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  • exponential decay  (2)
  • saponite  (2)
  • Springer  (4)
  • 1995-1999  (4)
  • 1950-1954
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Publisher
  • Springer  (4)
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Year
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Acta applicandae mathematicae 50 (1998), S. 207-224 
    ISSN: 1572-9036
    Keywords: viscoelasticity ; exponential decay ; initial boundary-value problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider the anisotropic and inhomogeneous thermo-viscoelastic equation. We prove that the first and second-order energy decay exponentially as time goes to infinity provided the relaxation function also decays exponentially to zero. While if the relaxation functions decay polynomially to zero, then the energy decays also polynomially. That is, the kernel of the convolution defines the rate of decay of the solution.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of inclusion phenomena and macrocyclic chemistry 31 (1998), S. 219-230 
    ISSN: 1573-1111
    Keywords: ethyl 2-oxocyclopentanecarboxylate ; saponite ; interlayer compounds
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The retention of ethyl 2-oxocyclopentanecarboxylate by a saponite has been studied. Intercalation compounds were prepared by two different methods: 1) in repose at room temperature and 2) heating at 60 °C under reflux. Contact times between 2 and 12 days were considered for each method. The intercalation compounds obtained were characterized by X-ray diffraction, infrared spectroscopy, chemical analyses and thermal analyses. This characterization indicates that the organic compound is retained both in the interlayer region and at the edge of the clay particles. The amount retained outside of the interlayer space is eliminated by careful washing with benzene and cyclohexane. The results obtained when using acid-activated saponite -obtained by treatment of the clay with dilute HCl solutions- in the intercalation experiments were similar to those obtained when using non-activated saponite.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of porous materials 6 (1999), S. 335-344 
    ISSN: 1573-4854
    Keywords: saponite ; acid treatment ; surface area ; porosity ; acid centres
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A new deposit of saponite, Vicálvaro (Madrid, Spain), has recently been described in the Madrid Basin (provinces of Madrid and Toledo, Central Spain). The acid treatment of such material and the characterization of the solids obtained are reported in the present paper. The surface area of the natural saponite is rather high, 197 m2/g, related to the very small size of the clay particles due to the sedimentary origin of the deposit. The treatment of the saponitic material at room temperature with 0.62 wt% HCl for times of between 2 and 48 h or with 1.25 wt% HCl solutions for times of up to 6 h produces a partial dissolution of the saponite structure, resulting in the formation of mixtures of unattacked saponite and free silica, with a high development of the textural properties of the solids. The treatment with 1.25 wt% HCl solutions for times of over 6 h results in an almost total dissolution of the structure of the clay, the obtained solids being mainly formed by some delaminated saponite sheets, free silica and insoluble impurities. Solids with a maximum surface area of 462 m2/g and a maximum number of acid centres of 0.98 mmol H+/g are obtained.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Journal of elasticity 44 (1996), S. 61-87 
    ISSN: 1573-2681
    Keywords: 35B40 ; 35L05 ; 35L70 ; viscoelasticity ; exponential decay ; initial boundary value problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract We consider the viscoelastic plate equation and we prove that the first and second order energies associated with its solution decay exponentially provided the kernel of the convolution also decays exponentially. When the kernel decays polynomially then the energy also decays polynomially. More precisely if the kernel g satisfies g(t) ⩽ -c0g(t)1+1/p and g,g1+1/p ∈ L1(ℝ) with p 〉 2, then the energy decays as 1/(1+t)p.
    Type of Medium: Electronic Resource
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