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Frank Klinker

Publications and source records attributed to Frank Klinker.

17 recordsLinked to original sources
arXiv2020

On the approximation of D.I.Y. water rocket dynamics including air drag

If you want to get accurate predictions for the motion of water and air propelled D.I.Y rockets, neglecting air resistance is not an option. But the theoretical analysis including air drag leads to a system of differential equations which can only be solved numerically. We propose an approximation which simply works by the estimate of a definite integral and which is even feasible for undergraduate physics courses. The results only slightly deviate from the reference data (received by the Runge-Kutta method). The motion is divided into several flight phases that are discussed separately and the resulting equations are solved by analytic and numeric methods. The different results from the flight phases are collected and are compared to data that has been achieved by well explained and documented experiments. Furthermore, we theoretically estimate the rocket's drag coefficient. The result is confirmed by a wind tunnel experiment.

physics.pop-ph↗
arXiv2020

Exponential moving average versus moving exponential average

In this note we discuss the mathematical tools to define trend indicators which are used to describe market trends. We explain the relation between averages and moving averages on the one hand and the so called exponential moving average (EMA) on the other hand. We present a lot of examples and give the definition of the most frequently used trend indicator, the MACD, and discuss its properties.

stat.OT↗
arXiv2020

Ein optimiertes Glättungsverfahren motiviert durch eine technische Fragestellung (An optimized smoothing method motivated by a technical problem)

Ausgehend von einer konkreten technischen Fragestellung diskutieren wir in dieser Notiz die Anwendung verschiedener Glättungsverfahren auf Datensätze mit vorgegebener Struktur. Wir stellen die Verfahren im Detail vor und besprechen die Vorund Nachteile. Insbesondere stellen wir hier die symmetrisierte exponentielle Glättung vor, die ein sehr gutes Glättungsverhalten mit einem hohen Maß~an Symmetrieerhaltung kombiniert. (Based on a specific technical question, we discuss the application of various smoothing methods to data sets with a particular structure. We present the methods in detail and discuss their advantages and disadvantages. In particular, we present the symmetrized exponential smoothing that combines very good smoothing behavior with a high degree of symmetry-conservation)

math.GM↗
arXiv2020

Supersymmetric Killing Structures

In this text we combine the notions of supergeometry and supersymmetry. We construct a special class of supermanifolds whose reduced manifolds are (pseudo) Riemannian manifolds. These supermanifolds allow us to treat vector fields on the one hand and spinor fields on the other hand as equivalent geometric objects. This is the starting point of our definition of {supersymmetric Killing structures}. The latter combines subspaces of vector fields and spinor fields, provided they fulfill certain field equations. This naturally leads to a superalgebra that extends the supersymmetry algebra to the case of non-flat reduced space. We examine in detail the additional terms that enter into this structure and we give a lot of examples.

math.DG↗
arXiv2018

A note on the regularity of matrices with uniform polynomial entries

In this text we study the regularity of matrices with special polynomial entries. Barring some mild conditions we show that these matrices are regular if a natural limit size is not exceeded. The proof draws connections to generalized Vandermonde matrices and Schur polynomials that are discussed in detail.

math.RT↗
arXiv2017

The general non-symmetric, unbalanced star circuit: On the geometrization of problems in electrical measurement

We provide the general solution of problems concerning AC star circuits by turning them into geometric problems. We show that one problem is strongly related to the Fermat-point of a triangle. We present a solution that is well adapted to the practical application the problem is based on. Furthermore, we solve a generalization of the geometric situation and discuss the relation to non-symmetric, unbalanced AC star circuits.

math-ph↗
arXiv2017

An explicit description of $SL(2,\mathbb{C})$ in terms of $SO^+(3,1)$ and vice versa

In this note we present explicit and elementary formulas for the correspondence between the group of special Lorentz transformation $SO^+(3,1)$, on the one hand, and its spin group $SL(2,\mathbb{C})$, on the other hand. Although we will not mention Clifford algebra terminology explicitly, it is hidden in our calculations by using complex $2\times2$-matrices. Nevertheless, our calculations are strongly motivated by the Clifford algebra $\mathfrak{gl}(4,\mathbb{C})$ of four-dimensional space-time.

