The Sumerian verb kušur, “to repair”

The article discusses a Sumerian verb, kušur, which can be interpreted as an Akkadian loanword and be related to the root *kšr attested in the verb kašāru/kuššuru, meaning “to repair (ruined or damaged walls, building, ...)”

A handbook from the Eduba'a: an Old Babylonian collection of model contracts

The Old Babylonian prism here published is a compendium of model contracts (and one legal provision) written in Sumerian and it is a direct expression of the scholastic legal tradition in Southern Mesopotamia

Another Old Babylonian barley loan from Gula’s temple

The article is the edition of a new Old Babylonian loan of barley from the Gula temple in Larsa

Becker and Lomnitz rheological models: a comparison

The viscoelastic material functions for the Becker and the Lomnitz rheological models, sometimes employed to describe the transient flow of rocks, are studied and compared. Their creep functions, which are known in a closed form, share a similar time dependence and asymptotic behavior. This is also found for the relaxation functions, obtained by solving numerically a Volterra equation of the second kind. We show that the two rheologies constitute a clear example of broadly similar creep and relaxation patterns associated with neatly distinct retardation spectra, for which analytical expressions are available.Comment: 7 pages, 4 figure

Two isomorphism criteria for directed colimits

Using the general notions of finitely presentable and finitely generated object introduced by Gabriel and Ulmer in 1971, we prove that, in any (locally small) category, two sequences of finitely presentable objects and morphisms (or two sequences of finitely generated objects and monomorphisms) have isomorphic colimits (=direct limits) if, and only if, they are confluent. The latter means that the two given sequences can be connected by a back-and-forth chain of morphisms that is cofinal on each side, and commutes with the sequences at each finite stage. In several concrete situations, analogous isomorphism criteria are typically obtained by ad hoc arguments. The abstract results given here can play the useful r\^ole of discerning the general from the specific in situations of actual interest. We illustrate by applying them to varieties of algebras, on the one hand, and to dimension groups---the ordered $K_0$ of approximately finite-dimensional C*-algebras---on the other. The first application encompasses such classical examples as Kurosh's isomorphism criterion for countable torsion-free Abelian groups of finite rank. The second application yields the Bratteli-Elliott Isomorphism Criterion for dimension groups. Finally, we discuss Bratteli's original isomorphism criterion for approximately finite-dimensional C*-algebras, and show that his result does not follow from ours.Comment: 10 page

The effect of round-off error on long memory processes

We study how the round-off (or discretization) error changes the statistical properties of a Gaussian long memory process. We show that the autocovariance and the spectral density of the discretized process are asymptotically rescaled by a factor smaller than one, and we compute exactly this scaling factor. Consequently, we find that the discretized process is also long memory with the same Hurst exponent as the original process. We consider the properties of two estimators of the Hurst exponent, namely the local Whittle (LW) estimator and the Detrended Fluctuation Analysis (DFA). By using analytical considerations and numerical simulations we show that, in presence of round-off error, both estimators are severely negatively biased in finite samples. Under regularity conditions we prove that the LW estimator applied to discretized processes is consistent and asymptotically normal. Moreover, we compute the asymptotic properties of the DFA for a generic (i.e. non Gaussian) long memory process and we apply the result to discretized processes.Comment: 44 pages, 4 figures, 4 table

Digital manufacturing in fiat group automobiles: virtual simulations for preliminary ergonomics optimization of workcells in the design phase of a new car model

New standards on work organization in the automotive industry, require a new concept of design methods: the human centred process. In Fiat Group Automobiles (FGA) the “Digital Manufacturing” (DM) project has started with the goal to create simulation tools and methods to improve the design of new cars’manufacturing processes giving a special attention to manual operations. The DM approach is based on a detailed “virtual plant” where virtual mannequins interact with digital models of car’s components, equipment, containers, etc. in order to simulate and improve working conditions with many benefits on ergonomics, safety, final product quality, work organization and general production costs. The key factor for this approach is that with DM methodologies, designers and engineers have, already in the design phase of a new car’s manufacturing process, a preliminary estimation of the numerical indices used in the plants to check if workcells are compliant to international standards and regional safety laws. In this way the most important ergonomic indices (like Niosh, Snook & Ciriello, EAWS, etc.) become a “design tool” that allow to change/improve project solutions (designing easy and comfortable work tasks, equipment, tools, etc.) and to distribute the work load in an optimal way between workers

Representation of Perfect and Local MV-algebras

We describe representation theorems for local and perfect MV-algebras in terms of ultraproducts involving the unit interval [0,1]. Furthermore, we give a representation of local Abelian lattice-ordered groups with strong unit as quasi-constant functions on an ultraproduct of the reals. All the above theorems are proved to have a uniform version, depending only on the cardinality of the algebra to be embedded, as well as a definable construction in ZFC. The paper contains both known and new results and provides a complete overview of representation theorems for such classes

A generalization of the Becker model in linear viscoelasticity: Creep, relaxation and internal friction

We present a new rheological model depending on a real parameter $\nu \in [0,1]$ that reduces to the Maxwell body for $\nu=0$ and to the Becker body for $\nu=1$. The corresponding creep law is expressed in an integral form in which the exponential function of the Becker model is replaced and generalized by a Mittag-Leffler function of order $\nu$. Then, the corresponding non-dimensional creep function and its rate are studied as functions of time for different values of $\nu$ in order to visualize the transition from the classical Maxwell body to the Becker body. Based on the hereditary theory of linear viscoelasticity, we also approximate the relaxation function by solving numerically a Volterra integral equation of the second kind. In turn, the relaxation function is shown versus time for different values of $\nu$ to visualize again the transition from the classical Maxwell body to the Becker body. Furthermore, we provide a full characterization of the new model by computing, in addition to the creep and relaxation functions, the so-called specific dissipation $Q^{-1}$ as a function of frequency, which is of particularly relevance for geophysical applicationsComment: 18 pages, 8 figures. arXiv admin note: text overlap with arXiv:1701.0306