Based on the hydrogen-helium similarity theory, the leakage experiments using helium instead of hydrogen can effectively reduce the risk of hydrogen deflagration, but the experimental results show that there is a larg...
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Based on the hydrogen-helium similarity theory, the leakage experiments using helium instead of hydrogen can effectively reduce the risk of hydrogen deflagration, but the experimental results show that there is a large difference between the concentration of hydrogen and helium in initial period of leakage base on this theory. This paper focuses on leakage experiments under turbulent conditions in enclosed spaces. Based on the hydrogen-helium similarity theory, helium is used to replace hydrogen to find out the concentration of helium at multiple leakage speeds. A comparison is made between helium concentration values and hydrogen concentration values, and a polynomial correction algorithm is used to shrink the difference. The results show that this correction method can reduce the concentration average error between the helium and the hydrogen from 14.06% to 7.94% for the Reynolds number range of 3500-9500. Therefore, a polynomial fitting algorithm based on this theory can improve the accuracy of experiment using helium instead of hydrogen.
In the article, we consider undirected multiple graphs of any natural multiplicity k > 1. A multiple graph contains edges of three types: ordinary edges, multiple edges, and multiedges. Each edge of the last two ty...
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In the article, we consider undirected multiple graphs of any natural multiplicity k > 1. A multiple graph contains edges of three types: ordinary edges, multiple edges, and multiedges. Each edge of the last two types is a union of k linked edges, which connect 2 or (k + 1) vertices, correspondingly. The linked edges should be used simultaneously. If a vertex is incident to a multiple edge, then it can be incident to other multiple edges, and it can also be the common end of k linked edges of a multiedge. If a vertex is the common end of a multiedge, then it cannot be the common end of another multiedge. As for an ordinary graph, we can define the integer function of the length of an edge for a multiple graph and set the problem of the shortest path joining two vertices. Any multiple path is a union of k ordinary paths adjusted on the linked edges of all multiple and multiedge edges. In this article, the previously obtained algorithm for finding the shortest path in an arbitrary multiple graph is optimized. We show that the optimized algorithm is polynomial. Thus, the shortest path problem is polynomial for any multiple graph.
In this paper, we present an efficient algorithm for minimizing an Mp-convex function under a color -induced budget constraint. The algorithm extends the algorithms by Gabow and Tarjan for finding a minimum-weight bas...
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In this paper, we present an efficient algorithm for minimizing an Mp-convex function under a color -induced budget constraint. The algorithm extends the algorithms by Gabow and Tarjan for finding a minimum-weight base of a matroid and by Gottschalk et al. for minimizing a separable discrete convex function on a polymatroid under a color-induced budget constraint. It can also be recognized as an extension of a greedy algorithm for unconstrained Mp-convex function minimization by Murota and Shioura.(c) 2023 Elsevier B.V. All rights reserved.
Graph theory is used in many areas of chemical sciences, especially in molecular chemistry. It is particularly useful in the structural analysis of chemical compounds and in modeling chemical reactions. One of its app...
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Graph theory is used in many areas of chemical sciences, especially in molecular chemistry. It is particularly useful in the structural analysis of chemical compounds and in modeling chemical reactions. One of its applications concerns determining the structural formula of a chemical compound. This can be modeled as a variant of the well-known graph realization problem. In the classical version of the problem, a sequence of natural numbers is given, and the question is whether there exists a graph in which the vertices have degrees equal to the given numbers. In the variant considered in this paper, instead of a sequence of natural numbers, a sequence of sets of natural numbers is given, and the question is whether there exists a multigraph such that each of its vertices has a degree equal to a number from one of the sets. This variant of the graph realization problem matches the nature of the problem of determining the structural formula of a chemical compound better than other variants considered in the literature. We propose a polynomial time exact algorithm solving this variant of the problem.
A digraph is eulerian if it is connected and every vertex has its in-degree equal to its out-degree. Having a spanning eulerian subdigraph is thus a weakening of having a hamiltonian cycle. In this paper, we first cha...
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A digraph is eulerian if it is connected and every vertex has its in-degree equal to its out-degree. Having a spanning eulerian subdigraph is thus a weakening of having a hamiltonian cycle. In this paper, we first characterize the pairs (D,a) $(D,a)$ of a semicomplete digraph D $D$ and an arc a $a$ such that D $D$ has a spanning eulerian subdigraph containing a $a$. In particular, we show that if D $D$ is 2-arc-strong, then every arc is contained in a spanning eulerian subdigraph. We then characterize the pairs ( D , a ) $(D,a)$ of a semicomplete digraph D $D$ and an arc a $a$ such that D $D$ has a spanning eulerian subdigraph avoiding a $a$. In particular, we prove that every 2-arc-strong semicomplete digraph has a spanning eulerian subdigraph avoiding any prescribed arc. We also prove the existence of a (minimum) function f ( k ) $f(k)$ such that every f ( k ) $f(k)$-arc-strong semicomplete digraph contains a spanning eulerian subdigraph avoiding any prescribed set of k $k$ arcs. We conjecture that f ( k ) = k + 1 $f(k)=k+1$ and establish this conjecture for k <= 3 $k\le 3$ and when the k $k$ arcs that we delete form a forest of stars. A digraph D $D$ is eulerian-connected if for any two distinct vertices x , y $x,y$, the digraph D $D$ has a spanning ( x , y ) $(x,y)$-trail. We prove that every 2-arc-strong semicomplete digraph is eulerian-connected. All our results may be seen as arc analogues of well-known results on hamiltonian paths and cycles in semicomplete digraphs.
