Motivated by entanglement-assisted quantum error-correcting codes, where the hull dimension determines the number of required pre-shared entangled pairs, we study hulls of two families of 𝔽_q-linear codes defined by q-polynomial operators over 𝔽_q^m. Our main tool is a unified Gram-matrix method. For image codes 𝒞()=imΦ_, with Φ_=∑_iα_iF_i, we prove the master hull–rank formula Hull(𝒞())=rank(Φ_)-rank(G()), where G() is the associated Gram matrix over 𝔽_q. Specializing to C_λ,μ=im(λx+μL(x)), we obtain a quadratic Gram pencil λ^2G_0+λμG_1+μ^2G_2 whose determinant describes the LCD locus in ℙ^1(𝔽_q). We also treat 𝔽_q^m-linear rank-distance codes 𝒞=⟨ X,F_1,…,F_k⟩_𝔽_q^m with the Delsarte inner product, where a k× k Gram matrix over 𝔽_q^m determines the hull dimension. For L(X)=X^q^k, with d=(k,m), the resulting circulant Gram matrices yield a closed-form discriminant and a complete classification in three of the four bijectivity configurations over ℙ^1(𝔽_q^m). In the remaining case, the hull dimension equals δ=_𝔽_q(imϕ_λ,μ∩_λ,μ^†), and the extremal condition δ=d is characterized by an explicit trace-isotropy criterion. We conclude with an exact count of LCD and non-LCD points, showing that the LCD density tends to 1 as q→∞, together with a worked example over 𝔽_64 and a SageMath verification.
In this paper, we analyze a linearized model for incompressible transversely isotropic dispersive fiber-reinforced materials in which both the elastic and dispersive properties depend on the direction of the fibers. We investigate the motions in bodies made of these materials that are subjected to prescribed shear or normal action on part of the rigid boundaries. In the case where the motion is induced by shear stresses acting at the boundary, we provide the analytical solution for the displacement field from which we derive the components of the stress tensor. In the case where the motion is due to the action of normal stresses at the boundary, the initial and boundary value problem is solved using a projection algorithm based on spectral methods. In both cases, we quantify how anisotropic dispersion and material stiffness affect the displacement field.
The present guideline summarizes all aspects of patch testing for the diagnosis of contact allergy in patients suspected of suffering, or having been suffering, from allergic contact dermatitis or other delayed-type hypersensitivity skin and mucosal conditions. Sections with brief descriptions and discussions of different pertinent topics are followed by a highlighted short practical recommendation. Topics comprise, after an introduction with important definitions, materials, technique, modifications of epicutaneous testing, individual factors influencing the patch test outcome or necessitating special considerations, children, patients with occupational contact dermatitis and drug eruptions as special groups, patch testing of materials brought in by the patient, adverse effects of patch testing, and the final evaluation and patient counselling based on this judgement. Finally, short reference is made to aspects of (continuing) medical education and to electronic collection of data for epidemiological surveillance.
Hermetia illucens (Diptera: Stratiomyidae), also known as black soldier fly (BSF), offers an important sustainable approach to waste management and resource recovery, since its larvae can reduce organic waste volumes, transform them into biomass, and generate protein-rich feed, biodiesel precursors, and organic fertilizers. Despite the abundance of information on its larval stage, the reproductive biology of the adult is still poorly understood. The present study, through behavioural tests, cryo-scanning electron microscopy analysis and centrifugal force tester experiments, deepens the knowledge on the mechanical interaction between male tarsi and the body of conspecifics during mating and competition, describes the sexual dimorphism in BSF tarsal attachment devices and provides information on the attachment ability of both sexes to artificial surfaces with different features in terms of roughness and wettability. Further studies comparing adult behaviour in rearing conditions and in the wild are necessary to optimise BSF mass-rearing facilities.
The use of appropriate models for environmental decision-making is crucial for supporting soil conservation strategies, particularly in erosion-prone systems such as Mediterranean basins. In this study, the suitability of the Sediment Delivery Distributed (SEDD) model at the event scale was evaluated in a 231 ha basin in Central Italy, where rainfall-runoff-sediment yield data from four erosive events were available. The model was applied by subdividing the basin into morphological units, defined as areas with uniform aspect, length, and slope steepness. Model parameterization involved the estimation of a single coefficient, beta(e), embedded in the sediment delivery ratio of each morphological unit. The variability of beta(e) with rainfall-runoff event intensity was analysed. The resulting relationship reflects the physical mechanism whereby sediment transport along hillslopes becomes more efficient as event intensity increases, as represented by the runoff coefficient Q(R). Analysis of the empirical cumulative frequency distribution of the sediment delivery ratio for each morphological unit suggests that the influence of the runoff coefficient on beta(e) may vanish during the most erosive events. Under this hypothesis, for Q(R) > 0.15, the variability of sediment delivery processes is governed solely by the structural component of sediment connectivity, while the functional component becomes invariant and characteristic of the investigated basin.
