**Author details**

Pavel Loskot ZJU-UIUC Institute, Haining, Zhejiang, China

\*Address all correspondence to<EMAIL_ADDRESS>
© 2022 The Author(s). Licensee IntechOpen. 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.

*Bayesian Methods and Monte Carlo Simulations DOI: http://dx.doi.org/10.5772/intechopen.108699*


**5. Bactericidal effect**

Until a recent past, the radiation effects on the bacterial load and removal of noxious chemical compounds had only been performed in small samples of sludge irradiated under laboratory conditions and mainly address either only the microbiological or the chemical effect of radiation in a sample of sludge [16–20]. Processing and disposal of wastewater sludge is a critical problem worldwide [18] and especially in large metropolitan such as Washington DC in the USA and Tokyo in Japan. Therefore, new technologies to solve the problem of safely disposing of sewage sludge are constantly being sought. An attractive solution for the disposal of wastewater sludge is its utilization in crop fields and landscaping as a fertilizer due to its high content in natural nitrogen compounds. However, in order to be used as such, it must be converted into a class A biosolid [21] which is a form of treated sludge that is deemed safe for humans and animals. In recent years, electron beam technology have shown to be an economically alternative that could be used to meet these regulations by considerably reducing the number of potentially harmful bacteria such as the fecal coliform bacteria and helminth ova such as A*scaris ova* which are both ubiquitous contaminants present in the sewage sludge. The fecal coliform bacteria are a group of bacteria that are released in the environment through the fecal excrement of humans, wildlife, and livestock. They typically occur in the digestive tract of humans and warm-blooded animals. When present in sewage sludge, they are indicative of the presence of human and animal pathogens including some strains of *Escherichia coli*, *Shigella flexneri*, and *Salmonella typhimurium*. Among the fecal coliforms, the *E. coli O157:H7* strain which was responsible for many outbreaks has retain attention of media in the past several years. Indeed, *E. coli O157:H7* was found contaminating drinking water and vegetables, causing cases of stomach cramping, vomiting, and bloody diarrhea in patients. However, in most cases infections with the *E. coli O157:H7* strain were mild or with no symptoms. Most people infected with *S. typhimurium* develop diarrhea, stomach cramping, and fever which could cause the patient to experience fatigues and dehydration. An infection with *S. flexneri* is much more serious with severe stomach pain, dehydration, severe diarrhea, and fever. Patients suffering for shigellosis feel very sick and stay in bed at the pick of the infection. In farming areas where livestock is grown, beside occurrence of fecal coliforms, ascaris ova that when ingested by a person or an animal would hatch and develop into adult worms, *Ascaris lumbricoides* cause stomach pain, nausea, vomiting, and fatigue. In patients who are heavily infested with ascaris worms, the parasites could be expelled through feces and/or vomit.

Additionally, the electron beam technology could be used to reduce the concentration of volatile organic sulfides and other volatile organic compounds (VOCs) responsible for the unpleasant odor in sewage sludge. Moreover, electron beam treatment of sludge is not an energy intensive process which means that it has a small footprint and the processing times are usually short. The main effect of radiation on sewage sludge is in the radiolysis of water producing OH\* and H\* radicals and hydrated electrons, highly reactive chemical species which rapidly react with organic compounds in the sludge. The main intermediates in this process are:

$$\mathrm{H\_2O} \rightarrow \mathrm{[2.7]} \mathrm{OH^\*} + \mathrm{[2.6]} e\_{aq}^- + \mathrm{[0.6]} H^\* + \mathrm{[2.6]} H\_3 \mathrm{O^\*} + \mathrm{[0.7]} H\_2 \mathrm{O\_2} + \mathrm{[0.45]} H\_2 \tag{1}$$

The effect of electron beam irradiation on the microbial reduction in sludge is accomplished by a two-fold effect of the irradiation on the sludge [22]. The first one is the direct effect of radiation on the microorganisms disrupting the structural integrity of DNA molecule and eventually killing them. The other one is the indirect effect caused by the radiolysis of water described above. The chemical active species which are produced in water because of the irradiation will cause oxidative damage on nucleic acids, proteins, and lipids in microorganisms leading to their death. Typically, at a given electron beam radiation dose, the killing of microorganisms occurs at a constant rate over time. Similarly, the effectiveness of the killing of the microbial populations including that of bacteria increases with the radiation dose. The effectiveness of electron beam radiation on the killing of microorganisms is better represented by the so called *D10* value which is the dose of radiation required to kill 90% of the population of microorganisms present in the sludge sample. Because of the difference in structural complexity of microorganisms, *D10* values may vary more or less significantly from one microorganism to another. Thus, for *Ascaris ova,* that *D10* value was determined to be in the order of 0.39 kGy [23]. For other microbial contaminants of sludge including *S. typhimurium* and *E. coli*, these *D10* values were determined to be 0.3 and 0.34 kGy respectively [4]. Recent studies performed by Engohang-Ndong and his research collaborators have shown that the electron beam technology could be used at industrial scale to eliminate potential microbial pathogens from sewage sludge [9]. The US-based research team showed that a dose of 25.7 kGy was enough to eliminate *Ascaris ova* to a level that is not detectable to available technique used to count the helminth eggs in sewage sludge including the use of Sedgwick Rafter cells to count the detectable ascaris ova. Thus, at that electron beam radiation dose, it was possible to achieve a class A sludge. According to the US Environmental Protection Agency (EPA) standards, to be considered class A biosolids, the sewage sludge must contain less than one *Ascaris* ovum per four gram of sludge dry weight [21]. The dose needed to eliminate fecal coliforms to the norm set by the US EPA to convert sewage sludge to class A biosolids is much lower. The experimental dose determined by Engohang-Ndong and collaborators is 6.7 kGy. In other words, when risks of contamination of sewage sludge by helminth eggs is reduced such as in heavily urbanized areas, the doses needed to convert sewage sludge to class A biosolids that in turn could be used to enrich the soil for landscaping and agricultural purposes is very beneficial and requires low consumption of energy.

