**2.2 Plant responses to cold stress**

Plants acclimatize to survive metabolic lesions because of intracellular ice formation, as well as to survive the dehydrative effects of frost (Kacperska, 1984). Fowler *et al.,* (1996) found that after the vernalization requirement was met in wheat (*Triticum aestivum* L.) and rye (*Secale cereale* L.), cold acclimation declined. Laroche *et al.,* (1992) did not observe this reduction in cold acclimation in rapeseed but they estimated cell survival on excised leaves to determine freezing tolerance and not crown meristem survival.

The relationship between vernalization requirements and cold tolerance is not clear as different observations have been reported. While Markowski and Rapacz (1994) found little relationship between these traits by comparing vernalization requirements and frost resistance of winter rape lines derived from doubled haploid, Rapacz and Markowski (1999) found a significant correlation between vernalization requirement and both frost resistance and field survival when looking at older, high erucic acid cultivars. Long vernalization requirements are expected to delay a plant from entering the reproductive growth phase, a cold sensitive plant growth stage (Fowler et al., 1996). Rife and Zeinali (2003) found that rapeseed plants may withstand cold temperatures under field conditions more effectively prior to vernalization saturation than after the vernalization requirement has been met.

Under field conditions, rapeseed plants often survive cold events in December and January only to be killed by less severe cold events in February and March (Rife and Zeinali, 2003). One theory to explain this is that after vernalization saturation takes place, rapeseed plants do not have the same ability to recover after a warming event as unvernalized plants. This has been documented in winter cereals. Fowler et al., (1996) found reductions in lethal temperature 50's (LT50s) of 5°C or more for many cultivars between Day 49 and 84 of

Prospects for Transgenic and Molecular

potential treatments.

observed in polymer coat treatments.

with field-evaluated frost damage.

Breeding for Cold Tolerance in Canola (*Brassica napus* L.) 9

than the better areas by one to two weeks. Plant counts at harvest averaged 43 plants/m2. The thin crop that was questioned in spring eventually yielded 2,128 kg/ha gross with 2 to 3% green. Although this crop probably would have yielded higher if frost had not occurred, the yield was satisfactory and equivalent or better than reseeded canola. Early spring germinated stands can suffer damage due to subsequent heavy spring frosts. Polymercoated seeds show promise to reduce the untimely germination but carry extra costs (Canola Council of Canada, 2011). However, Christian *et al.,* (2004)) observed that by decreasing osmotic potential and temperature, germination significantly reduced on both coated and uncoated canola seeds. Polymer-coated seeds exhibited delayed germination even in the absence of moisture stress, an effect that was magnified at more negative water potentials and at a lower temperature. Median germination time of polymer-coated seed was significantly higher than for uncoated control seed throughout all temperature and osmotic

Several types of polymer seed coats have recently been developed with the intent to extend the fall planting period (Zaychuk and Enders, 2001). The polymers are specifically designed to prevent germination of canola seeds until spring by absorbing water into the polymer coat matrix but preventing the passage of sufficient amounts of water to the seed coat to begin germination. After water entry into the polymer coat matrix, freezing is required to create microfractures in the polymer coat that act as water channels for imbibition. Polymer seed coats have been shown to decrease imbibition (Chachalis and Smith, 2001) and final germination percentages (Valdes and Bradford, 1987). This may also be a problem with the polymer coats developed specifically for fall seeding canola as Gan et al., (2001) observed reduced canola emergence during a dry spring following a dry fall. Lower yields were also

To make early spring seeding feasible, suitable canola cultivars must be selected. The suitable cultivars must have quick germination, emergence, and establishment at low temperatures, and seedlings must be tolerant to early spring freezing and thawing events. Freezing on the functionality of the photosynthetic apparatus can be used to assess the cold tolerance of plant genotypes. The photosynthetic apparatus function can be evaluated by measuring the Fv/Fm, which indicates the efficiency of the excitation capture by open Photosystem II reaction centers (Rizza et al., 2001). Rizza *et al* (2001) observed a significant reversible decrease in Fv/Fm in all genotypes of oat (*Avena sativa* L.) during acclimation to low, nonfreezing temperatures, and Fv/Fm measurement was found to be highly correlated

The late freeze of April 5-9, 2007, in Northern Alabama, resulted in significant economic damage to most of the winter canola cultivars that were evaluated for the National Winter Canola Variety Trials at the Hazel Green, Alabama location (Cebert and Rufina, 2007). Five consecutive nights of low temperatures: 0.6, 1.1, -5.6, -5.6, and 0.6ºC with chilling hours of 8, 16, 18, 24, and 17occurred from April 5-9, 2007, respectively. These dates correspond to days 192, 193, 194, 195, and 196 after planting, when all cultivars were beyond 50% blooming (Figures 4-9). Damage on the primary stem was highest in early blooming cultivars (Figure 5). Cultivars which were in full bloom between days 178-183 (March 22-27) suffered a complete loss. Seeds per pod and days to 50% blooming were the two factors other than the extent of freeze damage which influenced seed yield (Table 1). In Alabama

acclimation at 4°C. This study suggested that this may not be the case in three rapeseed cultivars: A112, Ceres, and Plainsman. However, the spike of increased cold tolerance was more pronounced in unvernalized seedlings. Under the variable temperature conditions present during Great Plains winters, this phenomenon could have a substantial impact on winter survival before vernalization saturation and selecting genotypes with increased vernalization requirements could have a positive effect on winter survival.

Early seeding between late March and mid April has been proposed as the key to achieve a good and stable canola seed yield in central Montana, USA (Chengci *et al.,* 2005). This study indicated that the optimal seeding rate for early spring seeded canola is 32 to 65 seeds m-2. Although early spring seeded canola is expected to encounter cold soil temperatures and frequent frosts, canola can germinate at less than 4°C and requires 42 to 81 growing degree days (GDD) for 50% flowering for emergence. Further studies are needed to test the threshold temperature and duration of canola genotypes to cold stress. Several genotypes were found to have favorable characteristics for the semi-arid region in the northern Great Plains, such as low Tb, fast emergence, relatively cold tolerant, early flowering, and good seed yield and oil content. Further, Chengci *et al*., (2005) observed that a high Fv/Fm and low EL reading after a snowstorm event indicated less effect on Photosynthetic System II and cell membranes by cold stress. A large recovery of Fv/Fm and slow leakage rate (longer time to reach 50% total leakage) also indicate a frost tolerance of the plants. There were variances observed among the cultivars in Fv/Fm, Δ(Fv/Fm), EL, and hours to 50% total leakage (HTL50). However, as the authors noted, there was no evidence of cell membrane damage by the snowstorm, EL readings ranged from 12.7 to 20.4 μS cm−1, and the time to reach 50% of the total leakage (≈600 μS cm−1 after autoclaving) ranged from 212 to 276 h. Several cultivars had greater Fv/Fm readings and less Δ(Fv/Fm) than others. Neither EL nor the Fv/Fm readings were correlated with seed yield. However, the positive correlations between Δ(Fv/Fm) and biomass indicated that cultivars having faster biomass growth may be sensitive to cold stress. Results in this study also indicated that canola did not suffer severe frost damage by the snowstorm on 12 May 2004. Canola seedlings at the early seeding dates encountered several snowstorms in May and early June over 3 yr from 2002 to 2004, but no severe frost damage to the seedlings was observed. Canola was also found to have the ability to withstand subzero temperatures in other studies after reclamation. Kirkland and Johnson (2000) found fall-seeded canola survived eight consecutive nights of frost with the temperature dropping as low as −8°C in 1994. Further, Johnson *et al.* (1995) observed that canola seedlings were able to tolerate temperatures of −6°C without significant reductions in plant stands in North Dakota

#### **2.3 Effect of cold stress during flowering and pod formation**

Farmers in central Alberta experienced a record string of killing frosts for their Canola plants in late May to early June, 2000. Seedling canola was severely injured by these frosts and significant reseeding occurred. The surviving density was on average 32 to 43 plants/m2 and about 11/m2 in the worst areas. Continuing frosts hampered the recovery of the canola seedling but eventually new growth appeared after 10 days. The canola stand had a slow recovery for a few weeks following damage, but initially looked quite poor. By flowering, the stand began to fill in but differences in maturity were evident between areas that suffered different amounts of stand thinning. The stand continued to improve through flowering and pod fill. The crop matured in September with the thin areas maturing later

acclimation at 4°C. This study suggested that this may not be the case in three rapeseed cultivars: A112, Ceres, and Plainsman. However, the spike of increased cold tolerance was more pronounced in unvernalized seedlings. Under the variable temperature conditions present during Great Plains winters, this phenomenon could have a substantial impact on winter survival before vernalization saturation and selecting genotypes with increased

Early seeding between late March and mid April has been proposed as the key to achieve a good and stable canola seed yield in central Montana, USA (Chengci *et al.,* 2005). This study indicated that the optimal seeding rate for early spring seeded canola is 32 to 65 seeds m-2. Although early spring seeded canola is expected to encounter cold soil temperatures and frequent frosts, canola can germinate at less than 4°C and requires 42 to 81 growing degree days (GDD) for 50% flowering for emergence. Further studies are needed to test the threshold temperature and duration of canola genotypes to cold stress. Several genotypes were found to have favorable characteristics for the semi-arid region in the northern Great Plains, such as low Tb, fast emergence, relatively cold tolerant, early flowering, and good seed yield and oil content. Further, Chengci *et al*., (2005) observed that a high Fv/Fm and low EL reading after a snowstorm event indicated less effect on Photosynthetic System II and cell membranes by cold stress. A large recovery of Fv/Fm and slow leakage rate (longer time to reach 50% total leakage) also indicate a frost tolerance of the plants. There were variances observed among the cultivars in Fv/Fm, Δ(Fv/Fm), EL, and hours to 50% total leakage (HTL50). However, as the authors noted, there was no evidence of cell membrane damage by the snowstorm, EL readings ranged from 12.7 to 20.4 μS cm−1, and the time to reach 50% of the total leakage (≈600 μS cm−1 after autoclaving) ranged from 212 to 276 h. Several cultivars had greater Fv/Fm readings and less Δ(Fv/Fm) than others. Neither EL nor the Fv/Fm readings were correlated with seed yield. However, the positive correlations between Δ(Fv/Fm) and biomass indicated that cultivars having faster biomass growth may be sensitive to cold stress. Results in this study also indicated that canola did not suffer severe frost damage by the snowstorm on 12 May 2004. Canola seedlings at the early seeding dates encountered several snowstorms in May and early June over 3 yr from 2002 to 2004, but no severe frost damage to the seedlings was observed. Canola was also found to have the ability to withstand subzero temperatures in other studies after reclamation. Kirkland and Johnson (2000) found fall-seeded canola survived eight consecutive nights of frost with the temperature dropping as low as −8°C in 1994. Further, Johnson *et al.* (1995) observed that canola seedlings were able to tolerate temperatures of −6°C

vernalization requirements could have a positive effect on winter survival.

