**1. Introduction**

*Anoectochilus roxburghii* (Wall.) Lindl., also called "Jin Xianlian" and "Jin Xianlan" is a perennial herb of the genus *Anoectochilus* of the Orchidaceae family. It is widespread in southern China and considered a famous drug in the provinces of Jiangxi, Taiwan, Guangdong, Guizhou, Zhejiang, and Fujian which is its main markets [1]. The herb is a valuable Chinese medicinal material that is known as the "King Medicine", the "Golden Grass", and the "Bird Ginseng" by countryfolk [2]. The whole plant is used as a medicine and has the efficacy to clear the heat, cool the blood, eliminate dampness, and detoxification. Many pharmacological studies have demonstrated its wide range of pharmacological effects including its antioxidant [3,4], hepatoprotective [3], anti-diabetic [5,6], anti-rheumatoid arthritis [7], anti-hyperglycemic [4,8], anti-inflammatory [9] and many other properties. Due to the fact of its high medical values, *A. roxburghii* is not only widely used in medicine and health care but also in beauty and drinking products with an increasing market demand. The average annual demand in South Korea and Japan is more than 1000 t, 70% of which depend on imports [10]. The vigorous market demand results in excessive harvesting and exploitation of the plant, leading to resource depletion. Thus, tissue culture has become the main source of commercial *A. roxburghii*.

Most orchids form mycorrhizae with mycorrhizal fungi [11]. The fungal hyphae form coiled structures termed "peloton" inside the cells of the plant roots which play a key role in the nutrients' exchange and absorption between the orchid and its mycorrhizal fungi [12]. The process is unique and complex involving various processes related to growth and development, such as colonization, increasing the survival rate and morphological growth. Moreover, the mycorrhizal fungal elicitor can rapidly induce the expression of relative genes that are related to secondary metabolic pathways which result in a significant accumulation of active ingredients in the host plant [13]; this was demonstrated in orchid by a few studies. The symbiosis between *Dendrobium nobile* and *Mycena* sp. MF23 caused the accumulation of dendrobine and polysaccharide [14,15]. *Mycena* sp. MF23 could also stimulate the accumulation of flavonoid and kinsenoside in *A. formosanus* [16]. For *A. roxburghii*, the major bioactive components include polysaccharides, kinsenosides, steroids, triterpenes, amino acids, alkaloids, and flavonoids that have been regarded as the quality standard of *A. roxburghii* [10]. However, *A. roxburghii* contains a very limited number of flavonoids, which limits the development and utilization of *A. roxburghii*-based medicines. In order to improve the content of flavonoid in *A. roxburghii* and to avoid excessive exploitation, many methods have recently been put forward by researchers [17–19]; the role of mycorrhizal fungi in the accumulation of flavonoid in *A. roxburghii* has been gradually recognized. Wang et al. reported that flavonoid accumulated significantly in *A. roxburghii* growth for 8 weeks treated with different fungi such as *Rhizoctonia* sp. cw-6 and cw-13, *Exophila pisciphila* (cw-8), *Nemania* sp. (cw-10), and *Umbelopsis* sp. (cw-1) [20]. However, few studies investigated the effects of mycorrhizal fungi on flavonoid accumulation in *A. roxburghii* during different growth stages.

The flavonoid biosynthetic pathway has been well characterized in some medicinal plants such as *Gnetum parvifolium* [21], *Chrysanthemum morifolium* [22], *Lotus japonicus* [23]. Its biosynthesis can be divided into two stages: phenylpropanoid and flavonoid pathways. Phenylalanine ammonia-lyase (PAL) is the first enzyme of the phenylpropanoid pathway which can convert phenylalanine into cinnamic acid [24]. Cinnamic acid is then converted into p-coumaric acid by trans-cinnamate 4-hydroxylase (C4H). Next, 4-coumarate CoA ligase (4CL) converts coumaric acid into its CoA ester. 4CL is one of the key branch point enzymes in the phenylpropanoid pathway and its products are subsequently used by various oxygenases, reductases, and transferases for the biosynthesis of lignin, flavonoids, anthocyanins, aurones, stilbenes, coumarins, suberin, cutin, and sporopollenin [25]. Chalcone synthase (CHS) and chalcone isomerase (CHI) are involved in two step condensation reaction, producing naringenin chalcone and naringenin, respectively. Then, flavanone is catalyzed by flavonoid 3 -hydroxylase (F3 H) and other enzymes. Subsequently, flavanone produces the branches of flavone and dihydroflavonol under the catalysis of flavone synthase (FNS) and flavanone 3-hydroxylase (F3H), respectively. Next, flavonol synthase (FLS) catalyzes C-3 hydroxylation in the structure of dihydroflavonols to form various flavonols, and flavonol-glycosides are formed by flavonoid 3-O-glucosyltransferase (GT) and rhamnosyltransferase (RT) or GT.

With the rapid development of high-throughput sequencing technology and systems biology, multi-omics technology has become an indispensable research method in the field of life science [26,27]. It can provide the dynamic changes of the plant's growth and development from the cell to the individual level. The metabolome is a powerful approach to qualitatively and quantitatively analysis all the small-molecule metabolites (mass ≤ 1000 Da) in the cells or tissues of an organism at any

physiological period using different analysis technologies including nuclear magnetic resonance (NMR) spectroscopy, liquid chromatograph-mass spectrometer (LC-MS), and gas chromatography-mass spectrometer (GC-MS) [28]. In other words, this method could provide the global metabolic changes. Similarly, the transcriptome means the detection of all RNA transcripts in a sample and reflects gene expression differences between different treatments [29]. Integrated transcriptome and metabolome analyses have been successfully applied to study the metabolic pathways of some substances [30,31], the color formation of vegetables, fruits, and flowers [32,33], the stress resistance mechanisms [34,35], and the growth and development mechanisms of the plants [36,37]. The combination can not only elucidate changes in the content of a series of metabolites, but it can also analyze the corresponding differentially expressed genes.

To investigate the changes of metabolites in *A. roxburghii* that is infected with mycorrhizal fungus, we performed metabolome and transcriptome analyses on six-month growth data of the mycorrhizal *A. roxburghii* (M) and non-mycorrhizal ones (NM). The results indicated that AR2 significantly promoted flavonoid biosynthesis in the plant. During the growth stage, the flavonoid content (two flavones: nobiletin and tangeretin; two flavonols: quercetin and isorhamnetin; five flavonol-glycosides: narcissin, rutin, isorhamnetin-3-O-beta-d-glucoside, quercetin 7-o-glucoside, and kaempferol 3-O-glucoside) in different metabolites and the expression of the genes that were related to the biosynthesis of flavonoid were further tested over a period of six months using high-performance liquid chromatography coupled with tandem mass spectrometry (HPLC-MS/MS) then quantitative real-time polymerase chain reaction (qRT-PCR). These will provide valuable information to reveal the effects of *Ceratobasidium* sp. AR2 on the flavonoid accumulation in *A. roxburghii*.


**4. Exploring bandwidth and extracting optimal spectral bands using hierarchical band merging**

Works in the previous section were dedicated to the identification of a FS score. It was used for band selection, that is to say to select a subset of original bands out of a hyperspectral data set (without optimizing their weights). This section will focus on band extraction and will consider band subsets composed of spectral bands with different spectral widths. Indeed, optimizing spectral width is important to design a spectral sensor, as having wider bands is a way to limit signal noise while having too wide bands can also lead to a loss a useful information.


**Phase Diagram and Membrane Desalination**

Ayman Taha Abd El-aziem El-gendi

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/60419

#### **Abstract**

[14] N. Hilal, L. Al-Khatib, B.P. Atkin, V. Kochkodan, N. Potapchenko, Photochemical modification of membrane surfaces for (bio)fouling reduction: a nano-scale study us‐

[15] M.N. Abu Seman, D. Johnson, S. Al-Malek, N. Hilal, Surface modification of nanofil‐ tration membrane for reduction of membrane fouling, Desalination and Water Treat‐

[16] A.C. Talla-Nwafo, Modification of NF membranes for improved salt rejection, Ho‐

[17] A.H. Mohd Yusof, M. Ulbricht, Polypropylene-based membrane adsorbers via pho‐ to-initiated graft copolymerization: Optimizing separation performance by prepara‐

[18] M. Taniguchi, G. Belfort, Low protein fouling synthetic membranes by UV-assisted surface grafting modification: varying monomer type, Journal of Membrane Science,

[19] J. Pieracci, J.V. Crivello, G. Belfort, UV-Assisted graft polymerization of N-vinyl-2 pyrrolidinone onto poly(ether sulfone) ultrafiltration membranes using selective UV

[20] S.-i. Kuroda, I. Mita, K. Obata, S. Tanaka, Degradation of aromatic polymers: Part IV--Effect of temperature and light intensity on the photodegradation of polyether‐

[21] B. Kaeselev, P. Kingshott, G. Jonsson, Influence of the surface structure on the filtra‐ tion performance of UV-modified PES membranes, Desalination, 146 (2002) 265-271.

[22] B. Van der Bruggen, Chemical modification of polyethersulfone nanofiltration mem‐ branes: A review, Journal of Applied Polymer Science, 114 (2009) 630-642.

[23] L. Puro, M. Manttari, A. Pihlajamaki, M. Nystrom, Characterization of modified nanofiltration membranes by octanoic acid permeation and FTIR analysis, Chemical

[24] V. Yangali-Quintanilla, A. Sadmani, M. McConville, M. Kennedy, G. Amy, A QSAR model for predicting rejection of emerging contaminants (pharmaceuticals, endo‐ crine disruptors) by nanofiltration membranes, Water Research, 44 (2010) 373-384. [25] R. Malaisamy, A. Talla-Nwafo, K.L. Jones, Polyelectrolyte modification of nanofiltra‐ tion membrane for selective removal of monovalent anions, Separation and Purifica‐

tion conditions, Journal of Membrane Science, 311 (2008) 294-305.

wavelengths, Chemistry of Materials, 14 (2001) 256-265.

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tion Technology, 77 (2011) 367-374.

sulfone, Polymer Degradation and Stability, 27 (1990) 257-270.

