Related papers: Divisors computing the minimal log discrepancy on …
Two planar sets are circularly separable if there exists a circle enclosing one of the sets and whose open interior disk does not intersect the other set. This paper studies two problems related to circular separability. A linear-time…
Sorting and separation of microparticles is a challenging problem of interdisciplinary nature. Existing technologies can differentiate microparticles by their bulk properties, such as size, density, electric polarizability, etc. The next…
Defined mathematically as critical points of surface area subject to a volume constraint, constant mean curvatures (CMC) surfaces are idealizations of interfaces occurring between two immiscible fluids. Their behavior elucidates phenomena…
Let $S$ be a minimal surface of general type with $p_g(S)=2$ and $K^2_S=1$, so called by a minimal $(1,2)$-surface. Then we obtain that the global log canonical threshold of the surface $S$ via $K_S$ is greater than equal to $\frac{1}{2}$.…
Thermo-osmotic flow around a microparticle in a liquid is characterized by observing and analyzing the distribution of tiny particles, i.e., tracers, near the microparticle's surface. First, an optical trapping laser is used to localize the…
Let $\Gamma$ be a finite set, and $X\ni x$ a fixed klt germ. For any lc germ $(X\ni x,B:=\sum_{i} b_iB_i)$ such that $b_i\in \Gamma$, Nakamura's conjecture, which is equivalent to the ACC conjecture for minimal log discrepancies for fixed…
We construct a sequence of embedded minimal disks in a ball where the curvatures blow up only at the center. The sequence converges to a limit which is not smooth and not proper.
There are many practical applications based on the Least Square Error (LSE) approximation. It is based on a square error minimization 'on a vertical' axis. The LSE method is simple and easy also for analytical purposes. However, if data…
Three methods of least squares are examined for fitting a line to points in the plane. Two well known methods are to minimize sums of squares of vertical or horizontal distances to the line. Less known is to minimize sums of squares of…
In this short note we provide an unbiased multilevel Monte Carlo estimator of the log marginal likelihood and discuss its application to variational Bayes.
We study a least squares estimator for an unknown parameter in the drift coefficient of a path- distribution dependent stochastic differential equation involving a small dispersion parameter epsilon greater than zero. The estimator, based…
It is shown that given a set of $N$ points in the plane or on the sphere, there is a subset of size $\gtrsim N^{1/3}/\log N$ with all pairwise distances between points distinct.
It is shown that the log-canonical threshold of a curve with an isolated singularity is computed by the term ideal of the curve in a suitable system of local parameters at the singularity. The proof uses the Enriques diagram of the…
The displacement field of an object surface can be measured by using speckle interferometry. This technique is based on the phenomenon of laser speckle and consists in correlating speckle interferograms taken after and before the…
Writing correct distributed programs is hard. In spite of extensive testing and debugging, software faults persist even in commercial grade software. Many distributed systems, especially those employed in safety-critical environments,…
The logarithmic relation between interfacial separation and squeezing pressure between randomly rough surfaces, has been predicted by both theory and experiment. However, the experimental slope between interfacial separation and logarithmic…
Computing a quasi-developable strip surface bounded by design curves finds wide industrial applications. Existing methods compute discrete surfaces composed of developable lines connecting sampling points on input curves which are not…
We believe we have made progress in the age-old problem of divisibility rules for integers. Universal divisibility rule is introduced for any divisor in any base number system. The divisibility criterion is written down explicitly as a…
We investigate the notion of the $p$-divisor for foliations on a smooth algebraic surface defined over a field of positive characteristic $p$ and we study some of their properties. We present a structure theorem for the $p$-divisor of…
We prove a base point free theorem for nef and log big divisors on log canonical surfaces.