without significant reductions in plant stands in North Dakota

**2.3 Effect of cold stress during flowering and pod formation**

Farmers in central Alberta experienced a record string of killing frosts for their Canola plants in late May to early June, 2000. Seedling canola was severely injured by these frosts and significant reseeding occurred. The surviving density was on average 32 to 43 plants/m2 and about 11/m2 in the worst areas. Continuing frosts hampered the recovery of the canola seedling but eventually new growth appeared after 10 days. The canola stand had a slow recovery for a few weeks following damage, but initially looked quite poor. By flowering, the stand began to fill in but differences in maturity were evident between areas that suffered different amounts of stand thinning. The stand continued to improve through flowering and pod fill. The crop matured in September with the thin areas maturing later than the better areas by one to two weeks. Plant counts at harvest averaged 43 plants/m2. The thin crop that was questioned in spring eventually yielded 2,128 kg/ha gross with 2 to 3% green. Although this crop probably would have yielded higher if frost had not occurred, the yield was satisfactory and equivalent or better than reseeded canola. Early spring germinated stands can suffer damage due to subsequent heavy spring frosts. Polymercoated seeds show promise to reduce the untimely germination but carry extra costs (Canola Council of Canada, 2011). However, Christian *et al.,* (2004)) observed that by decreasing osmotic potential and temperature, germination significantly reduced on both coated and uncoated canola seeds. Polymer-coated seeds exhibited delayed germination even in the absence of moisture stress, an effect that was magnified at more negative water potentials and at a lower temperature. Median germination time of polymer-coated seed was significantly higher than for uncoated control seed throughout all temperature and osmotic potential treatments.

Several types of polymer seed coats have recently been developed with the intent to extend the fall planting period (Zaychuk and Enders, 2001). The polymers are specifically designed to prevent germination of canola seeds until spring by absorbing water into the polymer coat matrix but preventing the passage of sufficient amounts of water to the seed coat to begin germination. After water entry into the polymer coat matrix, freezing is required to create microfractures in the polymer coat that act as water channels for imbibition. Polymer seed coats have been shown to decrease imbibition (Chachalis and Smith, 2001) and final germination percentages (Valdes and Bradford, 1987). This may also be a problem with the polymer coats developed specifically for fall seeding canola as Gan et al., (2001) observed reduced canola emergence during a dry spring following a dry fall. Lower yields were also observed in polymer coat treatments.

To make early spring seeding feasible, suitable canola cultivars must be selected. The suitable cultivars must have quick germination, emergence, and establishment at low temperatures, and seedlings must be tolerant to early spring freezing and thawing events. Freezing on the functionality of the photosynthetic apparatus can be used to assess the cold tolerance of plant genotypes. The photosynthetic apparatus function can be evaluated by measuring the Fv/Fm, which indicates the efficiency of the excitation capture by open Photosystem II reaction centers (Rizza et al., 2001). Rizza *et al* (2001) observed a significant reversible decrease in Fv/Fm in all genotypes of oat (*Avena sativa* L.) during acclimation to low, nonfreezing temperatures, and Fv/Fm measurement was found to be highly correlated with field-evaluated frost damage.

The late freeze of April 5-9, 2007, in Northern Alabama, resulted in significant economic damage to most of the winter canola cultivars that were evaluated for the National Winter Canola Variety Trials at the Hazel Green, Alabama location (Cebert and Rufina, 2007). Five consecutive nights of low temperatures: 0.6, 1.1, -5.6, -5.6, and 0.6ºC with chilling hours of 8, 16, 18, 24, and 17occurred from April 5-9, 2007, respectively. These dates correspond to days 192, 193, 194, 195, and 196 after planting, when all cultivars were beyond 50% blooming (Figures 4-9). Damage on the primary stem was highest in early blooming cultivars (Figure 5). Cultivars which were in full bloom between days 178-183 (March 22-27) suffered a complete loss. Seeds per pod and days to 50% blooming were the two factors other than the extent of freeze damage which influenced seed yield (Table 1). In Alabama

Prospects for Transgenic and Molecular

Carvallo *et al.,* 2011).

species (Kott *et al.,* 1988).

Fig. 10. The Triangle of U, by Woo Jang-choon (Nagaharu U, 1935).

Breeding for Cold Tolerance in Canola (*Brassica napus* L.) 11

especially with the use of model plant *Arabidopsis thaliana* (Yamaguchi-Shinozaki and Shinozaki, 1994; Jaglo-Ottosen *et al.,* 1998; Lee *et al.,* 2001; Taji *et al.,* 2002; Zhang *et al.,* 2004b;

However, contribution towards the improvement of *Brassica* species, which eventually led to the development of canola, is the creation of the Triangle of U (Figure 10) by Nagaharu, U (1935). The interpretation of three common diploid species (*B. campestris*, *B. nigra* and *B. oleracea*) being the origin of the current tetraploid *Brassica* species continues to be the foundation for contemporary development and enhancement for both vegetables and oilseed crops within the genus, indicative in improvement of *B. rapa* by Ofori *et al.,* (2008). An extensive assortment of loci for various physiological and morphological traits in the different *Brassicica* species have been determined and identified through both classical and molecular methods. Through the use of embryo rescue techniques, interspecific and intergeneric hybridization hindrances such as male-sterility and self-incompatibility were overcome (Nishi *et al.,* 1959; Quazi, 1988; Mohaptra and Bajaj, 1987). As delineated by Harberd (1969), the tedious procedures for embryo rescue in *Brassica* species resulted in the exchange of genes to produce cultivars with improved resistance for pests, variation for seed coat color, changes in fatty-acids composition and tolerance to herbicide. Sacristan and Gerdemann (1986), successfully transferred blackleg resistance to *B. napus* from *B*. *juncea* using embryo culture, while similar techniques were successfully employed to transfer both aphid-resistance and triazine herbicide-resistance among and between the various *Brassica*

†Means with the same letter are not significantly different at a = 0.05

Table 1. Estimated freeze damage and yield (Kg ha-1) of canola cultivars following late spring frost damage and exceptional drought conditions in National Winter Canola Variety Trial, Alabama A&M University, USA 2007.

A&M University, U.S. experimental plots, Cebert and Rufina (2007) reported an inverse response among cultivars between freeze damage and seed yield. Cultivars Kadore, Kalif and Plainsman with the highest seed yields were also the last ones to reach 50% blooming, approximately five days before the freeze.

### **3. Breeding for crop improvement**

#### **3.1 Genetics**

As described by Nakashima and Yamaguchi-Shinozaki (2006), the basic characteristics of plants forced them to survive in environments with variable environmental stresses such as cold stress and osmotic stress, which includes drought and high salinity. Plants, therefore exhibit an increase in freezing tolerance in response to low, non-freezing temperatures. This concept of acclimating to stressful environmental conditions has been widely investigated,

**Cultivar Estimated freeze damage (%) Estimated yield (Kg ha-1)**

Baros 80.0a† 374.6i Virginia 65.0ab 685.7hi Viking 60.0abc 838.9fghi Hybrista 56.7abc 782.8ghi Abilene 55.0abcd 851fghi Taurus 53.3abcd 902.7fghi Trabant 53.3abcd 893.6fghi Baldur 40.0bcde 1195.6defgh Rasmus 35.0bcdef 972.2fgh Falstaff 28.3cdef 1332.5defg Summer 26.7cdef 924.7fghi Ceres 21.7def 1399.2cdef Wichita 21.7def 1721.2bcd Satori 16.7ef 1392.3cdef Jetton 16.7ef 1061.8efgh Kalif 16.7ef 2094.6ab Ovation 10.0ef 1578bcde Kronos 8.3ef 1624.8bcd Kadore 1.7f 2552.0a Plainsman 1.7f 1900.6bc

†Means with the same letter are not significantly different at a = 0.05

Trial, Alabama A&M University, USA 2007.

approximately five days before the freeze.

**3. Breeding for crop improvement**

**3.1 Genetics**

Table 1. Estimated freeze damage and yield (Kg ha-1) of canola cultivars following late spring frost damage and exceptional drought conditions in National Winter Canola Variety

A&M University, U.S. experimental plots, Cebert and Rufina (2007) reported an inverse response among cultivars between freeze damage and seed yield. Cultivars Kadore, Kalif and Plainsman with the highest seed yields were also the last ones to reach 50% blooming,

As described by Nakashima and Yamaguchi-Shinozaki (2006), the basic characteristics of plants forced them to survive in environments with variable environmental stresses such as cold stress and osmotic stress, which includes drought and high salinity. Plants, therefore exhibit an increase in freezing tolerance in response to low, non-freezing temperatures. This concept of acclimating to stressful environmental conditions has been widely investigated, especially with the use of model plant *Arabidopsis thaliana* (Yamaguchi-Shinozaki and Shinozaki, 1994; Jaglo-Ottosen *et al.,* 1998; Lee *et al.,* 2001; Taji *et al.,* 2002; Zhang *et al.,* 2004b; Carvallo *et al.,* 2011).

