Spectral bounds for infinite dimensional polydiagonal symmetric matrix operators on discrete spaces

In this thesis, we prove a variety of discrete Agmon Kolmogorov inequalities and apply them to prove Lieb Thirring inequalities for discrete Schrodinger operators on ℓ[superscript 2](ℤ). We generalise these results in two ways: Firstly, to higher order difference operators, leading to spectral bounds for Tri-, Penta- and Polydiagonal Jacobi-type matrix operators. Secondly, to ℓ[superscript 2]-spaces on higher dimensional domains, specifically on ℓ[superscript 2](ℤ[superscript 2]), ℓ[superscript 2](ℤ[superscript 3]) and finally ℓ[superscript 2](ℤ[superscript d]). In the Introduction we discuss previous work on Landau Kolmogorov inequalities on a variety of Banach Spaces, Lieb Thirring inequalities in ℓ[superscript 2](ℝ[superscript d]), and the use of Jacobi Matrices in relation to the discrete Schrodinger Operator. We additionally give our main results with some introduction to the notation at hand. Chapters 2, 3 and 4 follow a similar structure. We first introduce the relevant difference operators and examine their properties. We then move on to prove the Agmon Kolmogorov and Generalised Sobolev inequalities over ℤ of order 1, 2 and σ respectively. Furthermore, we prove the Lieb Thirring inequality for the respective discrete Schrodinger-type operators, which we subsequently lift to arbitrary moments. Finally we apply this inequality to obtain spectral bounds for tri-, penta- and polydiagonal matrices. In Chapter 5, we prove a variety of Agmon Kolmogorov inequalities on ℓ[superscript 2](ℤ[superscript 2]) and ℓ[superscript 2](ℤ[superscript 3]). We use these intuitive ideas to obtain 2[superscript d-1] Agmon Kolmogorov inequalities on ℓ[superscript 2](ℤ[superscript d]). We continue from here in the same manner as before and prove the discrete Generalised Sobolev and Lieb Thirring inequalities for a variety of exponent combinations on ℓ[superscript 2](ℤ[superscript d]).Open Acces

A study on the relationship between upstream and downstream conditions in swirling two-phase flow

Inline fluid separation is a concept, which is used in the oil and gas industry. Inline fluid separators typically have a static design and hence changing inlet conditions lead to less efficient phase separation. For introducing flow control into such a device, additional information is needed about the relationship of upstream and downstream conditions. This paper introduces a study on this relationship for gas/liquid two-phase flow. The downstream gas core development was analyzed for horizontal device installation in dependence of the inlet gas and liquid flow rates. A wire-mesh sensor was used for determining two-phase flow parameters upstream and a high-speed video camera to obtain core parameters downstream the swirling device. For higher accuracy of the calculated void fraction, a novel method for wire-mesh sensor data analysis has been implemented. Experimental results have shown that void fraction data of the wire-mesh sensor can be used to predict the downstream behavior for a majority of the investigated cases. Additionally, the upstream flow pattern has an impact on the stability of the gas core downstream which was determined by means of experimental data analysis

Controlled inline fluid separation based on smart process tomography sensors

Today's mechanical fluid separators in industry are mostly operated without any control to maintain efficient separation for varying inlet conditions. Controlling inline fluid separators, on the other hand, is challenging since the process is very fast and measurements in the multiphase stream are difficult as conventional sensors typically fail here. With recent improvement of process tomography sensors and increased processing power of smart computers, such sensors can now be potentially used in inline fluid separation. Concepts for tomography‐controlled inline fluid separation were developed, comprising electrical tomography and wire‐mesh sensors, fast and massive data processing and appropriate process control strategy. Solutions and ideas presented in this paper base on process models derived from theoretical investigation, numerical simulations and analysis of experimental data

International Children’s Rights: Reflections on a Complex, Dynamic, and Relatively Young Area of Law