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ment, 10 (2009) 298-305.

36 Desalination Updates

ward University, 2009.

231 (2004) 147-157.

Desalination technologies have made a significant impact in seawater and brackish water desalination. Recently, the evolution of membrane development has improved performance to lower operating costs and membranes have become the preferred technology for water desalination. Fortunately, different raw materials can be used for preparing membrane sheets which include either organic or inorganic materials, such as cellulose acetate, polyamide, polyimide, ceramic, natural, or artificial polymers. On the one hand, as a result of the variety of the raw materials which already exist in the entire world, different membrane separation processes might be applied dependent on the nature of the membrane sheet and the requirements of treatment process. On the other hand, there are different types of membranes can be used for membrane desalination by using different technologies such as reverse osmosis (RO), membrane distillation (MD), and forward osmosis (FO). The ternary phase diagram for membrane casting solution has an important role to get the required membranes.

**Keywords:** Desalination technologies, membrane, phase diagram, membrane sepa‐ ration processes

## **1. Introduction**

This chapter intends to focus on using membrane separation processes for desalination based on the selectivity of the membrane, such as the preferential permeation of water (classical selectivity) or the solute (reverse selectivity). Phase inversion process is the most important technique used to prepare asymmetric polymeric membranes. In addition, the morphology

© 2015 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

and performance of membranes depend on their effects, which also depend on the membrane preparation process parameters. From a thermodynamic point of view, study on polymer– solvent– nonsolvent system can be well depicted in a ternary phase diagram. The Flory-Huggins theory was found to be a convenient and useful framework for the thermodynamic analysis of component mixing in a membrane preparation system. As a result of the variety of the raw materials which already exist in the entire world, different membrane separation processes might be applied dependent on the nature of the membrane sheet and the require‐ ments of treatment process. In addition, there are different engineering forms which have been established for membranes that include flat, tubular, spiral wound or hollow fiber. Generally, the membrane preparation techniques are classified as a function of the raw materials used, the engineering forms and the characteristics of the required separation process. Over the past decades, the polymeric membranes have achieved commercial importance in a variety of separations applications in the chemical, food, pharmaceutical, and biotechnology industries. Today, the membrane industry is faced with the challenge of inventing new membrane materials.

In this chapter, we will focus particularly on membrane desalination techniques, such as reverse osmosis (RO), forward osmosis (RO) and membrane distillation for desalination. For these methods, as with any membrane process, the membrane is one of the most important characteristics which determines the usefulness and effectiveness of the entire process. For this reason, several targets of research have shifted in recent years towards developing new and more efficient materials that allow for a compromise between two fundamental properties of the separation, often antagonistic, namely the selectivity and permeability.

However, membrane processes are becoming economically competitive after the development of highly permeable polymer membranes. These membranes are less expensive than inorganic membranes and their implementation is much easier. Several types of polymers can be used such as cellulose acetate, polysulfones, polyamides and polyimides.

This chapter aims at preparing desalination membranes in order to get water selective membranes suitable for the retention of salts water mixtures. Hence two objectives must be reached: first, the selection of water selective materials well resistant in almost pure water and second, the preparation of high flux membranes needed for the recovery of water.

As a matter of fact, the preparation of polymeric membranes usually involves the phase inversion process, in which a homogeneous casting solution induces phase separation into a polymer-rich phase and a polymer-poor phase by the exchange of solvent with nonsolvent in an immersion bath (i.e: as water bath). Phase separation would continue to form the membrane structure until the polymer rich phase is solidified. Solidification during phase inversion could be induced by gelation and/or crystallization of the casted polymer solution. The equilibrium ternary phase diagram system is still a good tool for controlling the morphology and inter‐ preting the membrane structure. Significantly, knowledge of phase equilibria (cloud points, binodals, spinodals, and critical compositions) enables one to change the conditions for the preparation of membranes such as the compositions of the casting solution, the temperature and of the coagulation bath type to obtain an optimum membrane structure.

The phase diagram has an important role to report the agreement between experimental work in order to get the required membranes, and the ternary phase diagram miscibility gaps for the evaluations of membrane-forming system. In the ternary phase diagram (polymer (p)/ solvent (s)/nonsolvent (ns)) a miscibility gap with metastable regions exists. According to the theory of phase separation three modes of phase separation can take place in such ternary system: nucleation and growth of the polymer lean phase, spinodal phase separation and nucleation and growth of the polymer rich phase. Since polymer is one of the components of the ternary system, solidification of a part of the system can take place.


*4.1. Use of the OEE Indicator in Enterprises—Study Results*

The aim of the first stage of the research was to collect information on the use of lean maintenance methods and tools in enterprises, such as total productive maintenance (TPM), single minute exchange of die (SMED), 5S, and OEE indicator. The research, which was carried out in two stages, stage I—in 2010–2014 and stage II in 2014–2017, covered 150 production companies in the Podkarpackie Voivodship. The following criteria were taken into account when classifying the surveyed enterprises: size of the organization, production, type, industry, type of ownership, its capital, the company's condition, and the type of machines owned. Among the analyzed enterprises, there were those that carried out several types of production or operated in several industries. Among the analyzed enterprises, the biggest group were large enterprises (stage I: 46%, stage II: 52%). The next group were medium-sized enterprises (stage I: 27%, stage II: 32%). Among the surveyed enterprises, those from the metal processing industry dominated (stage I: 22.77%, stage II: 22.41%), followed by the aviation industry (stage I: 23.76%, stage II: 24.14%) and the automotive industry (stage I: 18.81%, stage II: 20.69%) (Figure 2). The majority were private enterprises (stage I: 94%, stage II: 98%) with Polish capital (stage I: 44%, stage II: 2%) or majority foreign capital (stage I: 44%, stage II: 25%) (Figure 3).

**Figure 2.** Structure of the surveyed research enterprises—type of industry.

**Figure 3.** Structure of the surveyed research enterprises—property and capital.

Unit production dominated among the surveyed enterprises (stage I: 28.44%, stage II: 28%) and low- and medium-batch production, respectively, (stage I: 24.77%, stage II: 24%) and (stage I: 21.10%, stage II: 28%) (Figure 4).

**Figure 4.** Structure of the surveyed research enterprises—type of production.

A survey method was used for the research. The designed questionnaires allowed us to obtain the data in the same form from all the respondents who did them independently. The survey included the representatives of medium and top management as well as the workers directly responsible for the supervision process of technological machines and devices and the chosen machine operators. The survey was realized in the form of conjunctive closed questions, which included a list of the prepared, provided-in-advance answers presented to a respondent with a multiple response item in which more than one option might be chosen. Additionally, other answers could be given if they were not among the provided options.

Within the conducted survey, the identification of the measures used for the effectiveness assessment of the implemented LM methods and tools as well as the benefits from their use noticed by enterprises were thoroughly analyzed. Collecting the information on the used types of measures for the effectiveness assessment of machine operation was the area of the conducted studies. The OEE indicator is one of the measures recommended in the literature. While assessing the effectiveness of the possessed machines and the implementation of the TPM method, this parameter is crucial. However, as the studies show, it is not always used [47,48]. The OEE indicator was one of the main study areas. The aim of the studies was to investigate if the OEE indicator was calculated in enterprises and how its value changed after the TPM method implementation.

Figure 5 shows that most of the analyzed enterprises still do not apply the OEE indicator (stage II: 60.38%, stage I: 73.96%). Only a few percent of the enterprises use this indicator for all machines (stage II: 7.55%, stage I: 5.21%).

**Figure 5.** Is the overall equipment effectiveness (OEE) indicator calculated?—study results.

Figure 6 shows the size of the enterprises where this indicator in not used. The second stage of the studies indicates that the indicator is the most often not used in the medium size enterprises (stage I: 7.55%, stage II: 5.21%). However, its use increased significantly in micro companies (stage I: 10.26%, stage II: 5.88%).

In addition, the fact this indicator is not most often used in the enterprises with unit production (stage I: 29.49%, stage II: 29.41%) as well as with medium-batch production (stage I: 23.08%, stage II: 29.41%) was identified. Its use increased significantly in mass production (stage I: 8.97%, stage II: 2.94%). Furthermore, the indicator is most often not used in the enterprises of aviation, metal processing, and automotive industries. However, all the enterprises of the food industry that took part in the second stage of the studies declared its application. A crucial issue during the conducted studies was to obtain the information on the rate of calculating the OEE indicator. The rate of obtaining such information is essential, because the OEE indicator values inform us on an ongoing basis about productivity of the possessed machines. If the information is collected too seldom, a prompt reaction will not be possible in cases when the use of machines decreases.

**Figure 6.** The percentage of enterprises that do not use the OEE indicator—the enterprise size.

The conducted studies show that in many enterprises the OEE indicator is calculated once a month (stage I: 26.09%, stage II: 25.00%). However, more and more often, the OEE indicator is calculated once per shift—the increase of over 17%, less often once a day—the decrease of over 16%. The obtained results show that large enterprises calculate the OEE value once per shift most often, medium enterprises once a month, small and micro enterprises once a week. The rate of calculating the indicator does not differ significantly in case of conventional and numerical machines (most often once per shift). Comparing the study results from the stages I and II, the rate of calculating changed from once a month to once a week for the machines described as "other".

Another element of the realized studies was collecting the information, which considered the value of the OEE indicator. Its value is important, because it allows us to conduct initially a general analysis of the effectiveness of the possessed machines. The value over 85% is considered as the world level value of this indicator [49]. Analyzing the obtained results, it was stated that the number of companies that declared an average value of the OEE indicator at the level of 50–70% (stage I: 18.18%, stage II: 33.33%) and at the level of 30–50% (stage I: 9.09%, stage II: 25.00%) increased significantly. In stage II of the studies, none of the analyzed companies declared the OEE values below 30%. The highest OEE indicator values of over 70% are obtained in large enterprises for numerical machines, in the aviation and automotive industry with major foreign capital. The lowest OEE indicator values, below 30%, are obtained in small enterprises for the machines described as "other", in the metal processing industry with Polish capital.

