| 1. |
- Maligranda, Lech
(författare)
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Some remarks on the triangle inequality for norms
- 2008
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Ingår i: Banach Journal of Mathematical Analysis. - : Springer Science and Business Media LLC. - 1735-8787. ; 2:2, s. 31-41
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Tidskriftsartikel (refereegranskat)abstract
- Remarks about strengthening of the triangle inequality and its reverse inequality in normed spaces for two and more elements are collected. There is also a discussion on Fischer-Musz´ely equality for n-elements in a normed space. Some other estimates which follow from the triangle inequality are also presented.
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| 2. |
- Hyun, Sang-Min, et al.
(författare)
-
Preparation, characterization, and evaluation of celecoxib eutectic mixtures with adipic acid/saccharin for improvement of wettability and dissolution rate
- 2019
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Ingår i: International Journal of Pharmaceutics. - : Elsevier. - 0378-5173 .- 1873-3476. ; 554, s. 61-71
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Tidskriftsartikel (refereegranskat)abstract
- Celecoxib (CEL) is a selective cyclooxygenase-2 (COX-2) inhibitor therapeutically indicated for the treatment of rheumatoid arthritis, osteoarthritis, acute pain, and inflammation. However, its poor solubility and dissolution rate significantly hinders its broader application. In this study, eutectic mixtures, as binary pharmaceutical compositions of CEL with adipic acid (ADI) and saccharin (SAC), were identified through a phase diagram and Tammann’s triangle intended to improve the wettability and dissolution rate of poorly water-soluble CEL. The contact angles at 0s in the liquid-solid interface were approximately θs (theta) 79.7° ± 0.50° and 86.65° ± 0.45° for CEL-ADI and CEL-SAC, respectively, which were much lower than the value obtained for CEL (92.05° ± 0.75° θ). Moreover, a comparison of the disk intrinsic dissolution rate and powder dissolution properties demonstrated that eutectic mixtures significantly increased the dissolution rate compared with CEL and physical mixtures. A general relationship was elucidated and indicated that the dissolution rate was increased as the contact angle decreased (correlation coefficient, r = 0.9966 ± 0.0031). Therefore, CEL-ADI and CEL-SAC eutectics may offer a novel formulation strategy to enhance the solubility and oral bioavailability of CEL.
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| 3. |
- Maligranda, Lech
(författare)
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A simple proof of the real Riesz–Thorin interpolation theorem in the lower triangle
- 2023
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Ingår i: Colloquium Mathematicum. - : Institut Matematyczny Polskiej Akademii Nauk. - 0010-1354 .- 1730-6302. ; 172:1, s. 99-103
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Tidskriftsartikel (refereegranskat)abstract
- A simple proof of the real Riesz–Thorin interpolation theorem for operators of strong types (p0, q0) and (∞, ∞) in the lower triangle, that is, if 0 < p0 ≤ q0 < ∞ with the best estimate of the norms is presented.
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| 4. |
- Holmes, Thomas P., et al.
(författare)
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Fundamental Economic Irreversibilities Influence Policies for Enhancing International Forest Phytosanitary Security
- 2017
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Ingår i: Current Forestry Reports. - Cham : Springer. - 2198-6436. ; 3:3, s. 244-254
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Tidskriftsartikel (refereegranskat)abstract
- National and international efforts to manage forest biosecurity create tension between opposing sources of ecological and economic irreversibility. Phytosanitary policies designed to protect national borders from biological invasions incur sunk costs deriving from economic and political irreversibilities that incentivizes wait-and-see decision-making. However, the potential for irreversible ecological and economic damages resulting from failed phytosanitary policies argues for precautionary measures, creating sunk benefits while increasing the risk of over-investment in phytosanitary security. Here, we describe the inherent tension between these sources of irreversibility in economic terms, relate these forces to type I and type II errors, and use this framework to review national and international efforts to protect forests from biological invasions. Available historical evidence suggests that wait-and-see phytosanitary decision-making has dominated the adoption of precautionary measures in most regions and that willingness to under-regulate may sometimes be orders of magnitude greater than willingness to over-regulate. Reducing scientific uncertainty about threats to biosecurity may help mitigate the tendency to under-regulate, and phytosanitary security measures with relatively modest sunk costs could help protect forests as scientific learning advances. A fuller accounting of the costs associated with type II errors, particularly regarding the suite of non-market ecosystem services at risk, would help decision-makers better understand the trade-offs between the sunk costs of policies and long-term economic losses to stakeholders.
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| 5. |
- Barza, Sorina, et al.
(författare)
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Optimal estimates in lorentz spaces of sequences with an increasing weight
- 2013
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Ingår i: Proceedings of the Romanian Academy. - 1454-9069. ; 14:1, s. 20-27
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Tidskriftsartikel (refereegranskat)abstract
- We study the weighted Lorentz spaces of sequences to find optimal estimates between different equivalent quasi-norms. We also obtain the best constant in the triangle inequality.
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| 6. |
- Barza, Sorina, 1967-, et al.
