Refined inequalities on graded Lie groups

We construct a Littlewood–Paley decomposition associated to a Rockland operator on graded Lie groups, which allows us to deduce refined Gagliardo–Nirenberg, Sobolev and Hardy inequalities.     

Flamelet structure in turbulent premixed swirling oxy-combustion of methane

Two key flame macrostructures in swirling flows have been observed in experiments of oxy-combustion (as well as air-combustion); as the equivalence ratio is raised, the flame moves from being stabilized on just the inner shear layer (Flame III) to getting stabilized on both the inner and outer shear layers (Flame IV). We report results of an LES investigation of two different inlet oxy-fuel mixtures, in a turbulent swirling flow at $\text{Re}=20,000,$ that capture these two macrostructures. Previous work on the effects of heat loss have mostly focused on its impact on macro-scale observations. In this paper, we examine how heat loss impacts the flame microstructures as well for these two macrostructures. For both flames, the flamelet structure, as represented by a scatter plot of the normalized fuel concentration against the normalized temperature, depends on whether the combustor walls are adiabatic or non-adiabatic. For the adiabatic case, the flamelets of both macrostructures behave like strained flames. When wall heat transfer is included, Flame III microstructure is more bimodal. Since this flame extends farther downstream and part of it propagates along the walls, heat transfer has a greater impact on it’s microstructure. These results show that heat loss impacts not just the macro properties of the flame such as its shape or interactions with the wall, but also fundamentally changes its internal structure. Scatter plots of the turbulent flames are constructed and compared to different 1D laminar flame profiles (e.g., strained or with heat loss), and comparisons suggest the important role of the wall thermal boundary conditions in the accurate simulations of combustion dynamics and interpretations of experimental data, including data reduction and scaling.     

Protein regulators of eicosanoid synthesis: role in inflammation

A variety of factors contribute to the complex course of inflammation. Microbiological, immunological and toxic agents can initiate the inflammatory response by activating a variety of humoral and cellular mediators. In the early phase of inflammation, excessive amounts of cytokines and inflammatory mediators are released. These factors activate, in addition to other signaling pathways, the lipid synthesis pathways, which play a crucial role in the pathogenesis of organ dysfunction. Arachidonic acid (AA), the precursor of pro-inflammatory eicosanoids, is released from membrane phospholipids by the action of phospholipase A(2) (PLA(2)), and is metabolized to prostaglandins (PGs) and leukotrienes (LTs) by the action of cyclooxygenase (COX) and lipoxygenase (LO) enzymes, respectively. Disordered activation of PLA(2), LO and COX enzymes have been implicated in many inflammatory diseases. PLA(2) is activated by phospholipase-A(2)-activating protein (PLAP) and LO by 5-lipoxygenase-activating protein (FLAP). The inducible form of COX-2 enzyme, which is usually not present under basal conditions, is induced in inflammation. In this article the function of these enzymes in eicosanoid synthesis, their regulation, and their implication in inflammatory disorders will be reviewed. The properties, function and regulation of the protein activators PLAP and FLAP will also be discussed.     

Determination of Chromium (VI) in Airborne Particulate Matter by Electrothermal Atomic Absorption Spectrometry

Hexavalent chromium Cr(VI) is a well-established carcinogen associated with lung, nasal, and sinus cancer. Cr(VI) threshold limit values in workroom air have been recently lowered. Consequently, the currently available analytical methods are insufficiently sensitive or high cost. In this paper, a simple, cost-effective, sensitive, and reproducible method using solid-phase extraction with electrothermal atomic absorption spectrometry for determination of hexavalent chromium in airborne samples is reported. The method validation included selectivity, linearity, accuracy, and precision. Interferences from other ions likely to be present in airborne samples, including trivalent chromium, were tested and selectivity was demonstrated. The detection and quantification limits were, respectively, as low as 0.1 and 0.4?µg?L^?1. The linearity ranged from 0.5 to 50.0?µg?L^?1, with a regression coefficients exceeding 0.998. The extraction recovery exceeded 98%. The developed method was successfully compared with a reference spectrophotometric method. The performances achieved were similar to ion chromatography and high-performance liquid chromatography approaches. The novel method was tested on airborne samples collected from the workplace. The method’s performance suggests that it may be an alternative to high-cost techniques for monitoring occupational exposure to hexavalent chromium.     

