Hadamard partitioned difference families and their descendants

If $D$ is a $(4u^2,2u^2-u,u^2-u)$ Hadamard difference set (HDS) in $G$, then $\{G,G\setminus D\}$ is clearly a $(4u^2,[2u^2-u,2u^2+u],2u^2)$ partitioned difference family (PDF). Any $(v,K,\lambda)$-PDF will be said of Hadamard-type if $v=2\lambda$ as the one above. We present a doubling construction which, starting from any such PDF, leads to an infinite class of PDFs. As a special consequence, we get a PDF in a group of order $4u^2(2n+1)$ and three block-sizes $4u^2-2u$, $4u^2$ and $4u^2+2u$, whenever we have a $(4u^2,2u^2-u,u^2-u)$-HDS and the maximal prime power divisors of $2n+1$ are all greater than $4u^2+2u$

The Strategic Role of Marketing Communication in he SME: the Case of Fornari SpA

In this paper we discuss the strategic importance of communication and Intranet for theItalian Small and Medium Enterprise (SMEs). We analyse the case of Fornari SpA, an Italian medium size clothing and shoes manufacturer that uses internet as a communication tool. The aim of this study is to understand the potential of internet in a specific case and to understand whether internet is a strategic tool or only an operative tool. The firm currently uses two applications of internet: extranet and intranet. The analysis underlines the importance of marketing competences and training that are absolutely necessary to make the most effectiveand efficient use of the internet potential.SME, ICT, Internet Marketing.

On the full automorphism group of a Hamiltonian cycle system of odd order

It is shown that a necessary condition for an abstract group G to be the full automorphism group of a Hamiltonian cycle system is that G has odd order or it is either binary, or the affine linear group AGL(1; p) with p prime. We show that this condition is also sufficient except possibly for the class of non-solvable binary groups.Comment: 11 pages, 2 figure

Super-regular Steiner 2-designs

A design is additive under an abelian group $G$ (briefly, $G$-additive) if, up to isomorphism, its point set is contained in $G$ and the elements of each block sum up to zero. The only known Steiner 2-designs that are $G$-additive for some $G$ have block size which is either a prime power or a prime power plus one. Indeed they are the point-line designs of the affine spaces $AG(n,q)$, the point-line designs of the projective planes $PG(2,q)$, and the point-line designs of the projective spaces $PG(n,2)$. In the attempt to find new examples, possibly with a block size which is neither a prime power nor a prime power plus one, we look for Steiner 2-designs which are strictly $G$-additive (the point set is exactly $G$) and $G$-regular (any translate of any block is a block as well) at the same time. These designs will be called\break "$G$-super-regular". Our main result is that there are infinitely many values of $v$ for which there exists a super-regular, and therefore additive, $2$-$(v,k,1)$ design whenever $k$ is neither singly even nor of the form $2^n3\geq12$. The case $k\equiv2$ (mod 4) is a definite exception whereas $k=2^n3\geq12$ is at the moment a possible exception. We also find super-regular $2$-$(p^n,p,1)$ designs with $p\in\{5,7\}$ and $n\geq3$ which are not isomorphic to the point-line design of $AG(n,p)$.Comment: 31 page

Designs over finite fields by difference methods

One of the very first results about designs over finite fields, by S. Thomas, is the existence of a cyclic 2-(n, 3, 7)design over F2for every integer ncoprime with 6. Here, by means of difference methods, we reprove and improve a little bit this result showing that it is true, more generally, for every odd n. In this way, we also find the first infinite family of non-trivial cyclic group divisible designs over F2

Partitioned difference families: the storm has not yet passed

Two years ago, we alarmed the scientific community about the large number of bad papers in the literature on {\it zero difference balanced functions}, where direct proofs of seemingly new results are presented in an unnecessarily lengthy and convoluted way. Indeed, these results had been proved long before and very easily in terms of difference families. In spite of our report, papers of the same kind continue to proliferate. Regrettably, a further attempt to put the topic in order seems unavoidable. While some authors now follow our recommendation of using the terminology of {\it partitioned difference families}, their methods are still the same and their results are often trivial or even wrong. In this note, we show how a very recent paper of this type can be easily dealt with

evaluation of the variability contribution due to epistemic uncertainty on constitutive models in the definition of fragility curves of rc frames

Abstract In the framework of uncertainty propagation in seismic analyses, most of the research efforts were devoted to quantifying and reducing uncertainties related to seismic input. However, also uncertainties associated to the definition of constitutive models must be taken into account, in order to have a reliable estimate of the total uncertainty in structural response. The present paper, by means of incremental dynamic analyses on reinforced concrete frames, evaluates the effect of the epistemic uncertainty for plastic-hinges hysteretic models selection. Eleven different hysteretic models, identified based on literature data, were used and seismic fragility curves were obtained for three different levels of maximum interstorey drift ratio. Finally, by means of analysis of variance techniques, the paper shows that the uncertainty associated to the hysteretic model definition has a magnitude similar to that due to record-to-record variability

Fano Kaleidoscopes and their generalizations

In this work we introduce Fano Kaleidoscopes, Hesse Kaleidoscopes and their generalizations. These are a particular kind of colored designs for which we will discuss general theory, present some constructions and prove existence results. In particular, using difference methods we show the existence of both a Fano and a Hesse Kaleidoscope on $v$ points when $v$ is a prime or prime power congruent to 1$\pmod{6}$, $v\ne13$. In the Fano case this, together with known results on pairwise balanced designs, allows us to prove the existence of Kaleidoscopes of order $v$ for many other values of $v$; we discuss what the situation is, on the other hand, in the Hesse and general case.Comment: 19 page