**6.2. Deviation from the percentage optimum**

**1.** In the deficient range or zone the symptoms are visible and occur in soils (or substrates) very deficient in an element due to insufficient dosages. In these conditions the re‐ sponse in production of dry matter is high, the element concentration is not increased and it may even be diluted. The nutrient dilution effect caused by organic matter forma‐ tion is known as the Steembjerg effect. When the concentration of a plant nutrient is set

**2.** In the transition range or zone, deficiency symptoms are not visible (disguised hunger) but there is a direct relation between nutrient foliar concentration of and production. When the nutrient concentration allows an average of 80 to 95% of the maximum pro‐ duction, this level corresponds to the critical level. The relation of nutrient concentra‐ tions and maximal production (100%) is seen in soils (or substrates) with slight deficiency and with lower responses in growth and production when the nutrient is ap‐ plied. In these conditions the increases in foliar concentrations are proportional to growth and production, that is, greater absorption is compensated by increasing organ‐ ic material. A nutrient concentration in this range, considered between the critical level

**3.** In the luxury consumption range or zone, increasing element concentration does not in‐ crease production. This is observed in non-deficient soils receiving element dosages. Although plant tissues show absorption of the increased nutrient concentrations this is not expressed in increased growth. Thus, the element concentration in this range, which corre‐ sponds to maximal or optimal production and it is below the toxicity critical point, is consid‐

**4.** The toxicity range or zone starts when increased nutrient concentrations significantly reduce production. Reductions of 5% up to 20% indicate toxic levels. The condition is observed in soils (or substrates) with excess nutrients receiving additional dosages that are absorbed as shown by increased tissue concentrations but expressed in decreased

The critical level of deficiency is a factor largely employed in research and it corresponds to an optimal nutrient concentration. Below it the growth index (production or quality) is sig‐

After attaining maximal production, increased nutrient concentrations will not result in growth but in plant "luxury consumption". During this period nutrients accumulate in cell vacuoles and may be gradually liberated to supply eventual plant nutritional necessities. As already stated nutrient concentrations above the level of luxury consumption can lead to de‐

Interpretation of foliar nutrient concentrations based on the critical level and the sufficiency range is made directly by comparison with standard values. The plant nutritional status (de‐ ficiency, sufficiency, luxury consumption) is defined independently for each element by the range of values found for the sample. However, the plant mineral composition is the result of its adaptation to an environment under the action of several limiting factors. Lack of con‐

in this range it is considered deficient.

ered to be high.

128 Soil Fertility

and maximal production is interpreted as adequate.

growth and/or imbalance in relation to other nutrients.

creased production and characterize the toxicity range.

nificantly decreased and above it, production represents poor economics.

The deviation from the percentage optimum (DPO) is an improvement of the critical level method [19]. It evaluates each nutrient concentration in relation to the optimum value (me‐ dian of the sufficiency range) by the expression: DPO= [(Cx100/CR)-100] where C is an ele‐ ment concentration in the sample dry matter and CR it is the optimal concentration for the same conditions (culture, tissue analyzed, manipulation, plant development stage etc.). In the absence of the sufficiency range the critical level is taken as the optimum value.

This is a procedure not common in the literature but it permits the evaluation of the nutri‐ tional status of the plant and the arrangement of the elements as a function of the degree of deficiency. However, the limitation order is not representative because element interactions are not considered and the conventional table is still used.

### **6.3. Diagnosis and Recommendation Integrated System (DRIS)**

DRIS is an alternative to the conventional method for the determination of the nutritional status of a plant [20]. It considers nutrient interactions in the diagnostic process, which is conducted by the combination of all the relations in the form of ratios [20] or products [21]. In this technique indexes, which express nutrient equilibrium in a plant or culture are calcu‐ lated for each one, as a function of concentration ratios of each element and the total and compared in groups of two to other ratios considered standard or norms obtained in a pop‐ ulation of highly productive plants.

Foliar diagnosis, in this method, aims to adjust fertilization, so far only recommended by soil fertility and culture productivity, by additional production gains and correction of defi‐ ciencies. It also makes possible the management other nutrient availabilities, possibly reduc‐ ing them and permitting an equilibrated fertilization, in view of the culture nutritional necessities.

### **6.4. Diagnosis of nutritional composition (DNC)**

The method relates nutrient concentrations in a multivariable form, as a function of ratios of each nutrient concentration and the geometrical mean of the nutritional composition of the sampled tissue [23]. The method is not widely used although it deals with relations between all elements analyzed.

DNC and DRIS are independent calibration methods, since use of double or multi variable methods minimizes non controlled effects of accumulated biomass, in contrast to the critical level, which needs calibration assays conducted in places and different years, and maintain control on other production factors (including other nutrients) and on a supply adequate to full plant development [24].

However, it is important to emphasize that all methods that interpret foliar analysis re‐ sults are based on analysis of nutrient concentrations in plant dry matter. Thus, all pro‐ cedures described in the previous topics (excluding biotic and abiotic factors that may interfere in the collection, preparation and analysis of sample and results) should be well conducted, since no analytical or interpretative method will correct mistakes in these steps.

