Existence Results for Abstract Partial Neutral Integro-differential Equation with Unbounded Delay

In this paper we study the existence and regularity of mild solutions for a class of abstract partial neutral integro-differential equations with unbounded delay.

GLOBAL SOLUTIONS FOR ABSTRACT FUNCTIONAL DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

In this paper we study the existence of global solutions for a class of abstract functional differential equation with nonlocal conditions. An application is considered.

EXISTENCE RESULTS FOR ABSTRACT NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper we discuss the existence of solutions for a class of abstract partial neutral functional differential equations.

Pseudodifferential operators with C*-algebra-valued symbols: Abstract characterizations

Given a separable unital C*-algebra C with norm parallel to center dot parallel to, let E-n denote the Banach-space completion of the C-valued Schwartz space on R-n with norm parallel to f parallel to(2)=parallel to < f, f >parallel to(1/2), < f, g >=integral f(x)* g(x)dx. The assignment of the pseudodifferential operator A=a(x,D) with C-valued symbol a(x,xi) to each smooth function with bounded derivatives a is an element of B-C(R-2n) defines an injective mapping O, from B-C(R-2n) to the set H of all operators with smooth orbit under the canonical action of the Heisenberg group on the algebra of all adjointable operators on the Hilbert module E-n. In this paper, we construct a left-inverse S for O and prove that S is injective if C is commutative. This generalizes Cordes' description of H in the scalar case. Combined with previous results of the second author, our main theorem implies that, given a skew-symmetric n x n matrix J and if C is commutative, then any A is an element of H which commutes with every pseudodifferential operator with symbol F(x+J xi), F is an element of B-C(R-n), is a pseudodifferential operator with symbol G(x - J xi), for some G is an element of B-C(R-n). That was conjectured by Rieffel.

Total soil carbon and chemical attributes under different land uses in the Brazilian savanna

Total soil carbon and chemical attributes under different land uses in the Brazilian savanna. The Brazilian savanna region (Cerrado) is one of the largest cultivated areas of the world. The different land uses in the region can effectively change the quantities of soil organic matter and the cycling of nutrients. I-lie objective of this study was to evaluate the effect of different land use management systems on the relationship between soil organic carbon and the soil chemical attributes of a Red Latosol (Oxisol) under Cerrado in Rio Verde (Goias state). The treatments studied were native vegetation (cerrado), low-productivity pasture, conventional tillage with soybean, and no-tillage with soybean and maize. The smallest values for pH, available P, K, Ca and Mg were observed for the Cerradao treatment, even if the relatively high C levels increased the potential soil cation exchange capacity. The pasture, conventional tillage and no-tillage treatments showed higher K, Ca, Mg, available 13, and S concentrations in the soil. In the areas where soil tillage did not take place and lime and fertilizers were applied superficially, the stratification of the soil organic carbon provides the retention of the elements near to the surface, with significance correlations with the soil chemicals attributes.

Fermentation of cacao (Theobroma cacao L.) seeds with a hybrid Kluyveromyces marxianus strain improved product quality attributes

Fermentation of Theobroma cacao (cacao) seeds is an absolute requirement for the full development of chocolate flavor precursors. An adequate aeration of the fermenting cacao seed mass is a fundamental prerequisite for a satisfactory fermentation. Here, we evaluated whether a controlled inoculation of cacao seed fermentation using a Kluyveromyces marxianus hybrid yeast strain, with an increased pectinolytic activity, would improve an earlier liquid drainage (`sweatings`) from the fermentation mass, developing a superior final product quality. Inoculation with K. marxianus increased by one third the volume of drained liquid and affected the microorganism population structure during fermentation, which was detectable up to the end of the process. Introduction of the hybrid yeast affected the profile of total seed protein degradation evaluated by polyacrylamide gel electrophoresis, with improved seed protein degradation, and reduction of titrable acidity. Sensorial evaluation of the chocolate obtained from beans fermented with the K. marxianus inoculation was more accepted by analysts in comparison with the one from cocoa obtained through natural fermentation. The increase in mass aeration during the first 24 h seemed to be fundamental for the improvement of fermentation quality, demonstrating the potential application of this improved hybrid yeast strain with superior exogenous pectinolytic activity.

