Let V be a non empty zero structure. An element of Cthe carrier of V is said to be a C-linear combination of V if: (Def. 1) There exists a finite subset T of V such that for every element v of V such that v / ∈ T holds it(v) = 0. Let V be a non empty additive loop structure and let L be an element of Cthe carrier of V . The support of L yielding a subset of V is defined by: (Def. 2) The support...

Assume that G = (V, E) is an undirected graph with vertex set V and edge set E. The ball Br(v) denotes the vertices within graphical distance r from v. A subset C ⊆ V is called an (r,≤ l)-locating-dominating code of type B if the sets Ir(F ) = ⋃ v∈F (Br(v)∩C) are distinct for all subsets F ⊆ V \C with at most l vertices. A subset C ⊆ V is an (r,≤ l)-locatingdominating code of type A if sets Ir(...

Recently A. G. Ramm (1999) has shown that a subset of phase shifts δl, l = 0, 1, . . ., determines the potential if the indices of the known shifts satisfy the Müntz condition ∑ l =0,l∈L 1 l = ∞. We prove the necessity of this condition in some classes of potentials. The problem is reduced to an inverse eigenvalue problem for the half-line Schrödinger operators.

Let $$d\ge 2$$ and let K L be two convex bodies in $${{\mathbb {R}}^d}$$ such that $$L\subset {\text {int}}K$$ the boundary of does not contain a segment. If satisfy $$(d+1)$$ -equichordal property, i.e., for any line l supporting points $$\{\zeta _{\pm }\}$$ intersection with l, $$\begin{aligned} {dist}}^{d+1}(L\cap \zeta _+)+{\text _-)=2\sigma ^{d+1} \end{aligned}$$ holds, where constant $$\s...

(0, 1,2}. The set of three-valued logical functions (i.e., f: E” --t E for n=l,2,... ) is denoted by P3. A subset F of P3 is said to be closed if it contains all superpositions (i.e., compositions or substitutions) of its members (cf. [l, 1 l-131). For closed sets F and H such that FC H (proper inclusion), F is an H-maxima/ set if FC G c H for no closed set G. A subset F of H is complete in H i...

The objective of this work is to quantify the uncertainty in probability failure estimates resulting from incomplete knowledge distributions for input random variables. We propose a framework that couples widely used Subset simulation (SuS) with Bayesian/information theoretic multi-model inference. process starts data infer model inputs. Often such sets are small. Multi-model inference assess a...

A finite automaton can be either deterministic (DFA) or nondeterministic (NFA). An automaton-based task is in general more efficient when performed with a DFA rather than an NFA. For any NFA there equivalent that generated by the classical Subset Construction algorithm. When, however, large may transformed into series of actions operating directly on NFA, unnecessarily expensive computation, as...

Feature subset selection has become more and more a common topic of research. This popularity is partly due to the growth in the number of features and application domains. It is of the greatest importance to take the most of every evaluation of the inducer, which is normally the more costly part. In this paper, a technique is proposed that takes into account the inducer evaluation both in the ...