On Searching a Table Consistent with Division Poset

Suppose $P_n=\{1,2,...,n\}$ is a partially ordered set with the partial order defined by divisibility, that is, for any two distinct elements $i,j\in P_n$ satisfying $i$ divides $j$, $i<_{P_n} j$. A table $A_n=\{a_i|i=1,2,...,n\}$ of distinct real numbers is said to be \emph{consistent} with $P_n$, provided for any two distinct elements $i,j\in \{1,2,...,n\}$ satisfying $i$ divides $j$, $a_i< a_j$. Given an real number $x$, we want to determine whether $x\in A_n$, by comparing $x$ with as few entries of $A_n$ as possible. In this paper we investigate the complexity $\tau(n)$, measured in the number of comparisons, of the above search problem. We present a $\frac{55n}{72}+O(\ln^2 n)$ search algorithm for $A_n$ and prove a lower bound $({3/4}+{17/2160})n+O(1)$ on $\tau(n)$ by using an adversary argument.Comment: 16 pages, no figure; same results, representation improved, add reference

Value and selfhood: pragmatism, Confucianism, and phenomenology

This article articulates a dialogue between Edward Casey, Cheng Chung‐ying, and me that began at the Eastern Division annual meeting in Philadelphia of the American Philosophical Association, in a session sponsored by the International Society for Chinese Philosophy. There, we read brief versions of the papers presented in this issue and commented on one another. Casey represented Continental phenomenology, Cheng the Chinese tradition as he has developed it into onto‐generative hermeneutics, and I the melding of American pragmatic and Confucian traditions that I have been developing

COUPLED-CLUSTER CALCULATIONS FOR LOW-LYING ELECTRONIC STATES OF HEAVY-METAL CONTAINING MOLECULES

Coupled-cluster calculations of low-lying electronic states for heavy-metal containing diatomic molecules (e.g., PtH, ThO$^+$, ThN, BaO$^+$, CsF$^+$) are reported. Recently-developed relativistic quantum-chemical techniques have been used, including an atomic mean-field approach for efficent construction of spin-orbit integrals [1], a perturbative approach for treating spin-orbit coupling within exact-two-component equation-of-motion coupled-cluster methods [2], and a new implementation of two-component coupled-cluster methods for non-perturbative treatments of spin-orbit coupling [3]. Bond lengths, vibrational frequencies, and dipole moments of these molecules containing heavy metals are compared with experimental data to assess the accuracy and usefulness of the computational methods. \begin{thebibliography}{comment} \bibitem{Ref1} J. Liu and L. Cheng, J. Chem. Phys. submitted. \bibitem{Ref2} L. Cheng, F. Wang, J. F. Stanton, and J. Gauss, J. Chem. Phys. \textbf{148}, 044108 (2018). \bibitem{Ref3} J. Liu, Y. Shen, A. Asthana, and L. Cheng, J. Chem. Phys. \textbf{148}, 034106 (2018). \end{thebibliography

Ground state sign-changing homoclinic solutions for a discrete nonlinear pp-Laplacian equation with logarithmic nonlinearity

By using a direct non-Nehari manifold method from [X.H. Tang, B.T. Cheng. J. Differ. Equations. 261(2016), 2384-2402.], we obtain an existence result of ground state sign-changing homoclinic solution which only changes sign one times and ground state homoclinic solution for a class of discrete nonlinear $p$-Laplacian equation with logarithmic nonlinearity. Moreover, we prove that the sign-changing ground state energy is larger than twice of the ground state energy

Is intra-abdominal hypertension a missing factor that drives multiple organ dysfunction syndrome?

In a recent issue of Critical Care, Cheng and colleagues conducted a rabbit model study that demonstrated that intra-abdominal hypertension (IAH) may damage both gut anatomy and function. With only 6 hours of IAH at 25 mmHg, these authors observed an 80% reduction in mucosal blood flow, an exponential increase in mucosal permeability, and erosion and necrosis of the jejunal villi. Such dramatic findings should remind all caring for the critically ill that IAH may severely damage the normal gut barrier functions and thus may be reasonably expected to facilitate bacterial and mediator translocation. The potential contribution of IAH as a confounding factor in the efficacy of selective decontamination of the digestive tract should be considered