Extending the applicability of Secant methods and nondiscrete induction

We use nondiscrete mathematical induction to extend the applicability of the Secant methods for solving equations in a Banach setting. Our approach has the following advantages over earlier works under the same information: weaker sufficient convergence conditions; tighter error bounds on the distances involved and more information on the location of the solution. Numerical examples where our results apply but earlier ones fail to solve nonlinear equation as well as tighter error bounds are also provided in this study.     

Two Characterizations of Optimality in Dynamic Programming

It holds in great generality that a plan is optimal for a dynamic programming problem, if and only if it is “thrifty” and “equalizing.” An alternative characterization of an optimal plan, that applies in many economic models, is that the plan must satisfy an appropriate Euler equation and a transversality condition. Here we explore the connections between these two characterizations.     

Economic model predictive inventory routing and control

Central European Journal of Operations Research - The paper proposes an economic model predictive control (EMPC) strategy for the inventory routing problem under demand uncertainty. The strategy is...     

Modulus of curve families and extremality of spiral-stretch maps

We develop a method using the modulus of curve families to study minimisation problems for the mean distortion functional in the class of finite distortion homeomorphisms. We apply our method to prove extremality of the spiral-stretch mappings defined on annuli in the complex plane. This generalises results of Gutlyanskiĭ and Martio [12] and Strebel [23].     

A generalized Kantorovich theorem for nonlinear equations based on function splitting

The Kantorovich theorem is a fundamental tool in nonlinear analysis for proving the existence and uniqueness of solutions of nonlinear equations arising in various fields. In the present paper we formulate and prove a generalized Kantorovich theorem that contains as special cases the Kantorovich theorem and a weak Kantorovich theorem recently proved by Uko and Argyros. An illustrative example is given to show that the new theorem is applicable in some situations in which the other two theorems are not applicable.     

QuEChERS and solid phase extraction methods for the determination of energy crop pesticides in soil,plant and runoff water matrices

QuEChERS and solid phase extraction (SPE) methods were applied for determining four herbicides (metazachlor, oxyfluorfen, quizalofop-p-ethyl, quinmerac) and one insecticide (α(±)-cypermethrin) in runoff water, soil, sunflower and oilseed rape plant matrices. Determination was performed using gas chromatography mass spectrometry (GC-MS), whereas high-pressure liquid chromatography mass spectrometry (HPLC-MS) was used for quinmerac. In all substrates linearity was evaluated using matrix-matched calibration samples at five concentration levels (50–1000 ng L^?1 for water, 5–500 μg kg^?1 for soil and 2.5–500 μg kg^?1 for sunflower or oilseed rape plant). Correlation coefficient was higher than 0.992 for all pesticides in all substrates. Acceptable mean recovery values were obtained for all pesticides in water (65.4–108.8%), soil (70.0–110.0%) and plant (66.1–118.6%), with intra- and inter-day RSD% below 20%. LODs were in the range of 0.250–26.6 ng L^?1 for water, 0.10–1.8 μg kg^?1 for soil and 0.15–2.0 μg kg^?1 for plants. The methods can be efficiently applied for field dissipation studies of the pesticides in energy crop cultivations.     

Determination of Herbicides in Natural Waters Using Solid Phase Microextraction (SPME) and Gas Chromatography Coupled with Flame Thermionic and Mass Spectrometric Detection

Abstract

This study develops a method for solid phase microextraction (SPME) of ten widespread herbicides from water. The selected herbicides belong to different chemical groups are EPTC, molinate, propachlor, trifluralin, atrazine, propazine, terbuthylazine, prometryne, alachlor. Their determination was carried out by gas chromatography with flame thermionic and mass spectrometric detection. To perform the SPME, two types of fibre have been assayed: Carbowax-divinylbenzene (CW-DVB) of 65 μm thickness and polydimethylsiloxane-divinylbenzene (PDMS-DVB) of 65 μm thickness. The main factors affecting the SPME process such as pH, ionic strength, methanol content, memory effect, stirring rate and adsorption-time profile were studied. The method was applied to spiked natural waters such as ground water, sea water, lake water and river water in a concentration range of 0.1 to 10 μg/L. Limits of detection with each of the detectors were determined to be 1 – 20 ng/L in PDMS-DVB and 2–20 ng/L CW-DVB fibres. The recoveries of herbicides compared to distilled water were in relatively high levels 78.3–127.3 % and the average r² values of the calibration curves were above 0.99 for all the analytes. The SPME conditions were finally optimized in order to obtain maximum sensitivity and samples were applied for the trace-level determination in river water samples originating from Ioannina region (Greece).