(författare)
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Best constants between equivalent norms in Lorentz sequence spaces
- 2012
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Ingår i: Journal of Function Spaces and Applications. - : Hindawi Limited. - 0972-6802 .- 1758-4965. ; 2012
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Tidskriftsartikel (refereegranskat)abstract
- We find the best constants in inequalities relating the standard norm, the dual norm, and the norm ‖ 푥 ‖ ( 푝 , 푠 ) ∑ ∶ = i n f { 푘 ‖ 푥 ( 푘 ) ‖ 푝 , 푠 } , where the infimum is taken over all finite representations ∑ 푥 = 푘 푥 ( 푘 ) in the classical Lorentz sequence spaces. A crucial point in this analysis is the concept of level sequence, which we introduce and discuss. As an application, we derive the best constant in the triangle inequality for such spaces.
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| 7. |
- Klisinski, Marek, et al.
(författare)
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Discussion on application of piece-wise linear weight functions in 2D contact problems
- 2003
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Ingår i: Computer Assisted Mechanics and Engineering Sciences. - 1232-308X. ; 10:3, s. 321-337
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Tidskriftsartikel (refereegranskat)abstract
- Standard higher order finite elements often perform unsatisfactory in contact problems. The major difficulties are caused by uneven distribution of nodal forces resulting in oscillating contact pressures. The paper presents a new approach that eliminates this drawback. The weight functions are chosen in such a way that even distributions of nodal forces are obtained. It is achieved by applying piece-wise linear functions. Two new 2D isoparametric quadratic elements are derived: 6-node triangle and 8-node quadrilateral, and tested in many examples. The new elements have unsymmetric stiffness matrices, but the provided examples show their good performance in contact problems
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| 8. |
- Doggett, Michael, et al.
(författare)
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Adaptive view dependent tessellation of displacement maps
- 2000
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Ingår i: Proceedings, 2000 SIGGRAPH/EUROGRAPHICS Workshop on Graphics Hardware, Interlaken, Switzerland, August 21-22, 2000. - New York : Association for Computing Machinery (ACM). - 1581132573 ; , s. 59-66
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Konferensbidrag (refereegranskat)abstract
- Displacement Mapping is an effective technique for encoding the high levels of detail found in today's triangle based surface models. Extending the hardware rendering pipeline to be capable of handling displacement maps as geometric primitives, will allow highly detailed models to be constructed without requiring large numbers of triangles to be passed from the CPU to the graphics pipeline. We present a new approach based on recursive tessellation that adapts to the surface complexity described by the displacement map. We also ensure that the resolution of the displaced mesh is tessellated with respect to the current view point. Our tessellation scheme performs all tests only on triangle edges to avoid generating cracks on the displaced surface. The main decision for vertex insertion is based on two comparisons involving the average height surrounding the vertices and the normals at the vertices. Individually, the tests will fail to tessellate a mesh satisfactorily, but their combination achieves good results. We propose several additions to the typical hardware rendering pipeline in order to achieve displacement map rendering in hardware. The mesh tessellation is placed within the rendering pipeline so that we can take advantage of the pre-existing vertex transformation units to perform the setup calculations for our view dependent test. Our method adds only simple arithmetic and comparison operations to the graphics pipeline and makes use of existing units for calculations wherever possible
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| 9. |
- Hirche, Johannes, et al.
(författare)
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Hardware accelerated per-pixel displacement mapping
- 2004
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Ingår i: Graphics Interface 2004. - : A K Peters. - 1568812272 ; , s. 153-158
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Konferensbidrag (refereegranskat)abstract
- In this paper we present an algorithm capable of rendering a displacement mapped triangle mesh interactively on latest GPUs. The algorithm uses only pixel shaders and does not rely on adaptively adding geometry. All sampling of the displacement map takes place in the pixel shader and bi- or trilinear ltering can be applied to it, and at the same time as the calculations are done per pixel in the shader, the algorithm has automatic level of detail control. The triangles of the base mesh are extruded along the respective normal directions and then the resulting prisms are rendered by casting rays inside and intersecting them with the displaced surface. Two different implementations are discussed in detail.
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| 10. |
- Amor, Margarita, et al.
(författare)
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A meshing scheme for efficient hardware implementation of butterfly subdivision using displacement mapping
- 2005
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Ingår i: IEEE Computer Graphics and Applications. - 0272-1716 .- 1558-1756. ; 25:2, s. 46-59
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Tidskriftsartikel (refereegranskat)abstract
- Displacement mapping is an effective technique for encoding the high levels of detail of surface models using coarse triangle meshes and displacement maps. These maps are 2D representations containing the distances between the coarse mesh and the surface to represent. Displacement maps have been used in many applications such as ray tracing, image warping, and volume rendering. In this article, we propose modifications to our previous grouping strategy, a new subdivision strategy based on the Modified Butterfly algorithm and new heuristics for the adaptive subdivision procedure, and, finally, the corresponding modifications on our hardware proposal. A meshing scheme and an adaptive subdivision strategy based on displacement mapping reduce the bottleneck between the CPU and graphics pipeline common in high-performance graphics systems.
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