Traditional Chinese Medicine (TCM) is a complete medical system that has been practiced for more than 3000 years. Prescription number 1 (PN-1) consists of several Chinese medicines and is designed according to TCM theories to treat patients with neuropsychiatric disorders. The evidence of clinical practice suggests the benefit effects of PN-1 on cognitive deficits of dementia patients. We try t...

Motivated by the discovery that the eighth root of the theta series of the E8 lattice and the 24th root of the theta series of the Leech lattice both have integer coefficients, we investigate the question of when an arbitrary element f ∈ R (where R = 1 + xZ x ) can be written as f = gn for g ∈ R, n 2. Let Pn := {gn | g ∈R} and let μn := n∏p |n p. We show among other things that (i) for f ∈R, f ...

Let Al;k(n)?Sn denote the set of permutations [n] for which l consecutive numbers {k,k+1,?,k+l?1} appears in a positions. Under uniform probability measure Pn on Sn, one has Pn(Al;k(n))?l! nl?1 as n??. In part this paper we consider clustering under Mallows distributions Pnq, q>0. Because duality, it suffices to q?(0,1). We show that qn=1?c n?, with c>0 and ??(0,1), Pnq(Al;kn(n)) is order 1 n?(...

Depth-first proof-number search (df-pn) is powerful AND/OR tree search to solve positions in games. However, df-pn has a notorious problem of infinite loops when applied to domains with repetitions. Df-pn(r) cures it by ignoring proof and disproof numbers that may lead to infinite loops. This paper points out that df-pn(r) has a serious issue of underestimating proof and disproof numbers, while...

Oral absorption of a drug is modeled by the differential equations for dissolution, permeation and gastrointestinal transit processes. The purpose of the present study was to compare simple approximate analytical solutions with full numerical solutions for the calculation of the fraction of a dose absorbed (Fa). The GI compartment model for numerical integration consisted of 1 stomach, 7 intest...

Let Pn be a pentagonal chain with 2n pentagons in which two edges common can regarded as adding one vertex and to hexagon. Thus, the linear derivation chains QPn represent graph obtained by attaching four-membered rings every of Pn. In this article, Laplacian spectrum consisting eigenvalues symmetric matrices is determined. Next, formulas for invariants that represented spectrum, namely, Kirchh...

BACKGROUND The NHS Bowel Scope Screening (BSS) programme offers men and women aged 55 years a once-only flexible sigmoidoscopy (FS), a test that can help reduce colorectal cancer (CRC) incidence and mortality. However, the benefits of BSS are contingent on uptake. This National Institute for Health Research-funded single-stage phase II trial will test the feasibility of using patient navigation...

In this note, we derive an explicit formula for the equitable chromatic number of a complete n-partite graph Kp1 ;p2 ;:::;pn . Namely, if M is the largest integer such that pi (modM)¡ ⌈pi M ⌉ (i = 1; 2; : : : ; n) then e(Kp1 ;p2 ;:::;pn) = n ∑