**•** Deficiency symptoms may be different from the ones described in the literature or speci‐ alized publications. For example, symptoms may be light instead of the severe ones de‐

**•** Element deficiency signs may be different according to element and culture. Zn defi‐ ciency in fruit trees is expressed by smaller leaves and in corn cultures, new leaves

**•** Deficiency symptoms may be similar for different nutrients.

**•** Deficiencies of two or more nutrients prevents identification.

**•** Certain deficiencies may reduce production without plant symptoms.

**•** Excess of one nutrient may be mistakenly taken as the deficiency of another one.

**•** Adequate visual diagnosis must be conducted by technicians with significant experience

Furthermore, when the nutritional disorder is acute and visual symptoms of deficiency or excess are obvious and able to be differentiated a significant part of production (around 40-50%) may have been already compromised by a series of irreversible injuries to the physiology of the plant. Thus, visual diagnosis should not be used as a rule but

Foliar diagnosis is a direct evaluation method that utilizes nutrient concentrations in plant tissues as an indicator of nutritional status. However, indirect methods exist and are useful. When a deficient nutrient is part of an organic component or activates an enzymic activity this can be indirectly expressed. For example N deficiency may be shown by low chloro‐ phyll levels or low activity of nitrate reductase. A description of biochemical tests that may be employed to evaluate plant nutritional status has been reported in [8]. For N, reductase and glutamine synthetase activity, amide N and asparagine; for P, fructose-1,6-diphosphate and photosynthesis ; phosphatase activity; for K,amide concentrations; free amino-acids; for Mn, peroxidases and a/b chlorophyll ratios; for B, ATP-ase activity; for Zn, ribonuclease, car‐ bonic anhydrase, arginine concentration. In the case of P other studies indicate that Pi

cuole cells may indicate the nutritional status of the plant [25, 26]. These are additional tools to evaluate plant nutrition, which are not commonly used because some of the tests require special methods of sampling, storage and complex analytical procedures and costly equip‐ ment. Other methods, specifically for N, evaluate the index of green color by a portable de‐ vice called chlorophyll meter. This index is strongly correlated to the chlorophyll

concentration in leaves and N nutritional status of the plant.

in va‐

Plant Analysis

131

http://dx.doi.org/10.5772/53388

**•** Visual diagnosis does not quantify neither the deficiency level nor the excessive one.

scribed.

are bleached.

in cultures of the region.

only as complement.

**8. Other methods**


**1. Introduction**

In this paper, we intend to treat an elliptic PDE (Among the numerous textbooks on elliptic PDEs, we think that Gilbarg and Trudinger's book [1], first published in 1998 and then again in 2001 and 2015, is the main contribution to acquire the necessary knowledge on this fascinating topic. On the other hand, the main notions to tackle the typical mathematical physics problems can be found in [2], for example.) with a special focus on the property of the *degeneracy* of its spectrum.

To begin with, we consider the following elliptic PDE:

$$
\left[ -\frac{1}{2}\nabla^2 + \frac{r^2}{2} \right] f(x, y, z) = \lambda f(x, y, z),
\tag{1}
$$

where *r* = *x*2 + *y*2 + *z*2, and the function *f*(*x*, *y*, *z*) belongs to the following Hilbert space:

$$\mathcal{H} = \left\{ f(\cdot) \in L^2(\mathbb{R}^3) \cap \mathbb{C}^2(\mathbb{R}^3) \mid \lim\_{r \to \infty} f(x, y, z) = 0 \right\}. \tag{2}$$

As is known, ∇2 is the Laplacian operator:

$$
\nabla^2 = \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} + \frac{\partial^2}{\partial z^2}.
$$

The operator L := −1 2 ∇2 + *r*2 2 satisfies the property of rotational invariance, i.e., it is invariant under *SO*(3) transformations. Addressing the problem (1) in polar coordinates is not difficult, and it is well known that the eigenfuctions in H depend on three parameters, say, *l*, *m*, *n*, whereas the eigenvalues only depend on *n*, meaning that L is a degenerate operator. However, there are different kinds of degeneracy: If the eigenvalues *λi* are independent of *m*, that is called *natural degeneracy*. If *λi* are independent of *l*, *accidental*

**Citation:** De Marchis, R.; Palestini, A.; Patrì, S. Accidental Degeneracy of an Elliptic Differential Operator: A Clarification in Terms of Ladder Operators. *Mathematics* **2021**, *9*, 3005. https://doi.org/10.3390/ math9233005

Academic Editor: Andrea Scapellato

Received: 26 October 2021 Accepted: 22 November 2021 Published: 23 November 2021

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

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

*degeneracy* occurs. Namely, we focus on accidental degeneracy and on its relationship with ladder operators (a similar procedure applied to spherical hydrogen atom eigenfuctions can be found in [3]).

Recent papers in which the various types of degeneracy are treated are [4–6], just to cite a few.

The paper is organized as follows: In Section 2 the main notions and a selection of useful results on invariance and degeneracy are presented. In Section 3, the ladder operators are introduced and summarized. Section 4 intends to describe the accidental degeneracy of the operator L in detail. Section 5 features a final discussion and the possible future developments of this theory.


