2,411 research outputs found
Gurland's ratio for the gamma function
AbstractWe consider the ratio T(x, y) = г(x)г(y) / г2((x + y)/2) and its properties related to convexity, logarithmic convexity, Schur-convexity, and complete monotonicity. Several new bounds and asymptotic expansions for T are derived. Sharp bounds for the function x → x/(1 - e−x) are presented, as well as bounds for the trigamma function. The results are applied to a problem related to the volume of the unit ball in Rn and also to the problem of finding the inverse of the function x → T(1/x, 3/x), which is of importance in applied statistics
Numerical computation of transonic flows by finite-element and finite-difference methods
Studies on applications of the finite element approach to transonic flow calculations are reported. Different discretization techniques of the differential equations and boundary conditions are compared. Finite element analogs of Murman's mixed type finite difference operators for small disturbance formulations were constructed and the time dependent approach (using finite differences in time and finite elements in space) was examined
Scaling Interface Length Increase Rates in Richtmyer– Meshkov Instabilities
The interface area increase produced by large-amplitude wave refraction through an interface that separates fluids with different densities can have important physiochemical consequences, such as a fuel consumption rate increase in the case of a shock–flame interaction. Using the results of numerical simulations along with a scaling analysis, a unified scaling law of the interface length increase was developed applicable to shock and expansion wave refractions and both types of interface orientation with the respect to the incoming wave. To avoid a common difficulty in interface length quantification in the numerical tests, a sinusoidally perturbed interface was generated using gases with different temperatures. It was found that the rate of interface increase correlates almost linearly with the circulation deposited at the interface. When combined with earlier developed models of circulation deposition in Richtmyer–Meshkov instability, the obtained scaling law predicts dependence of interface dynamics on the basic problem parameters
Transient Thermal Response of Turbulent Compressible Boundary Layers
A numerical method is developed with the capability to predict transient thermal boundary layer response under various flow and thermal conditions. The transient thermal boundary layer variation due to a moving compressible turbulent fluid of varying temperature
was numerically studied on a two-dimensional semi-infinite flat plate. The compressible Reynolds-averaged boundary layer equations are transformed into incompressible form through the Dorodnitsyn–Howarth transformation and then solved with similarity transformations. Turbulence is modeled using a two-layer eddy viscosity model
developed by Cebeci and Smith, and the turbulent Prandtl number formulation originally developed by Kays and Crawford. The governing differential equations are discretized with the Keller-box method. The numerical accuracy is validated through grid-independence
studies and comparison with the steady state solution. In turbulent flow as
in laminar, the transient heat transfer rates are very different from that obtained from quasi-steady analysis. It is found that the time scale for response of the turbulent boundary layer to far-field temperature changes is 40% less than for laminar flow, and the turbulent local Nusselt number is approximately 4 times that of laminar flow at the final
steady state
End-to-End Formal Verification of Ethereum 2.0 Deposit Smart Contract
We report our experience in the formal verification of the deposit smart contract, whose correctness is critical for the security of Ethereum 2.0, a new Proof-of-Stake protocol for the Ethereum blockchain. The deposit contract implements an incremental Merkle tree algorithm whose correctness is highly nontrivial, and had not been proved before. We have verified the correctness of the compiled bytecode of the deposit contract to avoid the need to trust the underlying compiler. We found several critical issues of the deposit contract during the verification process, some of which were due to subtle hidden bugs of the compiler.Ope
Unifying Parsimonious Tree Reconciliation
Evolution is a process that is influenced by various environmental factors,
e.g. the interactions between different species, genes, and biogeographical
properties. Hence, it is interesting to study the combined evolutionary history
of multiple species, their genes, and the environment they live in. A common
approach to address this research problem is to describe each individual
evolution as a phylogenetic tree and construct a tree reconciliation which is
parsimonious with respect to a given event model. Unfortunately, most of the
previous approaches are designed only either for host-parasite systems, for
gene tree/species tree reconciliation, or biogeography. Hence, a method is
desirable, which addresses the general problem of mapping phylogenetic trees
and covering all varieties of coevolving systems, including e.g., predator-prey
and symbiotic relationships. To overcome this gap, we introduce a generalized
cophylogenetic event model considering the combinatorial complete set of local
coevolutionary events. We give a dynamic programming based heuristic for
solving the maximum parsimony reconciliation problem in time O(n^2), for two
phylogenies each with at most n leaves. Furthermore, we present an exact
branch-and-bound algorithm which uses the results from the dynamic programming
heuristic for discarding partial reconciliations. The approach has been
implemented as a Java application which is freely available from
http://pacosy.informatik.uni-leipzig.de/coresym.Comment: Peer-reviewed and presented as part of the 13th Workshop on
Algorithms in Bioinformatics (WABI2013
Lower bounds for the first eigenvalue of the magnetic Laplacian
We consider a Riemannian cylinder endowed with a closed potential 1-form A
and study the magnetic Laplacian with magnetic Neumann boundary conditions
associated with those data. We establish a sharp lower bound for the first
eigenvalue and show that the equality characterizes the situation where the
metric is a product. We then look at the case of a planar domain bounded by two
closed curves and obtain an explicit lower bound in terms of the geometry of
the domain. We finally discuss sharpness of this last estimate.Comment: Replaces in part arXiv:1611.0193
Community practice and religion at an Early Islamic cemetery in highland Central Asia
Archaeological studies of Early Islamic communities in Central Asia have focused on lowland urban communities. Here, the authors report on recent geophysical survey and excavation of an Early Islamic cemetery at Tashbulak in south-eastern Uzbekistan. AMS dating places the establishment of the cemetery in the mid-eighth century AD, making it one of the earliest Islamic burial grounds documented in Central Asia. Burials at Tashbulak conform to Islamic prescriptions for grave form and body deposition. The consistency in ritual suggests the existence of a funerary community of practice, challenging narratives of Islamic conversion in peripheral areas as a process of slow diffusion and emphasising the importance of archaeological approaches for documenting the diversity of Early Islamic communities.Introduction Background and rationale The site of Tashbulak Islamic burial The Tashbulak cemetery - Burial forms - Body treatment - Demographic profile - Chronology Discussion Conclusio
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