scholarly journals METHOD FOR ASSESSING THE STRUCTURAL RELIABILITY OF NETWORKS WITH UNDETERMINED TOPOLOGY

2020 ◽  
Vol 10 (1) ◽  
pp. 32-35
Author(s):  
Nina Kniazieva ◽  
Alexey Nenov ◽  
Irina Kolumba
Keyword(s):  
Lower Bounds ◽  
Reliability Index ◽  
Structural Reliability ◽  
Structural Characteristics ◽  
Scientific Research ◽  
Network Connectivity ◽  
Upper And Lower Bounds

This paper shows the relevance of the task of assessing the structural reliability of networks with undetermined topology. Proposed is a method for assessing the structural reliability of networks of undetermined topology based on taking into account the basic structural characteristics of the network (the number of nodes and branches, the degree of network connectivity, the maximum allowable rank of paths, and others). To obtain an estimate of the structural reliability for a network of any dimension and any topology, expressions are proposed in the scientific research to determine the number of paths of various ranks, which must be taken into account when calculating the structural reliability index by the upper and lower bounds method.

Reliability Based Assessment of Deck Elevations for Offshore Jacket Platforms

2004 ◽  
Vol 126 (4) ◽  
pp. 331-336 ◽  
Author(s):  
Ernesto Heredia-Zavoni ◽  
Dante Campos ◽  
Gallegher Ramı´rez
Keyword(s):  
Reliability Index ◽  
Structural Reliability ◽  
Failure Modes ◽  
Probability Of Failure ◽  
Upper And Lower Bounds ◽  
Series System ◽  
Wave Loading ◽  
System Components ◽  
Storm Wave ◽  
Wave Heights

Structural reliability analyses of fixed marine platforms subjected to storm wave loading are performed to assess deck elevations. Platforms are modeled as a series system consisting of the deck and jacket bays. The structural reliability analyses are carried out assuming dominant failure modes for the system components. Upper and lower bounds of the probability of failure are computed. The variation of the reliability index per bay component as a function of wave height, with a focus on those wave heights that generate forces on the deck, is analyzed. A comparison is given for the deck probability of failure and the lower bound probability of failure of the jacket in order to assess how the deck or the jacket controls the probability of failure of the system. Results are also given for reliability analyses considering different deck elevations. Finally, an analysis of the total probabilities of failure, unconditioned on wave heights, is given.

scholarly journals Some Refinements and Generalizations of I. Schur Type Inequalities

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Xian-Ming Gu ◽  
Ting-Zhu Huang ◽  
Wei-Ru Xu ◽  
Hou-Biao Li ◽  
Liang Li ◽  
...  
Keyword(s):  
Lower Bounds ◽  
Recent Literature ◽  
Structural Characteristics ◽  
Variable Parameter ◽  
Upper Bounds ◽  
Upper And Lower Bounds ◽  
Numerical Examples ◽  
Schur Inequality

Recently, extensive researches on estimating the value ofehave been studied. In this paper, the structural characteristics of I. Schur type inequalities are exploited to generalize the corresponding inequalities by variable parameter techniques. Some novel upper and lower bounds for the I. Schur inequality have also been obtained and the upper bounds may be obtained with the help ofMapleand automated proving package (Bottema). Numerical examples are employed to demonstrate the reliability of the approximation of these new upper and lower bounds, which improve some known results in the recent literature.

Structural Reliability Analysis with Uncertainty-but-Bounded Parameters Based on Meshless Method

2010 ◽  
Vol 163-167 ◽  
pp. 3034-3041
Author(s):  
Wei Zhao ◽  
J.K. Liu ◽  
Qiu Wei Yang
Keyword(s):  
Reliability Analysis ◽  
Meshless Method ◽  
Reliability Index ◽  
Structural Reliability ◽  
Strain Analysis ◽  
Optimization Theory ◽  
Upper And Lower Bounds ◽  
Probability Method ◽  
Structural Reliability Analysis ◽  
Interval Reliability

The structural reliability analysis with uncertainty-but-bounded parameters is considered in this paper. Each uncertain-but-bounded parameter is represented as an interval number or vector, an interval reliability index is defined and discussed. Due to the wide application of the Meshless method, it is used in structural stress and strain analysis. The target variable of requiring reliability analysis is estimated via Taylor expansion. Based on optimization theory and vertex solution theorem, the upper and lower bounds of the target variables are obtained, and also the interval reliability index. A typical elastostatics example is presented to illustrate the computational aspects of interval reliability analysis in comparison with the traditional probability method, it can be seen that the result calculated by the vertex solution theorem is consistent with that calculated by probability method.

scholarly journals On the Generalized Distance Energy of Graphs

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 17 ◽  
Author(s):  
Abdollah Alhevaz ◽  
Maryam Baghipur ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Connected Graph ◽  
Distance Matrix ◽  
Wiener Index ◽  
Diagonal Matrix ◽  
Upper And Lower Bounds ◽  
Star Graph ◽  
Extremal Graphs ◽  
Generalized Distance

The generalized distance matrix D α ( G ) of a connected graph G is defined as D α ( G ) = α T r ( G ) + ( 1 − α ) D ( G ) , where 0 ≤ α ≤ 1 , D ( G ) is the distance matrix and T r ( G ) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy E D α ( G ) . Some new upper and lower bounds for the generalized distance energy E D α ( G ) of G are established based on parameters including the Wiener index W ( G ) and the transmission degrees. Extremal graphs attaining these bounds are identified. It is found that the complete graph has the minimum generalized distance energy among all connected graphs, while the minimum is attained by the star graph among trees of order n.