**Acknowledgements**

This work was supported by the National Natural Science Foundation of China (grant number 11704314) and the China Postdoctoral Science Foundation (grant numbers 2018M631194 and 2020T130533).


**3. Results and discussion**

## **3.1. Characterization of ZnO-SEP catalysts**

## *3.1.1. XRD analysis*

washings and centrifugations (at 4000 rpm) were applied. The resulting catalysts were dried at 100°C for 12 h and then calcined at 500°C with a rate of 10°C min-1 for 5 h. Finally, the catalysts were ground into fine powder and named as 0.125 M ZnO-SEP, 0.25 M ZnO-SEP and 0.5 M

X-ray diffraction was used to monitor the formation of crystal planes and measure the crystalline size of ZnO nanoparticles. The analyses were recorded on a Rigaku-D/MAX-Ultima diffractometer using Cu-Kα radiation (λ=1.54 Å) operating at 40 kV and 40 mA and scanning rate of 2 min-1. Nitrogen sorption analysis was used to measure the surface areas, pore volumes

The nitrogen adsorption/desorption isotherms were obtained at 77 K using Quantachrome Nova 2200e automated gas adsorption system. The specific surface areas were determined using multi-point BET analysis and the pore sizes were measured by the BJH method of

The surface morphologies were determined using scanning electron microscopy (SEM) in combination with energy-dispersive X-ray analysis on an ESEM-FEG/EDAX Philips XL-30 instrument operating at 20 kV. The catalysts were fixed with carbon tape prior to the metalli‐

In X-ray photoelectron spectroscopy (XPS) tests, Thermo Scientific K-Alpha X-ray photoelec‐ tron spectrometer equipped with electron analyzer and Al-Kα micro-focused monochromator was used. The areas of peaks were estimated by calculating the integral of each peak after subtracting a Shirley background and fitting the experimental curve to a combination of Lorentzian/Gaussian lines. Binding energy shifts were observed in the samples and the instrument was calibrated using the carbon peak (C-1s) at 285 eV as in the other studies [20,21].

The UV-vis diffuse reflectance spectra (UV-vis DRS) of the supports, 0.25 M ZnO and sup‐ ported catalysts were obtained using UV-vis spectrophotometer (UV-2450, Shimadzu) equipped with an integrating sphere reflectance accessory. The baseline correction was done by BaSO4. The spectra were recorded in the range 200–600 nm for the catalysts and the FA

For the photocatalytic experiments, the details of reaction systems were given in our previous studies [22,23]. Briefly, a Pyrex flask reactor was located in an "irradiation box" equipped with eight black light lamps (Philips TL 15W/5BLB) with an emission maximum at λ=365 nm. The lamps were positioned to surround the flask with an incident photon flux of 4.7×1015 photons s-1. Then, 0.2 g of catalysts with 200 mL of 3.27 mg L-1 MO (unless the concentration effect of MO was controlled) was used as reaction solutions. The flask had an inlet for the air circulation and an outlet for the collection of aliquots. Prior to irradiation, suspensions were magnetically stirred in the dark for 30 min. UV-vis spectrophotometer (UV-2450, Shimadzu) was used to monitor the absorbance spectra of MO at 464 nm as a function of irradiation time. All experi‐ ments were performed at room temperature and without concerning the degradation inter‐ mediates. Also, measurements were conducted at least twice and the average value was

recorded. MO decolorization percentages were calculated by the following equation:

ZnO-SEP.

adsorption.

and pore diameters of the catalysts.

234 Advanced Catalytic Materials - Photocatalysis and Other Current Trends

using BaSO4 as a reference.

zation process with gold (Sputter Coater-Balzer SCD050).

The phase identification of the raw SEP and the supported catalysts were performed by XRD analysis from 0° τo 70° (2*θ*) (Figure 1). The characteristic d 110 reflection of the SEP was noticed with a basal spacing of 12.19 Å at 7.24° (2*θ*). ZnO loadings decrease the intensities of all SEP reflections. For the supported catalysts, alteration in ZnO concentrations did not modify the position of the SEP peaks due to the non-expandable nature of the SEP. Supported catalysts also exhibited wurtzite ZnO structure with d 100, d 002, d 101, d 102, d 110, d 103 and d 200 crystal planes at 31.9°, 34.6°, 36.4°, 47.7°, 56.7°, 63.1° and 66.6° (2*θ*), respectively. The broad and less intense ZnO peaks got sharper and more intense with the increments in ZnO loadings.

**Figure 1.** XRD patterns of SEP and supported catalysts (Z: ZnO).

The crystalline sizes (DZnO) calculated using Scherrer's equation for the broadening of d 101 reflection of ZnO were found as 16.1 nm (for 0.25 M ZnO), 13.4 nm (for 0.125 M ZnO-SEP), 12.3 nm (for 0.25 M ZnO-SEP) and 15.1 nm (for 0.5 M ZnO-SEP) (Table 1). The reduction in the ZnO crystalline sizes and the decrements in the intensities of SEP reflections may suggest highly dispersed ZnO nanoparticles over the surface and bulk.

a Calculated from the (101) diffraction peak of ZnO using the Scherrer equation.

b Determined from nitrogen adsorption-desorption isotherms using BET equation.

c Determined from cumulative adsorption pore volume using BJH method.

d Determined from adsorption pore size using BJH method.

