Positive\partial \bar \partial - closed currents and non-Kähler geometrycurrents and non-Kähler geometry

In this paper some new results on positive \(\partial \bar \partial - closed\) currents are applied to modifications \(f:\bar M \to M\) . The main result in this topic is that every smooth proper modification of a compact Kähler manifoldM is balanced. Moreover, under suitable hypotheses on the map, the Kähler degrees of \(\bar M\) corresponds to homological properties of the exceptional set of the modification. More examples ofp-Kähler manifolds are discussed in the last section of the paper.     

Trace cocharacters and the Kronecker products of Schur functions

It follows from the theory of trace identities developed by Procesi and Razmyslov that the trace cocharacters arising from the trace identities of the algebra M_r(F) of r×r matrices over a field F of characteristic zero are given by TC_r,n=∑_λΛr(n)χ^λχ^λ where χ^λχ^λ denotes the Kronecker product of the irreducible characters of the symmetric group associated with the partition λ with itself and Λ_r(n) denotes the set of partitions of n with r or fewer parts, i.e. the set of partitions λ=(λ₁λ_k) with kr. We study the behavior of the sequence of trace cocharacters TC_r,n. In particular, we study the behavior of the coefficient of χ^(ν,n−m) in TC_r,n as a function of n where ν=(ν₁ν_k) is some fixed partition of m and n−mν_k. Our main result shows that such coefficients always grow as a polynomial in n of degree r−1.     

Groups in which every non-abelian subgroup is permutable

A subgroupH of a groupG is said to bepermutable ifHX=XH for every subgroupX ofG. In this paper the structure of groups in which every subgroup either is abelian or permutable is investigated. This work was done while the last author was visiting the University of Napoli Federico II. He thanks the “Dipartimento di Matematica e Applicazioni” for its financial support.     

The Solow model improved through the logistic manpower growth law

In this paper the neo-classical economic Solow-Swan model (1956) has been improved replacing its Malthusian manpower law with the Verhulst (logistic) one. The relevant ordinary differential equation for the ratio capital/work has been then integrated in closed form via the Hypergeometric function₂ F ₁. The logistic growth injection for the manpower is detected to induce a more slow dynamics onto the Solow-Swan system, which keeps its stability. Increasing developments are displayed as the technologic progress rises. Further sceneries are tested and the congruence of the new solution with the classical one is shown switching to zero the selflimitation coefficent in the logistic law. Research supported by MURST grant:Metodi matematici in economia     

Sui principi variazionali nella meccanica dei continui classici

In this paper, along with the well established lines of the analytical mechanics, we aim to show an autonomous formulation of the fundamental principle of Lagrange-d'Alembert and of the subsequent Hamilton principle in classical mechanics of deformable continua in the sense that the afore—mentioned principles do not turn out to be a reformulation of the well known undefined equations of motion.     

Geometric dynamic recrystallization of austenitic stainless steel through linear plane-strain machining

ABSTRACT

Type 316L austenitic stainless steel was severely plastically deformed at room temperature using linear plane-strain machining in a single pass that imparted shear strains up to 2.2 at strain rates up to 2?×?10³ s^?1. The resulting microstructures exhibited significant grain size refinement and improved mechanical strength where geometric dynamic recrystallization was identified as the primary microstructural recrystallization mechanism active at high strain rates. This mechanism is rarely observed in low to medium stacking fault energy materials. The critical stress required for twin initiation is raised by the combined effects of refined grain size and the increase in stacking fault energy due to the adiabatic heating of the chip, thus permitting geometric dynamic recrystallization. The suppression of martensite formation was observed and is correlated to the significant adiabatic heating and mechanical stabilisation of the austenitic stainless steel. A gradient of the amount of strain induced martensite formed from the surface towards the interior of the chip. As the strain rate is increased from 4?×?10² s^?1–2?×?10³ s^?1, a grain morphology change was observed from a population of grains with a high fraction of irregular shaped grains to one dominated by elongated grain shapes with a microstructure characterised by an enhanced density of intragranular sub-cell structure, serrated grain boundaries, and no observable twins. As strain rates were increased, the combination of reduction in strain induced martensite and non-uniform intragranular strain led to grain softening where a Hall-Petch relationship was observed with a negative strengthening coefficient of ?0.08?MPa m^1/2.     

Modeling Transverse Relative Locality

We investigate some aspects of relativistic classical theories with “relative locality”, in which pairs of events established to be coincident by nearby observers may be described as non-coincident by distant observers. While previous studies focused mainly on the case of longitudinal relative locality, where the effect occurs along the direction connecting the distant observer to the events, we here focus on transverse relative locality, in which instead the effect is found in a direction orthogonal to the one connecting the distant observer to the events. Our findings suggest that, at least for theories of free particles, transverse relative locality is as significant as longitudinal relative locality both conceptually and quantitatively. And we observe that “dual gravity lensing” can be viewed as one of two components of transverse relative locality. We also speculate about a type of spacetime noncommutativity for which transverse relative locality could be particularly significant.     

The Suzuki homocoupling reaction under high-intensity ultrasound

The Pd-catalysed Suzuki homocoupling of boronic acids was successfully carried out in water under high-intensity ultrasound (HIU). Heterogeneous catalysis with Pd/C, facilitating work up and purification, could be used without adding phosphine ligands. Reaction rates and yields were strongly influenced by the oxidant employed; excellent results were obtained using either molecular oxygen or 3-bromo-4-hydroxycoumarin. 3-Arylation of the latter with the Suzuki procedure had failed, exclusively affording the homocoupling products, symmetric biaryls. Besides offering a number of operational advantages, the use of HIU broadens the field of application for the Suzuki reaction.     

Modelling the soundscape quality of urban waterfronts by artificial neural networks

The renewal of the urban waterfronts has become a major focus of attention for politicians and decision makers in the city’s management programs. The recognition of the patterns that define the waterfronts’ identity is essential to select new strategies of intervention for the environmental recovery. In order to create adequate environments for everyday life within a sustainable development, new links between human senses, human perception and design need to be created. Within this wide approach, the landscape and the soundscape play a significant role and can become a key driving force in the implementation of the changes. New techniques have to be tested to identify the sonic and visual parameters capable to explain the specificity of a waterfront. With this purpose, an artificial neural network (ANN) was developed, and the relative importance of the input variables was evaluated. The collected database was also analysed by multiple linear regression (MLR) to compare the outcomes of both models. The urban waterfront of Naples (Italy) was chosen as case study. The results obtained show that the performance of the neural network is better than the one of the linear regression (rANN = 0.949, rMLR = 0.639). The interpretation of the relative importance method is also quite satisfactory in the ANN.