#### *4.2. Identification of Factors Influencing the E*ff*ectiveness of Lean Maintenance Implementation*

The aim of this stage was to identify the factors, which have an influence on the OEE value in analyzed enterprises. For provided analyses, the statistical chi-squared test was used. The following hypotheses were proposed zero hypotheses (H0), which means that there is not a significant difference in the solutions used in particular enterprises and alternative hypotheses H1, as there is a difference in the solutions used in particular enterprises.

These hypotheses can be written as

$$\mathbf{H}0 = \mathbf{p}\_1 = \mathbf{p}\_2 = \mathbf{p}\_3 = \dots \dots = \mathbf{p}\_n \tag{1}$$

and

$$\mathbf{P} \text{ (H1)} = \mathbf{p}\_1 \neq \mathbf{p}\_2 \neq \mathbf{p}\_3 \neq \dots \dots \neq \mathbf{p}\_n \tag{2}$$

The obtained *p*-value decided about accepting or rejecting H0, and therefore about accepting the alternative Hypothesis H1. If:

Table 2 shows the posed research hypotheses for the values of the OEE indicator as well as the obtained *p*-values.

**Table 2.** Research hypotheses—the effects obtained for the implementation of the lean maintenance methods and tools.

For the analyzed Hypotheses 3 and 4, there is a statistically validated difference in the value of the OEE indicator (*p*-value OEE = 0.041 and OEE = 0.048—Hypothesis H0 rejected, Hypothesis H1 accepted). It means that, in the studied enterprises, the value of OEE depends on the type of ownership and the enterprise industry. In case of the concerned Hypothesis 13, there is also a statistically validated difference in the value of the OEE indicator (*p*-value OEE = 0.025, *p*-value LA = 0.005—Hypothesis H0 rejected, Hypothesis H1 accepted). It means that, in the studied enterprises, the value of OEE depends on the mean time to repair. The detailed results of the obtained studies were presented in the work [50].

On this basis, the following conclusions were drawn: the factors that influence the use of lean maintenance methods and tools are for example industry and the capital owned. The presented analyses allowed us to highlight the actual activities undertaken in the management of technical infrastructure and existing problems, and, thus, the possibility of identifying factors that increase the efficiency of lean maintenance. It should be noted that the studies often showed that single factors do not have a significant impact on the studied areas, although their interaction with other factors may have a substantial impact on the analyzed area. However, the problem is that analyzing a process with many variables is very difficult. Therefore, in the second stage of the study, the concept of using artificial intelligence (AI) methods in order to assess the effectiveness of the lean maintenance concept implementation was proposed.


**Single- and Multiple-Junction p-i-n Type Amorphous Silicon Solar Cells with p-a-Si1-xCx:H and nc-Si:H Films**

S. M. Iftiquar, Jeong Chul Lee, Jieun Lee, Juyeon Jang, Yeun-Jung Lee and Junsin Yi

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/51732

## **1. Introduction**

The p-a-Si1-xCx:H alloy is popularly knows as a wide band gap semiconducting alloy. It was demonstrated in the 1980s that application of the p-a-Si1-xCx:H alloy leads to improved per‐ formance of a solar cell with better blue response of its quantum efficiency (QE) [1]. There are few other well known wide band gap alloy materials available, however one interesting advantage of the p-a-Si1-xCx:H is that both the C and Si are four fold coordinated atoms, and hence a suitably prepared material may attain wider optical gap with good stability.

The p-i-n type diodes have been widely used in photovoltaic solar (PV) energy conversion. Incident light that falls on the diode is absorbed in the intrinsic layer and electron-hole (e-h) pairs are generated, producing the PV or electrical energy, while the p-type and n-type lay‐ ers produce built-in electric field to separate the e-h pairs, created in the i-type layer. Recent‐ ly the interest on PV energy has been growing because it can provide clean energy. However, the efficiency of a solar cell is lower than that is expected, although there is a con‐ tinuous improvement in solar cell efficiency (η) throughout the history of solar cell. One of the reasons for such a low efficiency has been loss of light at the front surface of the cell due to reflection, as well as part of the low energy photons remains unabsorbed in the cell. Thus, for a maximum utilization of the incident light for PV energy conversion, the structural and material properties are expected to play some important roles. Light absorption at the doped window layer is also considered loss of light.

Another challenge is the material and interface defects that can hinder the collection of the photo generated e-h pairs [2]. This defect can exist in the material or at the interface [3,4]. Reducing such defects is also one of the priorities of a solar cell fabrication. The collection of

© 2012 Iftiquar et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 Iftiquar et al.; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

the e-h pairs can also depend upon built-in electric field created by doped p-type and n-type layers [5], and thus degree and efficiency of doping of these layers are also important.

Hydrogenated nanocrystalline silicon (nc-Si:H) thin film is also known as hydrogenated mi‐ crocrystalline silicon (μc-Si:H) thin film. It is composed of amorphous phase and a few nm sized crystalline Si grains [25-27]. The p-type nc-Si:H is also a promising material for solar cell window layer [28] The nc-Si:H thin films have optical bandgap of around 1.1 eV, unlike the a-Si:H thin films that have band gap of about 1.7eV. Light induced degradation of nc-Si:H films are low [29, 30]. Having lower optical gap of this nc-Si:H films, it is possible to utilize longer wavelength radiation of solar spectra. The nc-Si:H has lower optical band gap and higher ab‐ sorption coefficient of longer wavelength light, for which it can be used in the bottom cell of a multiple-junction solar cell, preceded by a wider band gap top cell. Such a combination of amorphous and micro-crystalline cells can be called as a micromorph solar cell [31-32]. In a mi‐ cromorph solar cell, the bandgap of the top cell is ~ 1.7eV and that of bottom cell is 1.1eV. Usu‐ ally the thickness of a-Si:H top cell is thinner than a usual single p-i-n type cell. The thickness of

Single- and Multiple-Junction p-i-n Type Amorphous Silicon Solar Cells with p-a-Si1-xCx:H and nc-Si:H Films

http://dx.doi.org/10.5772/51732

291

the intrinsic layer of nc-Si:H layer is almost 10 times to that in the a-Si:H top cell [20].

performance of a MJ cell remains poor.

**2.1. Deposition of Silicon Alloy Films**

**2. Experimental**

solar cell, and characterize their performance.

Furthermore, tunneling and recombination junctions (TRJs) are necessary in a MJ cell [33]. In a p-i-n type MJ cell, multiple unit cells are joined in tandem. This leads to a junction between n-type layer of the top cell to the p-type layer of the bottom one (or p-n junction), that may act as a recifying diode placed opposite to the p-i-n cell. This may be deteriorative to cell performance. Using a TRJ type p-n junction is a solution to the problem, without this the

Thus, we try to explore various aspects of fabricating single and multiple junction thin film

We prepared amorphous type p-a-Si1-xCx:H, a-Si:H, n-a-Si:H and nano-crystalline p-nc-Si:H, i-nc-Si:H, n-ncSi:H films, characterized them and applied in single junction, double junction and triple junction solar cells. We used RF PECVD, VHF PECVD, HW-CVD, for depositing silicon alloy materials, sputtering for AZO film deposition and thermal evaporation for met‐ al electrode deposition. The silane (SiH4), methane (CH4), hydrogen (H2), diborane (B2H6) (1% in H2), phosphine (PH3)(1% in H2) were the source gases for various films, where the SiH4, CH4, H2 were used for a-Si1-xCx:H alloy materials, SiH4, H2 for a-Si:H and nc-Si:H films,

The p-a-Si1-xCx:H films were deposited by 13.56 MHz RF PECVD with CH4, SiH4, H2, B2H6

films were deposited on 25mm×25mm sized Corning 1737 glass substrates and for Fourier transform infra red (FTIR) spectroscopic study we used (100) oriented p-type c-Si wafers. Later, selective samples are used for the p-type layer of the p-i-n type solar cells. Prior to film deposition the substrates were cleaned in acetone, methanol and de-ionized water. A 10-8 Torr base pressure of the reaction chamber was maintained prior to the film depositions.

C. For optoelectronic characterization, the

B2H6 was used as a p-type dopant gas and PH3 as the n-type dopant one.

source gases, at substrate temperature (Ts) of 200o

Along with its wider optical gap, the doped window layer or the top p-layer is generally made thinner as well [6], so that more light can enter into the active region of the device. However, with a thinner p-type layer the output voltage also get reduced [7,8], leading to more recombination loss of the photo generated charge carriers. Similarly, if optical gap of the window layer is high, then also the absorption loss at the p-type layer reduces. So, a wider optical gap thicker p-type layer appears to be a good option for a solar cell window layer. However, it is known that with increased carbon content within the material, optical gap increases [9,10] and the wider optical gap is usually associated to lower dark conductiv‐ ity [11], and higher activation energy (Ea). As a result the higher optical gap of the p-type layer may lead to lower output voltage from the device.

There are several different types of window layer one can use, like hydrogenated amor‐ phous silicon oxide (a-SiO:H) [12], hydrogenated amorphous silicon carbide (a-Si1-xCx:H) [1,13], hydrogenated amorphous silicon (a-Si:H) [14] etc and micro-crystalline or nano-crys‐ talline version of these materials. Out of these, wide band gap a-Si1-xCx:H and nc-Si:H mate‐ rials are two of the most promising materials.

Being amorphous in nature and containing hydrogen (H) and carbon (C) atoms in the mate‐ rial the composition and local bonding structure of the characteristic property of the materi‐ al is thus partly determined by microstructure within the material. A microstructure is a local non-uniformity of the material, and is generally used to indicate the density of SiHn or CHn type poly-hydrides in the material, where 1 ≤ n ≤ 3. Such a microstructure can also be called a void structure as well, that may be deteriorative for the material [15,16].

The carbon-silicon bonds lead to higher optical gap of the material and thus the increased carbon fraction x in a-Si1-xCx:H leads to higher optical gap of the material [1,9,17,18]. This higher optical gap results in higher optical transparency of the material, making it more suitable for a transparent window layer of a p-i-n type solar cell. It is also known that boron doping of amorphous silicon alloy material leads to reduction in optical gap [19]. Thus, a suitable boron doped p-a-Si1-xCx:H can become one of the best suited window layers.