Fixed point results on a metric space endowed with a finite number of graphs and applications

In this paper, we consider self-mappings defined on a metric space endowed with a finite number of graphs. Under certain conditions imposed on the graphs, we establish a new fixed point theorem for such mappings. The obtained result extends, generalizes and improves many existing contributions in the literature including standard fixed point theorems, fixed point theorems on a metric space endowed with a partial order and fixed point theorems for cyclic mappings.     

Local Dispersive and Strichartz Estimates for the Schrödinger Operator on the Heisenberg Group

It was proved by Bahouri et al. [9] that the Schrödinger equation on the Heisenberg group $\mathbb{H}^d,$ involving the sublaplacian, is an example of a totally non-dispersive evolution equation: for this reason global dispersive estimates cannot hold. This paper aims at establishing local dispersive estimates on $\mathbb{H}^d$ for the linear Schrödinger equation, by a refined study of the Schrödinger kernel $S_t$ on $\mathbb{H}^d.$ The sharpness of these estimates is discussed through several examples. Our approach, based on the explicit formula of the heat kernel on $\mathbb{H}^d$ derived by Gaveau [19], is achieved by combining complex analysis and Fourier-Heisenberg tools. As a by-product of our results we establish local Strichartz estimates and prove that the kernel $S_t$ concentrates on quantized horizontal hyperplanes of $\mathbb{H}^d.$     

Stochastic equity volatility related to the leverage effect II: valuation of European equity options and warrants

We propose a general framework to assess the value of the financial claims issued by the firm, European equity options and warrantsin terms of the stock price. In our framework, the firm's asset is assumed to follow a standard stationary lognormal process with constant volatility. However, it is not the case for equity volatility. The stochastic nature of equity volatility is endogenous, and comes from the impact of a change in the value of the firm's assets on the financial leverage. In a previous paper we studied the stochastic process for equity volatility, and proposed analytic approximations for different capital structures. In this companion paper we derive analytic approximations for the value of European equity options and warrants for a firm financed by equity, debt and warrants. We first present the basic model, which is an extension of the Black-Scholes model, to value corporate securities either as a function of the stock price, or as a function of the firm's total assets. Since stock prices are observable, then for practical purposes, traders prefer to use the stock as the underlying instrument, we concentrate on valuation models in terms of the stock price. Second, we derive an exact solution for the valuation in terms of the stock price of (i) a European call option on the stock of a levered firm, i.e. a European compound call option on the total assets of the firm, (ii) an equity warrant for an all-equity firm, and (iii) an equity warrant for a firm financed by equity and debt. Unfortunately, to compute these solutions we need to specify the function of the stock price in terms of the firm's assets value. In general we are unable to specify this expression, but we propose tight bounds for the value of these options which can be easily computed as a function of the stock price. Our results provide useful extensions of the Black-Scholes model.     

Nonlinear model predictive control based on Nelder Mead optimization method

In this paper, a model predictive control (MPC) scheme based on Hammerstein model is carried on. The use of such nonlinear models complicates the implementation of the MPC in terms of computational time and burden since a nonlinear and so a nonconvex optimization problem will result. The Nelder Mead (NM) algorithm, as a free derivative method, is used to solve the resulting optimization problem. NM algorithm proves its efficiency in terms of computation time and global optimum seeking that can be successfully exploited especially with fast dynamic systems. A comparative study between the NM algorithm and the gradient-based method (GBM) based on computation time is established. The efficiency of the NM algorithm is illustrated with SISO and MIMO examples compared to GBM algorithm.