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Abstract

In [4], Császár has introduced the notions of weak structures and the structures α(w), π(w), σ(w), β(w). The main aim of this paper is to introduce and study properties of the structures r(w), α(w), π(w), σ(w) and β(w).

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Abstract

We define weak structures and show that these structures can replace in many situations generalized topologies or minimal structures.

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Abstract  

The properties of biologically active glasses in the system SiO2−P2O5−MgO−CaO were studied. Crystalline hydroxyapatite (HA) and β-wollastonite (β-W) were used after heat treatment (1100C). The influence of the glass particle size (0.071–2.5 mm) and of glass powder (d 50=15.1 μm) on the behaviour of the products during differential thermal analysis was followed. These analyses indicated that the β-W probably originates from surface nucleation, and HA from bulk nucleation. The differentiation was confirmed by calculation of the Avrami parameters (n) with the Pi-loyan-Borchardt analytical method. For HA and β-W, the calculated values ofn were 2.96 and 1.91. The surface-nucleated glasses exhibited predominant bidimensional crystal growth.

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Abstract  

The aim of the present work was to provide arguments to the almost ‘hystorical’ problem of what β-tungsten is. WO3was reduced in dry H2gas atmosphere in order to examine, whether β-tungsten formed in such a way contains oxygen as part of the lattice described as WxO (e.g. W20O) or is a pure metallic phase of tungsten. As a result of thermoanalytical measurements and of chemical analysis for oxygen, the assumption is supported that in the 600-800C temperature range of metal formation not the WxO (β-W)→W(α-W) transformation but the β-W→α-W structural rearrangement of materials with identical chemical composition is the most probable process. The earlier opinion that the formation of the β-W structure requires the presence of oxygen atoms was not verified by our results.

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Abstract  

Let X represent either the space C[-1,1] L p (α,β) (w), 1 ≦ p < ∞ on [-1, 1]. Then Xare Banach spaces under the sup or the p norms, respectively. We prove that there exists a normalized Banach subspace X 1 αβ of Xsuch that every f ∈ X 1 αβ can be represented by a linear combination of Jacobi polynomials to any degree of accuracy. Our method to prove such an approximation problem is Fourier–Jacobi analysis based on the convergence of Fourier–Jacobi expansions.

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cointegrating vector β w t − 1 ( β ) = β ' x t − 1 – error-correction term that needs to be stationary γ – threshold parameter Our paper observes bivariate ( p =   2 ) case of exports and imports in Romania, so Δ x t = [ Δ log ( X )   Δ log ( M ) ] . All

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