This paper is devoted to studying Hamilton-Jacobi-Bellman equations with distribution-valued coefficients, which are not well-defined in the classical sense and understood by using paracontrolled distribution method introduced (Gubinelli et al. Forum Math Pi 3(6):1, 2015). By a new characterization of weighted Hölder spaces Zvonkin’s transformation we prove some priori estimates, therefore esta...

Let $f(\mathbf z,\bar{\mathbf z})$ be a convenient Newton non-degenerate mixed polynomial with strongly polar non-negative weighted homogeneous face functions. We consider regular simplicial cone subdivision $\Sigma^*$ which is admissible for $f$ and take the toric modification $\hat{\pi} : X \to \mathbb{C}^n$ associated $\Sigma^*$. show that resolves topologically singularity of hypersurface g...

We investigate the distributions of the different possible values of polynomial maps Fq n −→ Fq , x 7−→ P (x) . In particular, we are interested in the distribution of their zeros, which are somehow dispersed over the whole domain Fq n . We show that if U is a “not too small” subspace of Fq n (as a vector space over the prime field Fp ), then the derived maps Fq /U −→ Fq , x + U 7−→ ∑ x̃∈x+U P (...

We give an upper bound on the number of vertices of PI, the integer hull of a polyhedron P, in terms of the dimension n of the space, the number m of inequalities required to describe P, and the size ~ of these inequalities. For fixed n the bound is O(mn~n-1). We also describe an algorithm which determines the number of integer points in a polyhedron to within a multiplicative factor of 1 qE in...

Let $$\Phi _n^{(k)}(x)$$ be the kth derivative of nth cyclotomic polynomial. We are interested in values _n^{(k)}(1)$$ for fixed positive integers n. D. H. Lehmer proved that _n^{(k)}(1)/ \Phi _n(1)$$ is a polynomial Euler totient function $$\phi (n)$$ and Jordan functions gave its explicit formula. In this paper, we give quick proof _n^{(k)}(1)/\Phi them without giving form. final section, ded...

‎This paper obtains the exact solutions of the wave equation as a second-order partial differential equation (PDE)‎. ‎We are going to calculate polynomial and non-polynomial exact solutions by using Lie point symmetry‎. ‎We demonstrate the generation of such polynomial through the medium of the group theoretical properties of the equation‎. ‎A generalized procedure for polynomial solution is pr...

abstract. suppose g is an nvertex and medge simple graph with edge set e(g). an integervalued function f: e(g) → z is called a flow. tutte was introduced the flow polynomial f(g, λ) as a polynomial in an indeterminate λ with integer coefficients by f(g,λ) in this paper the flow polynomial of some dendrimers are computed.

BIC is used to select the order of polynomial regression between 1 and 30. The estimated σ from the selected model is used to calculate the PI. Representative scatterplots at n = 200 with σ1 = 3, σ2 = 7 can be found in Figure 1. Note that the function estimate based on the selected model by BIC is visually more different from that based on the smaller model with one fewer term for the parametri...