Gorenstein modules of finite length

We study graded modules of finite length over the weighted polynomial ring R=k[x_{1},...,x_{n}], k any field, having a certain strongly selfdual resolution. We give a construction method of these Gorenstein modules via symmetric matrices in divided powers. Our main result is the following equivalence: Let n be an odd integer. A graded R-module of finite length has a selfdual minimal free resolution with a symmetric respectively skew symmetric middle matrix if and only if it can be defined by a symmetric respectively skew symmetric matrix in divided powers. The correspondence depends on the parity of (n-1)/2. We give applications, such as a proof of a conjecture of Eisenbud and Schreyer: Let R be trivially weighted. The monoid of Betti tables of free resolutions of graded Cohen-Macaulay modules over R depends on the characteristic of the base field k.Wir betrachten graduierte Moduln endlicher Länge über dem gewichteten Polynomring R=k[x_{1},...,x_{n}], k ein beliebiger Körper, die eine streng selbstduale Auflösung haben. Wir entwickeln eine Konstruktionsmethode für diese Gorenstein Moduln mit Hilfe symmetrischer Matrizen in dividierten Potenzen. Unser Hauptresultat ist die folgende Äquivalenz: Sei n eine ungerade natürliche Zahl. Ein graduierter R-Modul endlicher Länge besitzt eine selbstduale minimale freie Auflösung mit symmetrischer beziehungsweise schiefsymmetrischer mittlerer Matrix genau dann wenn er durch eine symmetrische beziehungsweise schiefsymmetrische Matrix in dividierten Potenzen definiert werden kann. Diese Korrespondenz hängt von der Parität von (n-1)/2 ab. Wir entwickeln eine Reihe von Anwendungen, zum Beispiel einen Beweis einer Vermutung von Eisenbud und Schreyer: Sei R nun der trivial gewichtete Polynomring. Der Monoid der Betti Diagramme von freien Auflösungen graduierter Cohen-Macaulay Moduln über R hängt von der Charakteristik des Grundkörpers k ab

Improved Direction of Arrival Estimation using Multiple Signal Classification (MUSIC) Algorithm with Decomposition and Normalization

It is important to determine the direction of arrival (DoA) of targets in various applications such as radar and sonar. Multiple Signal Classification (MUSIC), Estimation of Signal Parameters with Rotational In variance Technique (ESPRIT), and Weighted Subspace Fitting (WSF) are subspace-based methods that can be used to improve DoA estimation. MUSIC is effective for high-resolution, uncorrelated signals, but may struggle in cases where there are two nearby targets with a low signal-to-noise ratio (SNR). The goal of this research is to improve the performance of the MUSIC algorithm for DoA estimation with low SNR signals. The proposed solution involves decomposing and normalizing the signal during transmission. Simulations were conducted to test the modified procedure with MUSIC algorithm for DoA estimation, and it was found that received signal power improved though there is noisy environment as well as system can detect more number of targets. The proposed technique of decomposition and normalization could also be applied in other areas such as WiFi communication, autonomous vehicles and biomedical signal and image processing etc

Framework for reversible data hiding using cost-effective encoding system for video steganography

Importances of reversible data hiding practices are always higher in contrast to any conventional data hiding schemes owing to its capability to generate distortion free cover media. Review of existing approaches on reversible data hiding approaches shows variable scheme mainly focussing on the embedding mechanism; however, such schemes could be furthermore improved using encoding scheme for optimal embedding performance. Therefore, the proposed manuscript discusses about a cost-effective scheme where a novel encoding scheme has been used with larger block sizes which reduces the dependencies over larger number of blocks. Further a gradient-based image registration technique is applied to ensure higher quality of the reconstructed signal over the decoding end. The study outcome shows that proposed data hiding technique is proven better than existing data hiding scheme with good balance between security and restored signal quality upon extraction of data

Performance Driven FPGA Design Analysis with ASIC Perspective of Vector Quantization

AbstractThe paper presents and analysis two different approaches for the design of modular and optimized Vector Quantisation (VQ) architectural blocks for the generation of the winner Index from a set of Code vectors giving the best match to the input image vector. The two proposed methods are then analysed for area, logical and routing delays and the ease of redesign to suit specific requirements on the FPGA platform. If an FPGA design need be ported to an ASIC at a later stage it is also important to take this into account early in the design cycle so that the ASIC porting will be efficient. The structured and hierarchically design of VQ lead to the consideration of the dedicated parallel architectures in two ways, in the direction of Codebook size ‘N’ and the vector dimension ‘K’, that process with high efficiency. Flexibility in terms of Codebook size expansion and Input vector dimension makes the new design fast to re-configure and meet the specific and challenging needs of a single functioned, tightly constrained and real time VQ encoder. The soft IP core design was targeted on to Xilinx Virtex-5. Simulation result analyses indicate that the design with parallelism only in the direction of the codebook size ‘N’ gives the desirable performance and is cost effective even for an ASIC implementation performed in Cadence tool. The design satisfies the performance requirements of for a real time image processing. Reconfiguring the codebook size and vector dimension makes redesign simpler to suit applications requirements but at the cost of re-synthesis and is capable of even multiplexed image transmission due to reduction in the Bandwidt

Design and test of a 10kW ORC supersonic turbine generator

Manufactures are searching for possibilities to increase the efficiency of combustion engines by using the remaining energy of the exhaust gas. One possibility to recover some of this thermal energy is an organic Rankine cycle (ORC). For such an ORC running with ethanol, the aerothermodynamic design and test of a supersonic axial, single stage impulse turbine generator unit is described. The blade design as well as the regulation by variable partial admission is shown. Additionally the mechanical design of the directly coupled turbine generator unit including the aerodynamic sealing and the test facility is presented. Finally the results of CFD-based computations are compared to the experimental measurements. The comparison shows a remarkably good agreement between the numerical computations and the test data.Forschungsvereinigung Verbrennungskraftmaschinen e.V. (FVV)Forschungsvereinigung Antriebstechnik e.V. (FVA)Antriebstechnik und Entwicklungs GmbHSchaeffler, Herzogenaurauch/GermanyBarden Corp, Plymouth/UKSieb & Meyer, Lueneburg/German

The effect of CSF drain on the optic nerve in idiopathic intracranial hypertension

Background: Elevation of intracranial pressure in idiopathic intracranial hypertension induces an edema of the prelaminar section of the optic nerve (papilledema). Beside the commonly observed optic nerve sheath distention, information on a potential pathology of the retrolaminar section of the optic nerve and the short-term effect of normalization of intracranial pressure on these abnormalities remains scarce. Methods: In this exploratory study 8 patients diagnosed with idiopathic intracranial hypertension underwent a MRI scan (T2 mapping) as well as a diffusion tensor imaging analysis (fractional anisotropy and mean diffusivity). In addition, the clinical presentation of headache and its accompanying symptoms were assessed. Intracranial pressure was then normalized by lumbar puncture and the initial parameters (MRI and clinical features) were re-assessed within 26 h. Results: After normalization of CSF pressure, the morphometric MRI scans of the optic nerve and optic nerve sheath remained unchanged. In the diffusion tensor imaging, the fractional anisotropy value was reduced suggesting a tissue decompression of the optic nerve after lumbar puncture. In line with these finding, headache and most of the accompanying symptoms also improved or remitted within that short time frame. Conclusion: The findings support the hypothesis that the elevation of intracranial pressure induces a microstructural compression of the optic nerve impairing axoplasmic flow and thereby causing the prelaminar papilledema. The microstructural compression of the optic nerve as well as the clinical symptoms improve within hours of normalization of intracranial pressure