We show that the Gersten complex for the (improved) Milnor K-sheaf on a smooth scheme over an excellent discrete valuation ring is exact except at the first place and that exactness at the first ...place may be checked at the discrete valuation ring associated to the generic point of the special fibre. This complements results of Gillet-Levine for K-theory, Geisser for motivic cohomology and Schmidt-Strunk and the author for étale cohomology.
Online fountain codes have been proven to require lower overhead and fewer feedbacks than growth codes for successful decoding. In an attempt to improve the intermediate symbol recovery rate, the ...authors propose sending a number of degree-1 input symbols prior to the build-up phase based on a simple application of probability theory. In addition, during the completion phase, received encoded symbols with three neighbouring white (un-decoded) symbols are retained for decoding and updating the decoding graph later. The performance and characteristics of the proposed improved online fountain codes are compared to those of the original online fountain codes over an erasure channel. Simulation results reveal that the improved online fountain codes outperform the original fountain codes in terms of intermediate symbol recovery rate, average encoded symbols required to be generated by the sender, average feedback transmissions, and encoding/decoding efficiency.
Classical error-correcting codes under the Hamming metric are used to correct substitution and erasure errors. Motivated by the limitations of the reading process in high density data storage ...systems, a new class of codes called symbol-pair (metric) codes was designed to protect against pair errors in symbol-pair read channels. For a given alphabet of size <inline-formula> <tex-math notation="LaTeX">q </tex-math></inline-formula> and given values of <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">d </tex-math></inline-formula> with <inline-formula> <tex-math notation="LaTeX">1\leq d\leq n </tex-math></inline-formula>, let <inline-formula> <tex-math notation="LaTeX">A_{p}(n,d,q) </tex-math></inline-formula> denote the largest possible code size for which there exists a <inline-formula> <tex-math notation="LaTeX">q </tex-math></inline-formula>-ary code of length <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> with minimum pair-distance at least <inline-formula> <tex-math notation="LaTeX">d </tex-math></inline-formula>. In this paper, new upper and lower bounds on <inline-formula> <tex-math notation="LaTeX">A_{p}(n,d,q) </tex-math></inline-formula> are presented. Several examples are included to illustrate our main results; some examples are optimal in the sense that they meet the corresponding bounds, and the rest examples are meant to show that our bounds may perform better than some of the previously known ones in certain cases. In addition, we show that any symbol-pair code over <inline-formula> <tex-math notation="LaTeX">\mathbb {F}_{q} </tex-math></inline-formula> can be viewed as a Hamming metric code over <inline-formula> <tex-math notation="LaTeX">\mathbb {F}_{q^{2}} </tex-math></inline-formula> with the same parameters. Consequently, the theory of classical codes over <inline-formula> <tex-math notation="LaTeX">\mathbb {F}_{q^{2}} </tex-math></inline-formula> can be used directly to symbol-pair codes; in particular, by virtue of this result, some known results can be reobtained immediately.
The article addresses the issue of the unification of cartographic symbols in terms of graphics (visual) and interpretation in an international context. The motivation is the ongoing digitization of ...processes in the conditions of Industry 4.0, especially Construction 4.0, where geodesy and cartography have their irreplaceable share. The aim was both to design uniform cartographic symbols for the description of geographical objects on the map and to design a general method for the description of unified cartographic symbols so that it is independent of specific applications. The authors compared the symbols used in the map works of the Czech Republic and neighboring countries that are members of the EU and proposed a formal description of the graphics properties of the symbols, which is based on a general mathematical model. The description takes the form of a text string, and a Python algorithm was built to render the symbol and implemented in the QGIS environment. The article also presents a comparison of some cartographic symbols used in the Czech Republic and in selected EU countries and a proposal for their unification. The motivation is the effort to unify the cartographic language within the EU. The problem is in accordance with the INSPIRE directive (seamless map of Europe) at the international level and with the Digital Czechia 2018+ strategy at the national level.