### **6. Economic aspects**

An important aspect in the implementation of a new technology such as an electron accelerator in a wastewater treatment plant is to anticipate its impact on the operation costs of the facility and on the environment. With respect to the irradiation of sewage sludge several authors have addressed this issue. A team in Florida reported a cost of \$2.50 per 1000 gallons of sludge for a 1.5 MeV electron irradiation facility running at 160 gallons per minute [24], while another group compared gamma and electron beam irradiations for a sample of activated sludge and obtained treatment costs of \$4.20/m3 for gamma irradiation and \$2.10/m3 for electron beam irradiation, which are lower compared to \$4.85–\$5.19 when using conventional technology at the Central District Wastewater Treatment Facility in Miami Dade County [25]. Furthermore, a comparison was made between irradiation at a dose 6 kGy and incineration of sludge samples and showed a cost of \$60.87/ m3 for this latter compared to \$3.12/m3 when using gamma radiation. Similar results have been obtained by Engohang-Ndong et al. using a 3 MeV electron accelerator. In this case these authors reported that the cost to irradiate one cubic meter of sludge to a dose of 25.7 kGy will be \$1.26 [9]. That comparative cost analysis tends to show that electron beam irradiation of sludge consumes less energy than other technologies. Furthermore, electron beam irradiation requires processing times,

and very importantly more environmentally friendly technology compared to other technologies such as gamma radiation and incineration.


*1.3.1. Physical therapies for the urinary incontinence*

transobturator insertion (7%) compared to retropubic insertion (3%)(Barber, Kleeman et al.

Vulvovaginal pain can developed after bacterial vaginal infections or bacterial vaginosis. Infections change the vaginal ecosystem. Oestrogen deficiency in peri- and post-menopausal women can also lead to vulvar tissue atrophy and a subsequent irritation. Contact with irritanting agents such as soaps, detergents and topical preparations as well as vulvar trauma associated with accidents or surgery can lead to vulvar irritation and the development of

Urinary incontinence is an extremely common complaint worldwide. It causes a great deal of distress and embarrassment, as well as significant costs, to both individuals and societies (Lucas, Bosch et al. 2012). The standardization committee of the International Continence Society (ICS) has defined the female urinary incontinence as the involuntary urine loss, objectively demonstrable, which represents a social or hygienic problem (Abrahams, Blaivas

At least one out of four women in Europe suffers from a disorder associate with incontinence which often has been present for several years before consultation (Thomas, Plymat et al. 1980). In geriatric hospitals, the incidence of urinary incontinence I in women is 43% and as

Patients with 'complicated incontinence' are those with co-morbidities, a history of previous pelvic surgery, past surgery for incontinence, radiotherapy and associated genitourinary prolapse (Lucas, Bosch et al. 2012). Urinary incontinence is more common in women with UTIs and is also more likely in the first few days following an acute infection (Moore,

In women with incontinence, diagnosis of a UTI by positive leucocytes or nitrites using urine test strips had low sensitivity but high specificity (Semeniuk and Church 1999; Buchsbaum,

Incontinent women with symptoms of lower urinary tract or pelvic floor dysfunction and pelvic organ prolapse have a higher risk of of incomplete bladder emptying (elevated post void residual urine volume) compared to asymptomatic patients. Therefore it is suggested that the presence of post void residual should be ruled out in this patients (Fowler, Panicker et al.

In the elderly incontinence can be caused or worsened by underlying diseases including diabetes (Lee, Cigolle et al. 2009). A higher prevalence of incontinence was associated with higher age and body mass index (Sarma, Kanaya et al. 2009). A recent meta-analysis showed that systemic oestrogen therapy for post-menopausal women was associated with the devel‐ opment and worsening of urinary incontience (Cody, Richardson et al. 2009). Obesity appears

to confer a four-fold increased risk of UI (Chen, Gatmaitan et al. 2009).

2008; Lorenzo-Gómez, B et al. 2013).

294 Electrodiagnosis in New Frontiers of Clinical Research

**1.3. Urinary incontinence**

et al. 1988).

Jackson et al. 2008).

Albushies et al. 2004).

2009).

vulvovaginal pain (White, Jantos et al. 1997 Mar).

high as n 91% in psychogeriatric patients.

The treatment of lower urinary tract's disorders with pelvic floor exercises with or without biofeedback represents a risk-free option which can be applied in a great number of women. The correct function of the female pelvic floor depends on the position and mobility of the urethra and the urethrovesical junction. Pelvic floor muscle training increases urethral closure pressure and stabilises the urethra, preventing downward movement during moments of increased physical activity. There is evidence that increasing pelvic floor strength may help to inhibit bladder contraction in patients with an overactive bladder. This training may be augmented with biofeedback (Bidmead 2002).

