The Gyárfás–Sumner conjecture says that for every forest H $H$ , there is a function f ${f}_{H}$ such if G $G$ -free then χ ( ) ≤ ω $\chi (G)\le {f}_{H}(\omega (G))$ (where ,\omega $ are the chromatic number and clique of ). Louis Esperet conjectured that, whenever statement holds, can be chosen to polynomial. only known true modest set forests Esperet's almost no forests. For instance, it not ...

This paper presents a formula expressing Macaulay constants of numerical polynomial through its minimizing coefficients. From this, we obtain that Kolchin dimension polynomials do not decrease. For the minimal differential $$ {\omega}_{\mathcal{G}/\mathcal{F}} (this concept was introduced by W. Sitt) will prove criterion for to be equal. In this case, as our example shows, there are no bounds f...

We present the first polynomial time algorithm to learn nontrivial classes of languages of infinite trees. Specifically, our algorithm uses membership and equivalence queries to learn classes of ω-tree languages derived from weak regular ω-word languages in polynomial time. The method is a general polynomial time reduction of learning a class of derived ω-tree languages to learning the underlyi...

The Cohn-Umans group-theoretic approach to matrix multiplication suggests embedding matrix multiplication into group algebra multiplication, and bounding $\omega$ in terms of the representation theory of the host group. This framework is general enough to capture the best known upper bounds on $\omega$ and is conjectured to be powerful enough to prove $\omega = 2$, although finding a suitable g...

The $ k $-deck of a sequence is defined as the multiset all its subsequences length $. Let D_k(n) denote number distinct $-decks for binary sequences n For alphabet, we determine exact value small values and $, provide asymptotic estimates when fixed.Specifically, fixed introduce trellis-based method to compute in time polynomial We then \in \{3,4,5,6\} \leqslant 30 also improve upper bound on ...

We give a unified method to derive the strong convergence rate of backward Euler scheme for monotone SDEs in $L^p(\Omega)$-norm, with general $p \ge 4$. The results are applied SODEs polynomial growth coefficients. also generalize argument Galerkin-based SPDEs coefficients driven by multiplicative trace-class noise.

The CSP of a first-order theory $T$ is the problem of deciding for a given finite set $S$ of atomic formulas whether $T \cup S$ is satisfiable. Let $T_1$ and $T_2$ be two theories with countably infinite models and disjoint signatures. Nelson and Oppen presented conditions that imply decidability (or polynomial-time decidability) of $\mathrm{CSP}(T_1 \cup T_2)$ under the assumption that $\mathr...

Sumanene is a synthesized circulene molecule, with formula: 6:(5,6)3. We propose here units for periodic P-type surface networks, based on their stability, evaluated at the Hartree-Fock HF level of theory. Design of the yet hypothetical lattices was performed by using operations on maps, as provided by CVNET and Nano Studio software. The topology of the network was characterized by Omega polyno...

We study the regularity of viscosity solution u $u$ σ k $\sigma _k$ -Loewner–Nirenberg problem on a bounded smooth domain Ω ⊂ R n $\Omega \subset \mathbb {R}^n$ for ⩾ 2 $k \geqslant 2$ . It was known that is locally Lipschitz in $\Omega$ prove that, with d $d$ being distance function to ∂ $\partial \Omega$ and δ > 0 $\delta 0$ sufficiently small, { < ( x ) } $\lbrace d(x) \delta \rbrace$ first ...