In the above article <xref ref-type="bibr" rid="ref1">1 , we had mixed up the definition of the symbol <inline-formula> <tex-math notation="LaTeX">X_{c}(n) </tex-math></inline-formula> in formula ...<xref rid="deqn7" ref-type="disp-formula">(7) and formula <xref rid="deqn8" ref-type="disp-formula">(8) . This affected only the descriptions of formula <xref rid="deqn7" ref-type="disp-formula">(7) and formula <xref rid="deqn8" ref-type="disp-formula">(8) , and had no influence on the discussion and conclusions in the article. The correct definition and illustration are as follows:
We consider an approach for realizing radar sensing in orthogonal frequency division multiplexing (OFDM)-based joint communication and sensing (JCAS) systems. In such JCAS systems, the performance of ...radar sensing is limited by the OFDM cyclic prefix (CP) length. We propose a sensing system that exploits OFDM communication symbols, which are known by the sensing transceiver. These symbols have a CP length originally designed for communication. In the proposed method, a matrix using the transmitted communication symbols is constructed for radar sensing, avoiding the need of reserving sensing symbols. The proposed method results in achieving the maximum achievable range without loss of data throughput. In the scenario of our simulations, we show that the proposed method achieves a measurable distance approximately 14 times higher than a conventional OFDM radar sensing approach when no modifications are made in the transmitted data. When sensing symbols are reserved in the conventional approach to increase its maximum unambiguous distance, the proposed method shows a throughput gain of approximately 7% with respect to the conventional method.
Signifying Europe provides a systematic overview of the wide range of symbols used to represent Europe and Europeanness, both by the political elite and the broader public. Through a critical ...interpretation of the meanings of the various symbols—and their often contradictory or ambiguous dimensions—Johan Fornäs uncovers illuminating insights into how Europe currently identifies itself and is identified by others outside its borders. While the focus is on the European Union’s symbols, those symbols are also interpreted in relation to other symbols of Europe. Offering insight into the cultural dimensions of European unification, this volume will appeal to students, scholars and politicians interested in European policy issues, cultural studies and postnational cultural identity.
The research titled (Cultural Symbols in Graffiti art between Iraq and Italy - A Comparative Study) deals with the diversity of cultural symbols, their metaphors, and methods of expressing them for ...each people and is divided into four chapters. The first represents the methodological framework and includes the research problem, its importance, purpose, limits, and definition of terms. The second includes the theoretical framework and includes three topics: an intellectual introduction to culture and its relationships, the historical and conceptual root of Graffiti art, and the symbolic representations of culture in Graffiti art. The third chapter included research procedures and analysis of its sample, which included three drawings from each country. The researcher concluded a number of results such as. 1. Cultural symbols In Iraqi Graffiti art are characterized by specific metaphors and are limited to concrete isolation walls. While in Rome Cultural symbols are subject to a wide field of reference and are spread throughout most of the city’s spaces. 2. Most cultural symbols In Iraqi Graffiti art are characterized by iconic shapes and descriptive colors. While in Rome Most of the symbols are written and symbolic forms and conventional colors based on the concept of difference, breaking expectations, and achieving shock. 3. Cultural symbols In Iraqi Graffiti art establish decorative formations that perform a recreational function that do not reveal awareness of the cultural role of the system. While in Rome Cultural symbols establish aesthetic formations that perform a cultural expressive function and are aware of the cultural role of the system. Which were discussed and conclusions drawn.
This paper forms the basis for wireless constellation detection in seamless digital wireless-photonic receivers. The two intermediary stages in the proposed receiver model are discussed: ...Wireless-to-Optical (W-O) and Optical-to-Electrical (O-E) symbol mapping stages. The inherent barrier of erroneous constellation detection due to symbol degeneracy in the W-O and O-E mapping stages is reported. A receiver architecture with optical phase diversity is subsequently proposed to overcome the barrier of degeneracy. Breaking degeneracy not only lays the foundation for reliable detection of wireless constellations in seamless digital wireless-photonic receivers, but also ensures their compatibility with practical modulation schemes such as M-PSK and M-QAM.
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