scholarly journals Hadamard k-fractional inequalities of Fejér type for GA-s-convex mappings and applications

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Hui Lei ◽  
Gou Hu ◽  
Zhi-Jie Cao ◽  
Ting-Song Du
Keyword(s):  
Lower Bounds ◽  
Hypergeometric Functions ◽  
Upper And Lower Bounds ◽  
Weighted Inequalities ◽  
Convex Mappings ◽  
Special Means

Abstract The main aim of this paper is to establish some Fejér-type inequalities involving hypergeometric functions in terms of GA-s-convexity. For this purpose, we construct a Hadamard k-fractional identity related to geometrically symmetric mappings. Moreover, we give the upper and lower bounds for the weighted inequalities via products of two different mappings. Some applications of the presented results to special means are also provided.

scholarly journals On the Second-Largest Reciprocal Distance Signless Laplacian Eigenvalue

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 512
Author(s):  
Maryam Baghipur ◽  
Modjtaba Ghorbani ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Distance Matrix ◽  
Upper And Lower Bounds ◽  
Laplacian Eigenvalue ◽  
Signless Laplacian ◽  
Graph Parameters ◽  
Simple Connected Graph ◽  
Second Largest Eigenvalue ◽  
Reciprocal Distance Matrix

The signless Laplacian reciprocal distance matrix for a simple connected graph G is defined as RQ(G)=diag(RH(G))+RD(G). Here, RD(G) is the Harary matrix (also called reciprocal distance matrix) while diag(RH(G)) represents the diagonal matrix of the total reciprocal distance vertices. In the present work, some upper and lower bounds for the second-largest eigenvalue of the signless Laplacian reciprocal distance matrix of graphs in terms of various graph parameters are investigated. Besides, all graphs attaining these new bounds are characterized. Additionally, it is inferred that among all connected graphs with n vertices, the complete graph Kn and the graph Kn−e obtained from Kn by deleting an edge e have the maximum second-largest signless Laplacian reciprocal distance eigenvalue.

scholarly journals Multilevel Monte Carlo methods and lower–upper bounds in initial margin computations

2020 ◽  
Vol 26 (2) ◽  
pp. 131-161
Author(s):  
Florian Bourgey ◽  
Stefano De Marco ◽  
Emmanuel Gobet ◽  
Alexandre Zhou
Keyword(s):  
Monte Carlo ◽  
Lower Bounds ◽  
Asymptotic Optimality ◽  
Upper Bounds ◽  
Upper And Lower Bounds ◽  
Independent Random Variables ◽  
Outer Function ◽  
Control Problems ◽  
Multilevel Monte Carlo ◽  
Primal Dual

AbstractThe multilevel Monte Carlo (MLMC) method developed by M. B. Giles [Multilevel Monte Carlo path simulation, Oper. Res. 56 2008, 3, 607–617] has a natural application to the evaluation of nested expectations {\mathbb{E}[g(\mathbb{E}[f(X,Y)|X])]}, where {f,g} are functions and {(X,Y)} a couple of independent random variables. Apart from the pricing of American-type derivatives, such computations arise in a large variety of risk valuations (VaR or CVaR of a portfolio, CVA), and in the assessment of margin costs for centrally cleared portfolios. In this work, we focus on the computation of initial margin. We analyze the properties of corresponding MLMC estimators, for which we provide results of asymptotic optimality; at the technical level, we have to deal with limited regularity of the outer function g (which might fail to be everywhere differentiable). Parallel to this, we investigate upper and lower bounds for nested expectations as above, in the spirit of primal-dual algorithms for stochastic control problems.

scholarly journals A Lower Bound for the Query Phase of Contraction Hierarchies and Hub Labels and a Provably Optimal Instance-Based Schema

Algorithms ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 164
Author(s):  
Tobias Rupp ◽  
Stefan Funke
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Real World ◽  
Road Network ◽  
Upper And Lower Bounds ◽  
Bounded Degree ◽  
Shortest Path Routing ◽  
Graph Classes ◽  
Speed Up ◽  
To Come

We prove a Ω(n) lower bound on the query time for contraction hierarchies (CH) as well as hub labels, two popular speed-up techniques for shortest path routing. Our construction is based on a graph family not too far from subgraphs that occur in real-world road networks, in particular, it is planar and has a bounded degree. Additionally, we borrow ideas from our lower bound proof to come up with instance-based lower bounds for concrete road network instances of moderate size, reaching up to 96% of an upper bound given by a constructed CH. For a variant of our instance-based schema applied to some special graph classes, we can even show matching upper and lower bounds.

Localization of Discrete Spectrum of Multiparticle Schrödinger Operators

1985 ◽  
Vol 40 (10) ◽  
pp. 1052-1058 ◽  
Author(s):  
Heinz K. H. Siedentop
Keyword(s):  
Discrete Spectrum ◽  
Lower Bounds ◽  
Upper Bound ◽  
Schrödinger Operators ◽  
Upper And Lower Bounds ◽  
Schrodinger Operators

An upper bound on the dimension of eigenspaces of multiparticle Schrödinger operators is given. Its relation to upper and lower bounds on the eigenvalues is discussed.

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