Search results for "Block design"
showing 10 items of 18 documents
Four-Year Study on the Bio-Agronomic Response of Biotypes of Capparis spinosa L. on the Island of Linosa (Italy)
2021
The caper plant is widespread in Sicily (Italy) both wild in natural habitats and as specialized crops, showing considerable morphological variation. However, although contributing to a thriving market, innovation in caper cropping is low. The aim of the study was to evaluate agronomic and production behavior of some biotypes of Capparis spinosa L. subsp. rupestris, identified on the Island of Linosa (Italy) for growing purposes. Two years and seven biotypes of the species were tested in a randomized complete block design. The main morphological and production parameters were determined. Phenological stages were also observed. Analysis of variance showed high variability between the biotype…
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…
Bollettino di Matematica pura e applicata
2020
The paper emphasizes some the advances of knowledge in mathematics problems ad new applications. The Bollettino is open to the contribution of Italian or foreign researchers.
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.
On extremal intersection numbers of a block design
1982
K.N. Majumdar has shown that for a 2-(v, k, @l) design D there are three numbers @a, @t, and @S such that each intersection number of D is not greater than @S and not less than max{@a, @t}. In this paper we investigate designs having one of these 'extremal' intersection numbers. Quasisymmetric designs with at least one extremal intersection number are characterized. Furthermore, we show that a smooth design D having the intersection number @S or @a>0 is isomorphic to the system of points and hyperplanes of a finite projective space. Using this theorem, we can characterize all smooth strongly resolvable designs.
Short Form of Spanish Version of the WISC–IV for Intelligence Assessment in Elementary School Children
2014
In educational settings, quick assessments of intelligence are often required to screen children with potential special needs. The WISC–IV is administered individually and takes between one and two hours to complete. Given its widespread use in Spain, a short-form of the Spanish version is likely to be of use to professionals. The goal of this research was to develop a short form of the WISC–IV that can be performed in approximately half an hour. Data obtained in 100 elementary school children were analyzed following the criteria of Resnick and Entin (1971). The results showed that the most accurate estimation of intelligence was achieved with a combination of the Vocabulary, Block Design,…
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…
Über die Schnittzahlen mehrfach balancierter blockpläne
1991
Abstract For a finite incidence structure D with a set X of blocks let [ X ] be the number of points common with all blocks contained in X . We define the functions M(t)(B1,…; B1)=ΣB [B1, B]…[B1,B], and, for every partition ϖ = ϖ1,…,ϖ1) of t, the function Mϖ(B1,…,B1) = Σ Πm [Bi | i ϵ Rm], sum over all decompositions {l, …, t} = R1, ⊃ … ⊃ Rl, |Rm| = ϖm. We show: If D is t-fold balanced, then M(t) = Σϖ cϖMϖ, where the, coefficients cϖ are linear combinations of the parameters b1,…,bt, the constant numbers of blocks through any l,…, t distinct points. Conversely, if the rank of the b × b-matrix ([B, B∗])B,B∗ is equal to the number ν of points and M(t) is a rational linear combination of the fu…