We determine the best possible constants θ,ϑ,a and b such that the inequalities 2 + cos x 3 θ < sin x x < 2 + cos x 3 ϑ and π 2 π 2 − 4x 2 α < tan x x < π 2 π 2 − 4x 2 β are valid for 0 < × < π/2. Our results sharpen inequalities presented by Cusa, Becker and Stark.

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We report on the synthesis of a porous hierarchical disklike ZnO nanostructure fabricated via a simple low-temperature hydrothermal method for photovoltaic applications. The hierarchical ZnO nanostructures consist of porous ZnO nanowires growing in six symmetric directions and form a disklike shape. Owing to the enlarged surface area and natural electron collection routes of the ZnO hierarchical nanostructures, dye-sensitized solar cells based on these structures exhibit improved photovoltaic performance compared with that of the ZnO nanowire arrays. Our results suggest that porous hierarchical nanomaterials are promising materials for applications in dye-sensitized solar cells.

Background/Aims: The apolipoprotein E (ApoE) exon 4 polymorphism has been associated with vascular dementia (VaD) risk. Since not all studies confirm this finding, we explored this association in a case-control study. Methods: We genotyped ApoE in 144 VaD patients and 251 controls. Results: VaD patients were more likely than controls to have ApoE Ε3/Ε4 or Ε4/Ε4 genotypes: 23.6% versus 15.1%, odds ratio (OR) = 1.7, p = 0.036. This association remained significant after adjustment for age, sex, hypertension and diabetes by multiple logistic regression: OR = 1.9, p = 0.030. The association of Ε3/Ε4 or Ε4/Ε4 genotypes with VaD was strong among people with hypertension (OR = 2.9, p = 0.007) or diabetes (OR = 6.5, p = 0.011). The association was absent among people without hypertension (OR = 1.1, p = 0.79) or diabetes (OR = 1.3, p = 0.43). Conclusion: This interaction with hypertension and diabetes should be examined in other studies to confirm or refute this observation.

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The classical Bohr's inequality states that |z + w| 2 p|z| 2 + q|w| 2 for all z, w ∈ C and all p, q > 1 with 1 p + 1 q = 1. In this paper, Bohr's inequality is generalized to the context of Hilbert space operators for all positive conjugate exponents p, q ∈ R. In particular, the parallelogram law is recovered and some other interesting operator inequalities and established.

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Poly (methyl methacrylate) (PMMA) bone cement is widely used in vertebral body augmentation procedures such as vertebroplasty and balloon kyphoplasty. Filling high modulus PMMA increases the modulus of filled verterbra, increasing the risk of fracture in the adjacent vertebra. On the other hand, in porous PMMA bone cements, wear particle generation and deterioration of mechanical performance are the major drawbacks. This study adopts a new approach by utilizing linoleic acid coated strontium substituted hydroxyapatite nanoparticle (Sr-5 HA) and linoleic acid as plasticizer reducing bone cement's modulus with minimal impact on its strength. We determined the compressive strength (UCS) and modulus (Ec), hydrophobicity, injectability, in vitro bioactivity and biocompatibility of this bone cement at different filler and linoleic acid loading. At 20 wt % Sr5-HA incorporation, UCS and Ec were reduced from 63 ± 2 MPa, 2142 ± 129 MPa to 58 ± 2 MPa, 1785 ± 64 MPa, respectively. UCS and Ec were further reduced to 49 ± 2 MPa and 774 ± 70 MPa respectively when 15 v/v of linoleic acid was incorporated. After 7 days of incubation, pre-osteoblast cells (MC3T3-E1) attached on 20 wt % Sr5-HA and 20 wt % Sr5-HA with 15 v/v of linoleic acid group were higher (3.73 ± 0.01 x 10⁴, 2.27 ± 0.02 x 10⁴) than their PMMA counterpart (1.83 ± 0.04 x 10⁴). Incorporation of Sr5-HA with linoleic acid in monomer phase is more effective in reducing the bone cement's stiffness than Sr5-HA alone. Combination of low stiffness and high mechanical strength gives the novel bone cement the potential for use in vertebroplasty cement applications.