Diagnostic errors and repetitive sequential classifications in on-line process control by attributes

The procedure of on-line process control by attributes, known as Taguchi`s on-line process control, consists of inspecting the mth item (a single item) at every m produced items and deciding, at each inspection, whether the fraction of conforming items was reduced or not. If the inspected item is nonconforming, the production is stopped for adjustment. As the inspection system can be subject to diagnosis errors, one develops a probabilistic model that classifies repeatedly the examined item until a conforming or b non-conforming classification is observed. The first event that occurs (a conforming classifications or b non-conforming classifications) determines the final classification of the examined item. Proprieties of an ergodic Markov chain were used to get the expression of average cost of the system of control, which can be optimized by three parameters: the sampling interval of the inspections (m); the number of repeated conforming classifications (a); and the number of repeated non-conforming classifications (b). The optimum design is compared with two alternative approaches: the first one consists of a simple preventive policy. The production system is adjusted at every n produced items (no inspection is performed). The second classifies the examined item repeatedly r (fixed) times and considers it conforming if most classification results are conforming. Results indicate that the current proposal performs better than the procedure that fixes the number of repeated classifications and classifies the examined item as conforming if most classifications were conforming. On the other hand, the preventive policy can be averagely the most economical alternative rather than those ones that require inspection depending on the degree of errors and costs. A numerical example illustrates the proposed procedure. (C) 2009 Elsevier B. V. All rights reserved.

Effects of the preventive and corrective adjustments in economical designs for online process control for attributes with misclassification errors

The procedure for online process control by attributes consists of inspecting a single item at every m produced items. It is decided on the basis of the inspection result whether the process is in-control (the conforming fraction is stable) or out-of-control (the conforming fraction is decreased, for example). Most articles about online process control have cited the stoppage of the production process for an adjustment when the inspected item is non-conforming (then the production is restarted in-control, here denominated as corrective adjustment). Moreover, the articles related to this subject do not present semi-economical designs (which may yield high quantities of non-conforming items), as they do not include a policy of preventive adjustments (in such case no item is inspected), which can be more economical, mainly if the inspected item can be misclassified. In this article, the possibility of preventive or corrective adjustments in the process is decided at every m produced item. If a preventive adjustment is decided upon, then no item is inspected. On the contrary, the m-th item is inspected; if it conforms, the production goes on, otherwise, an adjustment takes place and the process restarts in-control. This approach is economically feasible for some practical situations and the parameters of the proposed procedure are determined minimizing an average cost function subject to some statistical restrictions (for example, to assure a minimal levelfixed in advanceof conforming items in the production process). Numerical examples illustrate the proposal.

Spatial Modeling of a Soil Fertility Index using Visible-Near-Infrared Spectra and Terrain Attributes

Our objective was to develop a methodology to predict soil fertility using visible near-infrared (vis-NIR) diffuse reflectance spectra and terrain attributes derived from a digital elevation model (DEM). Specifically, our aims were to: (i) assemble a minimum data set to develop a soil fertility index for sugarcane (Sarcharum officinarum L.) (SFI-SC) for biofuel production in tropical soils; (ii) construct a model to predict the SFI-SC using soil vis-NIR spectra and terrain attributes; and (iii) produce a soil fertility map for our study area and assess it by comparing it with a green vegetation index (GVI). The study area was 185 ha located in sao Paulo State, Brazil. In total, 184 soil samples were collected and analyzed for a range of soil chemical and physical properties. Their vis-NIR spectra were collected from 400 to 2500 nm. The Shuttle Radar Topographic Mission 3-arcsec (90-m resolution) DEM of the area was used to derive 17 terrain attributes. A minimum data set of soil properties was selected to develop the SFI-SC. The SFI-SC consisted of three classes: Class 1, the highly fertile soils; Class 2, the fertile soils; and Class 3, the least fertile soils. It was derived heuristically with conditionals and using expert knowledge. The index was modeled with the spectra and terrain data using cross-validated decision trees. The cross-validation of the model correctly predicted Class 1 in 75% of cases, Class 2 in 61%, and Class 3 in 65%. A fertility map was derived for the study area and compared with a map of the GVI. Our approach offers a methodology that incorporates expert knowledge to derive the SFI-SC and uses a versatile spectro-spatial methodology that may be implemented for rapid and accurate determination of soil fertility and better exploration of areas suitable for production.