**Table 1.** Crystalline sizes (DZnO), surface areas (BET), total pore volumes (Vpore) and pore radius (Rpore) of 0.25 M ZnO, SEP and supported catalysts.

## *3.1.2. Nitrogen adsorption desorption isotherms*

The textural characterization points out that 0.25 M ZnO had type II isotherms, which refer to non-porous materials (Figure 2A and 2B). However, the raw SEP and the supported catalysts had type IV nitrogen adsorption-desorption isotherms typical of mesoporous structures with hysteresis loops [24]. Almost similar pore radius was detected for all catalysts and the SEP (Table 1). The capillary condensation taking place within the mesopores in the high P/P0 range became more difficult with the formation of narrower loops, owing to the higher ZnO loading concentrations. Accordingly, 0.125 M ZnO-SEP shows almost similar surface area and pore volume with respect to the SEP, whereas 0.25 M ZnO-SEP and 0.5 M ZnO-SEP reveal lower values. The partial blockage of the pores by the ZnO nanoparticles on the supports' surface sites, edges and corners was expected to induce an easier attraction among MO molecules and the catalyst particles.

## *3.1.3. SEM (EDX) analysis*

Figure 3 illustrates the SEM and elemental mapping images of 0.25 M ZnO-SEP. The charac‐ teristic fibrous structure of SEP and pseudo-spherical shape of the as-prepared ZnO catalyst were reported previously [17,22]. The heterogeneously dispersed ZnO nanoparticles within the SEP matrix resulted in a different morphology in comparison to the raw SEP and unsup‐ ported catalyst. In the EDX analysis of 0.25 M ZnO-SEP (not shown), the reduction in the peak intensities and percentages of SiO2 and MgO (from 69.25% to 16.08% for SiO2 and from 28.92% to 10.93% for MgO) and also simultaneous detection of ZnO peak signified the in situ build236 Advanced Catalytic Materials - Photocatalysis and Other Current Trends 2 ZnO/Sepiolite Catalysts – Characterization and Photoactivity Measurements http://dx.doi.org/10.5772/61973 237

The crystalline sizes (DZnO) calculated using Scherrer's equation for the broadening of d 101 reflection of ZnO were found as 16.1 nm (for 0.25 M ZnO), 13.4 nm (for 0.125 M ZnO-SEP), 12.3 nm (for 0.25 M ZnO-SEP) and 15.1 nm (for 0.5 M ZnO-SEP) (Table 1). The reduction in the ZnO crystalline sizes and the decrements in the intensities of SEP reflections may suggest

 **g-1)**

0.25M ZnO 16.1 7.58 0.012 17.7 SEP - 104.5 0.140 14.9 0.125M ZnO-SEP 13.4 91 0.151 19.1 0.25M ZnO-SEP 12.3 47 0.077 20.2 0.5M ZnO-SEP 15.1 51 0.091 14.8

**Table 1.** Crystalline sizes (DZnO), surface areas (BET), total pore volumes (Vpore) and pore radius (Rpore) of 0.25 M

The textural characterization points out that 0.25 M ZnO had type II isotherms, which refer to non-porous materials (Figure 2A and 2B). However, the raw SEP and the supported catalysts had type IV nitrogen adsorption-desorption isotherms typical of mesoporous structures with hysteresis loops [24]. Almost similar pore radius was detected for all catalysts and the SEP (Table 1). The capillary condensation taking place within the mesopores in the high P/P0 range became more difficult with the formation of narrower loops, owing to the higher ZnO loading concentrations. Accordingly, 0.125 M ZnO-SEP shows almost similar surface area and pore volume with respect to the SEP, whereas 0.25 M ZnO-SEP and 0.5 M ZnO-SEP reveal lower values. The partial blockage of the pores by the ZnO nanoparticles on the supports' surface sites, edges and corners was expected to induce an easier attraction among MO molecules and

Figure 3 illustrates the SEM and elemental mapping images of 0.25 M ZnO-SEP. The charac‐ teristic fibrous structure of SEP and pseudo-spherical shape of the as-prepared ZnO catalyst were reported previously [17,22]. The heterogeneously dispersed ZnO nanoparticles within the SEP matrix resulted in a different morphology in comparison to the raw SEP and unsup‐ ported catalyst. In the EDX analysis of 0.25 M ZnO-SEP (not shown), the reduction in the peak intensities and percentages of SiO2 and MgO (from 69.25% to 16.08% for SiO2 and from 28.92% to 10.93% for MgO) and also simultaneous detection of ZnO peak signified the in situ build-

**b Vpore (cm3**

 **g-1)**

**c Rpore (Å)d**

highly dispersed ZnO nanoparticles over the surface and bulk.

a Calculated from the (101) diffraction peak of ZnO using the Scherrer equation. b Determined from nitrogen adsorption-desorption isotherms using BET equation. c Determined from cumulative adsorption pore volume using BJH method.

d Determined from adsorption pore size using BJH method.

