Related papers: Uniform Triangles with Equality Constraints

In the paper, the authors find the best possible constants appeared in two inequalities for bounding the Seiffert mean by the linear combinations of the arithmetic, centroidal, and contra-harmonic means.

Integer programs defined by two equations with two free integer variables and nonnegative continuous variables have three types of nontrivial facets: split, triangle or quadrilateral inequalities. In this paper, we compare the strength of…

An $N$-tiling of triangle $ABC$ by triangle $T$ (the `tile') is a way of writing $ABC$ as a union of $N$ copies of $T$ overlapping only at their boundaries. Let the tile $T$ have angles $(\alpha,\beta,\gamma)$, and sides $(a,b,c)$. This…

Constraints on the CKM angle \gamma are presented from GLW, ADS, and GGSZ analyses of B+- -> D K+- at the LHCb experiment. The branching fractions of B0 -> D0bar K+ \pi- and Bs -> D0bar K- \pi+ are also reported, measured relative to the…

For a C*-algebra A we consider the problem of when the set $TM_0(A)$ of all two-sided multiplications $x \mapsto axb$ ($a,b \in A$) on A is norm closed, as a subset of B(A). We first show that $TM_0(A)$ is norm closed for all prime…

We show that if a closed $C^1$-smooth surface in a Riemannian manifold has bounded Kolasinski--Menger energy, then it can be triangulated with triangles whose number is bounded by the energy and the area. Each of the triangles is an image…

We show that for a convex solid set of positive random variables to be tight, or equivalently bounded in probability, it is necessary and sufficient that it is radially bounded, i.e. that every ray passing through one of its elements…

The Bruss-Robertson inequality gives a bound on the maximal number of elements of a random sample whose sum is less than a specified value, and the extension of that inequality which is given here neither requires the independence of the…

We investigate the clustering transition undergone by an exemplary random constraint satisfaction problem, the bicoloring of $k$-uniform random hypergraphs, when its solutions are weighted non-uniformly, with a soft interaction between…

String theory in 4 dimensions has the unique feature that a topological term, the oriented self-intersection number, can be added to the usual action. It has been suggested that the corresponding theory of random surfaces wold be free from…

It is consistent that ZF+DC holds, the hypergraph of rectangles on a given Euclidean space has countable chromatic number, while the hypergraph of equilateral triangles in two-dimensional Euclidean space does not.

It has been pointed out by Gronau and Rosner that the angle gamma of the unitarity triangle could be determined by combining future results on B_s and B_d decays to K pi. Here we show that it is important to include in the analysis the…

We present a variation of the broken stick problem in which $n$ stick lengths are sampled uniformly at random. We prove that the probability that no three sticks can form a triangle is the reciprocal of the product of the first $n$…

Among the topics we discuss are certain joint densities (for sides and for angles), acuteness probabilities and bivariate Rice moments.

Time reversal symmetric triangular maps of the unit square are introduced with the property that the time evolution of one of their two variables is determined by a piecewise expanding map of the unit interval. We study their statistical…

Given a triangulation of a closed, oriented, irreducible, atoroidal 3-manifold every oriented, incompressible surface may be isotoped into normal position relative to the triangulation. Such a normal oriented surface is then encoded by…

We study solutions to the equation $a+b=c$, where $a,b,c$ form a triple of coprime natural numbers. The $abc$ conjecture asserts that, for any $\epsilon>0$, such triples satisfy $\mathrm{rad}(abc) \ge c^{1-\epsilon}$ with finitely many…

Let $ABC$ be an equilateral triangle. For certain triangles $T$ (the "tile") and certain $N$, it is possible to cut $ABC$ into $N$ copies of $T$. It is known that only certain shapes of $T$ are possible, but until now very little was known…

It is shown that the unique representation of positive integers in terms of tribonacci numbers and the unique representation in terms of iterated A, B and C sequences defined from the tribonacci word are equivalent. Two auxiliary…

We consider three modes $A$, $B$ and $C$ and derive continuous variable monogamy inequalities that constrain the distribution of bipartite entanglement amongst the three modes. The inequalities hold for all such tripartite states, without…