A generalization of a half-discrete Hilbert's inequality

Considering some parameters and by means of an inequality of Hadamard, we derive general half-discrete Hilbert-type inequalities. Then we highlight some special cases.Comment: This paper has been withdrawn by the author due to a conflict with my institute regulation

A Hardy space analysis of the B\'aez-Duarte criterion for the RH

In this article, methods from sub-Hardy Hilbert spaces such as the de Branges-Rovnyak spaces and local Dirichlet spaces are used to investigate B\'aez-Duarte's Hilbert space reformulation of the Riemann hypothesis (RH).Comment: 11 pages, final version, some typos on page 6 correcte

Iterative Method to Derive the Equivalent Centrifugal Compressor Performance at Various Operating Conditions: Part I: Modelling of Suction Parameters Impact

This paper introduces a new iterative method to predict the equivalent centrifugal compressor performance at various operating conditions. The presented theoretical analysis and empirical correlations provide a novel approach to derive the entire compressor map corresponding to various suction conditions without a prior knowledge of the detailed geometry. The efficiency model was derived to reflect the impact of physical gas properties, Mach number, and flow and work coefficients. One of the main features of the developed technique is the fact that it considers the variation in the gas properties and stage efficiency which makes it appropriate with hydrocarbons. This method has been tested to predict the performance of two multistage centrifugal compressors and the estimated characteristics are compared with the measured data. The carried comparison revealed a good matching with the actual values, including the stable operation region limits. Furthermore, an optimization study was conducted to investigate the influences of suction conditions on the stage efficiency and surge margin. Moreover, a new sort of presentation has been generated to obtain the equivalent performance characteristics for a constant discharge pressure operation at variable suction pressure and temperature working conditions. A further validation is included in part two of this study in order to evaluate the prediction capability of the derived model at various gas compositions

An Iterative Method to Derive the Equivalent Centrifugal Compressor Performance at Various Operating Conditions: Part II: Modeling of Gas Properties Impact

This is the second part of a study conducted to model the aerothermodynamic impact of suction parameters and gas properties on a multi-stage centrifugal compressor’s performance. A new iterative method has been developed in the first part to derive the equivalent performance at various operating conditions. This approach has been validated to predict the compressor map at different suction pressures and temperatures using the design characteristics as reference values. A further case is included in this paper in order to emphasize the validity of the developed approach to obtain the performance characteristics at various gas compositions. The provided example shows that the performance parameters at different gas mixtures can be predicted to within ±1.34%. Furthermore, the conducted optimization in this paper reveals that the proposed method can be applied for the compressor design evaluation corresponding to the expected variation in suction conditions. Moreover, the examined case study demonstrates the effect of gas properties’ variation on the operating point and aerodynamic stability of the entire compression system. In order to achieve that, a simple approach has been established to assess the contribution of gas properties’ variation to the inefficient and unstable compressor performance based on the available operational data