*3.1.2. Nitrogen adsorption desorption isotherms*

ZnO, SEP and supported catalysts.

the catalyst particles.

*3.1.3. SEM (EDX) analysis*

**Catalysts DZnO (nm)a BET (m2**

*figure\_2* **Figure 2.** (A) Nitrogen adsorption/desorption isotherms and (B) pore size distribution plots of 0.25 M ZnO, SEP and supported catalysts.

up of ZnO nanoparticles in the SEP structure. In mapping images, ZnO existence was proven by the dominating Zn signals within less dense regions of Si and Mg constituents.

**Figure 3.** SEM and mapping images of 0.25 M ZnO-SEP.

## *3.1.4. XPS analysis*

In order to control the presence of ZnO on the SEP host, the surface chemical composition was analyzed by the XPS method, focusing in particular on the binding energies of the typical lines of Zn and O (Figure 4). The survey scan of 0.5 M ZnO-SEP reveals Zn peaks in addition to the Mg (49.5 eV), Al (75.6 eV), Si (103 eV), O (531.47 eV) and some Auger peaks of the SEP (Figure 4A). Figure 4B depicts the presence of Zn ion with a doublet matching to Zn 2p3/2 and 2p1/2 core levels (Figure 4B). This shows the presence of Zn2+ ions in an oxide environment [25,26]. The O1s photoelectron peak is deconvoluted by three subspectral parts (Figure 4C). The peak at 527 eV is attributed to the lattice oxygen in a Zn-O-Zn network with 8.7% spectral area. The shift in the peak position with respect to ZnO binding energy of 530.5 eV can be due the complex configuration in the ZnO-SEP matrix. For the other two components, 64.7% spectral area refers to MgO and Al2O3 at 531 eV and 26.5% spectral area corresponds to SiO2 at 532.81 eV.

## *3.1.5. UV-vis DRS analysis*

UV-vis absorption spectroscopies of the SEP and supported catalysts are presented in Figure 5A. The raw SEP shows an extended profile in between 200 and 600 nm. In contrast, 0.25 M ZnO reveals its distinctive edge below 400 nm. The supported catalysts resemble this charac‐ teristic edge, which is more pronounced for the catalyst having the highest ZnO concentration. The UV activities of the supported catalysts are evidenced by the evaluated band-gap energies based on Kubelka-Munk transformed reflectance spectra as 3.08 eV for 0.125 M ZnO-SEP, 3.09 eV for 0.25 M ZnO-SEP and 3.16 eV for 0.5 M ZnO-SEP (Figure 5B).

ZnO/Sepiolite Catalysts – Characterization and Photoactivity Measurements http://dx.doi.org/10.5772/61973 239

**Figure 4.** XPS analysis of 0.5 M ZnO-SEP: (A) survey spectrum, (B) Zn 2p spectra and (C) O 1s spectra.

**Figure 5.** A) Diffuse reflectance spectra of SEP, 0.25 M ZnO and supported catalysts and (B) Kubelka-Munk trans‐ formed reflectance spectra of 0.25 M ZnO and supported catalysts.

### **3.2. Decolorization of MO by ZnO-SEP catalysts**

up of ZnO nanoparticles in the SEP structure. In mapping images, ZnO existence was proven

In order to control the presence of ZnO on the SEP host, the surface chemical composition was analyzed by the XPS method, focusing in particular on the binding energies of the typical lines of Zn and O (Figure 4). The survey scan of 0.5 M ZnO-SEP reveals Zn peaks in addition to the Mg (49.5 eV), Al (75.6 eV), Si (103 eV), O (531.47 eV) and some Auger peaks of the SEP (Figure 4A). Figure 4B depicts the presence of Zn ion with a doublet matching to Zn 2p3/2 and 2p1/2 core levels (Figure 4B). This shows the presence of Zn2+ ions in an oxide environment [25,26]. The O1s photoelectron peak is deconvoluted by three subspectral parts (Figure 4C). The peak at 527 eV is attributed to the lattice oxygen in a Zn-O-Zn network with 8.7% spectral area. The shift in the peak position with respect to ZnO binding energy of 530.5 eV can be due the complex configuration in the ZnO-SEP matrix. For the other two components, 64.7% spectral area refers

to MgO and Al2O3 at 531 eV and 26.5% spectral area corresponds to SiO2 at 532.81 eV.

eV for 0.25 M ZnO-SEP and 3.16 eV for 0.5 M ZnO-SEP (Figure 5B).

UV-vis absorption spectroscopies of the SEP and supported catalysts are presented in Figure 5A. The raw SEP shows an extended profile in between 200 and 600 nm. In contrast, 0.25 M ZnO reveals its distinctive edge below 400 nm. The supported catalysts resemble this charac‐ teristic edge, which is more pronounced for the catalyst having the highest ZnO concentration. The UV activities of the supported catalysts are evidenced by the evaluated band-gap energies based on Kubelka-Munk transformed reflectance spectra as 3.08 eV for 0.125 M ZnO-SEP, 3.09

by the dominating Zn signals within less dense regions of Si and Mg constituents.