We consider predicates on a finite set that are invariant with respect to an affine operation f(G), where G is some Abelian group. Such predicates are said to be multiaffine for the group G. Special attention is paid ...
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We consider predicates on a finite set that are invariant with respect to an affine operation f(G), where G is some Abelian group. Such predicates are said to be multiaffine for the group G. Special attention is paid to predicates that are affine for a group G(q) of addition modulo q = p(s), where p is a prime number and s = 1. We establish the predicate multiaffinity criterion for a group G(q). Then we introduce disjunctive normal forms (DNF) for predicates on a finite set and obtain properties of DNFs of predicates that are multiaffine for a group G(q). Finally we show how these properties can be used to design a polynomial algorithm that decides satisfiability of a system of predicates which are multiaffine for a group G(q), if predicates are specified by DNF.
Max-max, max-min, min-max and min-min optimization problems with a knapsack-type constraint containing a single numerical parameter are studied. The goal is to present optimal solutions for all possible values of the ...
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Max-max, max-min, min-max and min-min optimization problems with a knapsack-type constraint containing a single numerical parameter are studied. The goal is to present optimal solutions for all possible values of the parameter. algorithms with O (n log n) and O (n(2)) running times are proposed for the problems with a fixed parameter and for the general problem, respectively, where n is the number of items to be packed into the knapsack. The latter algorithm determines optimal solution values for all values of the parameter in O (n log(2) n) time. The problem of deciding whether there exists a single optimal solution for all values of the numerical parameter is proved to be NP-complete.
Since fuzzy discrete -event systems (FDESs) modeled by fuzzy automata were put forward, extensive research on FDESs has been successfully conducted from different perspectives. Recently, the safe codiagnosability of d...
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Since fuzzy discrete -event systems (FDESs) modeled by fuzzy automata were put forward, extensive research on FDESs has been successfully conducted from different perspectives. Recently, the safe codiagnosability of decentralized FDESs was introduced and an approach of constructing the safe codiagnoser to verify the safe codiagnosability was proposed. However, the complexity of constructing the safe codiagnoser of decentralized FDESs is exponential. In this paper, we present a polynomial verification. Firstly, the recognizer and the safe coverifier are constructed to recognize the prohibited strings in the illegal language and carry out safe diagnosis of decentralized FDESs, respectively. Then the necessary and sufficient condition for safe codiagnosability of decentralized FDESs is presented. In particular, an algorithm for verifying the safe codiagnosability of decentralized FDESs is proposed based on the safe coverifier. Notably, both complexities of constructing the safe coverifier and verifying the safe codiagnosability are polynomial in the numbers of fuzzy events and fuzzy states of FDESs. Finally, two examples are provided to illustrate the proposed algorithm and the derived results.
Skew-symmetrizable matrices play an essential role in the classification of cluster algebras. We prove that the problem of assigning a positive definite quasi-Cartan companion to a skew-symmetrizable matrix is in poly...
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Skew-symmetrizable matrices play an essential role in the classification of cluster algebras. We prove that the problem of assigning a positive definite quasi-Cartan companion to a skew-symmetrizable matrix is in polynomial class P. We also present an algorithm to determine the finite type Delta is an element of {A(n), D-n, B-n, C-n, E-6, E-7, E-8, F-4, G(2)} of a cluster algebra associated to the mutation-equivalence class of a connected skew-symmetrizable matrix B, if it has one.
The studied problem consists in selecting a group of k entities out of n entities such that their diversity is maximized. Each entity is assumed to be characterized by a single numerical attribute. The diversity is me...
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The studied problem consists in selecting a group of k entities out of n entities such that their diversity is maximized. Each entity is assumed to be characterized by a single numerical attribute. The diversity is measured by the total pairwise Euclidean or squared Euclidean distance. The problem appears in the formation of social or working groups. Under certain conditions, diversity is perceived as a positive factor influencing the group's effectiveness. We propose simple O(n + k log k) time algorithms to solve this problem for both the total Euclidean and squared Euclidean distances.
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