However, contribution towards the improvement of *Brassica* species, which eventually led to the development of canola, is the creation of the Triangle of U (Figure 10) by Nagaharu, U (1935). The interpretation of three common diploid species (*B. campestris*, *B. nigra* and *B. oleracea*) being the origin of the current tetraploid *Brassica* species continues to be the foundation for contemporary development and enhancement for both vegetables and oilseed crops within the genus, indicative in improvement of *B. rapa* by Ofori *et al.,* (2008). An extensive assortment of loci for various physiological and morphological traits in the different *Brassicica* species have been determined and identified through both classical and molecular methods. Through the use of embryo rescue techniques, interspecific and intergeneric hybridization hindrances such as male-sterility and self-incompatibility were overcome (Nishi *et al.,* 1959; Quazi, 1988; Mohaptra and Bajaj, 1987). As delineated by Harberd (1969), the tedious procedures for embryo rescue in *Brassica* species resulted in the exchange of genes to produce cultivars with improved resistance for pests, variation for seed coat color, changes in fatty-acids composition and tolerance to herbicide. Sacristan and Gerdemann (1986), successfully transferred blackleg resistance to *B. napus* from *B*. *juncea* using embryo culture, while similar techniques were successfully employed to transfer both aphid-resistance and triazine herbicide-resistance among and between the various *Brassica* species (Kott *et al.,* 1988).

Fig. 10. The Triangle of U, by Woo Jang-choon (Nagaharu U, 1935).

Prospects for Transgenic and Molecular

Breeding for Cold Tolerance in Canola (*Brassica napus* L.) 13

**DREB TFs Species Accession no. Stress response References**  DREB1A *Arabidopsis thaliana* AB007787 **Cold** Liu *et al.,* 1998 DREB2C *Arabidopsis thaliana* At2g40340 Salt, Mannitol, **Cold** Lee *et al.,* 2010 CBF1 *Arabidopsis thaliana* U77378 **Cold** Gilmour *et al.,*

CBF2 *Arabidopsis thaliana* AF074601 **Cold** Gilmour *et al.,*

CBF3 *Arabidopsis thaliana* AF074602 **Cold** Gilmour *et al.,*

OsDREB1B *Oryza sativa* AF300972 **Cold** Dubouzet *et al.,*

OsDREB2B *Oryza sativa* Heat, **Cold** Matsukura *et*

WCBF2 *Triticum aestivum* **Cold**, Drought Kume *et al*.,

HvDREB1 *Hordeum vulgare* DQ012941 Drought, Salt, **Cold** Xu *et al.,* 2009

PgDREB2A *Pennisetum glaucum* AAV90624 Drought, Salt, **Cold** Agarwal *et al*.,

GmDREBa *Glycine max* AY542886 **Cold**, Drought, Salt Li *et al*., 2005 GmDREBb *Glycine max* AY296651 **Cold**, Drought, Salt Li *et al.,* 2005

PNDREB1 *Arachis hypogea* FM955398 Drought, **Cold** Mei *et al.,* 2009

DmDREBa *Dendronthema3moriforlium* EF490996 **Cold**, ABA Yang *et al.,* 2009 DmDREBb *Dendronthema3moriforlium* EF487535 **Cold**, ABA Yang *et al.,* 2009 PeDREB2 *Populus euphratica* EF137176 Drought, Salt, **Cold** Chen *et al.,* 2009

Table 2. Transcription factors identified as regulators in the expression abiotic stress

OsDREBL *Oryza sativa* AF494422 **Cold** Chen *et al*., 2003

Wounding

ABA, Wound

Drought, Salt, faintly to **Cold**,

ABA

ABA

OsDREB1A *Oryza sativa* AF300970 **Cold**, Salt,

OsDREB2A *Oryza sativa* AF300971

OsDREB1C *Oryza sativa* AP001168 Drought, Salt, **Cold**,

OsDREB1F *Oryza sativa* Drought, Salt, **Cold**,

TaDREB1 *Triticum aestivum* AAL01124 **Cold**, Dehydration,

WDREB2 *Triticum aestivum* BAD97369 Drought, Salt, **Cold**,

ZmDREB2A *Zea mays* AB218832 Drought, Salt, **Cold**,

PpDBF1 *Physcomitrella patens* ABA43697 Drought, Salt, **Cold**,

DvDREB2A *Dendrathema* EF633987 Drought, Heat,

\*Adapted from: Lata and Prasad (2011).

including cold tolerance\*

1998

1998

1998

2003

2003

2003

2003

*al.*,2010

2005

2007

Egawa *et al.*, 2006

ABA Wang *et al.,* <sup>2008</sup>

ABA Shen *et al*., 2003

Heat Qin *et al.,*<sup>2007</sup>

ABA Liu *et al*., 2007

ABA, **Cold** Liu *et al.,*<sup>2008</sup>

Dubouzet *et al.,*

Dubouzet *et al.,*

Dubouzet *et al.,*

Microspore culture and protoplast fusion are other protocols which have been employed successfully in the development of improved *Brassica* cultivars. According to results obtained by Ryschka *et al.,* (2007), hybrid formation between haploid at the level of protoplasts fusion obtained from different species has the potential to combine divergent genomes which may not be possible otherwise. Traditional non-molecular systems provided the foundation to identify Quantitative Trait Loci (QTLs) for early genomic mapping. These systems of hybridization coupled with current biotechnology have energized the search for novel procedures to create distinctive desirable cultivars.

#### **3.2 Breeding for cold tolerance**

Current molecular tools such as SSRs (Single Sequence Repeats), SNPs (Single Nucleotide Polymorphism) and ESTs (Expressed Sequence Tags) are being used to identify genes of economic significance including cold tolerance in *Brassica* species as reported in studies by Ofori *et al.,* (2008) and Thomashow (1999). Specific genes that respond to cold and osmotic stress in plants have been elucidated by Zhang *et al.,* (2004a), and Shinozaki *et al.,* (2003) and summarized by Lata and Prasad (2011). Results from these findings along with molecular makers have enabled the creation of high density genetic and physical maps of new genes that will allow the enhancement of genetic variation for desired traits such as response to cold stress. The most recent of such results is the release of the *Brassica rapa* genomesequence by the "*Brassica* Genome Sequencing Project Consortium" (2011). Initiatives to identify stress related genes have provided significant results in understanding functional genomics of abiotic stress. The Genome Canada/Genome Prairie project studied a range of genomics and proteomics technologies to determine how plants respond to various environmental stresses at the gene level, particularly to cold. A general insight among the findings is the discernment that cold tolerance genes are induced under conditions other than low temperatures but also due to dehydration, high salt and other abiotic stress.

Many studies (Sangwan *et al.,* 2001; Zhu *et al.,* 2009; Chinnusamy *et al.,* 2010; Chen *et al.,* 2011) have reported significant findings that provide novel sources of cold tolerance genes which can be introgressed into new hybrids and open pollinated cultivars. New data are being generated with genomics tools to exploit the use of genetic maps derive from various *Brassica* species and those from *Arabidopsis*. The accumulation of ESTs and SNPs is producing significant information on genome polymorphism and sequence data for all stress related characteristics in *Brassica* species. Kreps *et al.,* (2002) used transcriptome changes for *Arabidopsis* to identify genes in response to stress treatment including cold. Their findings showed approximately 30% of the transcriptones demonstrated sensitivity to regulation to common stress, with most being unambiguous in response for specific stimuli. Genes identified as circadian controlled were also found to be associated in response to cold stress stimuli. Similar findings were also reported by Trischuk *et al.,* (2006) and Nakashima and Yamaguchi-Shinozaki (2006) who further indicated that cold acclimation, while primarily influenced by temperature, is also moderated by factors such as light intensity, day length, cultural practices, and other abiotic stresses such as drought, dehydration and salinity. Dehydration responsive element binding (DREBs) have been identified as important plant transcription factors (TFs) in regulating expression of many stress-inducible genes. These DREBs elements have been identified in many plant species as indicated in Table 2 in their response to cold stress (Lata & Prasad, 2011).

Microspore culture and protoplast fusion are other protocols which have been employed successfully in the development of improved *Brassica* cultivars. According to results obtained by Ryschka *et al.,* (2007), hybrid formation between haploid at the level of protoplasts fusion obtained from different species has the potential to combine divergent genomes which may not be possible otherwise. Traditional non-molecular systems provided the foundation to identify Quantitative Trait Loci (QTLs) for early genomic mapping. These systems of hybridization coupled with current biotechnology have energized the search for

Current molecular tools such as SSRs (Single Sequence Repeats), SNPs (Single Nucleotide Polymorphism) and ESTs (Expressed Sequence Tags) are being used to identify genes of economic significance including cold tolerance in *Brassica* species as reported in studies by Ofori *et al.,* (2008) and Thomashow (1999). Specific genes that respond to cold and osmotic stress in plants have been elucidated by Zhang *et al.,* (2004a), and Shinozaki *et al.,* (2003) and summarized by Lata and Prasad (2011). Results from these findings along with molecular makers have enabled the creation of high density genetic and physical maps of new genes that will allow the enhancement of genetic variation for desired traits such as response to cold stress. The most recent of such results is the release of the *Brassica rapa* genomesequence by the "*Brassica* Genome Sequencing Project Consortium" (2011). Initiatives to identify stress related genes have provided significant results in understanding functional genomics of abiotic stress. The Genome Canada/Genome Prairie project studied a range of genomics and proteomics technologies to determine how plants respond to various environmental stresses at the gene level, particularly to cold. A general insight among the findings is the discernment that cold tolerance genes are induced under conditions other

than low temperatures but also due to dehydration, high salt and other abiotic stress.

Table 2 in their response to cold stress (Lata & Prasad, 2011).

Many studies (Sangwan *et al.,* 2001; Zhu *et al.,* 2009; Chinnusamy *et al.,* 2010; Chen *et al.,* 2011) have reported significant findings that provide novel sources of cold tolerance genes which can be introgressed into new hybrids and open pollinated cultivars. New data are being generated with genomics tools to exploit the use of genetic maps derive from various *Brassica* species and those from *Arabidopsis*. The accumulation of ESTs and SNPs is producing significant information on genome polymorphism and sequence data for all stress related characteristics in *Brassica* species. Kreps *et al.,* (2002) used transcriptome changes for *Arabidopsis* to identify genes in response to stress treatment including cold. Their findings showed approximately 30% of the transcriptones demonstrated sensitivity to regulation to common stress, with most being unambiguous in response for specific stimuli. Genes identified as circadian controlled were also found to be associated in response to cold stress stimuli. Similar findings were also reported by Trischuk *et al.,* (2006) and Nakashima and Yamaguchi-Shinozaki (2006) who further indicated that cold acclimation, while primarily influenced by temperature, is also moderated by factors such as light intensity, day length, cultural practices, and other abiotic stresses such as drought, dehydration and salinity. Dehydration responsive element binding (DREBs) have been identified as important plant transcription factors (TFs) in regulating expression of many stress-inducible genes. These DREBs elements have been identified in many plant species as indicated in

novel procedures to create distinctive desirable cultivars.

