Uniform Interpretation: Notice of Nonconformity

This Article is about uniform interpretation as it pertains to the nonconformity notices under CISG Article 39.1 Article 39, which is one of the most heavily-litigated provisions of the CISG, provides in relevant part:2 The buyer loses the right to rely on a lack of conformity of the goods if he does not give notice to the seller specifying the nature of the lack of conformity within a reasonable time after he has discovered it or ought to have discovered it.I will focus chiefly on two aspects of Article 39(1): (1) what constitutes a “reasonable time” within which buyers must notify sellers of a “lack of conformity” and (2) what level of specification is required to establish “the nature of the lack of conformity.

Set-theoretical solutions of the Yang-Baxter and pentagon equations on semigroups

The Yang-Baxter and pentagon equations are two well-known equations of Mathematical Physic. If $S$ is a set, a map $s:S\times S\to S\times S$ is said to be a set theoretical solution of the Yang-Baxter equation if $$s_{23}\, s_{13}\, s_{12} = s_{12}\, s_{13}\, s_{23},$$ where $s_{12}=s\times id_S$, $s_{23}=id_S\times s$, and $s_{13}=(id_S\times \tau)\,s_{12}\,(id_S\times \tau)$ and $\tau$ is the flip map, i.e., the map on $S\times S$ given by $\tau(x,y)=(y,x)$. Instead, $s$ is called a set-theoretical solution of the pentagon equation if $$s_{23}\, s_{13}\, s_{12}=s_{12}\, s_{23}.$$ The main aim of this work is to display how solutions of the pentagon equation turn out to be a useful tool to obtain new solutions of the Yang-Baxter equation. Specifically, we present a new construction of solutions of the Yang-Baxter equation involving two specific solutions of the pentagon equation. To this end, we provide a method to obtain solutions of the pentagon equation on the matched product of two semigroups, that is a semigroup including the classical Zappa product

Solutions of the Yang-Baxter equation and strong semilattices of skew braces

We prove that any set-theoretic solution of the Yang-Baxter equation associated to a dual weak brace is a strong semilattice of non-degenerate bijective solutions. This fact makes use of the description of any dual weak brace $S$ we provide in terms of strong semilattice $Y$ of skew braces $B_\alpha$, with $\alpha \in Y$. Additionally, we describe the ideals of $S$ and study its nilpotency by correlating it to that of each skew brace $B_\alpha$

Inverse semi-braces and the Yang-Baxter equation

The main aim of this paper is to provide set-theoretical solutions of the Yang-Baxter equation that are not necessarily bijective, among these new idempotent ones. In the specific, we draw on both to the classical theory of inverse semigroups and to that of the most recently studied braces, to give a new research perspective to the open problem of finding solutions. Namely, we have recourse to a new structure, the inverse semi-brace, that is a triple $(S,+, \cdot)$ with $(S,+)$ a semigroup and $(S, \cdot)$ an inverse semigroup satisfying the relation $a \left(b + c\right) = a b + a\left(a^{-1} + c\right)$, for all $a,b,c \in S$, where $a^{-1}$ is the inverse of $a$ in $(S, \cdot)$. In particular, we give several constructions of inverse semi-braces which allow for obtaining solutions that are different from those until known.Comment: 43 page

Set-theoretical solutions of the pentagon equation on groups

Let $M$ be a set. A set-theoretical solution of the pentagon equation on $M$ is a map $s:M\times M\longrightarrow M\times M$ such that \begin{equation*} s_{23}\, s_{13}\, s_{12}=s_{12}\, s_{23}, \end{equation*} where $s_{12}=s\times id_M$, $s_{23}=id_M \times s$ and $s_{13}=(id_M \times \tau) s_{12}(id_M \times \tau)$, and $\tau$ is the flip map, i.e., the permutation on $M\times M$ given by $\tau(x,y)=(y,x)$, for all $x,y\in M$. In this paper we give a complete description of the set-theoretical solutions of the form $s(x,y)=(x\cdot y , x\ast y)$ when either $(M,\cdot)$ or $(M,\ast)$ is a group; moreover, we raise some questions.Comment: 12 page

