Let S be a set of n ideals of a commutative ring A and let Geven (respectively Godd) denote the product of all the sums of even (respectively odd) number of ideals of S. If n ≤ 6 the product of Geven and the intersection of all ideals of S is included in Godd. In the case A is an Noetherian integral domain, this inclusion is replaced by equality if and only if A is a Dedekind domain.

The concept of a 0-distributive poset is introduced. It is shown that a section semicomplemented poset is distributive if and only if it is 0-distributive. It is also proved that every pseudocomplemented poset is 0-distributive. Further, 0-distributive posets are characterized in terms of their ideal lattices.

Generalizing prior work of P. W. Anderson and E. R. Huggins, we show that a "detailed Josephson-Anderson relation" holds for drag on finite body held at rest in classical incompressible fluid flowing with velocity ${\bf V}.$ The relation asserts an exact equality between the instantaneous power consumption by drag, $-{\bf F}\cdot{\bf V},$ vorticity flux across potential mass current, $-(1/2)\in...

An important predictor of historical sound change, functional load, fails to capture insights from speech perception. Building on ideal observer models of word recognition, we devise a new definition of functional load that incorporates both a priori expectedness and perceptual information. We explore this new measure with a simple model and find that it outperforms tra-

Abstract For a skew left brace ( G , rspace="4.2pt">? ? stretchy="false">) {(G,\cdot\,,\circ)} , the map ? : ? Aut ? {\lambda:(G,\circ)\to\operatorname{Aut}(G,\cdot\,...

This paper concerns the chemotaxis-Navier-Stokes system \begin{document}$\begin{equation} \begin{cases} n_t+u\cdot {\nabla } n = \Delta - {{\nabla }\cdot}(n\chi(c) c),\\ c_t+u\cdot c -nf(c),\\ u_t+\kappa (u\cdot }) u + P +n }\Phi, \quad }\cdot} 0 \end{cases} \end{equation} \;\;\;\;\;\;\;\;\;\;\;\;(\star)$ \end{document} in a smoothly convex bounded domain under Neumann/Neumann/Dirichlet boundar...

The massive 3-loop fermion-loop corrections $\propto C_A N_f T_F^2$ and $C_F N_f T_F^2$ to the massive operator matrix elements $A_{Qg}$, $A_{Qq}^{\rm{PS}}$, $A_{qq,Q}^{\rm{PS}}$, $A_{qq,Q}^{\rm{NS}}$ and $A_{qq,Q}^{\rm{NS,TR}} have been obtained for general values of $N$. Thereby the corresponding contributions to the asymptotic heavy flavor Wilson coefficients of the structure function $F_2(x...

We give a maximal independent set (MIS) algorithm that runs in $O(\log \log \Delta)$ rounds in the congested clique model, where $\Delta$ is the maximum degree of the input graph. This improves upon the $O(\frac{\log(\Delta) \cdot \log \log \Delta}{\sqrt{\log n}} + \log \log \Delta )$ rounds algorithm of [Ghaffari, PODC '17], where $n$ is the number of vertices of the input graph. In the first ...

Fundamental mathematical constants like $e$ and $\pi$ are ubiquitous in diverse fields of science, from abstract mathematics to physics, biology chemistry. For centuries, new formulas relating fundamental have been scarce usually discovered sporadically. Here we propose a novel systematic approach that leverages algorithms for deriving help reveal their underlying structure. Our find dozens wel...