A facet model of targets is proposed to simulate inverse synthetic aperture radar (ISAR) images and radar back-scattering of moving targets with rigid and nonrigid motions. Targets are composed of solid objects which ...
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A facet model of targets is proposed to simulate inverse synthetic aperture radar (ISAR) images and radar back-scattering of moving targets with rigid and nonrigid motions. Targets are composed of solid objects which are modeled by triangular facets. It is shown that a facet can be treated as an equivalent point-scatterer whose radar cross section (RCS) and position depend on the shape of the triangle, the frequency, and the angle of incidence. A shadowing algorithm is also developed to detect the facets which actually have influence on the signal received by the radar. Besides, a facet division algorithm is implemented to improve the result of the shadowing algorithm and to have at least one facet per resolution cell. Finally, we apply our simulator to obtain the ISAR images of a ship and a helicopter and to calculate the micro-Doppler signature of a human.
We discuss controllability of systems that are initially given by boundary coupled PDEs of second order. These systems may be described by modules over particular rings of distributions and ultradistributions with com...
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We discuss controllability of systems that are initially given by boundary coupled PDEs of second order. These systems may be described by modules over particular rings of distributions and ultradistributions with compact support arising from the solution of the Cauchy problem of the PDE under consideration with data on the time axis. We show that those rings are Bezout domains. This property is utilized in order to derive algebraic and trajectory related controllability results.
This note develops and implements the theory of polynomial asymptotes to (graphs of) rational functions, as a generalization of the classical topics of horizontal asymptotes and oblique/slant asymptotes. Applications ...
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This note develops and implements the theory of polynomial asymptotes to (graphs of) rational functions, as a generalization of the classical topics of horizontal asymptotes and oblique/slant asymptotes. Applications are given to hyperbolic asymptotes. Prerequisites include the division algorithm for polynomials with coefficients in the field of real numbers and the elementary limit theorems from calculus. This note could be used as enrichment material in courses ranging from Calculus to Real Analysis to Abstract Algebra.
A fast method for ray tracing in high-frequency electromagnetic problems is proposed. The proposed method, which is based on adaptive space division using an octree structure, reduces the total CPU time needed to trac...
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A fast method for ray tracing in high-frequency electromagnetic problems is proposed. The proposed method, which is based on adaptive space division using an octree structure, reduces the total CPU time needed to trace each ray while providing the same accuracy as conventional ray-tracing algorithms.
The K-NN query algorithm is an important class of query algorithm in spatial database, the traditional K-NN query algorithm used the measurement distance and pruning strategy to search in the adopted index tree, the r...
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ISBN:
(纸本)9781424480333
The K-NN query algorithm is an important class of query algorithm in spatial database, the traditional K-NN query algorithm used the measurement distance and pruning strategy to search in the adopted index tree, the regional division algorithm based on the grid obtained the nearest neighbor objects by calculating the distance between the queried object and the data objects within the eight grids around the queried object, and carried on expanding inquiry scope outward layer by layer, in view of the advantage of the grid index, a new K-NN query algorithm based on the dynamic movement of spatial objects is proposed in this paper, it only carries on grid division to a small part of region around the queried object, when all the data objects in the current grid are already searched, make the cells in the grid empty, dynamically move the external data objects into the grid area continue to query according to the relative position of these objects, because the algorithm uses a fixed grid area to query the data objects in the whole region, so it can reduce the target storage space and the complexity degree of the algorithm calculation, the experiments show that the new query algorithm is superior to the traditional algorithms in the querying performance when the amount of data is increased, and the query efficiency is greatly increased.
Generalized quasi-cyclic (GQC) codes form a wide and useful class of linear codes that includes thoroughly quasi-cyclic codes, finite geometry (FG) low density parity check (LDPC) codes, and Hermitian codes. Although ...
