation to provide overview of information. However, these maps have also created barriers for many people, particularly people with visual impairments. Existing research on accessible maps such as tactile and acoustic maps focuses on providing solutions for blind persons to be able to perceive the information digital maps present. For people with low vision, who often rely on magnifier, good contrast and good navigation support, current digital map solutions present many challenges. In this paper we have studied two types of digital maps and their related surrounding text in the home page of disaster applications. The study focuse…
On the additivity of block designs
2016
We show that symmetric block designs $${\mathcal {D}}=({\mathcal {P}},{\mathcal {B}})$$D=(P,B) can be embedded in a suitable commutative group $${\mathfrak {G}}_{\mathcal {D}}$$GD in such a way that the sum of the elements in each block is zero, whereas the only Steiner triple systems with this property are the point-line designs of $${\mathrm {PG}}(d,2)$$PG(d,2) and $${\mathrm {AG}}(d,3)$$AG(d,3). In both cases, the blocks can be characterized as the only k-subsets of $$\mathcal {P}$$P whose elements sum to zero. It follows that the group of automorphisms of any such design $$\mathcal {D}$$D is the group of automorphisms of $${\mathfrak {G}}_\mathcal {D}$$GD that leave $$\mathcal {P}$$P in…