In a multiple- junction amorphous silicon solar cell, multiple p-i-n type structures are joined in tandem [20]. The multiple junction solar cells are also known as multi-junction solar cell. The advantage of such a solar cell is that the open circuit voltage (Voc) becomes higher, and a wider spectral range of solar radiation can be absorbed in aggregate to the component cells. In this re‐ spect double (DJ) and triple junction (TJ) cells have been extensively studied in recent past [21-24]. As purpose of the DJ or TJ cell is the PV energy conversion by utilizing a wider spectral range, so tailoring of the band gap of the component cells become very important part of the design. In a suitable design, the top cell should have wider optical gap so that shorter wave‐ length light can be absorbed but the longer wavelength light will remain unabsorbed, while the middle cell should absorb the middle part and the bottom cell should absorb the longer wavelength part of the solar spectra. Thus, for the single p-i-n type cell or multiple-junction cell, a wide band gap window layer becomes a very significant component of the device.

Hydrogenated nanocrystalline silicon (nc-Si:H) thin film is also known as hydrogenated mi‐ crocrystalline silicon (μc-Si:H) thin film. It is composed of amorphous phase and a few nm sized crystalline Si grains [25-27]. The p-type nc-Si:H is also a promising material for solar cell window layer [28] The nc-Si:H thin films have optical bandgap of around 1.1 eV, unlike the a-Si:H thin films that have band gap of about 1.7eV. Light induced degradation of nc-Si:H films are low [29, 30]. Having lower optical gap of this nc-Si:H films, it is possible to utilize longer wavelength radiation of solar spectra. The nc-Si:H has lower optical band gap and higher ab‐ sorption coefficient of longer wavelength light, for which it can be used in the bottom cell of a multiple-junction solar cell, preceded by a wider band gap top cell. Such a combination of amorphous and micro-crystalline cells can be called as a micromorph solar cell [31-32]. In a mi‐ cromorph solar cell, the bandgap of the top cell is ~ 1.7eV and that of bottom cell is 1.1eV. Usu‐ ally the thickness of a-Si:H top cell is thinner than a usual single p-i-n type cell. The thickness of the intrinsic layer of nc-Si:H layer is almost 10 times to that in the a-Si:H top cell [20].

Furthermore, tunneling and recombination junctions (TRJs) are necessary in a MJ cell [33]. In a p-i-n type MJ cell, multiple unit cells are joined in tandem. This leads to a junction between n-type layer of the top cell to the p-type layer of the bottom one (or p-n junction), that may act as a recifying diode placed opposite to the p-i-n cell. This may be deteriorative to cell performance. Using a TRJ type p-n junction is a solution to the problem, without this the performance of a MJ cell remains poor.

Thus, we try to explore various aspects of fabricating single and multiple junction thin film solar cell, and characterize their performance.


**2. Phytoremediation process**

Biological methods using plants for treatment of polluted environment may also provide an alternative to traditional techniques [23, 24]. Phytoremediation (phyto = plant, remediation = correct evil) means re-vegetation of land which is spoiled by toxic substances and phytoremediation might be successful when plant using for phytoremediation material can accumulate high concentration of heavy metals in their shoots parts [23–28]. Phytoremediation as a brand new remedy approach for environmental pollutants communally anticipated to advantage all contemporary crises in better performance and decrease environmental effect in addition to economically feasible. This rising inexperienced technology, were won many severe anthropogenic pollutants. Fair evaluation required for risks, which associated with this approach. Even specifying it for a selected waste remedy inclusive of municipal wastewater [29] may also supply the reply key for consciousness on benefits and the accent risks. Aquatic macrophytes are vegetation that stay in water or moist soil and develop generously in lakes and waterways. This vegetation offer numerous ecological niches (meals, shelter), significantly contribute to biodiversity on the atmosphere level, and maintain meals chains. Besides their big position in nutrient cycle, oxygen balance, purification of water [30], and a source of some biologically

*Potential of Aquatic Plants for Pesticide Removal in Wastewater: A Case Study… DOI: http://dx.doi.org/10.5772/intechopen.107064*

active substances like antibacterial and antifungal agents [31]. Emergent aquatic macrophytes constitute a numerous institution of flora with a giant cappotential for removal/degradation of a lot of toxic objects and pollutants [32]. Besides, aquatic macrophytes are greater appropriate for wastewater preparation than different terrestrial flora because of their quicker growth, manufacturing of greater biomass and a relative better cappotential of pollutant approval [33]. Phytoremediation is a rapidly developing method that uses plants to reduce, degrade, assimilate and metabolize environmental pollutants such as hydrocarbons, pesticides, etc. [34].

The main mechanisms of phytoremediation included phytoextraction, rhizofiltration, phytostabilization, phytodegradation, and phytovolatilization [13]. Generally, vegetation selected for phytoremediation had the possibility to concentrate on a wide range of or specific contaminants [35]. Phytoremediation is the direct use of living green plants and is an effective, cheap, non-invasive, and environmentally friendly technique used to transfer or stabilize all the toxic metals and environmental pollutants in polluted soil or ground [35, 36]. Furthermore, phytoremediation is concerned with the potential of a plant species to accumulate high concentrations of toxic pollutants in their tissues. A number of plant metabolic processes come into play to degrade various organic compounds. There are many types of phytoremediation for agricultural land and water Plants bodies, e.g., phytotransformation, rhizosphere bioremediation, phytostabilization, phytoextraction (phyto-accumulation), rhizofiltration, phytovolatization, phytodegradtion, and hydraulic control (**Figure 1**) [38–40]. After more than 20 years of development, phytoremediation has become mature and widely employed to refine contaminated soil, water, and atmosphere. Also, the achievement of phytoremediation relies upon upon a plant's potential to tolerate and to build up excessive portions of the contaminant, even as yielding a big plant biomass [25]. In herbal and man-made filtering systems, macrophytes play an crucial function withinside the biochemical approaches of water remedy in view that their presence should exert a few high quality outcomes on this environment [41].


*<IP_ADDRESS> Baits*

There are certain rodenticides existing for field usage and can only be used by certified pesticide applicators. However, aluminum phosphide tablets and gas cartridges could be used to fumigate pest burrows. Agrarians may use bait stations to evaluate rodent populations decline, afterward use of rodenticide across the plantation flooring and below the canopies of trees. Globally, rodent pests are maximally frequently controlled chemically and there is an augmented interest in biological control by avian predators. Several avian predators (*Tyto alba*, *Elanus axillaris*, *Falco tinnunculus*, *Falco cenchroides*, *Bubo bengalensis*, *Buteo rufinus*) are commonly quoted in the biological control of rodents; however, barn owl (*T. alba*) is the most cited species [54].


*Edited by Farid A. Badria*

With the increasing emergence of viral infections worldwide, researchers are working to develop new and non-conventional treatments for infectious diseases. This is particularly true for SARS-CoV-2, which initiated a pandemic in 2019. With a focus on coronavirus, this book provides an overview of antiviral agents and new approaches to drug design. It includes five chapters that address new avenues for drug discovery, reprofiling of current drugs, computer-aided drug design, and more.

ISBN 978-1-80355-330-6

Antiviral Drugs - Intervention Strategies

Published in London, UK © 2022 IntechOpen © Trinity Treft / unsplash


*Article* **Note on Common Fixed Point Theorems in Convex Metric Spaces**

**Anil Kumar 1,† and Aysegul Tas 2,\*,†**

**Abstract:** In the present paper, we pointed out that there is a gap in the proof of the main result of Rouzkard et al. (The Bulletin of the Belgian Mathematical Society 2012). Then after, utilizing the concept of (E.A.) property in convex metric space, we obtained an alternative and correct version of this result. Finally, it is clarified that in the theory of common fixed point, the notion of (E.A.) property in the set up of convex metric space develops some new dimensions in comparison to the hypothesis that a range set of one map is contained in the range set of another map.

**Keywords:** compatible maps; common fixed points; convex metric spaces; q-starshaped

### **1. Introduction**

A point on which a self-map remains invariant is called a fixed point for that map. Fixed point theory plays an important role in solving different kinds of problems of nonlinear analysis and so it has applications in engineering, medical science, physical science, computer science, etc. In 1922, Banach [1] proved that a contraction map in a complete metric space has a fixed point and this result is known as the Banach contraction principle. Due to the simplicity and usefulness of this result, fixed point theory became a more aggressive area of research. Many researchers so far have worked in this field, extending this contraction principle in several possible ways [2–4].

In 1976, Jungck [5] extended the Banach contraction principle for the pair of commuting self-maps by ensuring the existence of a common fixed point for this pair. Sessa [6] relaxed the condition of commutativity and introduced the class of weak commuting maps. Again, Jungck [7] gave the weaker version of the commutativity condition by introducing the class of compatible maps and proved that weak commuting maps are compatible but the converse is not true in general. After that, many authors obtained more comprehensive common fixed point theorems under some given hypothesis [8,9].

On the other side, Takahashi [10] defined the notion of a convex structure in a metric space and called such a space a convex metric space. Further, he studied several properties of this space and ensure the existence of a fixed point for nonexpansive maps in the setup of convex metric space. In the last forty years, many fixed point and common fixed point theorems in the context of convex metric space have been established; for example, see [11–15].

### **2. Preliminaries**

In the present section we recall some standard notations, basic definitions and auxiliary results, which are required in the sequel.

In 2014, inspired by the idea of Aamri and Moutawakil [16], the concept of (E.A.) property in the context of convex metric space was introduced by Kumar and Rathee [17].

**Citation:** Kumar, A.; Tas, A. Note on Common Fixed Point Theorems in Convex Metric Spaces. *Axioms* **2021**, *10*, 28. https://doi.org/10.3390/ axioms10010028

Academic Editor: Emil Saucan

Received: 8 February 2021 Accepted: 25 February 2021 Published: 27 February 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

In the present article, we shall show that there is a gap in the proof of the Theorem 1, which is one of the main results of Rouzkard et al. [18]. Then, we obtain a correct version of Theorem 1 by utilizing the concept of (E.A.) property in a convex metric space defined by Kumar and Rathee [17].