The evidence published in the guidelines regarding urinary incontinence suggests that UTI treatment does not correct the UI. It is unclear if improving the incontinence helps decrease recurrence rate of UTI.

Valid methods to evaluate the morphologic and electromyographic abnormalities of the levator ani muscle are necessary in order to better select women or the treatment with pelvic floor training and biofeedback (Bo, Larsen et al. 1988; Espuña-Pons 2002).

The most recently published systematic review in 2010 found that medication was less effective than behavioural therapy in a comparative effectiveness trial (81% vs. 69% reduction in UI episodes) (Goode, Burgio et al. 2010), therefore pelvic floor physiotherapy must always be the first line of treatment for stress incontinence and overactive bladder. Drugs must be prescribed if pelvic floor physiotherapy fails (Bidmead 2002).


**A Review of the Etiology Delirium**

Nese Kocabasoglu1, Gul Karacetin2, Reha Bayar1 and Turkay Demir3 *1Cerrahpasa Medical School, Department of Psychiatry*

*2Department of Child and Adolescent Psychiatry 3Cerrahpasa Medical School, Department of Child and Adolescent Psychiatry Turkey*


**5. Conclusion and future direction**

This work presents a novel FEOLED had further increase the luminous efficiency of OLEDs. The characteristics of an OLED constructed in the FEOLED device are optimized by inserting a thin Cs2CO3 electron injection layer between the Alq3 and Al electrode. Experimental results indicate that the external field emission electrons can enhance the luminance in FEOLED efficiently owing to balanced recombination of electrons and holes. Additionally, FEOLED achieves a higher luminous capability than that of OLED under the same current density. Mechanism detection of the FEOLED further reveals that the amounts of holes are more than that of electrons in the emission layer of an OLED device. Furthermore, the secondary electron material CsI deposited onto the Al electrode in a FEOLED can provide multiple electrons as well as prevent the organic layer from electrons bombardment. The proposed device's construction is extremely important for characterizing the emission mechanism of the FEOLED.

Another objective of this chapter is to provide background knowledge to readers from the different fields to stimulate new ideas. For example, the flexible photovoltaic OLED (PVOLED) and a tandem of organic solar cell (OSC) and white organic light emitting diode (WOLED), although not addressed here, are now emerging. In PVOLEDs, the power recycling efficiency of 10.133 % is achieved under the OLED of PVOLED operated at 9V and at a brightness of 2110 cd/m2,when the conversion efficiency of OSC is 2.3%.[52]. In a tandem of OSC and WOLED, which can be fabricated to generate electricity as well as lighting for domestic and commercial uses [53].

### **Author details**

38 Organic Light Emitting Devices

listed by Table 1, respectively.

As describe above, we can see that the characteristics of the OLED and the FEOLED are

**Table 1.** (1) The characteristics of the OLED and (2) The characteristics of the FEOLED

This work presents a novel FEOLED had further increase the luminous efficiency of OLEDs. The characteristics of an OLED constructed in the FEOLED device are optimized by inserting a thin Cs2CO3 electron injection layer between the Alq3 and Al electrode. Experimental results indicate that the external field emission electrons can enhance the luminance in FEOLED efficiently owing to balanced recombination of electrons and holes. Additionally, FEOLED achieves a higher luminous capability than that of OLED under the same current density. Mechanism detection of the FEOLED further reveals that the amounts of holes are more than that of electrons in the emission layer of an OLED device. Furthermore, the secondary electron material CsI deposited onto the Al electrode in a FEOLED can provide multiple electrons as well as prevent the organic layer from electrons bombardment. The proposed device's construction is extremely important for characterizing

Another objective of this chapter is to provide background knowledge to readers from the different fields to stimulate new ideas. For example, the flexible photovoltaic OLED (PVOLED) and a tandem of organic solar cell (OSC) and white organic light emitting diode (WOLED), although not addressed here, are now emerging. In PVOLEDs, the power recycling efficiency of 10.133 % is achieved under the OLED of PVOLED operated at 9V and at a brightness of 2110 cd/m2,when the conversion efficiency of OSC is 2.3%.[52]. In a tandem of OSC and WOLED, which can be fabricated to generate electricity as well as

**5. Conclusion and future direction**

the emission mechanism of the FEOLED.

lighting for domestic and commercial uses [53].

Meiso Yokoyama

*Department of Electronic Engineering, I-Shou University, Kaohsiung City, Taiwan*

#### **6. References**

[18] M. Nikl, "Wide Band Gap Scintillation Materials: Progress in the Technology and Material Understanding" phys. stat. sol., vol. 179, pp. 595-620, (2000)

Field Emission Organic Light Emitting Diode 41

[34] M. Pfeiffer, K. Leo, X. Zhou, et al "Doped organic semiconductors: Physics and application in light emitting diodes" Organic Electronics, vol. 4, pp. 89-103, (2003) [35] W. A. de Heer , A. Châtelain, D. Ugarte "A Carbon Nanotube Field-Emission Electron

[36] S. Iijima "Helical microtubules of graphitic carbon", Nature, vol. 354, pp. 56-58.(1991) [37] T. 1V. Vorburger, D. Penn, and E. W. Plummer, "Field emission work functions" Surface