math-ph↗
arXiv2015

A family of non-restricted $D=11$ geometric supersymmetries

We construct a two parameter family of eleven-dimensional indecomposable Cahen-Wallach spaces with irreducible, non-flat, non-restricted geometric supersymmetry of fraction $ν=\tfrac{3}{4}$. Its compactified moduli space can be parametrized by a compact interval with two points corresponding to two non-isometric, decomposable spaces. These singular spaces are associated to a restricted $N=4$ geometric supersymmetry with $ν=\tfrac{1}{2}$ in dimension six and a non-restricted $N=2$ geometric supersymmetry with $ν=\tfrac{3}{4}$ in dimension nine.

math.DG↗
arXiv2014

Eleven-dimensional symmetric supergravity backgrounds, their geometric superalgebras, and a common reduction

We present two different families of eleven-dimensional manifolds that admit non-restricted extensions of the isometry algebras to geometric superalgebras. Both families admit points for which the superalgebra extends to a super Lie algebra; on the one hand, a family of $N=1$, $ν={}^3\!/\!_4$ supergravity backgrounds and, on the other hand, a family of $N=1$, $ν=1$ supergravity background. Furthermore, both families admit a point that can be identified with an $N=4$, $ν={}^1\!/\!_2$ six-dimensional supergravity background.

hep-th↗
arXiv2014

Connections on Cahen-Wallach spaces

We systematically discuss connections on the spinor bundle of Cahen-Wallach symmetric spaces. A large class of these connections is closely connected to a quadratic relation on Clifford algebras. This relation in turn is associated to the symmetric linear map that defines the underlying space. We present various solutions of this relation. Moreover, we show that the solutions we present provide a complete list with respect to a particular algebraic condition on the parameters that enter into the construction.

math.DG↗
arXiv2011

Generalized duality for k-forms

We give the definition of a duality that is applicable to arbitrary $k$-forms. The operator that defines the duality depends on a fixed form $Ω$. Our definition extends in a very natural way the Hodge duality of $n$-forms in $2n$ dimensional spaces and the generalized duality of two-forms. We discuss the properties of the duality in the case where $Ω$ is invariant with respect to a subalgebra of $\mathfrak{so}(V)$. Furthermore, we give examples for the invariant case as well as for the case of discrete symmetry.

math.DG↗
arXiv2008

SUSY structures on deformed supermanifolds

We construct a geometric structure on deformed supermanifolds as a certain subalgebra of the vector fields. In the classical limit we obtain a decoupling of the infinitesimal odd and even transformations, whereas in the semiclassical limit the result is a representation of the supersymmetry algebra. In the case of mass preserving structure we describe all high energy corrections to this algebra.

math.DG↗
arXiv2008

Polynomial poly-vector fields

In this text we give a decomposition result on polynomial poly-vector fields generalizing a result on the decomposition of homogeneous Poisson structures. We discuss consequences of this decomposition result in particular for low dimensions and low degrees. We provide the tools to calculate simple cubic Poisson structures in dimension three and quadratic Poisson structures in dimension four. Our decomposition result has a nice effect on the relation between Poisson structures and Jacobi structures.

math.DG↗
arXiv2007

The decomposition of the spinor bundle of Grassmann manifolds

The decomposition of the spinor bundle of the spin Grassmann manifolds $G_{m,n}=SO(m+n)/SO(m)\times SO(n)$ into irreducible representations of $\mathfrak{so}(m)\oplus\mathfrak{so}(n)$ is presented. A universal construction is developed and the general statement is proven for $G_{2k+1,3}$, $G_{2k,4}$, and $G_{2k+1,5}$ for all $k$. The decomposition is used to discuss properties of the spectrum and the eigenspaces of the Dirac operator.

math.DG↗
arXiv2006

The Torsion of Spinor Connections and Related Structures

In this text we introduce the torsion of spinor connections. In terms of the torsion we give conditions on a spinor connection to produce Killing vector fields. We relate the Bianchi type identities for the torsion of spinor connections with Jacobi identities for vector fields on supermanifolds. Furthermore, we discuss applications of this notion of torsion.

math.DG↗
arXiv2003

The spinor bundle of Riemannian products

In this note we compare the spinor bundle of a Riemannian manifold $(M=M_1\times...\times M_N,g)$ with the spinor bundles of the Riemannian factors $(M_i,g_i)$. We show, that - without any holonomy conditions - the spinor bundle of $(M,g)$ for a special class of metrics is isomorphic to a bundle obtained by tensoring the spinor bundles of $(M_i,g_i)$ in an appropriate way.

math.DG↗