The Limiting Density of Unit Root Test Statistics: A Unifying Technique

In this note we introduce a simple principle to derive a constructive expression for the density of the limiting distribution, under the null hypothesis, of unit root statistics for an AR(1)-process in a variety of situations. We consider the case of unknown mean and reconsider the well-known situation where the mean is zero. For long-range dependent errors we indicate how the principle might apply again. We also show that in principle the method also works for a near unit root case. Weak convergence and subsequent Karhunen-Loeve expansion of the weak limit of the partial sum process of the errors plays an important role, along with the evaluation of a certain normal type integral with complex mean and variance. For independent and long range dependent errors this weak limit is ordinary and fractional Brownian motion respectively.
AMS 1991 subject classification. Primary 62M10; secondary 62E20.     

Inverse electromagnetic scattering by cylindrical bodies buried in a slab or a half-space

An exact theory of the inverse scattering problems related to cylindrical bodies buried in a slab is established in two-dimensional scalar case. The theory dwells on two functional equations interrelating the outgoing wave solutions of the wave equation, which can be observed physically, with incoming wave solutions that are physically meaningless and irrealizable. One of these functional equations involves the measured radiation pattern in its kernel (material relation) while the other is independent of the measured data (universal relation). To establish the material relation one has to make far-field measurements with various incidence angles at various observation points and frequencies. The universal relation which guarantees some analytical properties of the field function results in a Stieltjes type integral equation. By solving these equations one gets the location, shape and permittivity of the inaccessible body. When the material of the half-space below the slab is made identical to that of the slab, then the results are reduced to that of the bodies buried in a half-space.     

Characterization of products evolved from supercritical water gasification of xylose (principal sugar in hemicellulose)

The catalyst decomposition of xylose (the principal sugar in hemicellulose) was examined in supercritical water for temperature from 400 to 600°C. Experiments were performed in the absence and presence of three main types of catalysts [alkali catalysts (K₂CO₃ and KOH) and metal impregnated activated carbons (Ni/AC) and (Ru/AC)] with a reaction time of 1h. Gasification yield reaches maximum values by using K₂CO₃ and KOH at the highest temperature of 600°C. The highest H₂ yield and the highest CH₄ yield were obtained by using Ru/AC and Ni/AC, respectively. Acetic acid and 5-methyl furfural were determined as the main aqueous products and reached maximum value by using Ru/AC.     

Optimal temperature control of solar heating systems

Temperature control systems based on solar and wind energy differ in two important ways from existing fossil fuel systems. One is that solar systems, at least active solar systems, all have some kind of energy storage, the other is that the source of energy in a solar and wind energy system is variable and uncontrollable. Because of these added complications and the high capital investment required for solar and wind energy systems, considerably more sophisticated techniques are required for the design of those systems. In this study, a new technique is applied to the optimal control problem of solar heating systems.     

Design of highly effective multilayer feedforward neural network by using genetic algorithm

This paper presents a highly effective and precise neural network method for choosing the activation functions (AFs) and tuning the learning parameters (LPs) of a multilayer feedforward neural network by using a genetic algorithm (GA). The performance of the neural network mainly depends on the learning algorithms and the network structure. The backpropagation learning algorithm is used for tuning the network connection weights, and the LPs are obtained by the GA to provide both fast and reliable learning. Also, the AFs of each neuron in the network are automatically chosen by a GA. The present study consists of 10 different functions to accomplish a better convergence of the desired input–output mapping. Test studies are performed to solve a set of two-dimensional regression problems for the proposed genetic-based neural network (GNN) and conventional neural network having sigmoid AFs and constant learning parameters. The proposed GNN has also been tested by applying it to three real problems in the fields of environment, medicine, and economics. Obtained results prove that the proposed GNN is more effective and reliable when compared with the classical neural network structure.     

Elimination of boron and lithium coexisting in geothermal water by adsorption-membrane filtration hybrid process

Direct release of geothermal waters to the environment may cause some damages to some plants because they contain toxic species such as boron, arsenic, fluoride etc. along with valuable minerals including lithium. In this study, a hybrid process combining adsorption and membrane filtration was used to separate boron and lithium simultaneously from geothermal water. According to the results obtained, separation efficiencies for lithium and boron from geothermal water were 100% and 83% using boron selective ion exchange resin Dowex XUS-43594.00 and lithium selective λ-MnO₂ adsorbent, respectively. The kinetic data of lithium and boron adsorption have been evaluated using pseudo-first order and pseudo-second-order kinetic models.     

Separation of fluoride from aqueous solution by electrodialysis: effect of process parameters and other ionic species

Removal of fluoride from aqueous solution by electrodialysis was studied. Applied voltage, feed flow rate, fluoride concentration in the solution and effect of the other anions as sulfate, chloride were investigated as experimental parameters on fluoride removal from aqueous solution. The separation performance was evaluated in terms of mass transfer and energy consumption. It was obtained that the separation performance increased when the initial concentration of fluoride in the feed solution increased. Percent removal of fluoride increased as the applied potential increased. However, the effect of feed flow rate was not apparent in the range of applied feed flow rate. Separation of fluoride was influenced by chloride but not by sulfate ions.     

A fully on-chip LDO voltage regulator with 37 dB PSRR at 1 MHz for remotely powered biomedical implants

This article presents a fully on-chip low-power LDO voltage regulator dedicated to remotely powered wireless cortical implants. This regulator is stable over the full range of alternating load current and provides fast load regulation achieved by applying a time-domain design methodology. Moreover, a new compensation technique is proposed and implemented to improve PSRR beyond the performance levels which can be obtained using the standard cascode compensation technique. Measurement results show that the regulator has a load regulation of 0.175 V/A, a line regulation of 0.024%, and a PSRR of 37 dB at 1 MHz power carrier frequency. The output of the regulator settles within 10-bit accuracy of the nominal voltage (1.8 V) within 1.6 μs, at full load transition. The total ground current including the bandgap reference circuit is 28 μA and the active chip area measures 290 μm × 360 μm in a 0.18 μm CMOS technology.     

Biodiesel production using gel‐type cation exchange resin at different ionic forms

In this study, a strong acidic‐type cation exchange resin was used in the transesterification of corn oil to fatty acid methyl esters (FAME). The gel‐type cation exchange resin (Purolite‐PD206) was used in H⁺ and Na⁺ forms to utilize ion‐exchange resin as effective heterogeneous catalyst in the production of biodiesel. Effect of ionic forms of ion exchange resin on free fatty acid (FFA) conversion and composition was investigated by using different amounts of ion exchange resin (12, 16, and 20 wt%), various mole ratios of methanol to oil (1:6, 1:12, and 1:18 mol/mol), reaction temperatures (63, 65, and 67°C), and reaction time (24, 36, and 48 h) during transesterification reaction. The highest FFA conversions of 73.5% and 79.45% were obtained at conditions of 20 wt% of catalyst, 65°C of reaction temperature, 18:1 as methanol to oil ratio, and 48 h of reaction time for H⁺ and Na⁺ forms of ion exchange resin, respectively. These results were obtained from regression equations established by using analysis of variance (ANOVA) model according to the experimental results of selected parameters. Gas chromatography analysis revealed that FAME is mainly composed of C16:0 (palmitic), C18:1 (oleic), and C18:2 (linoleic) acids of methyl ester.