[38] S. R. C. Vivekchand, L. M. Cele, F. L. Deepak, et al "Carbon nanotubes by nebulized

[39] W. B. Choi, D. S. Chung, J. H. Kang, et al "Fully sealed, high-brightness carbonnanotube field-emission display" Appl. Phys. Lett., vol. 75, pp. 3129-3131,(1999) [40] L. Zhu, J. Xu, Y. Xiu, et al "Growth and electrical characterization of high-aspect-ratio

[41] Z. Wu, Z. Chen, Xu Du, et al "Transparent, Conductive Carbon Nanotube Films"

[42] R. H. Schmidt, I. A. Kinloch, A. N. Burgess, and A. H. Windle "The Effect of Aggregation on the Electrical Conductivity of Spin-Coated Polymer/CarbonNanotube

[43] H. J. Jeong, H. K. Choi, G. Y. Kim, et al "Fabrication of efficient field emitters with thin multi-walled carbon nanotubes using spray method" Carbon, vol. 44, pp. 2689-2693.

[44] L.S.Hung, C.W.Tang, M.G.Mason, P.Raychaudhuri, and J. Madathil, "Application of an ultrathin LiF/Al bilayer in organic surface-emitting diodes", J.Appl.Phys.,

[45] Q.Liu, L.Duan,Y.Li,J.Qiao, Z. Yu, D. Zhang, L. Wang, G, Dong, and Y. Qiu, "Study on the electron injection mechanism of thermally decomposable Cs2CO3", Jpn. J. Appl.

[46] X. L. Zhu, J. X. Sun, H. J. Peng, et al "Vanadium pentoxide modified polycrystalline silicon anode for active-matrix organic light-emitting diodes" Appl Phys Lett., vol. 87,

[47] C. H. Chen, and C. W. Tang, "Efficient green organic light-emitting diodes with stericly hindered coumarin dopants" Appl. Phys. Lett., Vol. 79, No. 22, pp.3711-3713. (2001) [48] A. Buzulutskov, A. Breskin, and R. Chechik, "Field enhancement of the photoelectric and secondary electron emission from Csl" J. Appl. Phys. vol. 77 no.5, pp. 2138-

[49] H. J. Jeong, H. K. Choi, G. Y. Kim, et al "Fabrication of efficient field emitters with thin multi-walled carbon nanotubes using spray method" Carbon, vol. 44, pp. 2689-

[50] Q. Liu, L. Duan, Y. Li, J. et al "Study on the Electron Injection Mechanism of Thermally Decomposable Cs2CO3" Jpn. J. Appl. Phys., vol. 48, pp. 102302 (4 pages), (2009)

spray pyrolysis" Chemical Physics Letters, vol. 386, pp.313-318.(2004)

carbon nanotube arrays" Carbon, vol. 44, pp.253-258, (2006)

Composite Films" Langmuir, vol. 23, pp. 5707-5712 (2004)

Source" Science, Vol. 270, pp. 1179-1180, (1995)

Science, vol. 48, pp. 417-431,(1975)

Science, vol. 305, pp. 1273-1276, (2004)

vol.78,no.4,pp.544-546, (2000).

pp. 153508 (3 pages),(2005)

2145,(1995)

2693,( 2006)

Phys., vol.48, pp.102302-4, October (2009).

(2006)

[34] M. Pfeiffer, K. Leo, X. Zhou, et al "Doped organic semiconductors: Physics and application in light emitting diodes" Organic Electronics, vol. 4, pp. 89-103, (2003)

40 Organic Light Emitting Devices

[18] M. Nikl, "Wide Band Gap Scintillation Materials: Progress in the Technology and

[19] J. S. Yoo and J. D. Lee, "The effects of particle size and surface recombination rate on the brightness of low-voltage phosphor" J. Appl. Phys., vol. 81, pp. 2810-2813, (1997) [20] M. Pope, H. P. Kallmann, and P. Magnante , "Electroluminescence in Organic Crystals"

[21] J. H. Burroughes, D. D. C. Bradley, A. R. Brown, et al, "Light-emitting diodes based on

[22] W. Tang, and S. A. VanSlyke, "Organic electroluminescent diodes" Appl. Phsy. Lette.,

[23] P. Dannetun, M. Lögdlund, C. Fredriksson, et al "Reactions of low work function metals Na, Al, and Ca on α, ω diphenyl tetra decaheptaene. Implications for metal/polymer

[24] R. G. Kepler, P. M. Beeson, S. J. Jacobs et al. "Electron and hole mobility in tris(8 hydroxyquinolinolato-N1,O8) aluminum" Appl. Phys. Lett., Vol. 66, pp.3618-3620,

[25] P. E. Burrows, G. Gu, V. Bulovi6 et al "Achieving full-color organic light-emitting devices for lightweight, flat-panel displays" IEEE Transactions on Electron Dev. Vol. 44,

[26] C. L. Lin, H. W. Lin, and C. C. Wu"Examining microcavity organic lightemittingdevices having two metal mirrors" Appl. Phys. Lett., vol. 87, pp.021101 (1-3),

[27] Y. J. Lee, S. H. K, J. Huh, et al "A high-extraction-efficiency nano patterned organic

[28] H. Kanno, Y. Sun, and S. R. Forrest,"High-efficiency top-emissive white-light-emitting organic electro-phosphorescent devices" Appl. Phys. Lett., vol. 86, pp. 263502 1-3.

