let $r=k[x_1,x_2,cdots, x_n]$ be a polynomial ring over a field $k$. we prove that for any positive integers $m, n$, $text{reg}(i^mj^nk)leq mtext{reg}(i)+ntext{reg}(j)+text{reg}(k)$ if $i, j, ksubseteq r$ are three monomial complete intersections ($i$, $j$, $k$ are not necessarily proper ideals of the polynomial ring $r$), and $i, j$ are of the form $(x_{i_1}^{a_1}, x_{i_2}^{a_2}, cdots, x_{i_l...

We consider the operation of intersecting with a locally principal Cartier divisor (i.e., a Cartier divisor which is principal on some neighborhood of its support). We describe this operation explicitly on the level of cycles and rational equivalences and as a corollary obtain a formula for rational equivalence between intersections of two locally principal Cartier divisors. Such canonical rati...

The currently available queue model for multilane traffic control is based on priority discipline. This priority discipline based technique is not suitable to be applied for multilane-multiple intersections, since all vehicles in each lane move simultaneously according to its respective signal phase. In view of this scenario, a new general traffic model for multilane-multiple intersections base...

1 Hook turn (HT) is a unique traffic regulation rule for right-turning vehicles at intersections (in the 2 system where driving is on the left), which was proposed in Melbourne to improve the safety level 3 and operational efficiency of intersections. However, existing coordination plans for HT 4 intersections are fixed and determined empirically, which restricts the further improvements of the...

Carbohydrates are important molecular components of living matter. While spectroscopic and computational studies have been performed on carbohydrates in the electronic ground state, the lack of a chromophore complicates the elucidation of the excited-state properties and the photochemistry of this class of compounds. Herein, we report on the first computational investigation of the singlet phot...

BACKGROUND Racial/ethnic differences in the associations of smoking with uncontrolled blood pressure (BP) and its subtypes (isolated uncontrolled systolic BP (SBP), uncontrolled systolic-diastolic BP, and isolated uncontrolled diastolic BP (DBP)) have not been investigated among diagnosed hypertensive subjects. METHODS A sample of 7,586 hypertensive patients aged ≥18 years were selected from ...

Abstract: The introduction of uncontrollable renewable energy is having a positive impact on our health, the climate, and the economy, but it is also pushing the limits of the power system. The main reason for this is that, in any power system, the generation and consumption must match each other at all times. Thus, if we want to further introduce uncontrollable generation, we need a large abil...

We establish two criteria for certain local algebras to be complete intersections. These criteria play an important role in A. Wiles’s proof that all semi-stable elliptic curves over Q are modular. Introduction In this paper we discuss two results in commutative algebra that are used in A. Wiles’s proof that all semi-stable elliptic curves over Q are modular [11]. We first fix some notation tha...