Related papers: The p-widths of $RP^2$

The number of essentially different square polyominoes of order n and minimum perimeter p(n) is enumerated.

Pseudo-Riemannian metrics with Levi-Civita connection in the projective class of a given torsion free affine connection can be obtained from (and are equivalent to) the maximal rank solutions of a certain overdetermined projectively…

Let $p$ be a real number greater than one and let $X$ be a locally compact, noncompact metric measure space that satisfies certain conditions. The $p$-Royden and $p$-harmonic boundaries of $X$ are constructed by using the $p$-Royden algebra…

In this article, we introduce the notion of $\mathcal P$-triviality of topological manifolds and give a complete description of the $\mathcal P$-triviality of stunted real and complex projective spaces.

Let A be a based subspace of Y. Under the assumptions that Y is path-connected and that the reduced diagonal map of A induces the zero map in all mod 2 reduced homology groups, we compute a formula for the mod 2 reduced Poincar\'{e} series…

In this paper we present an extension of the classical Root-Locus (RL) method where the points are calculated in the real projective plane instead of the conventional affine real plane; we denominate this extension of the Root-Locus as…

Let I = p_1^{m_1} \cap ... \cap p_s^{m_s} be the defining ideal of a scheme of fat points in P^{n_1} x ... x P^{n_k} with support in generic position. When all the m_i's are 1, we explicitly calculate the Castelnuovo-Mumford regularity of…

In the first part we study deviation of a polynomial from its mathematical expectation. This deviation can be estimated from above by Carbery--Wright inequality, so we investigate estimates of the deviation from below. We obtain such…

The numerical radius of the general $2\times2$ complex matrix is calculated.

We calculate the dimension of the locus of elliptic surfaces over P^1 with a section and a given Picard number, in the corresponding moduli space.

We consider the pointwise in space Lp-type regularity for elliptic and parabolic equations of order m in Rn. We provide pointwise Schauder estimates for the general range of Lp exponents, extending previous results from p > n/m to 1 < p <…

If a bounded domain can be covered by the polydisk through a rational proper holomorphic map, then the Bergman projection is $L^p$-bounded for $p$ in a certain range depending on the ramified rational covering. This result can be applied to…

In the 19th International Symposium on Advances in Robot Kinematics the author introduced a novel class of continuous flexible discrete surfaces and mentioned that these so-called P-hedra (or P-nets) allow direct access to their spatial…

We compute the Kodaira dimension of the universal Picard variety P_{d,g} parameterizing line bundles of degree d on curves of genus g under the assumption that (d-g+1,2g-2)=1. We also give partial results for arbitrary degrees d and we…

All rational homology groups of unordered configuration spaces of the Moebius strip and the projective plane are calculated

We give a lower bound for the numerical index of two-dimensional real spaces with absolute and symmetric norm. This allows us to compute the numerical index of the two-dimensional real $L_p$-space for $3/2\leq p\leq 3$.

In this paper we give an algorithm to calculate the coefficients of the p-adic expansion of a rational numbers, and we give a method to decide whether this expansion is periodic or ultimately periodic.

In this paper we provide a priori error estimates with explicit constants for both the $L^2$-projection and the Ritz projection onto spline spaces of arbitrary smoothness defined on arbitrary grids. This extends the results recently…

We prove an inequality of Bonnesen type for the real projective plane, generalizing Pu's systolic inequality for positively-curved metrics. The remainder term in the inequality, analogous to that in Bonnesen's inequality, is a function of…

We consider products of uniform random variables from the Stiefel manifold of orthonormal $k$-frames in $\mathbb{R}^n$, $k \le n$, and random vectors from the $n$-dimensional $\ell_p^n$-ball $\mathbb{B}_p^n$ with certain $p$-radial…