[29] Y. J. Tung, M. M.-H. Lu, M. S. et al "High-Efficiency White Phosphorescent OLEDs for

[30] Y. J. Lu, C. H. Chang, C. L. Lin, et al "Achieving three-peak white organic light-emitting devices using wavelength-selective mirror electrodes" Appl. Phys. Lett., vol. 92, pp.

[31] C. S. Li, S. H. Su, H. Y. Chi, and M. Yokoyama "Application of highly ordered carbon nanotubes templates to field-emission organic light-emitting diodes" Journal of

[32] C. S. Li, S. H. Su, T. M. Lin , H. Y. Chi, and M. Yokoyama, "Luminous Efficiency Enhancement of Organic Light-Emitting Diodes by an External Electron Source", IEEE

[33] G. T. Chen, S. H. Su, and M. Yokoyama, "Field-Emission Organic Light-Emitting Device Using Oxide-Coated Cathode as Electron Source" Electrochemical and Solid-

light-emitting diode" Appl. Phys. Lett., vol. 82, pp. 3779-3781,(2003)

Lighting" Proc. of SPIE, vol. 5214, pp.114-123,(2004)

Crystal Growth, vol. 311, pp. 615-618, (2009)

State Letters, vol. 10, pp. J41-J44, (2007)

International Nano Electronics Conference (INEC).(2010)

Material Understanding" phys. stat. sol., vol. 179, pp. 595-620, (2000)

J.Chem. Phys, vol. 38, pp. 2042-2043, (1963)

vol. 51, pp. 913-915 (1987)

pp. 1188-1203, (1997)

(1995)

(2005)

(2005)

123303 (1-3),(2008)

conjugated polymers" Nature vol. 347, pp. 539-541, (1990)

interfaces" J. Chem. Phys., vol. 100, pp. 6765-6771.(1994)

	- [51] W. A. de Heer, A. Chatelain, D. Ugarte "A Carbon Nanotube Field-Emission Electron Source" Science, vol. 270, pp. 1179-1180, (1995)

**Chapter 3**

© 2012 Park, licensee InTech. This is an open access chapter 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 Park, 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.

**Polarized Light-Emission**

Additional information is available at the end of the chapter

Byoungchoo Park

**1. Introduction**

applications.

http://dx.doi.org/10.5772/54233

**from Photonic Organic Light-Emitting Devices**

Since the early pioneering work on efficient Organic Light-Emitting Devices (OLEDs) that was based on both small molecules and polymers, OLEDs have attracted a great deal of research interest due to their promising applications in full-color flat-panel displays and solid-state lighting [1-5]. Intensive research has been conducted into the development of OLEDs for realizing strong and efficient electroluminescent (EL) emission. To date, almost all previous work carried out on organic EL emission has involved unpolarized EL emission. Nevertheless, a number of researchers have reported the results of experiments in which linearly polarized EL emissions have been observed [6-17]. This particular avenue of research has been considered to be important because polarized EL emission from OLEDs is of potential use in a range of applications, not just those limited to high-contrast OLED displays, but also in efficient backlight sources in liquid crystal (LC) displays, optical data storage, optical communication, and stereoscopic 3D imaging systems [17]. In order to design and manufacture these novel light-emitting devices, a high degree of polarization ratio (*PR*) of emitting light is required, which has to be at least 30 ~ 40:1, between the brightness of two linearly polarized EL emissions that are parallel and perpendicular to the polarizing axis. Most cases of linearly polarized EL emission have been achieved through the use of uniaxially oriented materials, such as LC polymers or oligomers, incorporated within emissive layers. Methods that are commonly used for the uniaxial alignment of such layers include the Langmuir-Blodgett technique [6], rubbing/shearing of the film surface [7, 8], mechanical stretching of the film [9, 10], orientation on pre-aligned substrates [11, 12], precursor conversion on aligned substrates [13], epitaxial vapor deposition [14], and the friction-transfer process approach [15, 16]. Although there have been a number of such efforts to achieve linearly polarized EL emission, the polarization ratio and the device performance (in terms of brightness and efficiency) reported are still insufficient for most


**3.1. Growth rate and rate of development**

The Tv-T3 (1) and Th-T4 (3) strains of *Trichoderma* spp. presented a cottony texture with abundant density and abundant mycelium, a dark green and white coloration, whereas the Tav-T7 (2) strain presented a regular density, regular mycelium and a green/yellow coloration. For the *F. oxysporum* strain in this case (Fo-A) presented a velvety texture with a regular density and mycelium of pink white color, as described by Guzman [35], in addition its mycelium is formed by septate hyphae and the conidiophores present clusters of macroconidia where chlamydospores are observed.

