Related papers: On partial barycentric subdivision
Hausdorff dimension of level sets of generic continuous functions defined on fractals can give information about the "thickness/narrow cross-sections" "network" corresponding to a fractal set, $F$. This lead to the definition of the…
Special birational transformations $\Phi:\p^r\da Z$ defined by quadric hypersurfaces are studied by means of the variety of lines $\mathcal L_z\subset\p^{r-1}$ passing through a general point $z\in Z$. Classification results are obtained…
Let k be an algebraically closed field of characteristic 0 and let D be a division algebra whose center F contains k. We shall say that D can be reduced to r parameters if D = D_0 tensor_{F_0} F, where D_0 is a division algebra, the center…
We introduce a definition of the fractional Laplacian $(-\Delta)^{s(\cdot)}$ with spatially variable order $s:\Omega\to [0,1]$ and study the solvability of the associated Poisson problem on a bounded domain $\Omega$. The initial motivation…
Let $\{K_t\}_{t>0}$ be the semigroup of linear operators generated by a Schr\"odinger operator $-L=\Delta - V(x)$ on $\mathbb R^d$, $d\geq 3$, where $V(x)\geq 0$ satisfies $\Delta^{-1} V\in L^\infty$. We say that an $L^1$-function $f$…
A classical question in PL topology, asked among others by Hudson, Lickorish, and Kirby, is whether every linear subdivision of the d-simplex is simplicially collapsible. The answer is known to be positive for d<4. We solve the problem up…
Let $L_H$ denote the set of all normalized locally one-to-one and sense-preserving harmonic functions in the unit disc $\Delta$. It is well-known that every complex-valued harmonic function in the unit disc $\Delta$ can be uniquely…
In this paper we investigate fractional differential equations with Hilfer fractional derivative of order $1<\gamma<2$ and type $\delta \in [0,1]$ in a Banach space. We introduce a family of general fractional cosine operator functions of…
We prove the $L^2$-Euler characteristic has the invariance under the barycentric subdivision only for finite acyclic categories. And we extend the definition of $L^2$-Euler characteristic and prove the extended $L^2$-Euler characteristic…
Results of R. Stanley and M. Masuda completely characterize the h-vectors of simplicial posets whose order complexes are spheres. In this paper we examine the corresponding question in the case where the order complex is a ball. Using the…
The spectrum of the Laplacian of successive Barycentric subdivisions of a graph converges exponentially fast to a limit which only depends on the clique number of the initial graph and not on the graph itself. The proof uses an explicit…
We generalize the fractional Caputo derivative to the fractional derivative ${^CD^{\alpha,\beta}_{\gamma}}$, which is a convex combination of the left Caputo fractional derivative of order $\alpha$ and the right Caputo fractional derivative…
We present the first calculation on the $\Delta$ axial-vector and pseudoscalar form factors using lattice QCD. Two Goldberger-Treiman relations are derived and examined. A combined chiral fit is performed to the nucleon axial charge, N to…
We consider the longitudinal polarization of Lambda and Lambda-bar produced in the current fragmentation region of polarized deep inelastic scattering. We show how the various cross sections can be used to test the underlying parton…
We study the spectral stability of a 2D discrete Schr\"{o}dinger equation on a square lattice, in the simultaneous presence of a fractional Laplacian and $\cal{PT}$ symmetry. For that purpose, we compute the plane-wave spectrum in closed…
We obtain computational hardness results for f-vectors of polytopes by exhibiting reductions of the problems DIVISOR and SEMI-PRIME TESTABILITY to problems on f-vectors of polytopes. Further, we show that the corresponding problems for…
A new definition of a fractional derivative has recently been developed, making use of a fractional Dirac delta function as its integral kernel. This derivative allows for the definition of a distributional fractional derivative, and as…
A Fenchel-Moreau type duality for proper convex and lower semi-continuous functions $f\colon X\to \overline{L^0}$ is established where $(X,Y,\langle \cdot,\cdot \rangle)$ is a dual pair of Banach spaces and $\overline{L^0}$ is the set of…
For a simplicial complex $\Delta$, the graded Betti number $\beta_{i,j}(k[\Delta])$ of the Stanley-Reisner ring $k[\Delta]$ over a field $k$ has a combinatorial interpretation due to Hochster. Terai and Hibi showed that if $\Delta$ is the…
We generalize the fractional Caputo derivative to the fractional derivative ${{^CD}^{\alpha,\beta}_{\gamma}}$, which is a convex combination of the left Caputo fractional derivative of order $\alpha$ and the right Caputo fractional…