Spatial patterns of soil attributes and components in a mangrove system in Southeast Brazil (Sao Paulo)

Purpose Among environmental factors governing innumerous processes that are active in estuarine environments, those of edaphic character have received special attention in recent studies. With the objectives of determining the spatial patterns of soil attributes and components across different mangrove forest landscapes and obtaining additional information on the cause-effect relationships between these variables and position within the estuary, we analyzed several soil attributes in 31 mangrove soil profiles from the state of So Paulo (Guaruja, Brazil). Materials and methods Soil samples were collected at low tide along two transects within the CrumahA(0) mangrove forest. Samples were analyzed to determine pH, Eh, salinity, and the percentages of sand, silt, clay, total organic carbon (TOC), and total S. Mineralogy of the clay fraction (< 2 mm) was also studied by X-ray diffraction analysis, and partitioning of solid-phase Fe was performed by sequential extraction. Results and discussion The results obtained indicate important differences in soil composition at different depths and landscape positions, causing variations in physicochemical parameters, clay mineralogy, TOC contents, and iron geochemistry. The results also indicate that physicochemical conditions may vary in terms of different local microtopographies. Soil salinity was determined by relative position in relation to flood tide and transition areas with highlands. The proportions of TOC and total S are conditioned by the sedimentation of organic matter derived from vegetation and by the prevailing redox conditions, which clearly favored intense sulfate reduction in the soils (similar to 80% of the total Fe is Fe-pyrite). Particle-size distribution is conditioned by erosive/deposition processes (present and past) and probably by the positioning of ancient and reworked sandy ridges. The existing physicochemical conditions appear to contribute to the synthesis (smectite) and transformation (kaolinite) of clay minerals. Conclusions The results demonstrate that the position of soils in the estuary greatly affects soil attributes. Differences occur even at small scales (meters), indicating that both edaphic (soil classification, soil mineralogy, and soil genesis) and environmental (contamination and carbon stock) studies should take such variability into account.

Evaluation of the Importance of Attributes in Customer Satisfaction with Supermarkets in the Mid-Valley Region of the Itajai - SC

In a dynamic atmosphere of competitiveness, customer satisfaction is a key factor in the long term success of a business relationship. From this perspective, the objective of the article was to evaluate the importance of attributes and customer satisfaction with Supermarkets in the Mid-Valley region of the ltajai/SC. Research methodology is characterized as descriptive, of the survey type, with a quantitative, cross section approach. The research instrument used was a questionnaire structured with open and closed questions, according to Lickert`s scale. By means of this, the degree of importance of supermarket attributes and the level of customer satisfaction with them were verified. In regard to the importance of the attributes, cleaning, parking, safety and variety of products are the most important, while the attributes Of purchase through the internet and taste samples are the least significant ones. The results of satisfaction point to the fact that the Supermarkets Big and Angeloni presented a greater degree of satisfaction in relation to the general average in practically all of the attributes, while Bistek presented the smallest degree of satisfaction, only surpassing the average in regard to the attribute of store lighting.

Asymptotically almost periodic solutions for abstract neutral integro-differential equations

We study the existence of asymptotically almost periodic classical solutions for a class of abstract neutral integro-differential equation with unbounded delay. A concrete application to partial neutral integro-differential equations which arise in the study of heat conduction in fading memory material is considered. (C) 2011 Elsevier Inc. All rights reserved.

EXISTENCE OF S-ASYMPTOTICALLY omega-PERIODIC SOLUTIONS FOR ABSTRACT NEUTRAL EQUATIONS

A bounded continuous function it u : [0, infinity) -> X is said to be S-asymptotically omega-periodic if lim(t ->infinity)[u(t + omega) - u(t)] = 0. This paper is devoted to study the existence and qualitative properties of S-asymptotically omega-periodic mild solutions for some classes of abstract neutral functional differential equations with infinite delay, Furthermore, applications to partial differential equations are given.

On recent developments in the theory of abstract differential equations with fractional derivatives

This note is motivated from some recent papers treating the problem of the existence of a solution for abstract differential equations with fractional derivatives. We show that the existence results in [Agarwal et al. (2009) [1], Belmekki and Benchohra (2010) [2], Darwish et al. (2009) [3], Hu et al. (2009) [4], Mophou and N`Guerekata (2009) [6,7], Mophou (2010) [8,9], Muslim (2009) [10], Pandey et al. (2009) [11], Rashid and El-Qaderi (2009) [12] and Tai and Wang (2009) [13]] are incorrect since the considered variation of constant formulas is not appropriate. In this note, we also consider a different approach to treat a general class of abstract fractional differential equations. (C) 2010 Elsevier Ltd. All rights reserved.

EXISTENCE RESULTS FOR ABSTRACT DEGENERATE NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper we discuss the existence of solutions for a class of abstract degenerate neutral functional differential equations. Some applications to partial differential equations are considered.