*T. harzianum* presented the highest growth rate with a mean of 1.25 cm/day, followed by *T. viridae* with 0.75 cm/day, with the *T. atroviridae* strain being the lowest growth rate with 0.64 cm/day. For *F. oxysporum* the growth was 0.83 mm/day, results similar to those found by Amaro-Leal [36], with a speed between 70 and 73 mm/day in PDA, results similar to those of the present investigation.

by *T. viridae* with (PIRG) 79.61% and finally *T. atroviridae* with (PIRG) 73.41%. Reports of the percentage inhibition of *Fusarium* by *Trichoderma* show values from 22.5 to 86.44% [37]. The values obtained from inhibition are higher than those obtained by Michel [38], who at evaluating the antagonistic effect of native *Trichoderma* spp., on mycelial growth and reproductive potential of *F. oxysporum* and *Fusarium subglutinans*, presented inhibition of 47.6 and 73.0%, respectively. Snyder and Hansen [39], reported a percentage inhibition of 77.8% for *F. oxysporum,* when compared with *Trichoderma viridae* isolates, results lower than those reported in

Biological Control of *Fusarium oxysporum* in Tomato Seedling Production with Mexican Strains…

http://dx.doi.org/10.5772/intechopen.72878

161

The results of the interaction of the most representative paired cultures are presented in **Figure 2**. The *F. oxysporum* Fo-A strain was given 2 days advantage because of its slow growth compared to *Trichoderma*; the days after the first contact between hyphae, the behavior was determined, which was very heterogeneous and highly significant (P = 0.0001). Most of the *Trichoderma* isolates showed a visible overgrowth zone with the hyphae of *F*. *oxysporum*; the greater the area of overgrowth, the greater the aggressiveness of the antagonistic fungus [29]. In this sense, Michel [36], reported antagonism 1, 2 and 3 of *F. subglutinans* and *F. oxysporum*,

The treatment inoculated with *F. oxysporum* showed symptoms of the disease in the root and aerial part (**Table 4**), presenting the highest values in incidence and severity, this in comparison with the other treatments evaluated in this study. These results coincide with that observed by Kim [40], who point out the damage caused by *Phytophthora* sp., at the root and crown of the stem of chile plants under greenhouse conditions, similar results in this research. In the present investigation, the lowest incidence and severity was obtained in the treatment based on *T. harzianum* with 6%, presenting slight dry circular lesions in the root and without symptomatology in the aerial part. *T. harzianum* has the ability to produce enzymes such as cellulases, β-1,3-glucanase and chitinases, which degrade the cell wall of phytopathogens [41]. Treatments based on *T. harzianum*, *T*. *atroviridae* and *T*. *viridae*. used in this research work, present antagonistic efficacy against *F. oxysporum* with a survival ranging from 62.7 to 76.4% in comparison to the control treatment (**Figure 3**), which had a survival rate of 46%; while

**Figure 2.** Antagonistic capacity, according to the scale of Bell for *Trichoderma* spp. on *F. oxysporum*. (A and B = *T. harzianum* and *T*. *atroviridae* overlapping *F. oxysporum*, has a type II interaction, covers 2/3 of the surface of the medium, stops its growth and can overgrow it, and C = *T. viridae* presents an interaction of type I, where it covers the entire surface of the

the present investigation.

similar results in the present investigation.

**3.3. Greenhouse antagonism tests**

medium and stops its growth).

**Table 3.** Macroscopic characterization of the colonies of Mexican strains *Trichoderma* spp. and *F. oxysporum* in culture PDA.

The highest development rate was 5.69 mm/day for *T. harzianum*, followed by *T*. *viridae* at 5.04 mm/day and *T*. *atroviridae* at 4.85 mm/day; with respect to strain of *F. oxysporum* Fo-A had a rate of 3.80 mm/day, where a significant difference (p = 0.023) occurs among strains of *Trichoderma* spp. (**Table 3**).

#### **3.2. Confrontation of** *Trichoderma spp.* **on** *F. oxysporum in vitro*

The results of the percentage of inhibition of *Trichoderma* spp. strains on *F. oxysporum* by the dual culture method are shown in **Figure 1**, the Mexican strains of *Trichoderma* spp. inhibited the growth of the pathogenic fungus, where they presented a percentage of inhibition of radial significant growth (PIRG) [p = 0.056] at the Fo-A strain of *F. oxysporum*, with *T. harzianum* which showed higher antagonistic activity, with an average value of 81.50% (PIRG), followed

**Figure 1.** Percentage of radial growth inhibition (PICR) in replicates of *Trichoderma* spp., on *F. oxysporum* in dual culture. \*Different letters in the columns mean statistical differences in percent inhibition with Tukey's test (p < 0.05).

by *T. viridae* with (PIRG) 79.61% and finally *T. atroviridae* with (PIRG) 73.41%. Reports of the percentage inhibition of *Fusarium* by *Trichoderma* show values from 22.5 to 86.44% [37]. The values obtained from inhibition are higher than those obtained by Michel [38], who at evaluating the antagonistic effect of native *Trichoderma* spp., on mycelial growth and reproductive potential of *F. oxysporum* and *Fusarium subglutinans*, presented inhibition of 47.6 and 73.0%, respectively. Snyder and Hansen [39], reported a percentage inhibition of 77.8% for *F. oxysporum,* when compared with *Trichoderma viridae* isolates, results lower than those reported in the present investigation.

The results of the interaction of the most representative paired cultures are presented in **Figure 2**. The *F. oxysporum* Fo-A strain was given 2 days advantage because of its slow growth compared to *Trichoderma*; the days after the first contact between hyphae, the behavior was determined, which was very heterogeneous and highly significant (P = 0.0001). Most of the *Trichoderma* isolates showed a visible overgrowth zone with the hyphae of *F*. *oxysporum*; the greater the area of overgrowth, the greater the aggressiveness of the antagonistic fungus [29].