**Figure 3.** SEM and mapping images of 0.25 M ZnO-SEP.

238 Advanced Catalytic Materials - Photocatalysis and Other Current Trends

*3.1.4. XPS analysis*

*3.1.5. UV-vis DRS analysis*

Control experiments were performed under dark conditions for 0.25 M ZnO and 0.25 M ZnO-SEP (Figure 6). The remaining MO percentage was found as 83% in the presence of 0.25 M ZnO after 60 min, and then no significant variation was detected. The supported catalyst, however, shows a lower percentage (73%) in 80 min. The interaction between the SEP matrix and ZnO nanoparticles facilitated the adsorption of MO molecules. The low isoelectric point of the SEP (IEPSEP~2) increased the contact possibility of positively charged Zn2+ ions or ZnO (with high isoelectric point ~9) [18]. The attraction between positively charged Zn2+ ions and negatively charged MO moiety decreased the intensity of absorption band at 464 nm, which is responsible from the destruction of the chromophoric (-N=N-) group. The negligible photolysis of MO proves the active role of ZnO nanoparticles within the supported catalyst system. It is also noted that the raw SEP does not participate in the decolorization of MO (not shown).

The photoactivities of the supported catalysts were examined under irradiation (Figure 6, inset). The highest MO remaining percentage (43%) was obtained in the presence of 0.125 M ZnO-SEP within 120 min. The percentage of MO decreased upon the loading concentration of ZnO. The synergy established on the mixed structures of ZnO and SEP improved the catalyst performance. Accordingly, 0.5 M ZnO-SEP shows the best activity with the lowest MO remaining percentage (19.8%) in solution.

**Figure 6.** Photolysis and dark adsorption experiments. Inset: Photocatalytic activities of the supported catalysts.

The whole mechanism starts with the illumination of ZnO nanoparticles and production of electron-hole pairs (Eq. (1)).

$$\text{ZnO} + \text{h}\gamma \text{(UV)} \rightarrow \text{e}\_{\text{CB}} + \text{h}\_{\text{VB}} \text{ \textdegree \tag{1}$$

The main active species in such processes are known as hvb+ , ⋅ OH and O2 ⋅− [27,28]. The radicals may form either by the reactions of photogenerated holes or electrons. The photogenerated electron (ecb− ) can be easily transferred to the O2 molecules promoting the O2 ⋅− formation and then converted to the active ⋅ OH via hydrogen peroxide and hydroperoxyl radical generations (Eqs. (2)–(5)).

nanoparticles facilitated the adsorption of MO molecules. The low isoelectric point of the SEP (IEPSEP~2) increased the contact possibility of positively charged Zn2+ ions or ZnO (with high isoelectric point ~9) [18]. The attraction between positively charged Zn2+ ions and negatively charged MO moiety decreased the intensity of absorption band at 464 nm, which is responsible from the destruction of the chromophoric (-N=N-) group. The negligible photolysis of MO proves the active role of ZnO nanoparticles within the supported catalyst system. It is also

The photoactivities of the supported catalysts were examined under irradiation (Figure 6, inset). The highest MO remaining percentage (43%) was obtained in the presence of 0.125 M ZnO-SEP within 120 min. The percentage of MO decreased upon the loading concentration of ZnO. The synergy established on the mixed structures of ZnO and SEP improved the catalyst performance. Accordingly, 0.5 M ZnO-SEP shows the best activity with the lowest MO

noted that the raw SEP does not participate in the decolorization of MO (not shown).

**Figure 6.** Photolysis and dark adsorption experiments. Inset: Photocatalytic activities of the supported catalysts.

( ) - + ZnO + h UV e + h CB VB

g

The main active species in such processes are known as hvb+

The whole mechanism starts with the illumination of ZnO nanoparticles and production of

may form either by the reactions of photogenerated holes or electrons. The photogenerated

) can be easily transferred to the O2 molecules promoting the O2

® (1)

OH and O2

⋅− [27,28]. The radicals

⋅− formation and

, ⋅

remaining percentage (19.8%) in solution.

240 Advanced Catalytic Materials - Photocatalysis and Other Current Trends

electron-hole pairs (Eq. (1)).

electron (ecb−

$$\bullet \bullet\_{2} \text{+} \text{e}^{\cdot} \rightarrow \bullet \text{\_{2}}^{\cdot \text{-}} \tag{2}$$

$$\text{O}\_2\text{"} \text{"} \text{H}^+ \rightarrow \text{HO}\_2^\cdot\text{"}\tag{3}$$

$$\text{2HO}\_2^\* \to \text{H}\_2\text{O}\_2 \text{\textquotedblleft O}\_2 \tag{4}$$

$$\mathrm{H\_2O\_2} + \mathrm{O\_2}^- \rightarrow \mathrm{"OH} + \mathrm{O\_2} + \mathrm{OH}^- \tag{5}$$

