More than half a century ago Martin Gardner popularized a question leading to the benchmark problem of determining the minimum side length of a square into which the squares of sizes 1, 2, ..., n can be packed without...
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More than half a century ago Martin Gardner popularized a question leading to the benchmark problem of determining the minimum side length of a square into which the squares of sizes 1, 2, ..., n can be packed without overlap. Constructions are known for a certain range of n, and summing up the areas yields that a packing in a square of size smaller than N := root n(n + 1)(2n + 1)/6) is not possible. Here we prove that an asymptotically minimal packing exists in a square of size N + cn + O(root n) with c < 1, and such a packing is achievable with guillotine-cuts. An improved construction is also given for the case where the constraint of guillotine cutting is dropped.
This paper proposes an accurate and computationally efficient implementation of the IEEE Standard 1459-2000 for power measurements. The algorithm has two stages. In the first algorithm stage, the voltage and current s...
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This paper proposes an accurate and computationally efficient implementation of the IEEE Standard 1459-2000 for power measurements. The algorithm has two stages. In the first algorithm stage, the voltage and current signals are processed in parallel, and their spectrums are estimated independently of each other. Signal harmonics are estimated in a wide range of frequency using an efficient algorithm with reduced complexity. The algorithm is based on a recently introduced common structure for recursive discrete transforms and consists of digital resonators embedded in a common negative feedback loop. In the second algorithm stage, the unknown power components and other power quality indices are calculated according to definitions in the IEEE Standard 1459-2000. To demonstrate the efficiency of the proposed algorithm, the results of computer simulations and laboratory testing are presented. The laboratory results show accurate input power component estimates for a nonlinear load with rapid input current amplitude changes. In addition, a simple LabView implementation, based on the point-by-point processing feature, demonstrates the technique's modest computation requirements and confirms that the proposed algorithm is suitable for real-time applications.
作者：
Flammang, ValerieUniv Lorraine
UMR CNRS Ist Elie Cartan Lorraine 7502 Dept Math UFR MIM Site Metz F-57073 Metz France
Let alpha be a nonzero algebraic integer of degree d with conjugates alpha 1 = alpha, ... ,alpha(d). It is well known that Sk(alpha) = Sigma(d)(i=1) alpha(k)(i) . Here, we define S-k'(alpha) = Sigma(d)(i=)(1)verti...
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Let alpha be a nonzero algebraic integer of degree d with conjugates alpha 1 = alpha, ... ,alpha(d). It is well known that Sk(alpha) = Sigma(d)(i=1) alpha(k)(i) . Here, we define S-k'(alpha) = Sigma(d)(i=)(1)vertical bar alpha(i)vertical bar(k) and s(k)' (alpha) = S-k'(alpha) /d. Then, we focus our attention on the case k= 2 when a is an algebraic integer all of whose conjugates lie in a sector vertical bar argz vertical bar <= theta, 0 < theta < pi/2. We compute the greatest lower bound c(theta) of s(2)' (alpha) for theta belonging to eleven subintervals of [0, pi/2). Moreover, among these subintervals, there are twice two consecutive and complete subintervals. We use the method of explicit auxiliary functions for which the involved polynomials are found by our recursive algorithm.
This paper considers the computation problems in feature selection. A recursive computation procedure is presented for feature selection and ordering by using the indirect measures such as the Bhattacharyya distance a...
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This paper considers the computation problems in feature selection. A recursive computation procedure is presented for feature selection and ordering by using the indirect measures such as the Bhattacharyya distance and mutual information. Both binary and quantized measurements are considered. Supporting computer results are provided.
The finite-time convergence problem of an nth nonlinear system with unmatched disturbance is primarily studied in this paper. During the recursive procedure, a new finite-timecontroller is designed and proven by addin...
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The finite-time convergence problem of an nth nonlinear system with unmatched disturbance is primarily studied in this paper. During the recursive procedure, a new finite-timecontroller is designed and proven by adding a sign function and a power integrator. Meanwhile, a C1 positive definite and proper Lyapunov function, which satisfies the finite-timeLyapunov stability law, is designed. Finally, the designed finite-time controller is appliedto some examples and an application of integrated guidance and control system to testand verify its advantage and practicability.
