Branch identification and motion domain analysis of Stephenson type six-bar linkages

2007 ◽  
Vol 221 (5) ◽  
pp. 589-604 ◽  
Author(s):  
C-C Tsai ◽  
L-C T Wang
Keyword(s):  
Lower Bounds ◽  
Polynomial Equation ◽  
Domain Analysis ◽  
Upper And Lower Bounds ◽  
Computer Implementation ◽  
Input Output ◽  
Complicated Case ◽  
Sturm Theorem ◽  
The Dead ◽  
Selection Of

A general approach for branch identification and motion domain analysis of Stephenson type six-bar linkages is presented. By applying the Sturm theorem to the input-output polynomial equation, the dead-centre positions of the linkage are first evaluated and classified into two groups in order to discriminate the upper and lower bounds of the motion domains. The circuits of the linkage are then identified by matching the dead centres to the branches, which are attributed in accordance with the case where the input is assigned to a joint within the four-bar chain. Finally, the branches and motion domains of the more complicated case where the input is given through one of the uncoupled joints within the five-bar chain, are identified by mapping the circuits onto the domain of the specified input joint. This approach does not rely on the coupler curve of the constituent four-link mechanism. This is also suitable for computer implementation and can be systematically applied to all types of Stephenson linkages, regardless of the types of joints and the selection of input-output pair.

On the Dead-Center Positions of Stephenson Six-Bar Linkage

2011 ◽  
Vol 52-54 ◽  
pp. 915-919
Author(s):  
Yan Huo Zou ◽  
Xiao Ning Guo ◽  
Jin Kui Chu
Keyword(s):  
Analytical Method ◽  
Input Parameter ◽  
Polynomial Equation ◽  
New Method ◽  
Necessary Condition ◽  
Input Output ◽  
Simple Analytical Method ◽  
Condition Equation ◽  
The Dead

A new method for identifying the dead-center positions of the Stephenson six-bar linkage is presented by this article. This method uses the input-output polynomial equation of the linkage and the corresponding Sylvester's resultant to formulate the necessary condition of the dead-center configurations as a polynomial equation in terms of the input parameter; then through a simple analytical method to obtain all the truly dead-center positions among the double roots to the condition equation. An example is given to demonstrate the validity of this method.

On the dead-centre position analysis of Stephenson six-link linkages

2006 ◽  
Vol 220 (9) ◽  
pp. 1393-1404 ◽  
Author(s):  
C-C Tsai ◽  
L T Wang
Keyword(s):  
Input Parameter ◽  
Polynomial Equation ◽  
Necessary Condition ◽  
Input Output ◽  
Single Degree Of Freedom ◽  
Real Solutions ◽  
Geometric Conditions ◽  
Condition Equation ◽  
The Dead ◽  
Dead Centre

A new method for analysing the dead-centre positions of Stephenson type six-bar linkages is presented in this article. This method uses the input-output polynomial equation of the linkage and the corresponding Sturm functions to formulate the necessary condition of the dead-centre configurations as a polynomial equation in terms of the input parameter only. A simple analytical method for identifying the true dead-centre positions among the real solutions to the condition equation is also developed. The proposed method is conceptually straightforward and does not rely on any structure-related geometric conditions; therefore, it can be systematically applied to all types of Stephenson linkages and other multiple-loop, single degree-of-freedom linkages regardless of the selections of the input-output pair and the type of the joints.

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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