Effective Storm-Relative Helicity and Bulk Shear in Supercell Thunderstorm Environments

2007 ◽  
Vol 22 (1) ◽  
pp. 102-115 ◽  
Author(s):  
Richard L. Thompson ◽  
Corey M. Mead ◽  
Roger Edwards
Keyword(s):  
Lower Bounds ◽  
Broad Spectrum ◽  
Model Analysis ◽  
Vertical Shear ◽  
Upper And Lower Bounds ◽  
Wide Range ◽  
Equilibrium Level ◽  
Supercell Thunderstorm ◽  
Convective Inhibition ◽  
Minimum Constraints

Abstract A sample of 1185 Rapid Update Cycle (RUC) model analysis (0 h) proximity soundings, within 40 km and 30 min of radar-identified discrete storms, was categorized by several storm types: significantly tornadic supercells (F2 or greater damage), weakly tornadic supercells (F0–F1 damage), nontornadic supercells, elevated right-moving supercells, storms with marginal supercell characteristics, and nonsupercells. These proximity soundings served as the basis for calculations of storm-relative helicity and bulk shear intended to apply across a broad spectrum of thunderstorm types. An effective storm inflow layer was defined in terms of minimum constraints on lifted parcel CAPE and convective inhibition (CIN). Sixteen CAPE and CIN constraint combinations were examined, and the smallest CAPE (25 and 100 J kg−1) and largest CIN (−250 J kg−1) constraints provided the greatest probability of detecting an effective inflow layer within an 835-supercell subset of the proximity soundings. Effective storm-relative helicity (ESRH) calculations were based on the upper and lower bounds of the effective inflow layer. By confining the SRH calculation to the effective inflow layer, ESRH values can be compared consistently across a wide range of storm environments, including storms rooted above the ground. Similarly, the effective bulk shear (EBS) was defined in terms of the vertical shear through a percentage of the “storm depth,” as defined by the vertical distance from the effective inflow base to the equilibrium level associated with the most unstable parcel (maximum θe value) in the lowest 300 hPa. ESRH and EBS discriminate strongly between various storm types, and between supercells and nonsupercells, respectively.

scholarly journals Best possible rates of distribution of dense lattice orbits in homogeneous spaces

2018 ◽  
Vol 2018 (745) ◽  
pp. 155-188 ◽  
Author(s):  
Anish Ghosh ◽  
Alexander Gorodnik ◽  
Amos Nevo
Keyword(s):  
Lower Bounds ◽  
Diophantine Approximation ◽  
Upper Bound ◽  
Homogeneous Spaces ◽  
Automorphic Representation ◽  
Upper And Lower Bounds ◽  
Duality Principle ◽  
Wide Range ◽  
Dense Orbits

Abstract This paper establishes upper and lower bounds on the speed of approximation in a wide range of natural Diophantine approximation problems. The upper and lower bounds coincide in many cases, giving rise to optimal results in Diophantine approximation which were inaccessible previously. Our approach proceeds by establishing, more generally, upper and lower bounds for the rate of distribution of dense orbits of a lattice subgroup Γ in a connected Lie (or algebraic) group G, acting on suitable homogeneous spaces G/H. The upper bound is derived using a quantitative duality principle for homogeneous spaces, reducing it to a rate of convergence in the mean ergodic theorem for a family of averaging operators supported on H and acting on G/Γ. In particular, the quality of the upper bound on the rate of distribution we obtain is determined explicitly by the spectrum of H in the automorphic representation on L^{2} (Γ \setminus G). We show that the rate is best possible when the representation in question is tempered, and show that the latter condition holds in a wide range of examples.

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.

SET-VALUED PERFORMANCE APPROXIMATIONS FOR THE QUEUE GIVEN PARTIAL INFORMATION

2020 ◽  
pp. 1-23
Author(s):  
Yan Chen ◽  
Ward Whitt
Keyword(s):  
Steady State ◽  
Decay Rate ◽  
Waiting Time ◽  
Partial Information ◽  
Upper And Lower Bounds ◽  
Interarrival Time ◽  
Limited Information ◽  
Wide Range ◽  
The Mean ◽  
Third Moment

In order to understand queueing performance given only partial information about the model, we propose determining intervals of likely values of performance measures given that limited information. We illustrate this approach for the mean steady-state waiting time in the $GI/GI/K$ queue. We start by specifying the first two moments of the interarrival-time and service-time distributions, and then consider additional information about these underlying distributions, in particular, a third moment and a Laplace transform value. As a theoretical basis, we apply extremal models yielding tight upper and lower bounds on the asymptotic decay rate of the steady-state waiting-time tail probability. We illustrate by constructing the theoretically justified intervals of values for the decay rate and the associated heuristically determined interval of values for the mean waiting times. Without extra information, the extremal models involve two-point distributions, which yield a wide range for the mean. Adding constraints on the third moment and a transform value produces three-point extremal distributions, which significantly reduce the range, producing practical levels of accuracy.

scholarly journals An exact expression of positive periodic solution for a first-order singular equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yun Xin ◽  
Xiaoxiao Cui ◽  
Jie Liu
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Lower Bounds ◽  
Topological Degree ◽  
Order Differential Equation ◽  
Positive Periodic Solution ◽  
Exact Expression ◽  
Upper And Lower Bounds ◽  
Singular Equation ◽  
First Order

Abstract The main purpose of this paper is to obtain an exact expression of the positive periodic solution for a first-order differential equation with attractive and repulsive singularities. Moreover, we prove the existence of at least one positive periodic solution for this equation with an indefinite singularity by applications of topological degree theorem, and give the upper and lower bounds of the positive periodic solution.

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