On the notion of Cohen–Macaulayness for non-Noetherian rings

There exist many characterizations of Noetherian Cohen–Macaulay rings in the literature. These characterizations do not remain equivalent if we drop the Noetherian assumption. The aim of this paper is to provide some comparisons between some of these characterizations in non-Noetherian case. Toward solving a conjecture posed by Glaz, we give a generalization of the Hochster–Eagon result on Cohen–Macaulayness of invariant rings, in the context of non-Noetherian rings.     

Resource allocation with stochastic optimal control approach

A control-theoretic decision making system is proposed for an agent (decision maker) to “optimally” allocate and deploy his/her resources over time among a dynamically changing list of opportunities (e.g., financial assets), in an uncertain market environment. The solution is a sequence of actions with the objective of optimizing total reward function. This control-theoretic approach is unique in a sense that it solves the problem at distinct time epochs over a finite time horizon and strategies are discovered directly. Rather than basing a decision making system on forecasts or training via a reinforcement learning algorithm using current state data, we train our system via a Q-learning algorithm using Geometric Brownian Motion as an asset price function. While the above problem is quite general, we focus solely on the problem of dynamic financial portfolio management with the objective of maximizing the expected utility for a given risk level. The performance functions that we consider for our system are realized mean return, drawdown and standard deviation. We find that our model achieves a better return and drawdown compared to a known market index as a benchmark.     

On the Hysteresis Phenomenon of Turbulent Lifted Diffusion Methane Flame

This paper reports an experimental investigation on the flow characteristics upstream of a lifted turbulent diffusion flame in the presence of a coflow. Three fuel nozzles made of a long pipe with different outlet geometry were examined. One pair of these nozzles has the same orifice diameter but different normalized lip thickness, and another pair has the same normalized lip thickness but different orifice diameter. The strength of the co-airflow was also varied to assess its impact on the liftoff height of the jet diffusion flame. Previously published studies reported the existence of a hysteresis phenomenon in the liftoff height of a turbulent diffusion flame in the presence of a high co-airflow. That is, as the fuel velocity decreases, the lifted flame base would first move upstream (toward the burner) to a local minima followed by a downstream movement before its reattachment. The results of the present study, however, showed that such a phenomenon does not appear for a fuel pipe having a very small lip thickness. The present results also revealed that in the hysteresis region, the flame base sits where the turbulence intensity experiences its local maxima in the upcoming unburnt mixture. This corroborates the premixed stability theory which is based on turbulence intensity. Based on this, a correlation was found between the flame liftoff height in the hysteresis region and the fuel and co-airflow velocity at the nozzle exit. This relationship predicts successfully the liftoff height trend as a function of the fuel jet and co-airflow velocity and nozzle geometry. Away from the hysteresis region, however, the flame base location tends more toward the outside of the local turbulence intensity maxima. This indicates the limitations of the premixed stability theory in predicting the flame behavior in this region where the effect of the flow large-scale structures becomes important.     

Capable Lie algebras with the derived subalgebra of dimension 2 over an arbitrary field

In this paper, we classify all capable nilpotent Lie algebras with the derived subalgebra of dimension 2 over an arbitrary field. Moreover, the explicit structure of such Lie algebras of class 3 is given.     

Symplectic hypersurfaces in the complement of an isotropic submanifold

Using Donaldson's approximately holomorphic techniques, we construct symplectic hypersurfaces lying in the complement of any given compact isotropic submanifold of a compact symplectic manifold. We discuss the connection with rational convexity results in the K?hler case and various applications. Received: 9 January 2001 / Published online: 19 October 2001     

Electromyography Activity of Vastus Medialis Obliquus and Vastus Lateralis Muscles During Lower Limb Proprioceptive Neuromuscular Facilitation Patterns in Individuals with and without Patellofemoral Pain Syndrome

Objective: Exercise therapy to strengthen quadriceps muscle is recommended in rehabilitation program for people with patellofemoral pain syndrome (PFPS). This study aimed to investigate the electromyography (EMG) activity of vastus medialis obliquus (VMO), vastus lateralis (VL) and VMO/VL ratio during PNF in individuals with and without PFPS. Methods: 26 persons with PFPS and 26 healthy subjects participated to study. All subjects performed PNF patterns (Flexion-Adduction-External Rotation (D₁FL), Extension-Adduction-External Rotation (D₂EX), D₁FL+ load, D₂EX+ load) and straight leg raise (SLR). The normalized EMG activity of VMO, VL and VMO/VL ratio were measured and analyzed using repeated measure ANOVA. Results: There were significant main effects of group and exercises for the both VMO and VL (p<0.05). It was found that except SLR and D₂EX, in the other motions PFPS group had lower VMO activity compared to healthy group (p<0.05). For VL except SLR, in the other motions PFPS group had lower VL activity too (p<0.05). The PNF patterns activated VMO more than SLR, however it was not significant (p>0.05). Also; there weren''t any significant difference between the two groups in VMO/VL activation ratios. Also, performing the PNF patterns with load increased VMO and VL muscles activity significantly (p<0.05). It also found that in PFPS group the VMO/VL ratio values in PNF patterns were significantly more than SLR and the highest VMO/VL ratio value (0.96) was found during D₂EX. Conclusion: The PNF patterns due to provide optimal VMO/VL ratio value than SLR and proper balance between these two muscles can be recommended in rehabilitation of individuals with PFPS.     

CaCl2 as a bifunctional reusable catalyst: diversity-oriented synthesis of 4H-pyran library under ultrasonic irradiation

CaCl₂ is applied as an efficient reusable and eco-friendly bifunctional catalyst for the one-pot three-component synthesis of 4H-pyrans under ultrasonic irradiation. A broad range of substrates including the aromatic and heteroaromatic aldehydes, indoline-2,3-dione (isatin) derivatives, acenaphthylene-1,2-dione (acenaphthenequinone) and 2, 2-dihydroxy-2H-indene-1,3-dione (ninhydrin) were condensed with carbonyl compounds possessing a reactive ??-methylene group and alkylmalonates. All reactions are completed in short times, and the products are obtained in good to excellent yields. The catalyst could be recycled and reused several times without any loss of efficiency.     

Head-on quenching of laminar premixed methane flames diluted with hot combustion products

Transient head-on quenching of laminar premixed methane flames diluted with hot combustion products is analyzed using full-chemistry 1D DNS. The impact of the dilution level, pressure and wall temperature on carbon monoxide (CO) emissions is investigated. Increasing dilution level and pressure reduce peak average near-wall CO concentrations, and reduce the near-wall CO reduction rate. However, the peak average near-wall CO and near-wall CO reduction rate increase with increasing wall temperature. Analysis of the species transport budget for CO near the wall before, during and after quenching indicates that there are conditions where diffusion is the dominant transport term. As a consequence, it may be possible to model the near-wall CO using only the integrated diffusion term within certain spatial regions. Dilution increases the size of these regions, whereas increasing pressure reduces this size.