Group of Isometries of Niederreiter-Rosenbloom-Tsfasman Block Space

Let P = ({1, 2, ..., n}, ≤) be a poset that is an union of disjoint chains of the same length and V = F^N_q be the space of N-tuples over the finite field Fq. Let Vi = F^{k_i}_q , with 1 ≤ i ≤ n, be a family of finite-dimensional linear spaces such that k_1 + k_2 + ... + k_n = N and let V = V_1×V_2×...×V_n endow with the poset block metric d_(P,π) induced by the poset P and the partition π = (k_1, k_2, ..., k_n), encompassing both Niederreiter-Rosenbloom-Tsfasman metric and error-block metric. In this paper, we give a complete description of group of isometries of the metric space (V, d_(P,π)), also called the Niederreiter-Rosenbloom-Tsfasman block space. In particular, we reobtain the group of isometries of the Niederreiter-Rosenbloom-Tsfasman space and obtain the group of isometries of the error-block metric space.

Edge Detection Using the Bhattacharyya Distance with Adjustable Block Space

In this paper, we propose a new edge detection method for color images, based on the Bhattacharyya distance with adjustable block space. First, the Wiener filter was used to remove the noise as pre-processing. To calculate the Bhattacharyya distance, a pair of blocks were extracted for each pixel. To detect subtle edges, we adjusted the block space. The mean vector and covariance matrix were computed from each block. Using the mean vectors and covariance matrices, we computed the Bhattacharyya distance, which was used to detect edges. By adjusting the block space, we were able to detect weak edges, which other edge detections failed to detect. Experimental results show promising results compared to some existing edge detection methods.

Lp estimates for maximal functions along surfaces of revolution on product spaces

This paper is concerned with establishing Lp estimates for a class of maximal operators associated to surfaces of revolution with kernels in Lq(Sn−1 × Sm−1), q > 1. These estimates are used in extrapolation to obtain the Lp boundedness of the maximal operators and the related singular integral operators when their kernels are in the L(logL)κ(Sn−1 × Sm−1) or in the block space $\begin{array}{} B^{0,\kappa-1}_ q \end{array}$(Sn−1 × Sm−1). Our results substantially improve and extend some known results.

Boundedness of Generalized Parametric Marcinkiewicz Integrals Associated to Surfaces

In this article, the boundedness of the generalized parametric Marcinkiewicz integral operators M Ω , ϕ , h , ρ ( r ) is considered. Under the condition that Ω is a function in L q ( S n - 1 ) with q ∈ ( 1 , 2 ] , appropriate estimates of the aforementioned operators from Triebel–Lizorkin spaces to L p spaces are obtained. By these estimates and an extrapolation argument, we establish the boundedness of such operators when the kernel function Ω belongs to the block space B q 0 , ν - 1 ( S n - 1 ) or in the space L ( l o g L ) ν ( S n - 1 ) . Our results represent improvements and extensions of some known results in generalized parametric Marcinkiewicz integrals.

Transaction Fees, Block Size Limit, and Auctions in Bitcoin

Confirmation of Bitcoin transactions is executed in blocks, which are then stored in the Blockchain. As compared to the number of transactions in the mempool, the set of transactions which are verified but not yet confirmed, available space for inclusion in a block is typically limited. For this reason, successful miners can only process a subset of such transactions, and users compete with each other to enter the next block by offering confirmation fees. Assuming that successful miners pursue revenue maximization, they will include in the block those mempool transactions that maximize earnings from related fees. In the paper we model transaction fees as a Nash Equilibrium outcome of an auction game with complete information. In the game the successful miner acts as an auctioneer selling block space, and users bid for shares of such space to confirm their transactions. Moreover, based on expected fees we also discuss what the optimal, revenue maximizing, block size limit should be for the successful miner. Consistently with the intuition, the optimal block size limit resolves the trade-off between including additional transactions (which possibly lower the unit fees collected) and keeping the block capacity limited (with, however, higher unit fees).

Washington will block international space weapon ban

Headline INTERNATIONAL: Washington will block space weapon ban

The Bitcoin Mining Game

This article deals with the mining incentives in the Bitcoin protocol. The mining process is used to confirm and secure transactions. This process is organized as a speed game between individuals or firms – the miners – with different computational powers to solve a mathematical problem, bring a proof of work, spread their solution and reach consensus among the Bitcoin network nodes with it. First, we define and specify this game. Second, we analytically find its Nash equilibria in the two-player case. We analyze the parameters for which the miners would face the proper incentives to fulfill their function of transaction processors in the current situation. Finally, we study the block space market offer.