Bose systems in linear traps: Exact calculations versus effective space dimensionality

2021 ◽  
Vol 47 (7) ◽  
pp. 577-583
Author(s):  
Z. Shvaika ◽  
P. Sapriianchuk ◽  
A. Rovenchak
Keyword(s):  
Exact Calculations

scholarly journals Pricing Perpetual American Put Options with Asset-Dependent Discounting

2021 ◽  
Vol 14 (3) ◽  
pp. 130
Author(s):  
Jonas Al-Hadad ◽  
Zbigniew Palmowski
Keyword(s):  
Value Function ◽  
Asset Price ◽  
Stopping Times ◽  
Martingale Measure ◽  
Put Options ◽  
American Put Options ◽  
Exact Calculations ◽  
Negative Exponential ◽  
American Put ◽  
The Value Function

The main objective of this paper is to present an algorithm of pricing perpetual American put options with asset-dependent discounting. The value function of such an instrument can be described as VAPutω(s)=supτ∈TEs[e−∫0τω(Sw)dw(K−Sτ)+], where T is a family of stopping times, ω is a discount function and E is an expectation taken with respect to a martingale measure. Moreover, we assume that the asset price process St is a geometric Lévy process with negative exponential jumps, i.e., St=seζt+σBt−∑i=1NtYi. The asset-dependent discounting is reflected in the ω function, so this approach is a generalisation of the classic case when ω is constant. It turns out that under certain conditions on the ω function, the value function VAPutω(s) is convex and can be represented in a closed form. We provide an option pricing algorithm in this scenario and we present exact calculations for the particular choices of ω such that VAPutω(s) takes a simplified form.

scholarly journals Tetrahedra of varying density and their applications

2021 ◽  
Author(s):  
Dennis R. Bukenberger ◽  
Hendrik P. A. Lensch
Keyword(s):  
Tetrahedral Mesh ◽  
Rotational Inertia ◽  
Exact Mass ◽  
Accurate Analysis ◽  
Exact Integration ◽  
Voronoi Cells ◽  
Current State ◽  
Chebyshev Norm ◽  
Exact Calculations ◽  
Vector Matrix

Abstract We propose concepts to utilize basic mathematical principles for computing the exact mass properties of objects with varying densities. For objects given as 3D triangle meshes, the method is analytically accurate and at the same time faster than any established approximation method. Our concept is based on tetrahedra as underlying primitives, which allows for the object’s actual mesh surface to be incorporated in the computation. The density within a tetrahedron is allowed to vary linearly, i.e., arbitrary density fields can be approximated by specifying the density at all vertices of a tetrahedral mesh. Involved integrals are formulated in closed form and can be evaluated by simple, easily parallelized, vector-matrix multiplications. The ability to compute exact masses and centroids for objects of varying density enables novel or more exact solutions to several interesting problems: besides the accurate analysis of objects under given density fields, this includes the synthesis of parameterized density functions for the make-it-stand challenge or manufacturing of objects with controlled rotational inertia. In addition, based on the tetrahedralization of Voronoi cells we introduce a precise method to solve $$L_{2|\infty }$$ L 2 | ∞ Lloyd relaxations by exact integration of the Chebyshev norm. In the context of additive manufacturing research, objects of varying density are a prominent topic. However, current state-of-the-art algorithms are still based on voxelizations, which produce rather crude approximations of masses and mass centers of 3D objects. Many existing frameworks will benefit by replacing approximations with fast and exact calculations. Graphic abstract

Exact calculations in the d-s nuclear shell

1966 ◽  
Vol 86 (2) ◽  
pp. 457-470 ◽  
Author(s):  
Ricardo A. Broglia ◽  
Ernesto E. Maqueda
Keyword(s):  
Exact Calculations ◽  
Nuclear Shell

POLYNOMIAL DEHN FUNCTIONS AND THE LENGTH OF ASYNCHRONOUSLY AUTOMATIC STRUCTURES

2002 ◽  
Vol 85 (2) ◽  
pp. 441-466 ◽  
Author(s):  
MARTIN R. BRIDSON
Keyword(s):  
Automorphism Group ◽  
Free Group ◽  
Dehn Function ◽  
Arbitrary Degree ◽  
Dehn Functions ◽  
Automatic Structures ◽  
Automatic Groups ◽  
Observed Behaviour ◽  
Exact Calculations ◽  
Do So

We extend the range of observed behaviour among length functions of optimal asynchronously automatic structures. We do so by means of a construction that yields asynchronously automatic groups with finite aspherical presentations where the Dehn function of the group is polynomial of arbitrary degree. Many of these groups can be embedded in the automorphism group of a free group. Moreover, the fact that the groups have aspherical presentations makes them useful tools in the search to determine the spectrum of exponents for second order Dehn functions. We contribute to this search by giving the first exact calculations of groups with quadratic and superquadratic exponents. 2000 Mathematical Subject Classification:20F06, 20F65, 20F69.

Exact calculations of N-d polarization

1972 ◽  
Vol 40 (6) ◽  
pp. 605-606 ◽  
Author(s):  
P. Doleschall ◽  
J.C. Aarons ◽  
I.H. Sloan
Keyword(s):  
Exact Calculations
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