Finally, we clarify the importance of the notion (E.A.) property in a convex metric space in comparison to the hypothesis that the range set of one map is contained in the range set of another map.

**Definition 1.** *[10] Let* (*S*, *ρ*) *be a metric space. A continuous mapping W* : *S* × *S* × [0, 1] → *S is called a convex structure on S, if for all x*, *y* ∈ *S and λ* ∈ [0, 1]*, we have*

$$d(\mathfrak{u}, \mathcal{W}(\mathfrak{x}, \mathfrak{y}, \lambda)) \le \lambda d(\mathfrak{u}, \mathfrak{x}) + (1 - \lambda)d(\mathfrak{u}, \mathfrak{y})$$

*for all u* ∈ *S. A metric space* (*S*, *ρ*) *equipped with a convex structure is called a convex metric space.*

Let *M* be a subset of a convex metric space (*S*, *ρ*). The set *M* is said to be

In addition, the map *I* : *M* → *M* is said to be

Clearly, each convex set *M* is *q*-starshaped for any *q* ∈ *M* but the converse assertion is not necessarily true (see Example 7 of [19]).

**Definition 2.** *[10] A convex metric space* (*S*, *ρ*) *is said to satisfy the Property (I), if for all x*, *y*, *z* ∈ *S and λ* ∈ [0, 1]*, we have ρ*(*W*(*x*, *z*, *λ*), *W*(*y*, *z*, *λ*)) ≤ *λρ*(*x*, *y*)*.*

Notice that Property (I) is always satisfied in a normed linear space and each of its convex subsets.

**Definition 3.** *[19] Let T*, *I* : *S* → *S be mappings on a metric space* (*S*, *ρ*)*. The pair* (*T*, *I*) *is said to be compatible if*

$$
\rho(TI\mathbf{x}\_n, IT\mathbf{x}\_n) \to o
$$

*whenever* {*xn*} *is a sequence in S such that*

$$T\mathbf{x}\_{n\prime} \ I\mathbf{x}\_n \to t \in S$$

**Definition 4.** *[16] Let T*, *I* : *S* → *S be mappings on a metric space* (*S*, *ρ*)*. The pair* (*T*, *I*) *is said to satisfy (E.A.) property if there is a sequence* {*xn*} ∈ *S such that*

$$T\mathbf{x}\_{n\prime} \ I\mathbf{x}\_n \to t \in S$$

**Definition 5.** *Let* (*S*, *ρ*) *be a metric space and T*, *I* : *S* → *S. Then the pair* (*T*, *I*) *is said to be reciprocally continuous if*

$$\lim\_{n \to +\infty} T I x\_n = T t \quad \text{and} \quad \lim\_{n \to +\infty} I T x\_n = I t$$

*whenever* {*xn*} *is a sequence in S such that* lim*n*→+∞ *Txn* = lim*n*→+∞ *Ixn* = *t for some t* ∈ *X.*

It is easy to see that if *T* and *I* are continuous, then the pair (*T*, *I*) is reciprocally continuous but the converse is not true in general (see Example 2.3 of [20]).

Moreover, in the setting of common fixed point theorems for compatible pairs of self-mappings satisfying some contractive conditions, continuity of one of the mappings implies their reciprocal continuity.

**Definition 6.** *A pair* (*T*, *I*) *of self-maps of a metric space* (*S*, *ρ*) *is said to be sub-compatible if there exists a sequence* {*xn*} *such that*

$$\lim\_{n \to +\infty} \operatorname{Tx}\_n = \lim\_{n \to +\infty} I \mathbf{x}\_n = t \text{ for some } t \in \mathcal{X} \text{ and } \lim\_{n \to +\infty} \rho(T \mathbf{1} \mathbf{x}\_n, IT \mathbf{x}\_n) = 0.$$

Recently, Rouzkard et al. [18] proved the following common fixed point theorem for the pair of compatible maps in a convex metric space.

**Theorem 1.** *Let C be a nonempty closed convex subset of a convex metric space* (*X*, *ρ*) *satisfying the Property* (*I*)*. Denote* [*x*, *q*] = {*W*(*x*, *q*, *k*) : 0 ≤ *k* ≤ 1} *where W is a convex structure on the metric space.*

If *T* and *I* are compatible self-maps defined on *C* such that *I*(*C*) = *C*, *I* is *q*-affine and nonexpansive, which satisfy the inequality

$$
\rho(Tx, Ty) \le \rho(Ix, Iy) + \frac{(1 - k)}{k} \max\{\rho(Ix, [Tx, q]), \rho(Iy, [Ty, q])\} \tag{1}
$$

for all *x*, *y* ∈ *C*, where 1/2 < *k* < 1, then *T* and *I* have a common fixed point provided *cl*(*T*(*C*)) is compact and *T* is continuous.

#### **3. Results**

*3.1. Compatibility in Proof of Theorem 1.*

Let us recall the lines of the proof given in Rouzkard et al. [18]. First of all, for each *n* ∈ N, the authors define *Tn* : *C* → *C* by

$$T\_{\mathfrak{n}}\mathfrak{x} = \mathcal{W}(T\mathfrak{x}, \mathfrak{q}, k\_{\mathfrak{n}}) \text{ for all } \mathfrak{x} \in \mathbb{C}, \tag{2}$$

where *kn* is a sequence in ( 1 2 , 1) such that *kn* → 1. Afterward, to accomplish the compatibility of the maps *Tn* and *I* for each *n* ∈ N, the authors choose an arbitrary sequence {*xm*} in *C* such that

$$\lim\_{m \to +\infty} I\mathbf{x}\_m = \lim\_{m \to +\infty} T\_n \mathbf{x}\_m = t \in \mathbb{C} \tag{3}$$

Using the definition of *Tn*, it has been written that

$$\begin{aligned} \rho(Tx\_{\mathfrak{m}}, T\_{\mathfrak{n}}\mathfrak{x}\_{\mathfrak{m}}) &= \rho(Tx\_{\mathfrak{m}}, W(Tx\_{\mathfrak{m}}, q, k\_{\mathfrak{n}})) \\ &\leq \quad k\_{\mathfrak{n}} \rho(Tx\_{\mathfrak{m}}, Tx\_{\mathfrak{m}}) + (1 - k\_{\mathfrak{n}}) \rho(Tx\_{\mathfrak{m}}, q) \\ &= \quad (1 - k\_{\mathfrak{n}}) \rho(Tx\_{\mathfrak{m}}, q) .\end{aligned}$$

Then by taking *m* → +∞ and using (3), the authors get

$$\rho\left(\lim\_{m\to+\infty}T\mathbf{x}\_{m\prime},t\right)\leq(1-k\_{\hbar})\rho\left(\lim\_{m\to+\infty}T\mathbf{x}\_{m\prime},q\right).\tag{4}$$

Again, on making *n* → +∞ in (4), the authors wrote the following (see [18], page 323, line 20–21)

$$\rho(\lim\_{m\to+\infty} T\mathbf{x}\_{m\prime} \mathbf{t}) \le 0. \tag{5}$$

Then, by using this expression, the authors claim the compatibility of the maps *Tn* and *I* for each *n* ∈ N.

Here, it is pertinent to mention that the compatibility of the maps *Tn* and *I* is to be shown for each *n* ∈ N and so the compatibility of *Tn* and *I* is to be shown for arbitrarily fixed natural number *n*. If *n* is fixed, then it is superfluous to approach *n* → +∞, therefore (5) is not valid because this is obtained by taking *n* → ∞ in (4). So the compatibility of the maps *Tn* and *I* for each *n* ∈ N proved by this way is totally wrong. The same mistake occurred when the authors tried to prove the reciprocal continuity of *Tn* and *I* for each *n* ∈ *N* (see [18], page 324, line 3–15).

#### *3.2. Modified Version of Theorem 1*

The following definition given by Kumar and Rathee [17] is required to prove the modified version of Theorem 1.

**Definition 7.** *Let M be a q-starshaped subset of a convex metric space* (*S*, *ρ*) *and let T*, *I* : *M* → *M with q* ∈ *F*(*I*)*. The pair* (*T*, *I*) *is said to satisfy (E.A.) property with respect to q if there exists a sequence* {*xn*} *in M such that for all λ* ∈ [0, 1]*.*

$$\lim\_{n \to +\infty} I\mathbf{x}\_n = \lim\_{n \to +\infty} T\_\lambda \mathbf{x}\_n = \mathbf{t} \text{ for some } \mathbf{t} \in M\_\mathbf{t} \tag{6}$$

*where Tλx* = *W*(*Tx*, *q*, *λ*)*.*

The following lemma is a direct consequence of Theorem 3.2 of Rouzkard et al. [18].

**Lemma 1.** *Let T and I be self-maps of a metric space* (*S*, *ρ*)*. If the pair* (*T*, *I*) *is sub-compatible, reciprocally continuous and satisfies the inequality*

$$
\rho(Tx, Ty) \le a \, \rho(Ix, Iy) + (1 - a) \max \{ \rho(Ix, Tx), \rho(Iy, Ty) \} \tag{7}
$$

*for all x*, *y* ∈ *X, where* 0 < *α* < 1*. Then T and I have a unique common fixed point in X.*

Now we modify Theorem 1 by replacing the condition *I*(*M*) = *M* ⊇ *T*(*M*) with the assumption that the pair (*T*, *I*) satisfies (E.A.) property with respect to some *q* ∈ *M*.

**Theorem 2.** *Let M be a nonempty q-starshaped subset of a convex metric space* (*X*, *ρ*) *with Property (I) and let T and I be continuous self-maps of M such that the pair* (*T*, *I*) *satisfies (E.A.) property with respect to q. Assume that I is q-affine, cl*(*T*(*M*)) *is compact. If T and I are compatible and satisfy the inequality*

$$
\rho(Tx, Ty) \le \rho(Ix, Iy) + \frac{1-k}{k} \max\{\rho(Ix, [Tx, q]), \rho(Iy, [Ty, q])\}\tag{8}
$$

*for all x*, *y* ∈ *M, where* 1 2 < *k* < 1*, then T and I have a common fixed point in M.*

**Proof.** For each *n* ∈ N, we define *Tn* : *M* → *M* by

$$T\_n(\mathbf{x}) = \mathcal{W}(T\mathbf{x}, q, k\_n) \text{ for all } \mathbf{x} \in \mathcal{M}, \tag{9}$$

where *kn* is a sequence in ( 1 2 , 1) such that *kn* → 1.