This chapter reflects on the aim of the International Children’s Rights volume to provide those wishing to study, research, and practice international children’s rights law with a contemporary and comprehensive legal text. It recaps on the themes that emerged from the process of commissioning and editing the various contributions from some of the world’s leading and emerging legal scholars in the area of children’s rights. It marks the progress that has been made in the implementation of children’s rights law and the many challenges that still exist in the implementation of the CRC and associated international instruments. It notes that legal scholarship in the field of children’s rights is still developing and that, although multidisciplinary research and analysis is valuable, it is important to reaffirm children’s rights as a field of law and legal practice. International children’s rights is a complex, dynamic, and relatively young area of law. As the contributions to the collection show, it is diverse and evolving, with many new aspects and issues worthy of analysis and scrutiny. This chapter encapsulates the aspiration of the volume editors that the book contribute to the scrutiny of the legal implications of the CRC, recognizing the unique features of international children’s rights law, adding to the ongoing development of this important area of law.Effective Protection of Fundamental Rights in a pluralist worl

Monitoring and Implementation of Children's Rights

Effective Protection of Fundamental Rights in a pluralist worl

Carfilzomib and dexamethasone versus bortezomib and dexamethasone for patients with relapsed or refractory multiple myeloma (ENDEAVOR): And randomised, phase 3, open-label, multicentre study

Background: Bortezomib with dexamethasone is a standard treatment option for relapsed or refractory multiple myeloma. Carfilzomib with dexamethasone has shown promising activity in patients in this disease setting. The aim of this study was to compare the combination of carfilzomib and dexamethasone with bortezomib and dexamethasone in patients with relapsed or refractory multiple myeloma. Methods: In this randomised, phase 3, open-label, multicentre study, patients with relapsed or refractory multiple myeloma who had one to three previous treatments were randomly assigned (1:1) using a blocked randomisation scheme (block size of four) to receive carfilzomib with dexamethasone (carfilzomib group) or bortezomib with dexamethasone (bortezomib group). Randomisation was stratified by previous proteasome inhibitor therapy, previous lines of treatment, International Staging System stage, and planned route of bortezomib administration if randomly assigned to bortezomib with dexamethasone. Patients received treatment until progression with carfilzomib (20 mg/m2 on days 1 and 2 of cycle 1; 56 mg/m2 thereafter; 30 min intravenous infusion) and dexamethasone (20 mg oral or intravenous infusion) or bortezomib (1·3 mg/m2; intravenous bolus or subcutaneous injection) and dexamethasone (20 mg oral or intravenous infusion). The primary endpoint was progression-free survival in the intention-to-treat population. All participants who received at least one dose of study drug were included in the safety analyses. The study is ongoing but not enrolling participants; results for the interim analysis of the primary endpoint are presented. The trial is registered at ClinicalTrials.gov, number NCT01568866. Findings: Between June 20, 2012, and June 30, 2014, 929 patients were randomly assigned (464 to the carfilzomib group; 465 to the bortezomib group). Median follow-up was 11·9 months (IQR 9·3-16·1) in the carfilzomib group and 11·1 months (8·2-14·3) in the bortezomib group. Median progression-free survival was 18·7 months (95% CI 15·6-not estimable) in the carfilzomib group versus 9·4 months (8·4-10·4) in the bortezomib group at a preplanned interim analysis (hazard ratio [HR] 0·53 [95% CI 0·44-0·65]; p<0·0001). On-study death due to adverse events occurred in 18 (4%) of 464 patients in the carfilzomib group and in 16 (3%) of 465 patients in the bortezomib group. Serious adverse events were reported in 224 (48%) of 463 patients in the carfilzomib group and in 162 (36%) of 456 patients in the bortezomib group. The most frequent grade 3 or higher adverse events were anaemia (67 [14%] of 463 patients in the carfilzomib group vs 45 [10%] of 456 patients in the bortezomib group), hypertension (41 [9%] vs 12 [3%]), thrombocytopenia (39 [8%] vs 43 [9%]), and pneumonia (32 [7%] vs 36 [8%]). Interpretation: For patients with relapsed or refractory multiple myeloma, carfilzomib with dexamethasone could be considered in cases in which bortezomib with dexamethasone is a potential treatment option. Funding: Onyx Pharmaceuticals, Inc., an Amgen subsidiary