Prediction of the upper and lower bounds of electric potentials in a steady‐state current field with uncertain‐but‐bounded parameters

2018 ◽  
Vol 14 (1) ◽  
pp. 29-36
Author(s):  
Pengbo Wang ◽  
Jingxuan Wang
Keyword(s):  
Steady State ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Current Field ◽  
Steady State Current ◽  
Electric Potentials

scholarly journals Transient probability currents provide upper and lower bounds on non-equilibrium steady-state currents in the Smoluchowski picture

2019 ◽  
Vol 151 (17) ◽  
pp. 174108 ◽  
Author(s):  
Jeremy Copperman ◽  
David Aristoff ◽  
Dmitrii E. Makarov ◽  
Gideon Simpson ◽  
Daniel M. Zuckerman
Keyword(s):  
Steady State ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Transient Probability ◽  
Non Equilibrium

Taylor series expansion for evaluating the bounds of electric potentials in an electrostatic system with interval parameters

2018 ◽  
Vol 37 (2) ◽  
pp. 832-848
Author(s):  
Pengbo Wang ◽  
Jingxuan Wang
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Lower Bounds ◽  
Taylor Series ◽  
Taylor Series Expansion ◽  
Upper And Lower Bounds ◽  
Content Type ◽  
Interval Parameters ◽  
Electric Potentials ◽  
Electrostatic System

PurposeUncertainty is ubiquitous in practical engineering and scientific research. The uncertainties in parameters can be treated as interval numbers. The prediction of upper and lower bounds of the response of a system including uncertain parameters is of immense significance in uncertainty analysis. This paper aims to evaluate the upper and lower bounds of electric potentials in an electrostatic system efficiently with interval parameters. Design/methodology/approachThe Taylor series expansion is proposed for evaluating the upper and lower bounds of electric potentials in an electrostatic system with interval parameters. The uncertain parameters of the electrostatic system are represented by interval notations. By performing Taylor series expansion on the electric potentials obtained using the equilibrium governing equation and by using the properties of interval mathematics, the upper and lower bounds of the electric potentials of an electrostatic system can be calculated. FindingsTo evaluate the accuracy and efficiency of the proposed method, the upper and lower bounds of the electric potentials and the computation time of the proposed method are compared with those obtained using the Monte Carlo simulation, which is referred to as a reference solution. Numerical examples illustrate that the bounds of electric potentials of this method are consistent with those obtained using the Monte Carlo simulation. Moreover, the proposed method is significantly more time-saving. Originality/valueThis paper provides a rapid computational method to estimate the upper and lower bounds of electric potentials in electrostatics analysis with interval parameters. The precision of the proposed method is acceptable for engineering applications, and the computation time of the proposed method is significantly less than that of the Monte Carlo simulation, which is the most widely used method related to uncertainties. The Monte Carlo simulation requires a large number of samplings, and this leads to significant runtime consumption.

The Analysis of Gear Contact under Cyclical Load

2011 ◽  
Vol 86 ◽  
pp. 809-812
Author(s):  
Li Ping Wang ◽  
Ying Qiang Xu ◽  
Yuan Yuan
Keyword(s):  
Steady State ◽  
Residual Stresses ◽  
Lower Bounds ◽  
Frictional Coefficient ◽  
Upper And Lower Bounds ◽  
Shakedown Analysis ◽  
Local Coordinates ◽  
Gear Contact ◽  
Residual Stresses And Strains ◽  
Gear Profile

Shakedown analysis of gear contact is very important. Local coordinates are constructed on different meshing points because curvature of gear profile is not constant and then distributions of residual stresses and strains are given. Upper and lower bounds for the shakedown limits have been obtained. The steady-state residual stresses of gear under repeat meshing are calculated and relations between shakedown limits and frictional coefficient/meshing position are given. The results are useful information for the strength design of gear.

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.

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