In this sense, Michel [36], reported antagonism 1, 2 and 3 of *F. subglutinans* and *F. oxysporum*, similar results in the present investigation.


**1. Introduction**

The singular initial value problem

$$\begin{aligned} \frac{d^2y}{dx^2} + \frac{\chi}{\varkappa} \frac{dy}{d\varkappa} + r(\varkappa, y) &= s(\varkappa), \; 0 < \varkappa, \; \varkappa > 0\\ y(0) &= a, \frac{dy}{d\varkappa}(0) = 0, a \in \mathbb{R} \end{aligned} \tag{1}$$

for the Lane-Emden Eq. (1) models several phenomena such as the thermal behaviour of a spherical cloud of gas acting under the mutual attraction of its molecules [1], the temperature variation of a self gravitating star, the kinetics of combustion [2], thermal explosion in a rectangular slab [3] and the density distribution in isothermal gas spheres [4]. Moreover, Eq. (1) has been used many a time as a benchmark for new methods.

A particular case of Eq. (1) is the Emden-Fowler equation of the first kind:

$$\frac{d^2\mathbf{y}}{d\mathbf{x}^2} + \frac{2}{\mathbf{x}}\frac{d\mathbf{y}}{d\mathbf{x}} + \mathbf{y}^m = \mathbf{0}, \mathbf{y}(\mathbf{0}) = \mathbf{1}, \frac{d\mathbf{y}}{d\mathbf{x}}(\mathbf{0}) = \mathbf{0}, m \in \mathbb{N} \tag{2}$$

As mentioned in [5], Eq. (2) represents the dimensionless form of the governing equation for the gravitational potential of a Newtonian self-gravitating, spherically

symmetric, polytropic fluid. The equation provides a useful approximation for stars.

A more general form for Eq. (2) is the Emden-Fowler equation

$$\frac{d^2y}{d\mathfrak{x}^2} + \frac{\chi}{\mathfrak{x}}\frac{dy}{d\mathfrak{x}} + f(\mathfrak{x})\mathfrak{g}(y) = \mathbf{0} \tag{3}$$

on the problem domain 0, ½ � *L* and the method makes use of Radial basis functions.

In Section 2 we describe the MSRM for the model problem. In Section 3 we make use of examples to demonstrate the accuracy and computational efficiency of the

*x y*0 þ *f x*ð Þ*g y*ð Þ¼ 0, 0 <*x*≤*L*, *y*ð Þ¼ 0 *α*, *y*0

The method by Ramos proceeds by using the same linearisation method on the subintervals *Im*,ð Þ *m* ¼ 1, ⋯, *M* of *I* � *Iε*, i.e. *away from the singularity*. To this end, at the interface *xm*�1 of *Im*�1 and *Im* we make use the solution of Eq. (3) restricted to *Im*�1 to generate the initial conditions for Eq. (3) restricted to *Im*. This ensures continuity of the solution. In this chapter we avoid linearisation on *I* � *Iε* by making use of the SRM on the subintervals of *I* � *Iε*. However, as was done in [23] we make use of linearisation on *Iε*. This approach results in the MSRM.  Restrict problem (5) to 0, ½ � *ε* and

*m*¼1*Im* where *Im* ¼ ½ � *xm*�1, *xm* , *x*0 ¼ *ε* and*xM* ¼ *L* (6)

where *γ* >0, *L*, *α* are given constants and *f* and *g* are given functions. We follow the idea behind the solution method by Ramos [23], where the singularity at *x* ¼ 0 is isolated in a sufficiently small subinterval *Iε* ¼ ½ � 0, *ε* of *I* ¼ ½ � 0, *L* where *ε* >0. The point *x* ¼ *ε* splits interval *I* into two subintervals: *Iε* and *I* � *Iε* ¼ ½ � *ε*, *L* . A linearisation method is used to solve Eq. (5) restricted to *Iε*, i.e., *near the singularity* at *x* ¼ 0. In order to improve the accuracy of the method on the

ð Þ¼ 0 0 (5)

Unlike making use of collocation methods for solving Eq. (3) Van Gorder and Vajravelu [1] used the Runge–Kutta-Felhberg 4-5 (RKF45) method to validate the analytical solutions that they obtained from using the HAM and from using the traditional power series method. The RKF45 method is an embedded Runge–Kuttapair which makes use of an adaptive stepsize to control the method and to ensure stability properties such as *A*-stability. See [16] for more details on the RKF45 method. In this chapter we make use of a modified version of the spectral relation method (SRM) to solve an initial value problem for Eq. (3). We denote our method by MSRM. The SRM was successfully used to solve fluid flow problems by for example Motsa [17], Motsa *et al.* [18], Shateyi *et al.* [19] and Gangadhar *et al.* [20] to mention a few. In [17–20] the SRM was shown to be accurate, computationally efficient and easy to implement. Moreover, the SRM was applied only after transforming the governing partial differential differential equations to ordinary differential equations. However, not so long ago the SRM was modified in such a way that it was directly applicable to partial differential equations. See for example [21]. The SRM was used to solve other types of problems such as hyperchaotic systems [22]. It is to the best of our knowledge that the MSRM has not been used in existing literature. We chose the MSRM because it

*A Modified Spectral Relaxation Method for Some Emden-Fowler Equations*

*DOI: http://dx.doi.org/10.5772/intechopen.96611*

is not computationally intensive and it is easy to implement.