Use of Industrial Reclaimed Filler to Modify Asphalt Mixture and Binder Performances. Advanced rheological performance evaluation and 3D DEM Modeling of bituminous binders and mastics

The mechanical performance of an asphalt mixture is largely dependent on the properties of its constituents and by the way they reciprocally interact in the bituminous layer. In particular, the stress-strain response of the road pavements is closely related to the rheological behavior of the bituminous binder and of its interaction with the finest part of the lytic skeleton. Therefore, it is important to study in the laboratory by means of advanced rheological tests, how mastics (Bitumen-Filler Systems) and mortars (Bitumen-Filler-Sand Systems) react to dynamic loads and thermal stresses. Moreover, the understanding of the contacts mechanisms within the bitumen-filler system, through 3D micro-mechanical models, should allow for a deeper analysis of the mastic rheological behavior. Based on these considerations, in a socio-economic context in which it is necessary to reduce the environmental impact caused by the construction and maintenance of transportation infrastructures, bituminous mastics containing different reclaimed fillers from the industrial production wastes were studied. For this purpose, advanced rheological tests have been first validated and then implemented and combined with the 3D DEM models development. Results showed that the methods used to study the bituminous mastics and mortars allowed to understand the effects due to the addition of innovative and recycled fillers within the mixtures blend, highlighting as these can increase the asphalt mixture performance during its service life

Application of Mining Waste Powder as filler in Hot Mix Asphalt

Asphalt concrete mixtures are composed of two main components: aggregates and binder. The fraction of aggregates passing through the 63\u3bcm sieve is traditionally considered as filler. During years, several researches have shown the importance and the influence of filler in controlling the physical and mechanical properties of Hot Mix Asphalts (HMAs). The main objective of this research is to investigate and to assess the effects given by the use of Mining Waste Powder (MWP) within HMAs in total substitution of traditional limestone filler. The MWP used in this study is a residual of the tungsten extraction process in Panasqueira (Portugal) mine. The evaluation of properties conferred by the presence of the MWP filler within asphalt mixtures is based on a physical and mechanical laboratory characterization. For this purpose, tests have been performed both on bituminous mastics and on HMAs. Results indicate that the use of MWP in total substitution of limestone filler does not negatively affect the performances of HMAs and their bituminous mastics

PRESERVATION OF THE GOODS: COMPARISON OF ARTICLES 85-88 CISG AND COUNTERPART PROVISIONS OF THE PRINCIPLES OF EUROPEAN CONTRACT LAW

PRESERVATION OF THE GOODS: COMPARISON OF ARTICLES 85-88 CISG AND COUNTERPART PROVISIONS OF THE PRINCIPLES OF EUROPEAN CONTRACT LA

Investigation on performances of asphalt mixtures made with Reclaimed Asphalt Pavement: Effects of interaction between virgin and RAP bitumen

According to most recent surveys, the European area produced 265 mil tonnes of asphalt for road applications in 2014. In the same year, the amount of available RAP was more than 50 mil tonnes. The use of RAP in new blended mixes reduces the need of neat bitumen, making RAP recycling economically attractive. Despite the economic and environmental benefits, road authorities tend to limit the use of RAP in asphalt mixes due to uncertainty about field performances. The present study focuses on the interaction between neat and RAP bitumen in asphalt mixes made with different RAP content. The effects of RAP on physical and rheological properties of the final bituminous blend were investigated. This study is part of a wider research, where a specific type of asphalt mixture was produced with different RAP contents being 10%, 20% and 30% by mass of the mix. Bitumen was extracted and recovered from asphalt mixes, then it was subjected to the following laboratory tests: standard characterization, dynamic viscosity and rheological analysis with DSR. Findings showed that the effects of RAP bitumen on the final blend varied in proportion to RAP content. A threshold value of RAP content was found, below which bitumen was not subjected to significant changes in physical and rheological properties. Practical implications on production methods and paving of RAP mixes are also proposed. Keywords: Reclaimed Asphalt Pavement (RAP), Recycling, Bitumen blending, Bitumen rheolog