Related papers: Note on lower estimates of multiplicities
We show a lower estimate of the Milnor number of an isolated hypersurface singularity, via its Newton number. We also obtain analogous estimate of the Milnor number of an isolated singularity of a similar complete intersection variety.
We establish a quantitative lower bound on the reach of flat norm minimizers for boundaries in $\mathbb{R}^2$.
We present some new lower bound estimates for certain numbers in Laver table theory and introduce several related structures of interest.
Lower bounds for some explicit decision problems over the complex numbers are given.
The goal of this work is to prove a new sure upper bound in a setting that can be thought of as a simplified function field analogue. This result is comparable to a recent result of the author concerning almost sure upper bound of random…
New lower bounds involving sum, difference, product, and ratio sets for $A\subset \C$ are given.
Some monotone increasing sequences of the lower bounds for the minimum eigenvalue of $M$-matrices are given. It is proved that these sequences are convergent and improve some existing results. Numerical examples show that these sequences…
In this paper, we give estimates for both upper and lower bounds of eigenvalues of a simple matrix. The estimates are shaper than the known results.
We give upper bounds for volume of sublevel sets of real polynomials. Our method is to combine a version of global Lojasiewicz inequality with some well known estimate on volume of tubes around real algebraic sets. Some applications to…
Given a polynomial system f associated with a simple multiple zero x of multiplicity {\mu}, we give a computable lower bound on the minimal distance between the simple multiple zero x and other zeros of f. If x is only given with limited…
This paper gives a framework to produce the lower bound of eigenvalues defined in a Hilbert space by the eigenvalues defined in another Hilbert space. The method is based on using the max-min principle for the eigenvalue problems.
In this note we obtain lower bounds for $\P(\xi\geq 0)$ and $\P(\xi>0)$ under assumptions on the moments of a centered random variable $\xi$. The obtained estimates are shown to be optimal and improve results from the literature. The…
In order to provide a guaranteed precision and a more accurate judgement about the true value of the Cram\'{e}r-Rao bound and its scaling behavior, an upper bound (equivalently a lower bound on the quantum Fisher information) for precision…
We give lower bounds on the case of worst inhomogeneous approximation.
The saturation number $\text{sat}(n,\mathcal{F})$ is the minimum number of edges in any graph which does not contain a member of $\mathcal{F}$ as a subgraph, but will if any edge is added. We give a few upper and lower bounds for saturation…
The best known method to give a lower bound for the Noether number of a given finite group is to use the fact that it is greater than or equal to the Noether number of any of the subgroups or factor groups. The results of the present paper…
For an immersed minimal surface in $\mathbb{R}^3$, we show that there exists a lower bound on its Morse index that depends on the genus and number of ends, counting multiplicity. This improves, in several ways, an estimate we previously…
In this note, we shall give an improved lower bound for the argument of a power of a given algebraic number which has absolute value one but is not a root of unity.
In this paper, we obtain upper and lower bounds for the partition function $p(n)$ by using an elementary geometric inequality in Euclidean space, and we extend the method to generalizations of the partition function.
We solve a problem due to Recam\'an about the lower bound behavior of the maximum possible length among all arithmetic progressions in the least reduced residue system modulo $n$, as $n \to \infty$.