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Let A be a commutative noetherian non-positive DG-ring, ̄ an ideal of Ā : = H 0 (A) , and M ∈ D (A). In this paper, we introduce the notion of cohomological dimension of DG-modules and investigate the interplay between cd A ( ̄ , M) : = sup { cd Ā ( ̄ , H n (M)) + n | n ∈ ℤ } and sup R Γ ̄ (M). It is shown that cd A ( ̄ , M) = sup R Γ ̄ (M) for any 0 ≇ M ∈ D f − (A). As an application, we recover a DG-version of Grothendieck's vanishing and non-vanishing theorems for local cohomology. We also study the cohomological dimension of Koszul DG-modules and get some interesting results. [ABSTRACT FROM AUTHOR]

This paper introduces the notion of depth with respect to ideals for unbounded DG-modules, and gives a reduction formula and the local nature of this depth. As applications, we provide several bounds of the depth in special cases, and recover and generalize the known results about the depth of complexes. In addition, the width with respect to ideals for unbounded DG-modules is investigated and the depth and width formulas for DG-modules are generalized. [ABSTRACT FROM AUTHOR]

A series of N-isopropylacrylamide (NIPAAm) copolymer gels with different hydrophilicities were prepared from NIPAAm, hydrophilic acrylamide (AAm) and hydrophobic butyl methacrylate (BMA). The swelling and thermo-responsive properties of PNIPAAm P (NIPAm-co-BMA) and P(NIPAm- co-AAm) copolymer hydrogels were investigated. The drug loading and releasing behaviors for two kinds of model drug with different hydrophilicities were studied. The result shows that the copolymer gels present negative thermo-sensitivities. The lower critical solution temperature (LCST), equilibrium swelling degree and the initial swelling rate increase as the hydrophilicity of gels increases when the temperature is below the LCST. With increasing gel hydrophilicity the loading ratio for sodium salicylate increases, while for salicylic acid, the reverse is observed. The initial drug releasing rate of sodium salicylate and salicylic acid also increase with increasing gel hydrophilicity. The initial drug releasing rate of sodium salicylate is significantly higher than that of salicylic acid. For salicylic acid which is less hydrophilic, the equilibrium releasing ratio at high temperature is lower than that at low temperature while for sodium salicylate which is more hydrophilic, the equilibrium releasing ratio at high temperature is almost the same as that at low temperature. Equilibrium releasing ratios of the three gels are significantly different from each other for salicylic acid when the temperature is below LCST while the equilibrium releasing ratios of the three gels are all 100% for sodium salicylate. [ABSTRACT FROM AUTHOR]