Search results for "0101 mathematics"
showing 9 items of 2089 documents
A Cluster Analysis Approach to Profile Men and Women’s Volley Positions in Professional Tennis Matches (Doubles)
2021
(1) Background: Tennis ball tracking technology allows the aquirement of novel and reliable data about several performance indicators, such as volley positions. This information is key to understand match dynamics in doubles tennis and to better help preparing players for the demands they will face in match play. As such, the purpose of this study was to describe and compare the different types of volley positions in men’s and women’s doubles professional tennis. (2) Methods: Ball tracking data were collected for 46 women (Billie Jean King Cup) and 96 men’s doubles matches (Davis Cup). The variables used were the distance to the net, the distance to the centre of the court and the height of…
Radical Besinnung in Formale und transzendentale Logik (1929)
2018
This paper explicates Husserl’s usage of what he calls “radical Besinnung” in Formale und transzendentale Logik (1929). Husserl introduces radical Besinnung as his method in the introduction to FTL. Radical Besinnung aims at criticizing the practice of formal sciences by means of transcendental phenomenological clarification of its aims and presuppositions. By showing how Husserl applies this method to the history of formal sciences down to mathematicians’ work in his time, the paper explains in detail the relationship between historical critical Besinnung and transcendental phenomenology. Ultimately the paper suggests that radical Besinnung should be viewed as a general methodological fram…
A Time-Non-Homogeneous Double-Ended Queue with Failures and Repairs and Its Continuous Approximation
2018
We consider a time-non-homogeneous double-ended queue subject to catastrophes and repairs. The catastrophes occur according to a non-homogeneous Poisson process and lead the system into a state of failure. Instantaneously, the system is put under repair, such that repair time is governed by a time-varying intensity function. We analyze the transient and the asymptotic behavior of the queueing system. Moreover, we derive a heavy-traffic approximation that allows approximating the state of the systems by a time-non-homogeneous Wiener process subject to jumps to a spurious state (due to catastrophes) and random returns to the zero state (due to repairs). Special attention is devoted to the cas…
Husserl's Transcendentalization of Mathematical Naturalism
2020
Abstract The paper aims to capture a form of naturalism that can be found “built-in” in phenomenology, namely the idea to take science or mathematics on its own, without postulating extraneous normative “molds” on it. The paper offers a detailed comparison of Penelope Maddy’s naturalism about mathematics and Husserl’s approach to mathematics in Formal and Transcendental Logic (1929). It argues that Maddy’s naturalized methodology is similar to the approach in the first part of the book. However, in the second part Husserl enters into a transcendental clarification of the evidences and presuppositions of the mathematicians’ work, thus “transcendentalizing” his otherwise naturalist approach t…
Designing a graphics processing unit accelerated petaflop capable lattice Boltzmann solver: Read aligned data layouts and asynchronous communication
2016
The lattice Boltzmann method is a well-established numerical approach for complex fluid flow simulations. Recently, general-purpose graphics processing units (GPUs) have become available as high-performance computing resources at large scale. We report on designing and implementing a lattice Boltzmann solver for multi-GPU systems that achieves 1.79 PFLOPS performance on 16,384 GPUs. To achieve this performance, we introduce a GPU compatible version of the so-called bundle data layout and eliminate the halo sites in order to improve data access alignment. Furthermore, we make use of the possibility to overlap data transfer between the host central processing unit and the device GPU with com…
Hölder regularity for the gradient of the inhomogeneous parabolic normalized p-Laplacian
2018
In this paper, we study an evolution equation involving the normalized [Formula: see text]-Laplacian and a bounded continuous source term. The normalized [Formula: see text]-Laplacian is in non-divergence form and arises for example from stochastic tug-of-war games with noise. We prove local [Formula: see text] regularity for the spatial gradient of the viscosity solutions. The proof is based on an improvement of flatness and proceeds by iteration.
Regularity for nonlinear stochastic games
2015
We establish regularity for functions satisfying a dynamic programming equation, which may arise for example from stochastic games or discretization schemes. Our results can also be utilized in obtaining regularity and existence results for the corresponding partial differential equations. peerReviewed
Remarks on regularity for p-Laplacian type equations in non-divergence form
2018
We study a singular or degenerate equation in non-divergence form modeled by the $p$-Laplacian, $$-|Du|^\gamma\left(\Delta u+(p-2)\Delta_\infty^N u\right)=f\ \ \ \ \text{in}\ \ \ \Omega.$$ We investigate local $C^{1,\alpha}$ regularity of viscosity solutions in the full range $\gamma>-1$ and $p>1$, and provide local $W^{2,2}$ estimates in the restricted cases where $p$ is close to 2 and $\gamma$ is close to 0.
Fractional Hardy inequalities and visibility of the boundary
2013
We prove fractional order Hardy inequalities on open sets under a combined fatness and visibility condition on the boundary. We demonstrate by counterexamples that fatness conditions alone are not sufficient for such Hardy inequalities to hold. In addition, we give a short exposition of various fatness conditions related to our main result, and apply fractional Hardy inequalities in connection to the boundedness of extension operators for fractional Sobolev spaces.