At the same time, the photogenerated hvb+ can be captured on the catalyst surface undergoing charge transfer with adsorbed water molecules or with surface-bound hydroxide species to generate active ⋅ OH (Eqs. (6) and (7)) and results in the degradation of MO molecule (Eq. (8)).

$$\rm H\_{\rm vb}^{\cdot} + H\_2O \to H^{\prime} + \rm {}^{\bullet}OH \tag{6}$$

$$\text{CH}\_{\text{vb}}\text{}^{\text{+}}\text{OH}\text{'}\rightarrow\text{'OH}\tag{7}$$

$$\text{"OH} + \text{MO} \rightarrow \text{MO} \left( \text{decolorization and degradation} \right) \tag{8}$$

Thus, the separation of the charge carriers also enhanced the yield of hydroxyl radicals (highly reactive electrophilic oxidants) and improved the photocatalytic activity of the supported catalysts. The addition of the hydroxyl radical to the double bond of the azo group is referred to as the main reaction pathway, with the disappearance of the color. The second route followed the addition of hydroxyl radical to the aromatic rings [29,30]. Alternatively, hydroxyl radicals may attack the carbon atom bearing the azo bond [30]. Further attacks caused the formation of sulfonated intermediates, aromatic amine and phenolic compounds and ring open fragments [31].

Kinetic analysis was performed by varying the initial ΜΟ concentration from 16.2 to 3.27 mg L-1 in the presence of 0.5 M ZnO-SEP (not shown). The linearity obtained between ln(*C*0/*C*) versus *t* plot indicates pseudo-first-order kinetics, where *C*0 is the initial concentration of ΜΟ (mg L-1) and *C* is the concentration of ΜΟ (mg L-1) at irradiation time *t* (min) (Figure 7). The rate constants *k* (min-1) hence calculated (slopes of the lines) were found to decrease with increasing concentration of ΜΟ (from 0.01 (3.27 mg L-1) to 0.005 min-1 (16.2 mg L-1)). This can be a result of blocking of the photocatalytically active sites on the supported catalyst and reducing the interaction of photons with these sites.

**Figure 7.** Effect of initial MO concentration on the photoactivity of 0.5 M ZnO-SEP.

The stability of 0.5 M ZnO-SEP catalyst was examined by recycling experiments (Figure 8). For each run, 0.5 M ZnO-SEP was filtrated, washed and calcined at 500°C for 2 h. After four cycles, the percentage of MO remaining in solution was found to increase by only approximately 3% (from 19.8% to 22%). The slight increment in the percentage can be attributed to the catalyst loss during each collection and rinsing steps.

**Figure 8.** Reuse properties of 0.5 M ZnO-SEP.


2.2.6. Mantle Sills?

Although the mantle has proven far less heterogeneous than the crust, at least in terms of reflectivity, prominent mantle reflections have now been traced by a number of seismic reflection profiles. Perhaps the best known of these have been mapped by the BIRPS (British Institutions Reflection Profiling Syndicate) in northwestern Britain [79–81]. The mantle reflections which have received the most attention are dipping features, often interpreted as "fossil" subduction zones [82–85]. However, relative extensive subhorizontal reflections have also been observed in the mantle near Britain which resemble those in the upper crust that have been interpreted as sills (e.g., Figure 13). Some of these "flat" mantle reflections are spatially linked to the nearby dipping mantle reflections [86] and thus may be genetically related. In any case, they too may represent igneous sills, although other speculative explanations have been put forward (e.g., detachments [87]).

**Figure 13.** Strong, subhorizontal reflector in the mantle beneath northwest Great Britain from BIRPS marine data (After Snyder and Flack [86]). M indicates the position of the Moho at approximately 8 s (ca 25 km). Note that the top of this section corresponds to 5 s TWTT instead of the customary 0 s (surface).


*6.1.3 Sodium bicarbonate-based hydration*

The acidic PH promotes free radical production (which is found in tubular urine) [71], while elevated pH of normal extracellular fluid inhibits it [72, 73]. Since CM administration escalates the oxidative stress and increases the generation of free radicals and reactive oxygen species (ROS), alkalinizing renal tubular fluid with bicarbonate appears to be a logical strategy to protect against renal injury [74]. As a result of active reabsorption, bicarbonate concentration in the renal tubules lowers (to about 6mEq/L), and the tubular fluid pH is approximately 6.5 near the end of the proximal tubule in the renal medulla [75]. In the descending loop of Henle, water and chloride are passively reabsorbed. This elevates urine pH to ~7.4 at the tip of the papilla, and this part is spared from contrast nephropathy [76], which suggests that higher pH is protective. Also important is the observation that outer medulla is the most susceptible to CIN [62] and has acidic pH [72] that promotes activity of ROS. Superoxide, a ROS generated by ischemia, might react with medullary NO to produce the potent oxidant peroxynitrite [73]. At physiologic concentrations, bicarbonate scavenges peroxynitrite and other ROSs produced from NO [74]. Thus, several oxidant mechanisms of renal injury might be avoided using sodium bicarbonate. The useful effect of higher proximal tubular pH is approved by a report that acetazolamide, a carbonic-anhydrase inhibitor which blocks proximal tubular bicarbonate reabsorption, is protective in contrast-induced renal failure [77]. Merten et al. reported first study on the use of sodium bicarbonate in humans as a nephron-protective agent [78]. Patients received 154mEq/l of either NaCl (in 5% dextrose H2O) or sodium bicarbonate (in dextrose H2O), as a bolus of 3mL/kg/h for 1h before iopamidol contrast, followed by an infusion of 1mL/kg/h for 6h after the procedure. CIN occurred in 8 patients (13.6%) infused with NaCl but in only 1 (1.7%) of those receiving sodium bicarbonate (p = 0.02). Afterwards, many RCTs have compared the efficacy of sodium bicarbonate with saline hydration regarding the prophylaxis against CIN. These have been reviewed in multiple meta-analysis [79–82], which concluded that sodium bicarbonate-based saline hydration is more efficacious to saline hydration only.

