SUMS OF DUAL TOEPLITZ PRODUCTS ON THE ORTHOGONAL COMPLEMENTS OF FOCK-SOBOLEV SPACES

We consider dual Toeplitz operators on the orthogonal complements of the FockSobolev spaces of all nonnegative real orders.First,for symbols in a certain class containing all bounded functions,we study the problem of when an operator which is finite sums of the dual Toeplitz products is compact or zero.Next,for bounded symbols,we construct a symbol map and exhibit a short exact sequence associated with the C^(*)-algebra generated by all dual Toeplitz operators with bounded symbols.

Research on Ubiquitous Map Visualization for Ternary Space

In the era of information and communication technology (ICT) and big data, the map gradually shows a new qualitative feature of “spatiotemporal ubiquitous” with the extension of its object space, expression space and information source, which challenges the theory of cartographic visualization. This paper discusses the ubiquitous map visualization from the object content and expression form. Oriented to the ternary space, it divides the object dimension of ubiquitous map visualization and analyzes the expression characteristics of ubiquitous map visualization. Based on that, it constructs the variable system, symbol system and method system of ubiquitous map visualization. With three cases of the metro roadmap, the tag map, and the three-dimensional (3D) city map, the application of the proposed content is explained to illustrate its effectiveness. The research in this paper is expected to further enrich the theoretical basis of cartographic visualization and provide theoretical support for the expression and application of ubiquitous map visualization.

RCDS:a right-confirmable data-sharing model based on symbol mapping coding and blockchain

The problem of data right confirmation is a long-term bottleneck in data sharing.Existing methods for confirming data rights lack credibility owing to poor supervision,and work only with specific data types because of their technical limitations.The emergence of blockchain is followed by some new data-sharing models that may provide improved data security.However,few of these models perform well enough in confirming data rights because the data access could not be fully under the control of the blockchain facility.In view of this,we propose a right-confirmable data-sharing model named RCDS that features symbol mapping coding(SMC)and blockchain.With SMC,each party encodes its digital identity into the byte sequence of the shared data by generating a unique symbol mapping table,whereby declaration of data rights can be content-independent for any type and any volume of data.With blockchain,all data-sharing participants jointly supervise the delivery and the access to shared data,so that granting of data rights can be openly verified.The evaluation results show that RCDS is effective and practical in data-sharing applications that are conscientious about data right confirmation.

Concatenated Alamouti codes using multi-level modulation and symbol mapping diversity technique

A family of space-time block codes(STBCs)for systems with even transmit antennas and any number of receive antennas is proposed.The new codeword matrix is constructed by concatenating Alamouti space-time codes to form a block diagonal matrix,and its dimension is equal to the number of transmit antennas.All Alamouti codes in the same codeword matrix have the same information;thus,full transmit diversity can be achieved over fading channels.To improve the spectral efficiency,multi-level modulations such as multi-quadrature amplitude modulation(M-QAM)are employed.The symbol mapping diversity is then exploited between transmissions of the same information from different antennas to improve the bit error rate(BER)performance.The proposed codes outperform the diagonal algebraic space-time(DAST)codes presented by Damen[Damen et al.IEEE Transactions on Information Theory,2002,48(3):628–636]when they have the same spectral efficiency.Also,they outperform the 1/2-rate codes from complex orthogonal design.Moreover,compared to DAST codes,the proposed codes have a low decoding complexity because we only need to perform linear processing to achieve single-symbol maximum-likelihood(ML)decoding.