On line covers of finite projective and polar spaces

An $m$-$cover$ of lines of a finite projective space ${\rm PG}(r,q)$ (of a finite polar space $\cal P$) is a set of lines $\cal L$ of ${\rm PG}(r,q)$ (of $\cal P$) such that every point of ${\rm PG}(r,q)$ (of $\cal P$) contains $m$ lines of $\cal L$, for some $m$. Embed ${\rm PG}(r,q)$ in ${\rm PG}(r,q^2)$. Let $\bar{\cal L}$ denote the set of points of ${\rm PG}(r,q^2)$ lying on the extended lines of $\cal L$. An $m$-cover $\cal L$ of ${\rm PG}(r,q)$ is an $(r-2)$-dual $m$-cover if there are two possibilities for the number of lines of $\cal L$ contained in an $(r-2)$-space of ${\rm PG}(r,q)$. Basing on this notion, we characterize $m$-covers $\cal L$ of ${\rm PG}(r,q)$ such that $\bar{\cal L}$ is a two-character set of ${\rm PG}(r,q^2)$. In particular, we show that if $\cal L$ is invariant under a Singer cyclic group of ${\rm PG}(r,q)$ then it is an $(r-2)$-dual $m$-cover. Assuming that the lines of $\cal L$ are lines of a symplectic polar space ${\cal W}(r,q)$ (of an orthogonal polar space ${\cal Q}(r,q)$ of parabolic type), similarly to the projective case we introduce the notion of an $(r-2)$-dual $m$-cover of symplectic type (of parabolic type). We prove that an $m$-cover $\cal L$ of ${\cal W}(r,q)$ (of ${\cal Q}(r,q)$) has this dual property if and only if $\bar{\cal L}$ is a tight set of an Hermitian variety ${\cal H}(r,q^2)$ or of ${\cal W}(r,q^2)$ (of ${\cal H}(r,q^2)$ or of ${\cal Q}(r,q^2)$). We also provide some interesting examples of $(4n-3)$-dual $m$-covers of symplectic type of ${\cal W}(4n-1,q)$.Comment: 20 page

Modelling of thermo-chemical properties over the sub-solidus MgO–FeO binary, as a function of iron spin configuration, composition and temperature

Thermo-chemical properties and T–X phase relations diagram of the (Mg,Fe)O solid solution are modelled using mixing Helmholtz energy, ΔF(T,x)mixing, calculated by quantum mechanical and semi-empirical techniques. The sub-solidus MgO–FeO binary has been explored as a function of composition, with iron either in high-spin (HS) or low-spin (LS) configuration. Only the HS model provides physically sound results at room pressure, yielding a correct trend of cell edge versus composition, whereas LS’s issues are at variance with observations. Mixing Helmholtz energy has been parametrized by the following relationship: ΔF(T,x)mixing = x × y × [U0(T) + U1(T) × (x – y) + U2(T) × (x − y)2]−T × S(x,y)config, where y = 1−x and Uj(T) are polynomials in T of the second order. ΔF(T,x)mixing exhibits a quasi-symmetric behaviour and allows one to build the T–X phase relations diagram over the MgO–FeO join. The HS model including vibrational contribution to the Helmholtz energy predicts a solid solution’s critical temperature of some 950 K, remarkably larger than olivine’s and Mg–Fe garnet’s. All this points to a more difficult Mg–Fe mixing in periclase-like structure than olivine and garnet, which, in turn, provide more structure degrees of freedom for atomic relaxation. From ΔF(T,x)mixing, we have then derived ΔH(T,x)excess and ΔS(T,x)excess. The former, characterized by a quasi-regular behaviour, has been parametrized through W × x × (1−x), obtaining WH,Mg–Fe of 17.7(5) kJ/mol. ΔS(T,x)excess, in turn, increases as a function of temperature, showing absolute figures confined within 0.1 J/mol/K. Mixing Gibbs energy, calculated combining the present issues with earlier theoretical determinations of the magnesio-wüstite’s elastic properties, has shown that the HS configuration is stable and promote Mg–Fe solid solution up to ≈15 GPa

ORBIT CODES FROM FORMS ON VECTOR SPACES OVER A FINITE FIELD

In this paper we construct different families of orbit codes in the vector spaces of the symmetric bilinear forms, quadratic forms and Hermitian forms on an n-dimensional vector space over the finite field Fq. All these codes admit the general linear group GL(n, q) as a transitive automorphism group

A state-space partitioned time integration algorithm for real-time hybrid simulation with nonlinear numerical subdomains

This paper describes a state-space partitioned algorithm for real-time hybrid simulation. The state-space modeling is proposed to represent nonlinear numerical substructures. The effectiveness of the proposed method is demonstrated for a virtual bridge case study equipped with seismic isolation devices

Fe-periclase reactivity at Earth's lower mantle conditions: Ab-initio geochemical modelling