The concrete method of ‘surface spline interpolation’ is closely connected with the classical problem of minimizing a Sobolev seminorm under interpolatory constraints; the intrinsic structure of surface splines is a...
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The concrete method of ‘surface spline interpolation’ is closely connected with the classical problem of minimizing a Sobolev seminorm under interpolatory constraints; the intrinsic structure of surface splines is accordingly that of a multivariate extension of natural splines. The proper abstract setting is a Hilbert function space whose reproducing kernel involves no functions more complicated than logarithms and is easily coded. Convenient representation formulas are given, as also a practical multivariate extension of the Peano kernel theorem. Owing to the numerical stability of Cholesky factorization of positive definite symmetric matrices, the whole construction process of a surface spline can be described as a recursive algorithm, the data relative to the various interpolation points being exploited in sequence.
This paper presents a new method of converting a curve into chain-code representation. At every step of chain encoding, a predictive searching is conducted so that an optimal code direction is determined. Optimization...
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This paper presents a new method of converting a curve into chain-code representation. At every step of chain encoding, a predictive searching is conducted so that an optimal code direction is determined. Optimization is performed on the basis of a minimum mean-square-error criterion. This approach works very well for complex geometrical configuration with overlapping, crossing, and touching characteristics. We have applied this method with great success to computer analysis of chromosomes.
Let alpha be a nonzero algebraic integer of degree d, all of whose conjugates alpha(1) = alpha, alpha(2), ..., alpha(d) lie in a sector vertical bar arg z vertical bar <= theta, 0 < theta <= 90 degrees. We de...
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Let alpha be a nonzero algebraic integer of degree d, all of whose conjugates alpha(1) = alpha, alpha(2), ..., alpha(d) lie in a sector vertical bar arg z vertical bar <= theta, 0 < theta <= 90 degrees. We define the S-measure of alpha by S(alpha) = Sigma(d)(i=1) vertical bar alpha(i)vertical bar and the absolute S-measure of alpha by s(alpha) = S (alpha)/d. We compute the greatest lower bound c(theta) of s(alpha) for alpha belonging to twelve subintervals of (0, theta). Among these subintervals, three are complete. These computations use the principle of explicit auxiliary functions and our recursive algorithm.
作者：
Flammang, VUniv Lorraine
Dept Math UMR CNRS IECL 7502 UFR MIM Site Metz3 Rue Augustin FresnelBP 45112 F-57073 Metz 03 France
Thanks to our recursive algorithm developed in [Trace of totally positive algebraic integers and integer transfinite diameter, Math. Comp. 78(266) (2009) 1119-1125], we prove that, if a is a totally positive algebraic...
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Thanks to our recursive algorithm developed in [Trace of totally positive algebraic integers and integer transfinite diameter, Math. Comp. 78(266) (2009) 1119-1125], we prove that, if a is a totally positive algebraic integer of degree d >= 2 with minimum conjugate a l then, with a finite number of explicit exceptions, tr(alpha)/d >=alpha(1) + 1.68.
作者：
Flammang, VUniv Lorraine
UMR CNRS 7502 IECL Dept MathUFR MIM Site Metz3 Rue Augustin FresnelBP 45112 F-57073 Metz 03 France
We consider intervals of the form [r/s, u], where r, s are positive integers with gcd (r, s) = 1 and u is a real number, or of the form [0, (root a - root b)(2)], where a, b are positive integers. Thanks to a lemma of...
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We consider intervals of the form [r/s, u], where r, s are positive integers with gcd (r, s) = 1 and u is a real number, or of the form [0, (root a - root b)(2)], where a, b are positive integers. Thanks to a lemma of Chudnovsky, we give first a lower bound of the integer trans finite diameter of such intervals. Then, using the method of explicit auxiliary functions and our recursive algorithm, we explain how to get an upper bound for this quantity. We finish with some numerical examples. Secondly, we prove inequalities on the integer trans finite diameter of Farey intervals, i.e., intervals of the type [a/q, b/s], where vertical bar as - bq vertical bar = 1.
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