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61.
62.
This paper contains three parts where each part triggered and motivated the subsequent one. In the first part (Proper Secrets) we study the Shamir’s “k-out-of-n” threshold secret sharing scheme. In that scheme, the dealer generates a random polynomial of degree k−1 whose free coefficient is the secret and the private shares are point values of that polynomial. We show that the secret
may, equivalently, be chosen as any other point value of the polynomial (including the point at infinity), but, on the other
hand, setting the secret to be any other linear combination of the polynomial coefficients may result in an imperfect scheme.
In the second part ((t, k)-bases) we define, for every pair of integers t and k such that 1 ≤ t ≤ k−1, the concepts of (t, k)-spanning sets, (t, k)-independent sets and (t, k)-bases as generalizations of the usual concepts of spanning sets, independent sets and bases in a finite-dimensional vector
space. We study the relations between those notions and derive upper and lower bounds for the size of such sets. In the third
part (Linear Codes) we show the relations between those notions and linear codes. Our main notion of a (t, k)-base bridges between two well-known structures: (1, k)-bases are just projective geometries, while (k−1, k)-bases correspond to maximal MDS-codes. We show how the properties of (t, k)-independence and (t, k)-spanning relate to the notions of minimum distance and covering radius of linear codes and how our results regarding the
size of such sets relate to known bounds in coding theory. We conclude by comparing between the notions that we introduce
here and some well known objects from projective geometry.
相似文献
63.
Ali Barahmand 《International Journal of Mathematical Education in Science & Technology》2019,50(2):164-181
This article seeks to explore the most important obstacles of inflexibility in mathematics teachers’ behaviour in accepting new ideas, especially, while encountering a new situation. In so doing, the concept of equivalence between infinite sets, which is one of the challenging issues in mathematics teaching and learning, was selected as the subject matter of the study. The participants of the study were 64 high-school mathematics teachers. To collect the data, they were exposed to a challenging new situation involving equivalence between infinite sets. Then they were interviewed regarding the decisions they had made. The analysis of the data revealed that the main obstacles to accepting new ideas by mathematics teachers were preference to well-known procedures and tendency to work with methods with a more general extensive domain of the function. In addition, while the spirit of the article seems to imply that teachers are not flexible, in terms of accepting a new method, the data on teacher choices highlighted the positive results of teacher flexibility. 相似文献
64.
Mehdi Pourbarat 《Journal of Differential Equations》2019,266(4):2125-2141
It is shown that in the context of affine Cantor sets with two increasing maps, the arithmetic sum of both of its elements is a Cantor set otherwise, it is a closure of countable union of nontrivial intervals. Also, a new family of pairs of affine Cantor sets is introduced such that each element of it has stable intersection. At the end, pairs of affine Cantor sets are characterized such that the sum of elements of each pair is a closed interval. 相似文献
65.
本文讨论的是集值优化问题Benson真有效解的高阶Fritz John型最优性条件,利用Aubin和Fraukowska引入的高阶切集和凸集分离定理,在锥-似凸映射的假设条件下,获得了带广义不等式约束的集值优化问题Benson真有效解的高阶Fritz John型必要和充分性条件. 相似文献
66.
讨论自反Banach空间中的原——对偶锥线性优化问题的目标函数水平集的几何性质.在自反Banach空间中,证明了原目标函数水平集的最大模与对偶目标函数水平集的最大内切球半径几乎是成反比例的. 相似文献
67.
Redouane Kara Mourad Ahmane Jean Jacques Loiseau Said Djennoune 《Nonlinear Analysis: Hybrid Systems》2009,3(4):738-748
This paper deals with constrained regulation of continuous Petri nets under the so-called infinite servers semantics. Our aim is to design feedback gains that permit us to reach both desired stationary marking vector and desired asymptotic firing rate vector. The proposed approach takes into account constraints on the control, the marking of the Petri net, and the stability of the closed-loop system. The existence of a solution is first expressed geometrically, in terms of the inclusion of two polyhedral sets. They are reformulated algebraically as linear matrix inequalities, which provides an effective way to calculate feedback gains answering the problem. Finally, an application to an assembly production system is given. 相似文献
68.
Aldo Portela 《Bulletin of the Brazilian Mathematical Society》2009,40(1):53-75
It is known that not every Cantor set of S
1 is C
1-minimal. In this work we prove that every member of a subfamily of what we here call regular interval Cantor set is not C
1-minimal. We also prove that no member of a class of Cantor sets that includes this subfamily is C
1+∈-minimal, for any ∈ > 0.
Partially supported by CNPq-Brasil and PEDECIBA-Uruguay. 相似文献
69.
In this paper we study spectral sets which are unions of finitely many intervals in R. We show that any spectrum associated with such a spectral set Ω is periodic, with the period an integral multiple of the measure of Ω. As a consequence we get a structure theorem for such spectral sets and observe that the generic case is that of the equal interval case. 相似文献
70.
S. Alesker 《Geometriae Dedicata》1999,74(3):241-248
We present a characterization of continuous isometry covariant valuations on convex sets. The main result generalizes previous results of Hadwiger and Hadwiger and Schneider. 相似文献