MSRM. Section 4 concludes this chapter.

**2. The MSRM for the model problem**

We seek an approximate solution to

*y*00 þ *γ*

subinterval *I* � *Iε* we form a partition

*I* � *Iε* ¼ ∪*M*

of the MSRM is given in Sections 2.1 and 2.2.

**2.1 Near the singularity**

re-arrange to get

**117**

which can be written as

$$h(py')' + qy = h(\mathfrak{x}, \mathfrak{y}, \mathfrak{y}') \text{ where} \\ \mathrm{()}' = \frac{d}{d\mathfrak{x}}\, (\text{)}, \tag{4}$$

an equation which was discussed in [6]. An existence result for the solution is given therein under certain conditions on *p x*ð Þ, *q x*ð Þ and *h x*, *y*, *y*0 ð Þ.

Exact solutions are available for particular cases of Eq. (3) [7], but not for the general case according to the best of our knowledge. This is motivation enough for seeking approximate solutions. To this end several approximate analytical methods were used by other researchers to solve Eq. (3). Van Gorder [8] made use of the Homotopy analysis method (HAM) and its variant, the Optimal homotopy analysis method, to solve a boundary value problem for the Lane-Emden equation of the second kind. The two respective analytical solutions that they obtained were in strong agreement. The Homotopy perturbation method (HPM) is another variant of the HAM that was used by Chowdhury and Hashim [9] to solve an initial value problem for Eq. (3). Their analytical solutions were the same as those that were obtained by Wazwaz [10] using the Adomian decomposition method (ADM). Chowdhury and Hashim observed that the HPM was less computationally expensive than the ADM. Wazwaz [11] made use of the variational iteration method (VIM) to solve both initial value problems and boundary value problems for Eq. (3) and for some inhomogeneous Emden-Fowler equations. The results that they obtained demonstrated the reliability and effectiveness of the VIM.

Some numerical methods have been used by other researchers to approximate solutions to Eq. (3). Many of these numerical methods fall in the class of *collocation methods*. Examples of these collocation methods include but are not limited to the Chebyshev wavelet finite difference method (CWFDM) [12], the Haar wavelet collocation method (HWCM) [13], the Taylor wavelet method (TWM) [14] and the Radial basis function - differential quadrature method (RDF-DQM) [15]. One distinct feature of these collocation methods is the choice of collocation points for discretizing the problem domain. Another distinct feature is the choice of basis functions that are used either for constructing numerical solutions or for numerical differentiation. The CWFDM makes use of Chebyshev-Gauss-Lobatto collocation points and Chebyshev wavelet finite difference basis functions. The HWCM makes use of the collocation points

$$\mathbf{x}\_{j} = (\mathbf{j} - \mathbf{0}.\mathbf{5})/2\mathbf{M}, j = \mathbf{1}, \cdots, \mathbf{2M}$$

on the problem domain 0, ½ � *L* , and the method uses integrals of Haar wavelets as basis functions. The TWM uses roots of shifted Legendre polynomials as collocation points, and as basis functions the method uses Taylor wavelets which are special functions that defined in terms of Taylor polynomials. Convergence results for the Taylor wavelet solution were presented in [14]. The RDF-DQM uses collocation points

$$\mathbf{x}\_{j} = \frac{2}{L} \left( \mathbf{1} - \cos \left( \frac{j - 1}{N - 1} \right) \right), j = 1, \dots, N$$

#### *A Modified Spectral Relaxation Method for Some Emden-Fowler Equations DOI: http://dx.doi.org/10.5772/intechopen.96611*

on the problem domain 0, ½ � *L* and the method makes use of Radial basis functions. Unlike making use of collocation methods for solving Eq. (3) Van Gorder and Vajravelu [1] used the Runge–Kutta-Felhberg 4-5 (RKF45) method to validate the analytical solutions that they obtained from using the HAM and from using the traditional power series method. The RKF45 method is an embedded Runge–Kuttapair which makes use of an adaptive stepsize to control the method and to ensure stability properties such as *A*-stability. See [16] for more details on the RKF45 method.

In this chapter we make use of a modified version of the spectral relation method (SRM) to solve an initial value problem for Eq. (3). We denote our method by MSRM. The SRM was successfully used to solve fluid flow problems by for example Motsa [17], Motsa *et al.* [18], Shateyi *et al.* [19] and Gangadhar *et al.* [20] to mention a few. In [17–20] the SRM was shown to be accurate, computationally efficient and easy to implement. Moreover, the SRM was applied only after transforming the governing partial differential differential equations to ordinary differential equations. However, not so long ago the SRM was modified in such a way that it was directly applicable to partial differential equations. See for example [21]. The SRM was used to solve other types of problems such as hyperchaotic systems [22]. It is to the best of our knowledge that the MSRM has not been used in existing literature. We chose the MSRM because it is not computationally intensive and it is easy to implement.

In Section 2 we describe the MSRM for the model problem. In Section 3 we make use of examples to demonstrate the accuracy and computational efficiency of the MSRM. Section 4 concludes this chapter.