**3.2 Breeding for cold tolerance**

\*Adapted from: Lata and Prasad (2011).

Table 2. Transcription factors identified as regulators in the expression abiotic stress including cold tolerance\*

Prospects for Transgenic and Molecular

**4.1.1 Molecular markers**

losses after the divergence of *Arabidopsis* and *Brassica*.

Breeding for Cold Tolerance in Canola (*Brassica napus* L.) 15

The data indicated that the *Brassica* genome has undergone triplication and subsequent gene

Cheung *et al*. (2009) analyzed homoeologous regions of *Brassica* genomes at the sequence level. These represented segments of the *Brassica* A genome as found in *Brassica rapa* and *Brassica napus* and the corresponding segments of the *Brassica* C genome as found in *Brassica oleracea* and *B. napus*. Analysis of synonymous base substitution rates within modeled genes revealed a relatively broad range of times (0.12 to 1.37 million years ago) since the divergence of orthologous genome segments as represented in *B. napus* and the diploid species. Similar and consistent ranges were also identified for single nucleotide polymorphism and insertion-deletion variation. Genes conserved across the *Brassica* genomes and the homoeologous segments of the genome of *Arabidopsis thaliana* showed almost perfect collinearity. Numerous examples of apparent transduplication of gene fragments, as previously reported in *B. oleracea*, were also observed in *B. rapa* and *B. napus*, indicating that this phenomenon is widespread in *Brassica* species. They also concluded that the majority of the regions studied, the C genome segments were expanded in size relative to their A genome counterparts. Further, they observed considerable variation, even between the different versions of the same *Brassica* genome, for gene fragments and annotated putative genes suggesting that the concept of the pangenome might be particularly appropriate when considering *Brassica* genomes. Thus characterization of complete *Brassica* genome and comparative genome analyses with *Arabidopsis* using genomics approach will increase the knowledge of the biological mechanisms of the *Brassica* species that will allow targeted approaches to reduce the number and impact, which could enable a sustainable and environmentally-sound, farming policy.

Molecular markers have been used extensively to analyze genetic diversity and to create linkage maps in *Brassica* crops. Most importantly, they have been used widely to map agronomically important genes in *Brassica* genomes and to assist canola breeding and selection procedures. According to Snowdon and Friedt (2004), the major challenges that face *Brassica* geneticists and breeders are (i) the alignment of existing genetic and physical maps in order to agree on a consensus map with a standardized nomenclature, and (ii) to compile and integrate relevant phenological, morphological, and agronomic information with allelic information for *Brassica* oilseed germplasm. Therefore, association mapping can be used to exploit available genetic resources outside the narrow rapeseed gene pool. Molecular markers linked to agronomically important traits have been reported, and most of them are now integrated into oilseed breeding programmes. It is important to note that genome research and marker assisted applications in *Brassica* began to flourish in the late 1980s (Snowdon and Freidt, 2004), when the first restriction fragment length polymorphism (RFLP) linkage maps for *B. oleracea* (Slocum *et al.,* 1990), *B. rapa* (Song *et al*., 1991), and *B. napus* (Landry *et al.,* 1991) were developed. The development of PCR techniques over the last two decades has lead to the rise of new marker technologies, and this has enabled the generation of high-density molecular maps through the amplification of highly polymorphic anonymous PCR fragments. Some of the DNA-based marker systems that have been used in *Brassica* are random amplified polymorphic DNA markers (RAPD; Williams et al., 1990),

#### **3.3 Limitations of classical breeding**

*Brassica* species having characteristics such as sporophytic pollen self-incompatibility, male sterility along with restoration for cytoplasmic male sterility offered overwhelming possibilities for genetic modification. The production of haploids and doubled haploids using microspores has accelerated the production of homozygous lines in the *Brassica* species (Cardoza and Stewart, 2004). Somatic cell fusion has facilitated the development of interspecific and intergeneric hybrids in the sexually incompatible species of *Brassica*. Those characteristics have been further exploited by combining traditional non-molecular protocols with modern biotechnology including molecular markers in marker-assisted selection and breeding, and transformation technology to introduce desired genes into elite cultivars.

However, classical breeding which relies largely on homologous recombination between chromosomes to generate genetic diversity (Garcia *et al*., 1998), limits the extent of further improvement as it does not allow the precise understanding of genomic composition. The continuation of current technology in identifying selectable markers to aid in the assortment of segregating population is a major contribution that will extend the use of classical breeding. However, the use of plant transformation which allows the isolation and insertion of single genes into elite cultivars could accelerate crop improvement once the technology becomes routine.


**1.3 Food waste hierarchy**

Various options have been proposed to fight food waste, ranging from most to least preferable, including waste prevention, recycling, recovery, and disposal. Waste prevention involves strategies to avoid food waste from being generated in the first place, such as reducing the overproduction of perishable food products, optimising food manufacturing processes, and improving retail inventory management and storage practises. It also involves reduction strategies to limit the loss of food waste streams to worthless end point such as landfill, achieved through food recovery and redistribution approaches. Examples of this strategy include donating excess food to food bank organisations, marketing and selling imperfect-looking produce, or diverting food waste to animal feed applications. Waste recycling strategies involve the repurposing of food waste as an input into a subsequent process to create a product of higher value than the original waste stream. Examples of this strategy include the use of anaerobic digestion to produce biogas and biosolids, commercial composting to produce bio-fertiliser, or other bioconversion processes to generate valuable ingredients, chemicals, and materials [5]. Lastly, waste recovery aims to extract the residual energy stored within the biomass. **Figure 2** outlines the food waste hierarchy, which is presented to create an emphasis on moving food up the waste hierarchy.

**Figure 2.**

*Food waste hierarchy developed by Stop Food Waste Australia.*

#### **1.4 Food by-product upcycling through extrusion**

Based on the food waste hierarchy, by-product recycling into new food products is the second most preferable option behind waste prevention. A significant opportunity for waste upcycling is the incorporation of by-products into existing food manufacturing processes. There is a dual benefit for this approach, which includes: (1) Environmental sustainability benefits relating to reduced demand for existing food ingredients, which involves considerable resource use in terms of land, water, fertiliser, fuel, chemicals for pest and weed control, and fertile soil [6]; and (2) Health benefits by creating value-added food products that have a higher nutrient content, improved textural properties, and/or enhanced functionality.

Extrusion has emerged over the past decade as a processing option for food byproduct valorisation, as demonstrated by a 2014 review article into current options for food waste valorisation only mentioning extrusion once [7]. Extrusion is a food manufacturing technology that is emerging as a promising option for the incorporation of various types of biomass by-products [8]. The extrusion process involves a rotating single or twin-screw conveyor enclosed within a heated barrel, which cooks the food material through the application of temperature, pressure, and mechanical shearing. The product is formed into the desired shape through the choice of the die size and shape. Extrusion is widely used to manufacture various food products, such as breakfast cereals, snacks, pasta, noodles, plant-based meat substitutes, and animal feeds. The key benefit of this technology is its functionality and versatility, which allows an extruder machine to perform multiple processing functions (i.e. mixing, heating, shearing, cooking, material expansion, and product shaping), all in a single, continuous process. The process can be fine-tuned by adjusting temperature, moisture content, feeding rate, screw configuration, and screw speed, which directly affect the functional, nutritional, textural and sensory attributes of the final product. The food ingredients involved in extruded food production can vary depending on the specific product type being manufactured. However, some common ingredients include starch-based flour (i.e. corn, rice, wheat) for expanded snacks, plant proteins (i.e. soy, pea, peanut) for plant-based meat analogues, and fibre-rich components (i.e. bran, hulls).

## **2. Biomass by-product sources incorporated in extrusion**

In recent years, there has been growing interest in using alternative ingredients for extruded food production, such as food manufacturing by-products. These alternative ingredients are often rich in nutrients and have a lower starting cost compared to traditional ingredients. In fact, their utilisation may save costs in relation to waste management. Different types of biomass by-products have been incorporated into extruded foods, which include:

• Emerging extrusion feedstocks (i.e. insects)

Each of these types of biomass by-products will be discussed in the following sections, with **Table 1** summarising relevant journal articles that study the incorporation of these ingredients in extruded food products.

#### **Table 1.**

*Summary of publications investigating the impact of incorporating fruit and vegetable pomace by-products into extruded food products.*

#### **2.1 Fruit and vegetable pomace**


**1. Introduction**

At the present time, alterations in food production and consumption occur constantly. Stand‐ ardized food production gradually gives its place to mass tailor‐made production. Throughout this process, consumer needs also change and progress. In every aspect of life, the search for comfort increases its importance. Functional foods come to the light as a result of the search for comfort to fulfil certain needs. Functional food products become prominent within the several product groups particularly due to their direct effect on human health [1].

Functional foods are a highly important sector of the food market that grow rapidly. Within this concept, the interest towards the pro‐ and prebiotic foods increases by degrees. Foods that

© 2017 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. © 2017 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.

beyond their basic nutritional features make positive contribution to our health are named as 'functional foods'. The term functional food underlines the positive relation of nutrition with health [2–5]. The International Food Information Council (IFIC) defines functional foods as 'foods and food components that may provide benefits beyond basic nutrition'. According to the International Life Science Institute (ILSI), the concept of functional foods refers to the 'biologically active components in foods that have the potential to optimize physical and mental well being' [6–13].

The most important target groups of the functional foods are women and elders. The new conception assimilates Hippocrates, the founder of the medicine, nearly 2500 years old philosophy 'Let food be thy medicine and medicine be thy food', and therefore pays more attention to the healthy nutrition. Nowadays, due to reasons such as the increase in the treatment expenses, labour loss, length of life and the portion of the old people inside the population and people's desire of living a quality life, people start to expect more from the food items [14].

According to the data of the research that is made to reveal the consumers' awareness, acceptance and approach towards the functional foods, mineral water, whole‐grain diet biscuits and whole‐grain breakfast cereals are the most frequently consumed functional foods in the order. The functional food increases the level of the beneficial bacteria in the gut, helps lose weight and supports child development. These three features of the functional food are emphasized by customers as 'the top 3 factors that convince them to consume functional foods' in the research [15].