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Generalized quasi-cyclic (GQC) codes form a wide and useful class of linear codes that includes thoroughly quasi-cyclic codes, finite geometry (FG) low density parity check (LDPC) codes, and Hermitian codes. Although it is known that the systematic encoding of GQC codes is equivalent to the division algorithm in the theory of Grobner basis of modules, there has been no algorithm that computes Grobner basis for all types of GQC codes. In this paper, we propose two algorithms to compute Grobner basis for GQC codes from their parity check matrices;we call them echelon canonical form algorithm and transpose algorithm. Both algorithms require sufficiently small number of finite-field operations with the order of the third power of code-length. Each algorithm has its own characteristic. The first algorithm is composed of elementary methods and is appropriate for low-rate codes. The second algorithm is based oil a novel formula and has smaller computational complexity than the first one for high-rate codes with the number of orbits (cyclic parts) less than half of the code length. Moreover, we show that a serial-in serial-out encoder architecture for FG LDPC codes is composed of linear feedback shift registers with the size of the linear order of code-length;to encode a binary codeword of length it, it takes less than 2n adder and 2n memory elements.
In this paper. we introduce the Riesz-Dirichlet distribution on a symmetric cone as an extension of the Dirichlet distribution defined by the Wishart distribution. We also show that some projections of these distribut...
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In this paper. we introduce the Riesz-Dirichlet distribution on a symmetric cone as an extension of the Dirichlet distribution defined by the Wishart distribution. We also show that some projections of these distributions related to the Pierce decomposition are also Dirichlet. (c) 2008 Elsevier Inc. All rights reserved.
The main purpose of this note is to present and justify proof via iteration as an intuitive, creative and empowering method that is often available and preferable as an alternative to proofs via either mathematical in...
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The main purpose of this note is to present and justify proof via iteration as an intuitive, creative and empowering method that is often available and preferable as an alternative to proofs via either mathematical induction or the well-ordering principle. The method of iteration depends only on the fact that any strictly decreasing sequence of positive integers must terminate in finitely many steps. Four examples are presented using the method of iteration. These examples concern the factorization of integers or polynomials into products of primes, the calculation of quotients and remainders via the division algorithm (and, hence, of greatest common divisors via the Euclidean algorithm) and the rank of matrices via elementary row and column operations. We also justify the method of proof by iteration by showing that its validity is a logical consequence of the method of mathematical induction. Various parts of this material would be suitable for courses on Precalculus, Discrete Mathematics, Abstract Algebra or Matrix Theory/Linear Algebra.
We define generalized quasi-cyclic (GQC) codes as linear codes with nontrivial automorphism groups. Therefore, GQC codes, unlike quasi-cyclic codes, can include many important codes such as Hermitian and projective ge...
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ISBN:
(纸本)9781424434343
We define generalized quasi-cyclic (GQC) codes as linear codes with nontrivial automorphism groups. Therefore, GQC codes, unlike quasi-cyclic codes, can include many important codes such as Hermitian and projective geometry (PG) codes;this capability is important in practical applications. Further, we propose the echelon canonical form algorithm for computing Grobner bases from their parity check matrices. Consequently, by applying Grobner base theory, GQC codes can be systematically encoded and implemented with simple feedback shift registers. Our algorithm is based on Gaussian elimination and requires a sufficiently small number of finite-field operations, which is related to the third power of code-length. In order to demonstrate our encoder's efficiency, we prove that the number of circuit elements in the encoder architecture is proportional to the code-length for finite geometry (FG) LDPC codes (a class of GQC codes). We show that the hardware complexity of a serial-in-serial-out encoder architecture for FG-LDPC codes is related to the linear order of the code-length;less than 2n adder and 2n memory elements are required to encode a binary codeword of length n.
A divisibility test of Arend Heyting, for polynomials over a field in an intuitionistic setting, may be thought of as a kind of division algorithm. We show that such a division algorithm holds for divisibility by poly...
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A divisibility test of Arend Heyting, for polynomials over a field in an intuitionistic setting, may be thought of as a kind of division algorithm. We show that such a division algorithm holds for divisibility by polynomials of content 1 over any commutative ring in which nilpotent elements are zero. In addition, for an arbitrary commutative ring R, we characterize those polynomials g such that the R-module endomorphism of R[X] given by multiplication by g has a left inverse.
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