Now, we have to show that for each *n* ∈ N, the pair (*Tn*, *I*) is sub-compatible. Since *T* and *I* satisfy (E.A.) property with respect to *q*, there exists a sequence {*xm*} in *M* such that for all *λ* ∈ [0, 1]

$$\lim\_{m \to +\infty} I\mathbf{x}\_m = \lim\_{m \to +\infty} T\_\lambda \mathbf{x}\_m = t \in M,\tag{10}$$

where *Tλxm* = *W*(*Txm*, *q*, *λ*).

Since *kn* ∈ (0, 1), in light of (9) and (10), for each *n* ∈ *N*, we have

$$\begin{aligned} \lim\_{m \to +\infty} T\_n x\_m &= \lim\_{m \to +\infty} \mathcal{W}(T x\_m, q, k\_n) \\ &= \lim\_{m \to \infty} T\_{k\_n} x\_m = t \in M. \end{aligned}$$

Thus, we have

$$\lim\_{m \to +\infty} I\mathbf{x}\_m = \lim\_{m \to +\infty} T\_n \mathbf{x}\_m = t \in M. \tag{11}$$

Now using the fact that *I* is *q*-affine and Property (I) is satisfied, we get

$$\begin{aligned} \rho(T\_n I \mathbf{x}\_m, I \mathbf{I} T\_n \mathbf{x}\_m) &= \quad \rho(\mathcal{W}(T I \mathbf{x}\_m, q\_\prime k\_n), I(\mathcal{W}(T \mathbf{x}\_m, q\_\prime k\_n))) \\ &= \quad \rho(\mathcal{W}(T I \mathbf{x}\_m, q\_\prime k\_n), \mathcal{W}(I \mathbf{x}\_m, q\_\prime k\_n)) \\ &\le \quad k\_\mathbb{H} \, \rho(T I \mathbf{x}\_m, I \mathbf{I} \mathbf{x}\_\mathbb{m}). \end{aligned} \tag{12}$$

Since (*T*, *I*) satisfies (E.A.) property with *T* and *I* are compatible, in view of (10) we have

$$\lim\_{\mu \to +\infty} \rho(TI\mathbf{x}\_{m}, IT\mathbf{x}\_{m}) = 0.$$

Now, letting *m* → ∞ in (12), we obtain

$$\lim\_{m \to +\infty} \rho \left( T\_n I \mathbf{x}\_{m\prime} \, I T\_n \mathbf{x}\_m \right) = 0. \tag{13}$$

Hence, on account of (11) and (13), it follows that the pair (*Tn*, *I*) is sub-compatible for each *n* ∈ N. Since *T* and *I* are continuous, for each *n* ∈ N, the pair (*Tn*, *I*) is reciprocally continuous. Furthermore, by (8),

$$\begin{aligned} \rho(T\_n \mathbf{x}, T\_n \mathbf{y}) &= \rho(\mathcal{W}(T \mathbf{x}, q, k\_n), \mathcal{W}(T \mathbf{y}, q, k\_n)) \\ &\le \quad k\_n \, \rho(T \mathbf{x}, T \mathbf{y}) \\ &\le \quad k\_n [\rho(I \mathbf{x}, I \mathbf{y}) + \frac{1 - k\_n}{k\_n} \max\{\text{dist}(I \mathbf{x}, [T \mathbf{x}, q]), \text{dist}(I \mathbf{y}, [T \mathbf{y}, q])\}] \\ &\le \quad k\_n \, \rho(I \mathbf{x}, I \mathbf{y}) + (1 - k\_n) \max\{\rho(I \mathbf{x}, T\_n \mathbf{x}), \rho(I \mathbf{y}, T\_n \mathbf{y})\} \end{aligned} (14)$$

for each *x*, *y* ∈ *M* and 1 2 < *kn* < 1. By Lemma 1, for each *n* ∈ N, there exists *xn* ∈ *M* such that *xn* = *Ixn* = *Tnxn*.

Now the compactness of *cl*(*T*(*M*)) implies that there exists a sub-sequence {*Txm*} of {*Txn*} such that *Txm* → *z* as *m* → +∞. Further, it follows that

$$\mathbf{x}\_m = T\_m \mathbf{x}\_m = \mathcal{W}(T \mathbf{x}\_m, q, k\_m) \to z \quad \text{as} \quad m \to +\infty.$$

Then, by the continuity of *T* and *I*, we obtain *Iz* = *z* = *Tz* and so *z* is a common fixed point of *T* and *I*.

The following remark clarifies that in the context of a convex metric space, the notion of (E.A.) property introduced by Kumar and Rathee [17] for proving the common fixed point theorems has importance in comparison to the hypothesis that a range set of one map is contained in the range set of another map.

#### **Remark 1.**

(*a*) *In 2011, Haghi et al. [21] showed that several common fixed point generalizations in the theory of fixed point are not a real generalization because they can be obtained from the corresponding fixed point theorems. After the critical analysis of this paper, we reached the conclusion that* *the claim of Haghi et al. [21] is true only in the case if we make the assumption that the range set of one map is contained in the range set of another map.*

*So, keeping this in view, we replaced the condition I*(*M*) = *M* ⊇ *T*(*M*) *of Theorem 1 with the assumption that the pair* (*T*, *I*) *satisfies (E.A.) property with respect to some q* ∈ *M and due to this we have been able to obtain the modified and correct version of Theorem 1 in the form of Theorem 2.*

(*b*) *(see Example 17 of [16]) Let S* = R *with usual metric and M* = [0, 1]*. Define T*, *I* : *M* → *M by*

$$T(\mathbf{x}) = \begin{cases} \frac{1}{2} & \text{if } 0 \le \mathbf{x} \le \frac{1}{2} \\ \frac{x}{2} + \frac{1}{4} & \text{if } \frac{1}{2} \le x \le 1. \end{cases} \quad \text{and} \quad \begin{array}{c} I(\mathbf{x}) = \begin{cases} \frac{1}{2} & \text{if } 0 \le \mathbf{x} \le \frac{1}{2} \\ 1 - \mathbf{x} & \text{if } \frac{1}{2} \le \mathbf{x} \le 1. \end{cases}$$

*Then* (*S*, *ρ*) *is a convex metric space with W*(*x*, *y*, *λ*) = *λx* + (1 − *λ*)*y. It is easy to verify that the pair* (*T*, *I*) *satisfies (E.A.) property with respect to q* = 1 2 *, but the pair violates the condition that the range set of one map is contained in the range set of another map since T*(*M*)=[ 1 2 , 3 4 ] ⊆ [0, 1 2 ] = *I*(*M*) *and I*(*M*)=[0, 1 2 ] ⊆ [ 1 2 , 3 4 ] = *T*(*M*)*.*

In this way, we can say that there are certain pairs of self-maps, namely *T* and *I*, defined on a set (say *M*), which satisfies (E.A.) property in the set up of convex metric space but violates the condition *T*(*M*) ⊆ *I*(*M*). Thus, the common fixed point theorems in which the pair of maps satisfy (E.A.) property with some other hypotheses will ensure the existence of a common fixed point for such maps.

**Remark 2.** *As an application of Theorem 1, the authors in [18] obtained two more theorems (see Theorems 4.1 and 4.2 of [18]). Since we have quoted a gap in the proof of Theorem 1, Theorems 4.1 and 4.2 of [18] are no longer valid. Thus, these theorems can also be modified by using the notion of (E.A.) property in the set up of a convex metric space.*

#### **4. Conclusions**

In this work, a gap in the proof of the main result of Rouzkard et al. (The Bulletin of the Belgian Mathematical Society 2012) is detected. Then after, utilizing the concept of (E.A.) property in convex metric space, we obtained an alternative and correct version of this result.

In the set up of a convex metric space, the notion of (E.A.) property introduced by Kumar and Rathee [17] for proving the common fixed point theorems is more important than the hypothesis that a range set of one map is contained in the range set of another map and it develops some new extensions.

**Author Contributions:** Authors contributed equally to this work. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** This research did not report any data.

**Acknowledgments:** Thanks to Nasser Shahzad, King Abdulaziz University, Saudi Arabia, for providing us the preprint copy of Haghi et al. [21].

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


**1. Overview of the Issue: Remote Sensing Data Compression**

Announcing this Special Issue, the following was considered. First, a huge amount of data is acquired each day by different remote sensing systems and these data must be transferred to image processing centers, stored, and delivered to customers. Due to various restrictions, data compression is strongly desired or necessary. Second, there is a wide diversity of methods that can be used, requirements to compression and their priority, types, and properties of images to be processed, practical implementation aspects, etc. Our intention was to collect papers focused on advances in lossless and lossy compression, multi- and hyperspectral image compression, radar image compression, applications of remote sensing data compression; compression standards, practical implementation of image compression techniques, data compression hardware and software, impact of data compression on solving classification and identifications tasks.

As a result of our work as guest editors, 21 submissions have been received from which 6 have been rejected. The accepted publications cover a wide variety of questions.

Five papers relate to lossless and near lossless methods with application to multi- and hyperspectral data.

The paper "Analysis of Variable-Length Codes for Integer Encoding in Hyperspectral Data Compression with the k2-Raster Compact Data Structure" by Chow, K., Tzamarias, D.E.O., Hernández-Cabronero, M., Blanes, I., Serra-Sagristà, J. [1], examines various variable-length encoders that provide integer encoding to hyperspectral scene data within a k2-raster compact data structure. This structure leads to a compression ratio similar to that produced by some classical compression techniques while also providing direct access for query to its data elements without requiring any decompression. The selection of the integer encoder is critical for a competitive performance (compression ratio and access time). Different integer encoders, such as Rice, Simple9, Simple16, PForDelta codes, and DACs are investigated. Further, a method to determine an appropriate k value for building a competitive k2-raster compact data structure is discussed.