Education level has advanced hand in hand with the economic development; therefore, people's demand to healthy foods has increased alongside with these progressions. The concept of functional food occurred for the first time in Japan in the 1980s. Functional foods are put on display for customers as an active food trend at the beginning of the 1990s in America and in the middle of 1990s in the countries of Europe.

According to the Foods for Specified Health (FOSHU) affirmed in Japan in 1991, it is stipulated that in order for a product to get functional food licence it is required to meet with certain criteria. Some of these criteria are stated in relation to bee products. Functional foods should help the improvement of the quality of nourishment, and protection and preservation of health, the compound of the product should not differ from the similar type of foods' nutritional substance components within normal conditions, the product should be a well‐used food in daily diets, as all bee products have [16–19].


Case B (Case 10 in Table 1 and Table S2)

A 59-year-old woman presented with 0.7-cm nodules in the right lower lobe 1.5 years after undergoing right upper lobectomy for cancer. The tumors were round and had a smooth surface. Because of their morphology, they were suspected of being metastatic lesions. After 4 months of follow-up, there was no increase in the number of lung lesions, suggesting solitary intrapulmonary metastasis. Subsequently, wedge resection was performed. Although both tumors were pathologically papillary-predominant adenocarcinoma (Figure 4C,D), a lepidic pattern was observed in the periphery of the smaller nodule (Figure 4E), leading to a diagnosis of double primary lung cancers. However, the genetic mutation profile was consistent between the two tumors, suggesting them to be metastases (Figure 4F). The patient was positive for a mutation in the epidermal growth factor receptor (EGFR) gene (exon 19 deletion); hence, oral administration of an EGFR-tyrosine kinase inhibitor (gefitinib) was continued. The patient has remained alive without recurrence for 4 years after the second surgery.

**Figure 4.** Radiological, histopathological and genomic findings in case B. (**A**) Lung cancer in the right upper lobe. (**B**) A small nodule in the right lower lobe. (**C**) Histology of the lung cancer in the right upper lobe. (**D**,**E**) Histology of the nodule in the right lower lobe. A lepidic pattern was observed in the periphery of the small nodule. Each scale bar indicates 100 μm. (**F**) Heatmap of the gene mutations of the two lung tumors. The significant mutations identified in the right upper lobe tumor were homologous with those detected in the right lower lobe tumor. RU, right upper lobe; RL, right lower lobe; AF, allele fraction

Case C (Case 18 in Table 1 and Table S2)

A 74-year-old man presented with tumors measuring 4.0 cm and 1.8 cm in the left upper lobe, so left upper lobectomy was performed (Figure 5A,B). As both tumors were closely located and pathologically similar squamous cell carcinomas, they were assumed to be single origin pulmonary metastases (Figure 5C,D). However, the mutation profile was completely different between the two tumors genetically, suggesting double primary cancers (Figure 5E).

**Figure 5.** Radiological, histopathological and genomic findings in case C. (**A**,**B**) Two tumors, a large one (T1) and a small one (T2), were located in the left upper lobe in proximity to each other. (**C**,**D**) The tumors exhibited a similar histology of squamous cell carcinoma. Each scale bar indicates 100 μm. (**E**) Heatmap of the gene mutations of the two lung tumors. The mutation profiles of T1 and T2 were completely different. (**F**,**G**) Postoperatively, tracheobronchial lymph node enlargement was observed and the tumor was identified as a squamous cell carcinoma. Each scale bar indicates 100 μm. AF, allele fraction.


**2. Brain organoid protocols: general timeline, stages, strategies to improve outcome and classification**

Most of the current brain organoid protocols use the dissociation-re-aggregation method to form 3D aggregates from the stem cells. After some period of recovery and establishment of cell–cell contacts and maturation, these aggregates become EBs, which are used as a starting point for organoid formation and development. The EBs are not formed from every stem cell aggregate. So far, the studies have revealed a set of important variables [10, 11]. Firstly, the critical cell mass, i.e., a sufficiently large number of cells, is needed to form EB. Secondly, size and uniformity have a huge effect on the homogeneity and structure of the EBs and may impact the fate choice. Studies found that the addition of Y-27632 is beneficial for these results. To overcome these issues, geometric confinement approaches are often used. Thirdly, the time for aggregation also plays a critical role. These and other variables secure the establishment of an appropriate intra-EB microenvironment to trigger the intrinsic embryo developmental programs. The EBs are multicellular aggregates of stem cells, which resemble


*3.11. Cell Culture*

MC3T3E1 and L929 cells were obtained from a cell bank (Procell Life Science & Technology Co., Ltd., Wuhan, China) and HUVEC were received from an institute of zoology (Chinese academy of

sciences, Beijing, China). MC3T3E1 was grown as monolayer at 37 ◦C in a 5% CO2 incubator and cultured in Dulbecco's modified eagle medium (DMEM) containing 10% (*v*/*v*) fetal bovine serum (FBS) and 1% (*w*/*v*) penicillin-streptomycin. L929 and HUVEC cells were cultured in MEM and DMEM/F12 (1:1), respectively.


**Abstract**

Even though gold is inert in its bulk practice, greatly disseminated gold nanoparticles (Au NPs) with dimensions less than 5 nm have been found to be active for a number of oxygen transfer reactions, particularly for low-temperature CO oxidation. The catalytic activity not only be subject to the particle size of Au but also on the nature of the support and the synthesis method of the catalyst. These factors are frequently inter-related such that their separate contributions cannot be easily unraveled. Also, the activity of a supported Au catalyst is ruled by a complex combination of contributions of the particle morphology, metal dispersion, and electronic properties of the gold. Higher catalytic activity is being observed for Au NPs supported on reducible metal oxides such as TiO2, Co3O4, CeO2, and Fe2O3. However, silica is an inert, inexpensive, and convenient support that can be shaped into a host of attractive and varied morphologies. In this chapter, the study of CO oxidation catalyzed by mono- and bimetallic Au NPs over various silica supports is discussed in detail.

**Keywords:** gold nanoparticles, silica supports, mono-/bimetallic gold nanoparticles, CO oxidation, heterogeneous catalysis


**Author details**

*Advancement and New Understanding in Brain Injury*

epilepsy) are important [59, 62].

**6. Conclusions**

**Conflict of interest**

cerebral diseases, including consequences of TBI.

The authors declare no conflict of interest.

basis for potential optimization of neuroplasticity.

radical balance and prevention of excessive inflammatory processes, which is the

effect of the drug on the energy supply of brain tissue becomes clear [61].

Cortexin was demonstrated to be effective in the treatment of neurological, cognitive consequences of TBI and PTH in both pediatric and adult patients [56, 58]. Taking into account the risk of post-traumatic epilepsy in the long-term period of TBI, data on the dose-dependent antiepileptic activity of cortexin obtained in experiments in animals when modeling chronic convulsive activity (model of temporal

The potential multicomponent nature of cortexin, containing a multitude of different neuropeptides, may be favorable for simultaneous actions on multiple targets [58, 59]. The brain tissue specificity of these molecular mechanisms is important, as to a significant extent it determines the efficacy of the formulation in

Childhood and adolescence are periods of rapid physical and psychological growth, endocrine adjustment, and, at the same time, high risk of injuries. TBI is the most common and potentially the most deleterious type of injury in pediatric population. The consequences of TBI in children and adolescents can be represented in cognitive, behavioral, and paroxysmal disorders. These disorders may have a long-term and significantly negative impact on the success of school education and social adaptation in pediatric patients. Meanwhile, high levels of neuroplasticity in

children and adolescents may determine favorable outcomes of TBI.

Another study identified four brain proteins that interact with cortexin peptides [61]. The identified molecular partners of cortexin peptides are the cytoskeletal proteins actin and the brain-specific isoform of tubulin, the brain-specific adaptive protein 14-3-3 and creatine kinase—the first potential primary targets of the drug. All these proteins are involved in fundamentally important processes. The actin cytoskeleton is known to regulate important cellular processes in the brain, including division and proliferation, cell migration, cytokinesis, and differentiation. The neuronspecific protein tubulin β5, a component of the cytoskeleton microtubules, is critical for the emergence and maturation of neurons, their migration, differentiation, and integration into neural networks. Protein 14-3-3 (alpha/beta) is the important adaptive protein of the brain that interacts with a large number of proteins, determining their localization and function in the cell, and thereby affecting a variety of cellular and physiological processes. Regulating the activity of enzymes, protection from dephosphorylation of proteins, the formation of triple complexes and sequestration processes, protein 14-3-3 participates in pathogenesis and performs neuroprotective functions in neurodegenerative diseases and other neurological and mental disorders. If we assume that binding to cortexin peptides modulates the activity of creatine kinase type B, another molecular partner identified in this study, then the positive

**198**

Nikolay Zavadenko\*, Yuriy Nesterovskiy, Alexey Kholin and Irina Vorobyeva Neurology, Neurosurgery and Medical Genetics Department Named After Academician L.O. Badalian, Faculty of Pediatrics, N.I. Pirogov Russian National Research Medical University, Moscow, Russian Federation

\*Address all correspondence to<EMAIL_ADDRESS>
© 2020 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.


**Author details**

Cezar Francisco Araujo-Junior1,2\*, Vinicius Cesar Sambatti3 , João Henrique Vieira de Almeida Junior4 and Henrique Hiroki Yamada5

1 Agronomic Institute of the State of Paraná – IAPAR, Soils Area, Brazil

2 Post Graduate Programme in Conservation Agriculture, Londrina, Brazil

3 Post Graduate Programme in Conservation Agriculture with Support Scholarship Offered by Coordination for the Improvement of Higher Education Personnel (CAPES)—Finance Code 001, Londrina, Brazil

4 Agronomy at State University of Londrina—UEL, Scientific Initiation Programme at IAPAR—ProICI with Support Scholarship Offered by National Council for Scientific and Technological Development (CNPq), Brazil

5 Agronomy at Center University of Filadélfia—UNIFIL, Scientific Initiation Programme at IAPAR—ProICI with Support Scholarship Offered by National Council for Scientific and Technological Development (CNPq), Brazil

\*Address all correspondence to<EMAIL_ADDRESS>
© 2020 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.


