Related papers: A Wild Steiner-Lehmus Chase

This paper studies brachistochrone trajectories. Four rules are formulated as sufficient conditions. Two rules apply for a general conservative force. Two rules apply for a central force. A central force allows wire replacement. The wire is…

Sufficient and necessary conditions are presented for the comparison theorem of path dependent $G$-SDEs. Different from the corresponding study in path independent $G$-SDEs, a probability method is applied to prove these results. Moreover,…

Using Stein's method, we prove an abstract result that yields multivariate central limit theorems with a rate of convergence for time-dependent dynamical systems. As examples we study a model of expanding circle maps and a quasistatic…

As a first application of a very old theorem, known as Herschel's theorem, we provide direct elementary proofs of several explicit expressions for some numbers and polynomials that are known in combinatorics. The second application deals…

Let $v_1, ..., v_m$ be a finite set of unit vectors in $\RR^n$. Suppose that an infinite sequence of Steiner symmetrizations are applied to a compact convex set $K$ in $\RR^n$, where each of the symmetrizations is taken with respect to a…

All experiments attempting to verify the invariance of speed of light directly are based on two-way speed measurement. The challenge in one-way speed measurement, the requirement of spatially separated synchronised clocks, can be possibly…

Farkas established that a system of linear inequalities has a solution if and only if we cannot obtain a contradiction by taking a linear combination of the inequalities. We state and formally prove several Farkas-like theorems over…

The Erd\H{o}s similarity conjecture asserted that an infinite set of real numbers cannot be affinely embedded into every measurable set of positive Lebesgue measure. The problem is still open, in particular for all fast decaying sequences.…

While studying the motion of a heavy symmetric top, in general, constants of motion are used. Some students may want to understand the motion in terms of torque, which can lie on their routine based on the usage of Newton's second law.…

This paper discusses the formalization of proofs "by diagram chasing", a standard technique for proving properties in abelian categories. We discuss how the essence of diagram chases can be captured by a simple many-sorted first-order…

In this paper we extend results obtained in [3] and [5]. By considering a semi linear conservation law with velocity in $L^\infty$, we prove by fixed point arguments existence and uniqueness result and even in a penalized situation.

Fine's theorem concerns the question of determining the conditions under which a certain set of probabilities for pairs of four bivalent quantities may be taken to be the marginals of an underlying probability distribution. The eight CHSH…

The chase is a sound and complete algorithm for conjunctive query answering over ontologies of existential rules with equality. To enable its effective use, we can apply acyclicity notions; that is, sufficient conditions that guarantee…

The fundamental theorem of affine geometry says that a self-bijection $f$ of a finite-dimensional affine space over a possibly skew field takes left affine subspaces to left affine subspaces of the same dimension, then $f$ of the expected…

A class of backward doubly stochastic differential equations (BDSDEs in short) with continuous coefficients is studied. We give the comparison theorems, the existence of the maximal solution and the structure of solutions for BDSDEs with…

For a moving bicycle, the power can be modelled as a response to the propulsion of the centre of mass of the bicycle-cyclist system. On a velodrome, an accurate modelling of power requires a distinction between the trajectory of the wheels…

The study of the movement of flocks, whether biological or technological is motivated by the desire to understand the capability of coherent motion of a large number of agents that only receive very limited information. In a biological…

We create a new two-player game on the Sperner Triangle based on Sperner's lemma. Our game has simple rules and several desirable properties. First, the game is always certain to have a winner. Second, like many other interesting games such…

In a noise driving by a multivariate point process $\mu$ with predictable compensator $\nu$, we prove existence and uniqueness of the reflected backward stochastic differential equation's solution with a lower obstacle…

We derive a simple consistency relation from the running of the tensor-to-scalar ratio. This new relation is first order in the slow-roll approximation. While for single field models we can obtain what can be found by using other…