The paper "Using Predictive and Differential Methods with K2-Raster Compact Data Structure for Hyperspectral Image Lossless Compression" by Chow, K., Tzamarias, D.E.O., Blanes, I., Serra-Sagristà, J. [2] extends the previous paper by proposing a lossless coder for real-time processing and compression of hyperspectral images. After applying either a predictor or a differential encoder by exploiting the close similarity between neighboring bands, it uses the k2-raster compact data structure to further reduce the bit rate. Experiments show that using k2-raster alone already achieves much lower rates (up to 55% reduction), and with preprocessing, the rates are further reduced (up to 64%). Finally, experimental results show that prediction produces higher rates reduction than differential encoding.

The paper "Compression of Hyperspectral Scenes through Integer-to-Integer Spectral Graph Transforms" by Tzamarias, D.E.O., Chow, K., Blanes, I., Serra-Sagristà, J. [3] exploits the redundancies found between consecutive spectral components and within components themselves through the use of spectral graph filterbanks, such as the GraphBior transform. Such graph based filterbank transforms do not yield integer coefficients, making them appropriate only for lossy image compression schemes. In the paper, two integer-to-integer transforms are introduced for the purpose of the lossless compression, and its performance as a spatial transform is assessed.

The paper "Performance Impact of Parameter Tuning on the CCSDS-123.0-B-2 Low-Complexity Lossless and Near-Lossless Multispectral and Hyperspectral Image Compression Standard" by Blanes, I., Kiely, A., Hernández-Cabronero, M., Serra-Sagristà, J. [4] studies the performance impact related to different parameter choices for the new CCSDS-123.0-B-2 Low-Complexity Lossless and Near-Lossless Multispectral and Hyperspectral Image Compression standard. This standard supersedes CCSDS-123.0-B-1 and extends it by incorporating a new near-lossless compression capability, as well as other new features. Experimental results include data from 16 different instruments with varying detector types, image dimensions, number of spectral bands, bit depth, level of noise, level of calibration, and other image characteristics. Guidelines are provided on how to adjust the parameters in relation to their coding performance impact.

The paper "High-Performance Lossless Compression of Hyperspectral Remote Sensing Scenes Based on Spectral Decorrelation" by Hernández-Cabronero, M., Portell, J., Blanes, I., Serra-Sagristà, J. [5] investigates the most advantageous compression–complexity trade-off in hyperspectral image (HSI) compression. Compression performance and execution time results are obtained for a set of 47 HSI scenes produced by 14 different sensors in real remote sensing missions. Assuming only a limited amount of energy is available, obtained data suggest that the FAPEC algorithm yields the best trade-off. When compared to the CCSDS 123.0-B-2 standard, FAPEC is 5.0 times faster and its compressed data rates are on average within 16% of the CCSDS standard. In scenarios where energy constraints can be relaxed, CCSDS 123.0-B-2 yields the best average compression results.

There are three papers that deal with compression impact on classification and segmentation.

The paper "Lossy Compression of Multichannel Remote Sensing Images with Quality Control" by Lukin, V., Vasilyeva, I., Krivenko, S., Li F., Abramov, S., Rubel, O., Vozel, B., Chehdi, K., and Egiazarian, K. [6] studies a dependence between classification accuracy of maximum likelihood and neural network classifiers that have been applied to three-channel images and visual quality of compressed images. It is demonstrated that the classification accuracy starts to decrease faster when image quality due to increasing compression ratio reaches a distortion visibility threshold. In addition, classification accuracy depends essentially on the training methodology: training carried out for lossy compressed data seems preferable over training on undistorted data.

The paper "Lossy Compression of Multispectral Satellite Images with Application to Crop Thematic Mapping: A HEVC Comparative Study" by Miloš Radosavljevi´c, Branko Brkljaˇc, Predrag Lugonja, Vladimir Crnojevi´c, Željen Trpovski, Zixiang Xiong, and Dejan Vukobratovi´c [7] provides a comprehensive analysis of the HEVC still-image intra coding while applied to multispectral satellite images acquired by the Landsat-8- s OLI and Sentinel-2- s multispectral instrument. In the specific context of a crop classification application, HEVC's intra coding is shown to maintain approximately the same classification accuracy of a random forest pixel-based classifier for CR up to 150:1 while it is only up to 70:1 with JPEG 2000. It also achieves a better trade-off between compression gain and image quality, both visually and in terms of PSNR values, as compared to standard JPEG 2000.

The paper "Spectral Imagery Tensor Decomposition for Semantic Segmentation of Remote Sensing Data through Fully Convolutional Networks" by Josué López, Deni Torres, Stewart Santos, and Clement Atzberger [8] suggests a whole framework, called HOOI-FCN, to perform compression of an input RS-image followed by semantic classification. A Tucker decomposition-based mapping with preservation of the features of the classes of interest transforms the input third-order tensor into a core tensor with the same spatial resolution but a lower number of bands. This is done by means of the higher order orthogonal iteration (HOOI) algorithm. A fully convolutional network (FCN) is next considered to classify the core tensor at the pixel level. HOOI-FCN is shown to achieve high performance metrics competitive with some RS-multispectral images semantic segmentation state-of-the-art methods on Sentinel-2 images while significantly reducing computational complexity and processing time.

Lossy compression of data for unmanned aerial vehicle (UAV) is also attracting interest, as witnessed by two papers.

The paper "Real-Time Hyperspectral Data Transmission for UAV-Based Acquisition Platforms" by Melián, J.M., Jiménez, A., Díaz, M., Morales, A., Horstrand, P., Guerra, R., López, S., and López, J.F. [9] focuses on rapid compression of hyperspectral data prior to their transmission using two different NVIDIA boards—the Jetson Xavier NX and the Jetson Nano. The obtained results show the possibility of achieving real-time performance if the Jetson Xavier NX is used for all the configurations that could be applied in real missions.

The paper "FPGA-Based On-Board Hyperspectral Imaging Compression: Benchmarking Performance and Energy Efficiency against GPU Implementations" by Julián Caba, María Díaz, Jesús Barba, Raúl Guerra, Jose A. de la Torre, and Sebastián López [10] proposes a highly optimized implementation using integer arithmetic of the lossy compression algorithm for hyperspectral image systems. The purpose is to comply with the high-frame requirement imposed by a UAV-based sensing platform. The single-core version of the FPGA-based solution onto a heterogeneous Zynq-7000 SoC chip allows setting the baseline scenario of compressed hyperspectral image blocks at 200 FPS, using a small number of FPGA resources and low power consumption. Moreover, it is shown that a multicore FPGA-based version can reach the same level of performance as the most efficient embedded GPU-based implementations.

Two papers concern neural network use in image compression.

The paper "Reduced-Complexity End-to-End Variational Autoencoder for on Board Satellite Image Compression" by de Oliveira, V.A., Chabert, M., Oberlin, T., Poulliat, C., Bruno, M., Latry, C., Carlavan, M., Henrot, S., Falzon, F., and Camarero, R. [11] concentrates on design of a complexity-reduced variational autoencoder with attempt to meet the constraints dealing with board satellite compression, time, and memory complexities. A simplified entropy model that preserves the adaptability to the input image is proposed. It is shown that the designed complexity-reduced autoencoder provides a better ratedistortion trade-off compared to the Consultative Committee for Space Data Systems standard CCSDS 122.0-B.

The paper "Spectral–Spatial Feature Partitioned Extraction Based on CNN for Multispectral Image Compression" by Kong, F., Hu, K., Li, Y., Li, D., and Zhao, S. [12] puts forward a multispectral image compression framework that is fully based on a convolutional neural network (CNN). The novelty concerns the feature extraction module, divided into spectral and spatial parallel parts. The testing is carried out for datasets acquired by Landsat-8 and WorldView-3 satellites. A better performance is shown in comparison to JPEG 2000, 3D-SPIHT and ResConv, another CNN-based algorithm.

Compression acceleration is also addressed in the paper "An FPGA Accelerator for Real-Time Lossy Compression of Hyperspectral Images" by Daniel Báscones, Carlos González, and Daniel Mozos [13], which derives a custom FPGA implementation of the costliest part (tier 1 coder within JPEG2000) of the JYPEC algorithm, a lossy hyperspectral compression algorithm that combines PCA and JPEG2000. The main goal is to accelerate it significantly to bring the full algorithm execution time down as much as possible and even below the real-time constraint. An average acceleration of 3.6 is verified when the FPGA accelerated algorithm is applied to six hyperspectral images, four from the Spectrir library and two from the CCSDS 123 dataset.

Finally, two papers are devoted to compressive sensing.

The paper "Compressive Underwater Sonar Imaging with Synthetic Aperture Processing" by Choi, H., Yang, H., and Seong, W. [14] deals with synthetic aperture sonars (SAS) in underwater imaging. SAS imaging algorithms that employ compressive sensing are considered and verified through simulation and experimental data. A better resolution compared to the ω-k algorithms with minimal performance degradation by side lobes are demonstrated in simulations. Experimental data show the method's robustness with respect to sensor loss.

The paper "A Task-Driven Invertible Projection Matrix Learning Algorithm for Hyperspectral Compressed Sensing" by Dai, S., Liu, W., Wang, Z., and Li, K. [15] proposes a hyperspectral compressed sensing algorithm with low complexity and strong real-time performance. It is based on a task-driven invertible projection matrix learning algorithm aiming at solving the problems of long time-consuming and low reconstruction accuracy of compressed sensing-based reconstruction algorithms. Experiments performed on Indian Pine AVIRIS hyperspectral dataset show that, compared with the traditional compressed sensing algorithm, the proposed compressed sensing algorithm has higher reconstruction accuracy and improved real-time performance by more than a hundred times, thus leading to great application prospects in the field of hyperspectral image compression.

#### **2. Conclusions**

From the fifteen papers published in this Special Issue, we can state that compression of remote sensing data is today an active research area with new direction appearing and attracting attention of scientists engaged in the design of methods to meet customers' expectations. We hope that the readers will enjoy this Special Issue.