*3.2. Transesterification*

Into a cone flask with a cooled condenser, 12.5 g (0.0114 mol) of vegetable oil (Great Wall Business Co., Taiwan) was added, with various methanol (American Chemical Society grade, ECHO Chemical Co., Miaoli, Taiwan) to oil molar ratios (12-24) and catalyst quantities (2-10 wt.%) at 338 K for 4 h of transesterification. All of the experiments were performed under atmospheric pressure. An appropriate amount of deionized water was added into the sample to stop the transesterification reaction. After a period of time, the sample was cooled and separated through a typical filter paper. The extra methanol was removed from filtrate and water prior to the FAME analysis. The FAME composition of the biodiesel was determined by gas chromatography.


**3. Results**

#### *3.1. Model Training*

Multiple model training session revealed that tackling the objective of training an orthophoto patch encoder is inseparably related to preparing generator and discriminator neural networks that are complex enough to learn all the features present in the input orthophoto. The networks have to be able to produce high-quality artificial images and determine whether the image is artificially generated or not, respectively. This directly influences the following:

Initially chosen BiGAN architecture utilizes many concepts from previously designed networks such as deep convolutional GAN (DCGAN) [48] that, due to their simplicity, are not suitable for processing complex or large images. Therefore, their usefulness in the analysis of aerial imagery is limited. Although BiGAN offered all of the required earlier features, it was not capable of processing an orthophoto patch of size exceeding 32 pixels in both dimensions. This was a huge limitation due to the fact that, with a given 25 cm pixel ground sample distance, this method covered roughly the area of 64 m2. In consequence, the processed patch did not carry enough details to allow a reliable assessment of the similarity between real and artificial images. Attempts to increase the maximum processed input size led to swapping default BiGAN generator and discriminator models with other network types based on deep residual blocks [49] and inception modules [50]. The overall architecture of the generator and discriminator pair resembled BigGAN [51].

After multiple experiments, the authors confirmed that, despite the ability to generate images up to 512 px × 512 px, the network was not capable of learning a reliable bidirectional mapping between the image and the latent space. This was due to the fact that the encoder architecture was lacking in comparison with its powerful counterparts. This problem has been addressed and mitigated in the paper describing large adversarial features learning and the big bidirectional generative adversarial network (BigBiGAN) [44] by introducing intermediate discriminators and proposing a stronger encoder model (Supplementary Materials).


**2. Numerical simulation**

Follower displacement is calculated using SolidWorks software [9]. The follower moved with three degrees of freedom. Four values of the follower guide's from inside (I.D. = 16, 17, 18, 19 mm) at different cam speeds are used. The follower with the offset (O = 20, 30, 40, 50 mm) are chosen. The impact coefficient of restitution with the values (0.2, 0.3, and 0.4) is considered in the calculation of nonlinear response of the follower in the presence of follower offset. Cam follower mechanism is shown in **Figure 1**.

**Figure 1.** *Polydyne cam with an offset flat-faced follower.*

*Nonlinear Dynamics Phenomenon in a Polydyne Cam with an Offset Flat Faced Follower… DOI: http://dx.doi.org/10.5772/intechopen.106179*

**Figure 2.** *Nonlinear response mapping when the follower offsets to the right (O = 10 mm).*

The chaotic phenomenon in cam follower system is increased with the increasing of impact coefficient of restitution in which the impact will happen due the loss in potential energy of the follower and due to the increase in follower guide clearance value. **Figures 2** and **3** show the mapping of nonlinear response of the follower at

### **Figure 3.**

*Nonlinear response mapping when the follower offsets to the left (O = 10 mm).*

different cam speeds, different follower guides' clearances, and different impact coefficient of restitution when the follower offsets to the right and left respectively (O = 10 mm). The nonlinear response of the follower is periodic as shown in **Figure 2a** and both the cam and the follower are in permanent contact. The follower lost the contact with the cam at time (t = 13.58 s) and (t = 15.99 s) at detachment height

*Nonlinear Dynamics Phenomenon in a Polydyne Cam with an Offset Flat Faced Follower… DOI: http://dx.doi.org/10.5772/intechopen.106179*

(26.98 mm) and (27.43 mm) respectively. Due to the coefficient of restitution, the follower keep bouncing from the cam from (t = 0.36 s) to (t = 5.658 s) while the follower will regain energy and keep permanent contact with the cam for the period from (t = 9.208 s) to (t = 10.11 s) which is having a periodic motion as illustrated in **Figure 2b**. The chaotic motion is shown in **Figure 2c**–**f** which increased with the increasing of follower guides' clearances, cam speeds, and coefficient of restitution. There is an intangible impact when the coefficient of restitution (0.2) and the dissipation in potential energy is occurred due to sliding while the contact is still valid between the cam and the follower, as shown in **Figure 3a**. The periodic and chaotic motion is together shown in **Figure 3b** and **c**. The periodic motion is shown from the period (t = 6.1 s) to (t = 10.26 s) and from the period (t = 14.14 s) to (t = 19.55 s) as shown in **Figure 3b** while the periodic motion begins from the period (t = 1.264 s) to (t = 3.808 s) as shown in **Figure 3c**. The chaotic motion is shown in **Figure 3d**–**f**.

**Figure 4.** *Bifurcation diagram against cam speeds.*

**Figure 5.** *Bifurcation diagram when the follower offsets to the left (O = 50 mm).*


**7. Conclusions**

104 Soil Erosion Studies

**/Rainfall Years Author**

1000 mm 1 Mayor and Rodà,

1000 mm 1 Espelta et al.,

Henares, 416 mm 3 Rey et al., 2005,

300-400 mm 1 Alloza and

420 mm 40 www.creaf.uab.es/

391 mm 10 Badía et al., 2007

300 mm 1 Alloza and

300 mm 3 Maestro et al.,

277 mm 6 Cortina et al.,

391 mm 10 Badía et al., 2007

277 mm 6 Cortina et al.,

345 mm 1 Viñuales and

700 mm 1 Abril and Gracia,

300 mm 3 Maestro et al.,

391 mm 10 Badía et al., 2007

345 mm 1 Viñuales and

305 mm 1 Blanco, 1991

Henares, 416 mm 3 Rey et al., 2005,

Alcalá de

Spain

Alloza, Teruel

Alicante

Alcalá de

Alloza

Alicante

Fraga

Alloza, Teruel

Fraga

Table 7. Survival and growth of woody species used in restoration of areas affected by fires and other disturbances. Abbreviatures: S. Survival; HGR. Height growth rate; DGR.

1992

1993

Vallejo, 1999

iefc

Vallejo, 1999

2003

2004

2004

Badía, 1995.

1989

2003

Badía, 1995

**Species Survival and/or growth Location**

*Q. ilex* DGR: 0.87 mm/year Montseny

*Q. ilex* S: 92-70-38% Montseny

DGR: 1,4-2,7 mm/year

S: 58% (1992 year), 54% (1993) and 11% (1994)

*Q. ilex* DGR: 0,87-0,94 mm/year Almatret

cm/year. DGR=1,0-1,5 mm/year

*Q. coccifera* S: 40% (1993) and 0% (1994) España

*Q. coccifera* S: 10-20% Campello

DGR: 0,055-1,05 mm/year

DGR: 1,3-2,2 mm/year

80,9 % (70,4-86,7). HGR=6,1 cm/year (2,9-8,2). DGR= 2,1 mm/year (1,5-3,0)

DGR: 1,4 mm/year

DGR: 1,1 mm/year

*P. lentiscus* DGR: 1,9 mm/year Garraf

*P. lentiscus* S: 0-10% Campello

S: 61,7%(45,8-71,4).HGR=11,1 cm/year. (8,3-14,0). DGR=2,1 mm/year (1,7-2,6)

DGR: 0,1 mm/year

*J. phoenicea* S: 47% Peñaflor

*Q. ilex* S: 5-95%. HGR: 6,3-12,6 cm/year.

*Q. coccifera* S: 34,1 % (17,9-54,2). HGR=1,5-6,6

*Q. coccifera* S: <40 %. HGR: 1,6-4,7 cm/year.

*Q. coccifera* S: 2.5-80%. HGR: 3,5-12,4 cm/year.

*P. lentiscus* S: <40 % HGR: 5,3 cm/year.

*P. lentiscus* S: 100%; HGR: 5,02 cm/year.

*J. phoenicea* S: 94%. HGR: 2,51 cm/year.

*Q. ilex*

*P. lentiscus*

*J. phoenicea*

Diameter growth rate.

In the semi-arid environments of NE-Spain, there are different types of soil conditioned by the lithology of the substrate derived, and whose erosion reponse is significantly divergent. Thus the calcareous burned soils with low stoniness and loamy clay texture, as well as eroded gypsiferous soils, show runoff and erosion levels higher than gypsiferous soils, and especially that colluvial soils. The coverage provided by vegetation is a key element to stop sheet erosion on these soils. The combined effect of heat and ash incorporation involves a number of changes in physical, chemical and biological characteristics of soils affected by wildfire. These effects vary according to intensity of the fire, the amount of ash incorporated and soil characteristics starting. The protective measures such seeding and mulching treatments involve a significant reduction of sediment yield in the first years after fire, higher in eroded gypsiferous soils than in fertile calcareous ones. The remycorrhization is not effective when the soil mycorrhizal status has already been recovered from the effects of fire.

In the forest domain of the area there is a diversity of species whose response after the fire is clearly different. Those with resprouting shrub species tend to recover its previous status faster, the vegetal recovery is higher and temporarily stable. In mature Aleppo's pine forest, the germination of pine is high; the pine density is 3-times higher before than after fire, although it will be prgressively reduced. The shrub and woody species introduced show a differential response according to the soil in which they are implanted and restoration techniques, especially related to soil water conditions.