Intrinsic and extrinsic stability of the (Mg,Fe)O solid mixture in the Fe-Mg-Si-O system at high P, T conditions relevant to the Earth\u2019s mantle is investigated by the combination of quantum mechanical calculations (Hartree- 26 Fock/DFT hybrid scheme), cluster expansion techniques and statistical thermodynamics. Iron in the (Mg,Fe)O binary mixture is assumed to be either in the low spin (LS) or in the high spin (HS) state. Un-mixing at solid state is observed only for the LS condition in the 23\u201342 GPa pressure range, whereas HS does not give rise to un-mixing. LS (Mg,Fe)O un-mixings are shown to be able to incorporate iron by subsolidus reactions with a reservoir of a virtual bridgmanite composition, for a maximum total enrichment of 0.22 FeO. At very high P (up to 130/3150 GPa/K), a predominant (0.7 phase proportion), iron-rich Fe-periclase mixture (Mg0.50Fe0.50)O is formed, and it coexists, at constrained phase composition conditions, with two iron-poor assemblages [(Mg0.90Fe0.10)O and (Mg0.825Fe0.175)O]. These theoretical results agree with the compositional variability and frequency of occurrence observed in lower mantle Fe-periclase from diamond inclusions and from HP-HT synthesis products. The density difference among the Fe-periclase phases increases up to 10%, between 24 and 130 GPa. The calculated bulk Fe/Mg partitioning coefficient between the bridgmanite reservoir and Fe-periclase, Kd, is 0.64 at 24 GPa; it then drops to 0.19 at 80 GPa, and becomes quasi-invariant (0.18\u20130.16) in the lowermost portion of the Earth\u2019s mantle (80\u2013 130 GPa). These Kd-values represent an approximate estimate for the Fe/Mg-partitioning between actual bridgmanite and Fe-periclase. Consequently, our Kd-values agree with experimental measurements and theoretical determinations, hinting that iron preferentially dissolves in periclase with respect to all the other iron-bearing phases of the lower mantle. The continuous change up to 80 GPa (2000 km depth) of the products (compositions and phase proportions) over the MgO-FeO binary causes geochemical heterogeneities throughout the lower mantle, but it does not give rise to any sharp discontinuity. In this view, anomalies like the ULVZs, explained with a local and abrupt change of density, do not seem primarily ascribable to the mixing behavior and reactivity of (Mg,Fe)O at subsolidus

Mechanical properties of mortar containing waste plastic (PVC) as aggregate partial replacement

The purpose of this work is the reuse of polyvinyl chloride (PVC) deriving from waste electrical and electronic equipment (WEEE) used as a partial substitute for the mineral aggregate to produce lightened mortars. PVC was recovered from copper electrical cables, ground and used as replacement of mineral aggregate in 5, 10, 15 and 20 % vol. in mortar. A thermal characterization of the starting material was carried out to understand its composition. The mortar samples were mechanically tested both using class G cement and ordinary Portland cement. The results showed a worsening of the mechanical properties of around 50 % for only 5 % in volume of sand substituted with PVC waste. A likely explanation to this phenomenon was found in the mechanical characteristics of the PVC used and to its poor adhesion with the matrix, that resulted in the creation of porosity. However, the mortar prepared contributes to the conservation of natural resources and maintains mechanical properties adequate for the use in non-structural applications (e.g. screed or substrate)

Polyvinyl butyral-based composites with carbon nanotubes: Efficient dispersion as a key to high mechanical properties

Even if the carbon nanotubes (CNTs) and their derivatives are commonly used as reinforcing phase in composite materials, also in commercial products, their tendency to agglomerate generally determines a scarce dispersion, thus not maximizing the effect due to the second phase. In this article, a perfect dispersion of highly entangled nanotubes was achieved by using a very simple approach: exploiting the dispersing effect of a low-cost polymer, polyvinyl butyral (PVB), coupled with standard ultrasound sonication. Several dispersion approaches were tested in order to develop a consistent and widely applicable dispersion protocol. The tape casting technology was subsequently used to produce 100 to 300 μm thick PVB-matrix composite tapes, reinforced by multiwall CNTs dispersed according to the optimized protocol. Their mechanical properties were evaluated, and a simple model was used to demonstrate that the effective dispersion of CNTs is the key to obtain significantly improved properties

Associations between Objectively-measured Acoustic Parameters and Occupational Voice Use among Primary School Teachers☆

Abstract Previous studies on voice disorders among teachers have reported that this multidimensional phenomenon is associated with individual factors, external factors related with the audience and with the type of task and the occupation. This work deals with the long-term monitoring (1 to 4 days) of 31 primary school teachers and with the determination of the relationship between conversational and occupational voice parameters. Statistical analysis was performed to investigate the relationships between voice parameters and room acoustics-related factors