**Funding:** This research was partially funded by the Spanish Ministry of Economy and Competitiveness and the European Regional Development Fund under Grant RTI2018-095287-B-I00 and by the Catalan Government under Grant 2017SGR-463.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Acknowledgments:** We are grateful for having the opportunity to lead this Special Issue. We would like to thank the journal editorial team and reviewers for conducting the review process and all the authors for contributing their work.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


**5. Automaticity in writing and spelling**

Luria [67, 122] suggests that writing follows other mental processes in being a process which changes on a functional level through use and that changes on a functional level reflect greater functional integration in the brain. In the initial stages, writing depends on memorisation of the graphic form of each letter. With practice, the performance on each individual element becomes altered as writing develops into a single "kinetic melody," in which the structures underpinning the process of writing individual letters become automatised and integrated. Similar changes also take place in other higher mental processes to which the writing process is linked.

In the course of this development, it is not only the functional structure of the process which changes but also its cerebral organisation, as the activities of writing and spelling start to depend on different systems of concertedly working zones [123]. Following Vygotsky [7], this process of organisation would be based on new, intermediate structures of mental processes and new interfunctional relationships which would enable the performance of increasingly complex tasks by new methods. Automaticity would be central to the development of writing and spelling, as processes which enable their development into a single "kinetic melody" [67] capable of supporting the use of writing and spelling in higher mental activity.

Following Luria, assessment of writing and spelling would need to be linked to the assessment of reading ability. Luria [124] suggests that the investigation of writing should be conducted with a series of tests designed to analyse the state of the various elementary components and levels in writing. As writing is intimately connected with spelling, its assessment should also be linked to the investigation of phonetic analysis and synthesis of words and begin with the writing of individual letter, syllables and words. It should end with investigation of complex forms of written speech. In the course of these tests, the investigator would not only observe the quality of writing from dictation but also note the distinguishing features of the actual writing process.

On the level of instruction, Luria's theories would suggest that it would be important to develop both automaticity in reading and automaticity in writing and spelling, if these processes are not fluent. The work of the Spaldings [125–127] is based on the assumption that both writing and reading are stage-related and linked and that the rapid recognition of phonograms forms the basis through which writing is linked to the development of reading ability. Frith [128] has also suggested that the processes relating to the development of reading and the development of writing and spelling are stage-related and linked, as the following diagram suggests.

and components of, and issues surrounding, fluency and comprehension, will contribute to understanding of both reading development, and dyslexia subtypes. There would thus be justification on a theoretical level for incorporating assessment of oral reading fluency as one aspect of psychometric measurement of reading, together with other indicators of automatic-

At the same time, Moors and De Houwer [121] caution that there is wide usage of terms associated with automaticity as a concept, but no agreed definition as to what automaticity actually means. The author of this chapter follows Logan [50] in defining automaticity as relating to learned automatic processes, to which, following Luria [18, 19], fluency in speech

Luria [67, 122] suggests that writing follows other mental processes in being a process which changes on a functional level through use and that changes on a functional level reflect greater functional integration in the brain. In the initial stages, writing depends on memorisation of the graphic form of each letter. With practice, the performance on each individual element becomes altered as writing develops into a single "kinetic melody," in which the structures underpinning the process of writing individual letters become automatised and integrated. Similar changes also take place in other higher mental processes to which the writing process

In the course of this development, it is not only the functional structure of the process which changes but also its cerebral organisation, as the activities of writing and spelling start to depend on different systems of concertedly working zones [123]. Following Vygotsky [7], this process of organisation would be based on new, intermediate structures of mental processes and new interfunctional relationships which would enable the performance of increasingly complex tasks by new methods. Automaticity would be central to the development of writing and spelling, as processes which enable their development into a single "kinetic melody" [67]

Following Luria, assessment of writing and spelling would need to be linked to the assessment of reading ability. Luria [124] suggests that the investigation of writing should be conducted with a series of tests designed to analyse the state of the various elementary components and levels in writing. As writing is intimately connected with spelling, its assessment should also be linked to the investigation of phonetic analysis and synthesis of words and begin with the writing of individual letter, syllables and words. It should end with investigation of complex forms of written speech. In the course of these tests, the investigator would not only observe the quality of writing from dictation but also note the distinguishing features of the actual

On the level of instruction, Luria's theories would suggest that it would be important to develop both automaticity in reading and automaticity in writing and spelling, if these processes are not fluent. The work of the Spaldings [125–127] is based on the assumption

capable of supporting the use of writing and spelling in higher mental activity.

and language, as well as fluency in reading, writing and spelling, would be related.

ity, (for example, see [117–120]).

122 Learning Disabilities - An International Perspective

is linked.

writing process.

**5. Automaticity in writing and spelling**

The terms used in **Table 1** reflect Frith's contention that initially, pre-readers use logographic strategies, which involve the use of non-linguistic contextual cues, as well as the use of visual cues related to the whole shape of the word or to letter configurations within the word. This stage is primarily based on a visual route to learning, in that words are learned by rote memory through association of visual cues with the graphic representation of the word. The second alphabetic stage relies on a phonological route to learning which is more analytical. During this stage, both phonemes and graphemes become associated as children learn to sound out words [129].

Phonological processing then forms the basis for the establishment of an orthographic lexicon, in which alphabetic representations become precise enough to enable transfer from reading to spelling. The orthographic stage then develops after acquisition of phoneme-grapheme conversion knowledge, based on the application of phonological processing to spelling. At this stage, readers have learned to analyse words, and both letter groupings and word structure become important for increasingly fluid reading [129–131].

Frith suggests that there is initial dissociation between the strategies used in reading and writing in Stage 1 of each phase, whereas one and the same strategy is used in Stage 2 of each phase as children proceed from stage to stage in learning to read and spell [132]. Ehri [99] also suggests that spelling links closely with reading, but contends that beginning readers/spellers progress through phases of proficiency as opposed to stages. These phases are termed pre-alphabetic, partial alphabetic, full alphabetic and consolidated alphabetic and are related to the child's developing alphabetic and phonological knowledge. Ehri suggests that orthographic learning comes about through experience with printed language, in the process

Note that Frith's model assumes interplay between the evolving processes of reading and writing, which develop through logographic, alphabetic and orthographic stages. The numbers in the table indicate different stages in reading and writing development, whereas the arrows indicate how different stages in reading and writing development are linked. The small letters a and b indicate how the processes of reading and writing evolve in the different stages, become synchronised and ultimately become fluent.

**Table 1.** The six-step model of skills in reading and writing acquisition [128].

of which longer and longer letter strings become stored in memory. Children in the final consolidated alphabetic phase are able to read fluently as well as spell accurately, by relying upon these stored orthographic representations.

Besides requiring integration between the processes of instruction used to develop reading, writing and spelling [133], it would also be important to conceptualise the development of fluency in writing and spelling as a long-term process. Both Frith [132, 134] and Ehri [133, 135] are in agreement that considerable practice at reading by means of an alphabetic procedure is necessary to enable the reader to establish internal representations of word forms, as the basis for developing the ability to spell accurately and fluently.

Kellogg [136] suggests that mastering the mechanics of writing forms the foundations for a 10-year process of achieving fluency in the acquisition of knowledge, as well as written and spoken production in the telling of knowledge. This would then be followed by a second decade post school to advance from knowledge-telling to knowledge-transforming. As Kellogg observes, this is similar to the process of development involved in becoming an outstanding performer in music, chess, typewriting and other domains, in which deliberate practice needs to continue for a minimum of a decade for an individual to acquire expert standing [137, 138].


**Acknowledgements**

This research is part of the Cultural History of PaleoAsia - Integrative research on the formative processes of modern human cultures in Asia project and is supported by a Japan Society for the Promotion of Science Research Grant (Grant Number: 16H06409). Alfred Pawlik was supported by the University Research Council of Ateneo de Manila University and an AdMU Loyola Schools Research and Creative Writing (RCW) Faculty Grant. The research of Riczar Fuentes was funded by a Lisa Maskell Fellowship of the Gerda Henkel Foundation, Düsseldorf, Germany. The excavations of Leang Sarru and Goa Topogaro reported here would not be possible without the support and the administrative personnel of Pusat Penelitian Arkeologi Nasional (ARKENAS) and Balai Arkeologi Sulawesi Utara in Indonesia.

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**105**


**1. Introduction**

Fetal surgery or in utero therapy tries to prevents or corrects multiple congenital anomalies in the fetus to prevent their severe consequences on later fetal development. It started with open fetal surgery then innovations toward minimally invasive procedures have occurred. In this chapter, we discuss the basic principles of fetal surgery, the general history of its development, important specific conditions and procedures used to treat them, and the future of the field.


**1. Introduction**

82 Video Compression

Zhibo Chen, Jianfeng Xu, Yun He, Junli Zheng (2006) Fast integer-pel and fractional-pel

Vol.17,pp. 264–29,

motion estimation for H.264/AVC, *International Journal of Visual Communication*,

In this chapter, global motion estimation and its applications are given. Firstly we give the definitions of global motion and global motion estimation. Secondly, the parametric representations of global motion models are provided. Thirdly, global estimation approaches including pixel domain based global motion estimation, hierarchical global motion estimation, partial pixel set based global motion estimation, and compressed domain based global motion estimation are reviewed. Finally, four global motion based applications in video compression, sport video shot classification, video error concealment, and video text occluded region recovery are given.

Motion information is very important for video content analysis. In surveillance video, usually the camera is stationary, and the motions of the video frame are often caused by local motion objects. Thus detecting motions in the video sequences can be utilized in abnormal events detection. In sports video, the heavy motions are also related to highlights. Motion estimation and compensation is the core of video coding. Coding the residual component after motion compensated can save bit-rates significantly. In video sequences, the motion pattern can be classified into two types: local motion and global motion. The global motion is related to camera motion. Integrated with local motion, global motion is widely utilized in video object segmentation, video coding and error concealment. The rest of this chapter is organized as follows: the definition of global motion is given in Section 2. The global motion models are given in Section 3. Global motion estimation approaches are given in Section 4. Four applications based on global motion and local motion (GM/LM) information are introduced in Section 5. The applications are GM/LM based video coding, global view refinement for soccer video, GM/LM based error concealment and GM/LM based text occluded region recovery. And finally conclusions are drawn in Section 6.