Soil Erosion and Conservations Measures in Semiarid Ecosystems Affected by Wildfires 107

Badía, D., Martí, C., Aguirre, J., Echeverría, M.T. and Ibarra, P. (2008). Erodibility and

Barceló, M., Badía, D., Gracia, E. and Martí, C. (1994). Aplicación de endomicorrizas en la

Baeza, M.J., Pastor, A., Martín, J. and Ibañez, M. (1991a). Mortalidad post-implantación en

Baeza, M.J., Pastor, A., Martín, J. and Ibañez, M. (1991b). Evolución de la respuesta en

Blanco, E. (1991). Experiencia de trasplante de sabina, pp. 91–97, *Proceedings of Primer*

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**4. Summary**

length of life, the number of patients is expected to grow in the coming decades. Other types of brain tumors common in the elderly are primary CNS lymphomas (PCNSLs) and menin-

GBM comprise a rather heterogenic group of neoplasms, with two major types: primary glioblastomas (85–90%) and secondary GBMs that arise from low-grade astrocytomas (10–15%) [175]. Although both types are indistinguishable under the microscope, they appear to differ genetically. Genetically, primary GBMs exhibit by amplification and mutation of the *EGFR* gene, a lack of heterozygosity on chromosome 10q, inactivation of the *PTEN* homolog gene, and only rare occurrence of mutations in the *IDH* and *TP53* genes. Conversely, the genetics of secondary GBM are characterized by mutations in the *IDH* and/or *TP53* genes, as well as platelet-derived growth factor receptor activation [176]. A gene expression-based GBM classification was established by The Cancer Genome Atlas (TCGA) Research Network in 2010. The authors distinguished four subtypes of GBM. Characteristics that differentiate the subtypes at most were indicated as follows: proneural GBM has alterations of the *PDGFRA* gene and point mutations of *IDH1*, classical GBM has *EGFR* aberrations, and mesenchymal demonstrates GBM aberrations in *NF1*. The fourth subtype, neural GBM, is characterized by the expression of neuron markers such as *NEFL, GABRA1, SYT1*, and *SLC12A5*. Each subtype of GBM differs in its sensitivity to radiotherapy and chemotherapy, thus determining the genetic type of a surgically removed or biopsied lesion could protect patients against unnecessary ineffective therapy [177]. Unfortunately, GBMs are mostly incurable in the elderly, with most of these patients surviving less than 6 months [171]. Diagnosis of primary brain tumors in old age can be further complicated and delayed due to nonspecific symptoms that can be masked by physical and cognitive changes observed in the normal aging process [178]. Moreover, elderly patients are an underrepresented group in many clinical trials [179]. The literature data indicate that, at the close of the twentieth century, the chances of receiving a treatment, be that surgery and/ or radiotherapy, were decreasing as the patient got older. Treatment mostly took place for 82% of patients younger than 65 years of age, whereas only 47% of people older than 65 years and merely 25% of patients older than 75 were subjected to any kind of therapy. Additionally, patients treated with radiotherapy and/or surgery had a significantly lower survival rate as

Although pathological processes differ depending on the glioma subtype, there is a common core of molecular events. Growth factor receptor tyrosine kinases cause downstream signaling by activation of extracellular signal-regulated kinases (ERK) or protein kinase B (Akt) pathways. Lack of p53 activation is followed by the loss of the ability to activate DNA repair processes and cell death by apoptosis. An additional adverse characteristic occurring in GBM is that the cells provoke the secretion of vascular endothelial growth factor (VEGF), which is responsible for angiogenesis. The secretion of VEGF by GBM results in vascularization of the tumor, elevation of capillary permeability of the BBB, and creation of extracellular edema

[181]. Finally, due to vasculature growth, there is progression of tumor invasion [182].

Although these brain tumors are very invasive, it is important to note that, depending on the tumor subtype, they may be effectively treated in elderly patients by maximally safe surgical resection, radiotherapy, and/or chemotherapy with Temozolomide, a drug which is especially

giomas [174].

76 Senescence - Physiology or Pathology

they crossed the age border of 60 years [180].

The molecular mechanism of aging includes genome-wide changes such as genomic instability due to accumulation of mutations, telomere attrition, and epigenetic alterations. These changes collect over the years during the life of the organism, leading gradually to morphological and functional deterioration. The brain seems to be particularly vulnerable, as neurons generally do not divide and their pool decreases with the passage of time. Structural changes in the senescent brain affect mostly the cerebral WM and GM; these effects include progressive neuronal loss, decreased levels of neurotransmitters, increased inflammatory processes, and disrupted integrity of vessels and the BBB followed by infarction and microbleeds. These changes may lead to degenerative diseases, such as PD and dementias.

The frequently observed malnutrition and malabsorption syndrome in the elderly may cause decreased concentrations of the vitamins necessary for Hcy metabolism. This in turn results in increased injury to the cerebral vasculature, leading to degeneration and strokes. Consequently, progressive age-related vascular damage of the brain develops, additionally connected to an increased prevalence of epilepsy in the elderly.

An increased incidence of brain tumors may also be observed in old age, probably as an effect of the diminished efficiency of repair mechanisms. The inactivation of genes involved in DNA repair has been shown to advance with age. Such alterations, inflicted either by epigenetic changes or mutation, may cause further destabilization of immunologic systems and cellular repair mechanisms, thus increasing the susceptibility to ROS and spontaneous mutagenesis and resulting in uncontrolled cellular growth and age-related neoplasia (**Figure 2**).

**Figure 2.** Changes during the senescence process may be associated with neurological diseases. The pathological changes starting at the molecular level affect cells of the aging organism and lead to systemic deterioration, giving rise to age-related neurological diseases. ROS—reactive oxygen species, WM—white matter of the brain, and GM—gray matter of the brain.

In summary, the senescence mechanisms start at a molecular level and gradually lead to morphological disintegration and functional loss of brain cells. Finally, they lead to the deterioration of the CNS and an increased risk of developing neurological diseases.


**6. Conclusions**

We discussed the performance of an advanced supramolecular polymer-surfactant system, SAP-AP1, driven by β-cyclodextrin host-guest complexations as mobility control agent to displace heavy oil (i.e., 2560 cP at 25°C).

Heavy oil recovery displacement tests demonstrated that the SAP-AP1 system shows suitable propagation and low retention in unconsolidated sand-pack systems. The SAP-AP1 system displays superior mobility control efficiency when compared to the baseline AP1 polymer. The higher structural strength of the SAP-AP1 system makes it more effective in generating a stable viscous displacement front that results in a more efficient volumetric sweep, a faster WOR reduction, and accelerated heavy oil recovery. An average additional incremental oil recovery of 19% was achieved relative to the baseline AP1 polymer.

The important incremental oil recovery achieved by the supramolecular polymer-surfactant system is also attributed to the synergistic effect of greater mobility control functionality and decreased interfacial tension (IFT) between the oil-brine system offered by the SAP-AP1 system.

Overall, the SAP-AP1 system offers the potential for increasing heavy oil recovery at economically favorable conditions.


**5. Uniqueness of solutions of BVP**

Define the functions

$$W(\boldsymbol{u}) = \mathbf{0}, \mathsf{5C}\_{ij}^{nl} \boldsymbol{u}\_i, \boldsymbol{u}\_j \boldsymbol{u}\_l, \quad K(\boldsymbol{u}) = \mathbf{0}, \mathsf{5} \|\boldsymbol{u}\_i\|^2,$$

$$E(\boldsymbol{u}) = K(\boldsymbol{u}) + W(\boldsymbol{u}), \quad L(\boldsymbol{u}) = K(\boldsymbol{u}) - W(\boldsymbol{u}),$$

which are called the *densities of internal, kinetic, and total energy* of the system, respectively, and *L* is *the Lagrangian*.

**Theorem 5.1.** *If u is a classical solution of the Dirichlet (Neumann) boundary value problem, then*

$$\int\_{D\_t^-} L(u(\mathbf{x},t))dV(\mathbf{x},t) = \int\_{D\_t^-} G\_i(\mathbf{x},t)u\_i(\mathbf{x},t)dV(\mathbf{x},t) +$$

$$\int\_{D\_t} \left[ \mathbf{g}\_i(\mathbf{x},t)u\_i^S(\mathbf{x},t)d\mathbf{S}(\mathbf{x},t) - \int\_{\mathcal{S}^-} (u\_i(\mathbf{x},t)u\_{i\cdot\cdot t}(\mathbf{x},t) - u\_i^0(\mathbf{x})u\_i^1(\mathbf{x}))dV(\mathbf{x}) \right]$$

*Here and below, dV x*ð Þ¼ *dx*1 … *dxN*, *dV x*ð Þ¼ , *t dV x*ð Þ*dt*; *dS x*ð Þ, *and*, *dS x*ð Þ , *t are the differentials of the area of S and D, respectively*.

**Proof**. Multiplying (1) by *ui* and summing the result over *i*, after simple algebra, we obtain the expression

$$L = \left(\mathbf{C}\_{ij}^{ml}\boldsymbol{u}\_j, \boldsymbol{u}\_m\boldsymbol{u}\_i\right), \boldsymbol{l} - (\boldsymbol{u}\_i\boldsymbol{u}\_i, \boldsymbol{l}), \boldsymbol{t} + \mathbf{G}\_i\boldsymbol{u}\_i.$$

This equality is integrated over *Dt* taking into account the front discontinuities and using the Gauss-Ostrogradsky theorem and initial conditions (33) and (34) to obtain

*Mathematical Theorems - Boundary Value Problems and Approximations*

$$\begin{aligned} \int\_{D\_{i}^{-}} L(u(\mathbf{x},t))dV(\mathbf{x},t) &= \int\_{D\_{i}^{-}} \left(C\_{ij}^{ml}u\_{j,m}u\_{i}\right)\_{,l} - (u\_{i}u\_{i:t})\_{,l}dV(\mathbf{x},t) + \\ &+ \int\_{D\_{i}^{-}} G\_{i}(\mathbf{x},t)u\_{i}(\mathbf{x},t)dV(\mathbf{x},t) = \int\_{D\_{i}} \sigma\_{i}^{l}u\_{l}(\mathbf{x})u\_{i}(\mathbf{x},t)dS(\mathbf{x},t) - \\ &- \int\_{S} u\_{i}u\_{i:t}(\mathbf{x},t) - u\_{i}u\_{i:t}(\mathbf{x},0))dS(\mathbf{x},t) + \int\_{D\_{i}^{-}} G\_{i}(\mathbf{x},t)u\_{i}(\mathbf{x},t)dV(\mathbf{x},t) + \\ &+ \sum\_{k} \int\_{F\_{k}\cap D\_{i}^{-}} u\_{i} \left[\nu\_{l}^{k}\sigma\_{l}^{l}(\mathbf{x},t) - \nu\_{l}^{k}u\_{i:t}(\mathbf{x},t)\right]\_{F\_{k}}dF\_{k}(\mathbf{x},t) \end{aligned}$$

Here, *νk l* , *and νk t* are the components of the unit normal vector to the front *Fk*ð Þ *x*, *t* in *RN*þ1 , for which we have [17]

$$
\nu\_t^k = -c\_k / \left(\nu\_j^k \nu\_j^k\right)^{1/2},\tag{37}
$$

and *u*2, then their difference *u* ¼ *u*1 � *u*2 satisfies the system of equations with *G* ¼

*Singular Boundary Integral Equations of Boundary Value Problems for Hyperbolic Equations…*

*i* ð Þ¼ *x* 0 ð Þ *m* ¼ 0, 1 *:*

The vector *u* on the boundary *S* satisfies the homogeneous boundary conditions

Since the integrand is positive definite and by the conditions of the theorem, we

Let us assume that *S* is a smooth boundary with a continuous normal of a set *S*�.

