On the complexity of simple arithmetic expressions

Let $\text{E}$ be the set of all simple arithmetic expressions of the form E(x) = xT_l…T_k where x is a nonnegative integer variable and each T_i is a multiplication or integer division by a positive integer constant. We investigate the complexity of the inequivalence and the bounded inequivalence problems for expressions in $\text{E}$. (The bounded inequivalence problem is the problem of deciding for arbitrary expressions E₁(x) and E₂(x) and a positive integer l whether or not E₁(x) ≠ E₂(x) for some nonnegative integer x<l. If l = ∞, i.e., there is no upper bound on x, the problem becomes the inequivalence problem.) We show that the inequivalence problem (or equivalently, the equivalence problem) for a large subclass of $\text{E}$ is decidable in polynomial time. Whether or not the problem is decidable in polynomial time for the full class $\text{E}$ remains open. We also show that the bounded inequivalence problem is NP-complete even if the divisors are restricted to be equal to 2. This last result can be used to sharpen some known NP-completeness results in the literature. Note that if division is rational division, all problems are trivially decidable in polynomial time.     

A clay-vesicle system for water purification from organic pollutants

Vesicle-clay complexes in which positively charged vesicles composed of didodecyldimethylammonium bromide (DDAB) were adsorbed on montmorillonite removed efficiently anionic (sulfentrazone, imazaquin) and neutral (alachlor, atrazine) pollutants from water. These complexes (0.5% w:w) removed 92-100% of sulfentrazone, imazaquin and alachlor and 60% of atrazine from a solution containing 10mg/L of it. A synergistic effect on the adsorption of atrazine was observed when all pollutants were present simultaneously (30 mg/L each), its percentage of removal being 85.5. Column filters (18 cm) filled with a mixture of quartz sand and vesicle-clay (100:1, w:w) were tested. For the passage of 1L (25 pore volumes) of a solution including all the pollutants at 10mg/L each, removal was complete for sulfentrazone and imazaquin, 94% for alachlor and 53.1% for atrazine, whereas removal was significantly less efficient when using activated carbon. A similar advantage of the vesicle-clay filter was observed for the capacities of removal.     

Single‐source multibattery solar charger: case study and implementation issues

In this paper, design process and functionality of a portable single‐panel dual‐battery solar charger prototype are presented, achieving energy density of 571 W h kg⁻¹ during a typical 3‐day infantry mission. The device may instantaneously charge up to two Li‐ion MR‐2791 batteries, supporting plug‐and‐play operation. The system consists of a lightweight custom solar panel, based on 20% efficient monocrystalline photovoltaics, and an intelligent power processing module. The panel contains eight transparent polymer‐encapsulated and camouflaged series‐connected six solar cell packs with antiparallel diodes, allowing partial shading operation. The power processing module consists of two synchronous current‐mode‐controlled buck converters, digital signal processor, and a microcontroller, supporting both maximum power point tracking of the solar panel with partial shading detection and multimode charging of Li‐ion packs while instantaneously communicating with the batteries. Power management algorithmic design is presented, based on ensuring system stability while supporting the required operation modes. System implementation stages and underlying issues are thoroughly discussed, and utilized hardware components are presented in detail. Experimental results of system testing under real outdoor conditions are presented to demonstrate the device functionality and energy yield capabilities. Copyright © 2015 John Wiley & Sons, Ltd.     

Environmentally friendly slow release formulations of alachlor based on clay-phosphatidylcholine

A new clay-liposome complex was developed for reducing leaching of herbicides and contamination of groundwater. The liposomes were composed of the neutral and Environmental Protection Agency approved phospholipid phosphatidylcholine (PC). Adsorption of PC liposomes on the clay mineral montmorillonite could exceed the cation exchange capacity of the clay, and was well simulated by the Langmuir equation. X-ray diffraction results for 6 mM PC and 1.6 g/L clay (3 day incubation) yielded a basal spacing of 7.49 nm, which was interpreted as the formation of a supported planar bilayer on montmorillonite platelets. Fluorescence methods demonstrated structural changes which reflected adsorption of PC followed by loss of vesicle integrity as measured by the penetration of dithionite into the internal monolayer of fluorescently labeled liposomes, resulting in a decrease in fluorescence intensity to 18% of initial after 4 h. Energy transfer was demonstrated after 1 h from labeled liposomes to montmorillonite labeled by an acceptor. The neutral herbicide alachlor adsorbed on the liposome-clay complex, yielding a formulation of up to 40% active ingredient, and 1.6-fold reduction in herbicide release in comparison to the commercial formulation. Hence, the PC-montmorillonite complex can form a basis for environmentally friendly formulations of herbicides, which would yield reduced leaching.     

Biochemistry of lipoxygenase in relation to food quality

A renewed interest in lipoxygenase has led to detailed studies of its isoenzymes, substrate specificity, and the nature of its reaction products. Lipoxygenase is highly specific for cis,cis‐1,4‐pentadiene systems such as linoleic, linolenic, and arachidonic acid (or ester) and catalyzes the formation of the corresponding hydroperoxides with a cis,‐trans‐conjugated diene system. The hydroperoxides can then undergo enzymic or spontaneous degradation, producing a range of carbonyl compounds. This review will discuss the biochemical properties of this enzyme and its contribution to the quality of raw and processed food products. An attempt has been made to discuss both the desirable and undesirable effects associated with the action of lipoxygenase, citing specific food examples where appropriate.     

A learning curve model for an equivalent number of units

Conventional learning curve models are able to deal only with past data that includes an integer number of cycles and time per cycle. However, in real-life situations, the data collected are of a different nature: periodical information, which includes total work time, in-process inventory and completed units, for example. In such circumstances it would be wrong to consider just the completed units, disregarding the in-process inventory. The concept of Equivalent Number of Units (ENU) has been introduced to permit one to sum up all the work performed, and express it in a manner that allows one to use the learning curve model for such cases. Also, time per unit may not be given for single units and the ENU produced per reported period may not be an integer. In order to solve the above problems, a simple procedure was developed for periodical non-integer data. The end result of the procedure is the product learning curve parameters.     

Multigrid method for stability problems

The problem of calculating the stability of steady state solutions of differential equations is treated. Leading eigenvalues (i.e., having maximal real part) of large matrices that arise from discretization are to be calculated. An efficient multigrid method for solving these problems is presented. The method begins by obtaining an initial approximation for the dominant subspace on a coarse level using a damped Jacobi relaxation. This proceeds until enough accuracy for the dominant subspace has been obtained. The resulting grid functions are then used as an initial approximation for appropriate eigenvalue problems. These problems are solved first on coarse levels, followed by refinement until a desired accuracy for the eigenvalues has been achieved. The method employs local relaxation on all levels together with a global change on the coarsest level only, which is designed to separate the different eigenfunctions as well as to update their corresponding eigenvalues. Coarsening is done using the FAS formulation in a nonstandard way in which the right-hand side of the coarse grid equations involves unknown parameters to be solved for on the coarse grid. This in particular leads to a new multigrid method for calculating the eigenvalues of symmetric problems. Numerical experiments with a model problem that are presented demonstrate the effectiveness of the method proposed. Using an FMG algorithm a solution to the level of discretization errors is obtained in just a few work units (less than 10), where a work unit is the work involved in one Jacobi relaxation on the finest level.