The Heaviside function *H t*ð Þ is extended to zero by setting *H*ð Þ¼ 0 1*=*2. Define

*S* ð Þ *x* of a set *S*� is defined for *x*∈*S* as

. Similarly,

*i* ð Þ *x*, *t* denotes the Green's matrix, i.e. the fundamental solution of Eq. (1)

*i* ð Þ *x*, *t* ∗ *tH t*ðÞ ) *∂tV*^ *k*

Here and below, the star denotes the complete convolution with respect to ð Þ *x*, *t* , while the variable under the star denotes the incomplete convolution with respect to *x* or *t*, respectively. The convolution exists since the supports are semibounded with

*S* ð Þ¼ *x* 1*=*2 (38)

*S* ð Þ *x H t*ð Þ (39)

*D*ð Þ *x*, *t* , (40)

*D*ð Þ *x*, *t :* (41)

*i δ*ð Þ *x δ*ð Þ*t* and satisfies the conditions

*i* , *t*ð Þ¼ *x*, 0 0, *x* 6¼ 0 (42)

*i* ¼ *U*^ *k*

*i :* (43)

*i δ*ð Þ *x H t*ð Þ.

ð Þ¼ *x*, *t* 0*:*

ð Þ *K u*ð Þþ , *t W u*ð Þ , *t dS x*ð Þ¼ 0*:*

*ui*ð Þ¼ *x*, *t* 0 or *gi*

*S*

*H*�

*D*ð Þ¼ *x*, *t H*�

Accordingly, for *u* defined on *D*�, we introduce the generalized function

*u x* ^ð Þ¼ , *t uH*�

*G*^ *k*ð Þ¼ *x*, *t GkH*�

*H*�

*i* ð Þ¼ *x*, 0 0, *U*^ *k*

respect to *t*. Clearly, the convolution is the solution of Eq. (1) at *Fi* ¼ *δk*

For system (1), such a matrix was constructed in [10]. The primitive of Green's matrix with respect to *t* is defined as

*i* ð Þ¼ *x*, *t U*^ *k*

*um*

*E u*ð Þ , *t dS x*ð Þ¼ ð

**6. Analogues of the Kirchhoff and Green's formulas**

0 and the zero initial conditions, i.e.

*DOI: http://dx.doi.org/10.5772/intechopen.92449*

ð

*S*

have *u* � 0. The theorem is proved.

The characteristic function *H*�

the characteristic function of *D*� as

Let *U*^ *k*

**69**

which is defined on the entire space *RN*þ1

that corresponds to the function *Fi* ¼ *δk*

*V*^ *k*

*U*^ *k*

Theorem 5.2 yields

where *ck* is the velocity of the front. With the notation introduced, the relation (37) and the front condition (7) yield the assertion of the theorem.

It is easy to see that the following result holds true. **Corollary.** *If ui*ð Þ¼ *x*, 0 0, *ui*, *t*ð Þ¼ *x*, 0 0, *and*

$$\lim\_{l \to +\infty} u\_{i,l} \to 0, \quad \lim\_{l \to +\infty} u\_{i,l} \to 0, \quad x \in \mathbb{S}^-,$$

then

$$\int\_{D^{-}} L(u(\mathbf{x},t))dV(\mathbf{x},t) = \int\_{D^{-}} G\_i(\mathbf{x},t)u\_i(\mathbf{x},t)dV(\mathbf{x},t) + \int\_{D} \mathbf{g}\_i(\mathbf{x},t)u\_i^S(\mathbf{x},t)dS(\mathbf{x},t)$$

is proved in the following theorem [17]:

**Theorem 5.2.** *If u is a classical solution of the Dirichlet (Neumann) boundary value problem, then*

$$\int\_{\mathcal{S}^{-}} (E(\mathfrak{u}, t) - E(\mathfrak{u}, \mathbf{0}))dV(\mathfrak{x}) = $$

$$\int\_{D\_t^{-}} G\_i(\mathfrak{x}, t)u\_{i, t}(\mathfrak{x}, t)dV(\mathfrak{x}, t) + \int\_{D\_t} \mathfrak{g}\_i(\mathfrak{x}, t)u\_i^{\mathcal{S}},\_t(\mathfrak{x}, t)d\mathfrak{S}(\mathfrak{x}, t).$$

It is easy to see that this theorem implies the uniqueness of the solutions to the initial-boundary value problems in question.

**Theorem 5.3.** *If a classical solution of the Dirichlet (Neumann) boundary value problem exists and satisfies the conditions*

$$\lim\_{l \to +\infty} u\_{i,l} \to 0, \quad \lim\_{l \to +\infty} u\_{i,l} \to 0, \ \forall \mathfrak{x} \in \mathbb{S}^-,$$

*then this solution is unique*.

**Proof**. Since the problem is linear, it suffices to prove the uniqueness of the solution to the homogeneous boundary value problem. If there are two solutions *u*1 *Singular Boundary Integral Equations of Boundary Value Problems for Hyperbolic Equations… DOI: http://dx.doi.org/10.5772/intechopen.92449*

and *u*2, then their difference *u* ¼ *u*1 � *u*2 satisfies the system of equations with *G* ¼ 0 and the zero initial conditions, i.e.

$$
\mu\_i^m(\mathbf{x}) = \mathbf{0} \quad (m = \mathbf{0}, \mathbf{1}).
$$

The vector *u* on the boundary *S* satisfies the homogeneous boundary conditions

$$u\_i(\mathbf{x}, t) = \mathbf{0} \quad \text{or} \quad \mathbf{g}\_i(\mathbf{x}, t) = \mathbf{0}.$$

Theorem 5.2 yields

ð

*Lux* ð Þ ð Þ , *t dV x*ð Þ¼ , *t*

Here, *νk*

*Fk*ð Þ *x*, *t* in *RN*þ1

then

ð

*Lux* ð Þ ð Þ , *t dV x*ð Þ¼ , *t*

ð

*D*� *t*

*then this solution is unique*.

is proved in the following theorem [17]:

initial-boundary value problems in question.

*problem exists and satisfies the conditions*

*D*�

*problem, then*

**68**

*l* , *and νk*

ð

*Cml ij u j*, *mui* � �

*Mathematical Theorems - Boundary Value Problems and Approximations*

*Gi*ð Þ *x*, *t ui*ð Þ *x*, *t dV x*ð Þ¼ , *t*

*uiui*, *t*ð Þ� *x*, *t uiui*, *t*ð ÞÞ *x*, 0 *dS x*ð Þþ , *t*

ð Þ� *x*, *t νk t ui*, *t*ð Þ *x*, *t* � �

> *j νk j* � �1*=*2

where *ck* is the velocity of the front. With the notation introduced, the relation

lim*t*!þ∞ *ui*, *l* ! 0, lim*t*!þ∞ *ui*, *t* ! 0, *x*∈*S*�,

*Gi*ð Þ *x*, *t ui*ð Þ *x*, *t dV x*ð Þþ , *t*

**Theorem 5.2.** *If u is a classical solution of the Dirichlet (Neumann) boundary value*

ð Þ *E u*ð Þ� , *t E u*ð Þ , 0 *dV x*ð Þ¼

ð

*Dt gi* ð Þ *x*, *t uS*

It is easy to see that this theorem implies the uniqueness of the solutions to the

**Theorem 5.3.** *If a classical solution of the Dirichlet (Neumann) boundary value*

lim*t*!þ∞ *ui*, *l* ! 0, lim*t*!þ∞ *ui*, *t* ! 0, ∀*x*∈*S*�,

**Proof**. Since the problem is linear, it suffices to prove the uniqueness of the solution to the homogeneous boundary value problem. If there are two solutions *u*1

*t* are the components of the unit normal vector to the front

, *l* � *uiui*, ð Þ*t* , *tdV x*ð Þþ , *t*

ð

*nl*ð Þ *x ui*ð Þ *x*, *t dS x*ð Þ� , *t*

*dFk*ð Þ *x*, *t*

, (37)

*i* ð Þ *x*, *t dS x*ð Þ , *t*

*Gi*ð Þ *x*, *t ui*ð Þ *x*, *t dV x*ð Þþ , *t*

ð

*D*� *t*

*Fk*

ð

*D gi* ð Þ *x*, *t uS*

*i* , *t*ð Þ *x*, *t dS x*ð Þ , *t :*

*Dt σl i*

*D*� *t*

þ ð

� ð

þ X *k*

*S*

ð

*ui νk l σl i*

*νk*

(37) and the front condition (7) yield the assertion of the theorem.

*t* ¼ �*ck= νk*

*Fk* ∩ *D*� *t*

, for which we have [17]

It is easy to see that the following result holds true. **Corollary.** *If ui*ð Þ¼ *x*, 0 0, *ui*, *t*ð Þ¼ *x*, 0 0, *and*

ð

*D*�

ð

*S*�

*Gi*ð Þ *x*, *t ui*, *t*ð Þ *x*, *t dV x*ð Þþ , *t*

*D*� *t*

*D*� *t*

$$\int\_{S} E(u,t)dS(\mathbf{x}) = \int\_{S} (K(u,t) + W(u,t))dS(\mathbf{x}) = \mathbf{0}.$$

Since the integrand is positive definite and by the conditions of the theorem, we have *u* � 0. The theorem is proved.