#### *6.1.4 Pharmacological prophylaxis*

Various drugs have been assessed as prophylactic nephroprotective agents against contrast-induced acute kidney injury (CI-AKI) such as N-acetylcysteine (NAC) [36, 83], statins [84, 85], ascorbic acid [76, 86], and theophylline [87]. However, only statins have been approved for the prevention against the occurrence of CIN. Currently, the CM safety committee recommends the withdrawal of nephrotoxic drugs before CM administration [85].

#### *6.1.5 N-Acetylcysteine (NAC)*

NAC gives protection against CIN by improving the body's antioxidant abilities [88]. In vitro, NAC does this efficiently by scavenging hypochlorous acid as well as reacting with hydroxyl radicals [89]. In vivo due to its extensive degradation, it is likely that any antioxidant effect it exerts would be indirect, most probably by inducing glutathione synthesis. Different studies have suggested that NAC guards against glutathione depletion [90, 91] and elevates renal glutathione levels [92]; the latter has been demonstrated to result in the reduction of renal injury in ischemia reperfusion models [93, 94] and recently in CIN [95, 96]. Glutathione cannot enter the cell; instead, it must be formed inside the cell from glycine, glutamate, and cysteine [97]. Cysteine offers the active HS group which is crucial for the glutathione synthesis and thus is the rate-limiting factor in this process. NAC after deacylation produces cysteine that passes to the renal cells and serves as a precursor for glutathione synthesis. It can also produce vasodilator effects [98]. By ameliorating contrast-induced vasoconstriction, NAC can produce its nephron-protective role [99]. Increase in the medullary blood flow with NAC has also been demonstrated [100, 101]. The first clinical use of NAC for CIN was reported by Tepel et al. [83]. Eighty-three patients who had chronic renal impairment were randomly planned either to take oral NAC (600mg twice daily) and 0.45% saline intravenously, before and after administration of the CM, or to receive placebo and saline. NAC-receiving patients had lower incidence of CIN. Since then numerous studies have assessed the role of NAC against CIN. Those studies have been done mainly in patients undergoing coronary angiography [102]. Some 17 meta-analyses have been published as regards this subject [76, 86, 87, 103–116], 10 that approve its use (most of which were published early on). Most of these meta-analyses reported vast heterogeneity that makes it difficult to make clinical treatment recommendations relying on the provided data. Recently, results of the largest multicenter RCT of 2308 patients called "Acetylcysteine for Contrast-Induced Nephropathy Trial" (ACT) have been published [36]. It randomized patients in 46 centers in Brazil, to take 1200mg of oral NAC or placebo twice daily for 2 doses before and after the procedure. Intravenous hydration with normal saline, 1mL/kg/h, from 6–12h before to 6–12h after angiography, was strongly recommended. NAC was not able to significantly reduce the incidence of CIN (12.7% in the NAC group and 12.7% in the control group, p = 0.97) [117].

#### *6.1.6 Ascorbic acid*

Ascorbic acid serves as an antioxidant [118]. It does this via reacting with most biologically relevant free radicals and oxidants such as superoxide ions and hydroxyl ion [119]. It donates an electron to devastating oxidizing radicals [120]; this oneelectron oxidation leads to the formation of AHˉ the ascorbyl radical also called semidehydroascorbic acid [121]. Consequently, the reactive free radical is reduced [122]. Ascorbic acid has been reported to result in vasodilatation in coronary [123] and brachial arteries [124]. Thus, vitamin C can have favorable effects on vascular dilatation, through its antioxidant actions on nitric oxide, but these findings are not consistent [125]. Through which pathway vitamin C may offer nephron protection against CIN is still currently uninvestigated. The first clinical use of ascorbic

**129**

*6.2.2 Theophylline*

*Contrast-Induced Nephropathy*

*DOI: http://dx.doi.org/10.5772/intechopen.90457*

by the contrast media safety committee.

statins are warranted [129].

*6.2.1 High-dose versus low-dose statins*

**6.2 Statins**

acid for CIN prevention was reported by Spargias and his colleagues [116]. Two hundred and thirty-one patients were summoned and randomized to obtain either 3g of ascorbic acid supplied in chewable tablets or placebo at least 2h prior to the beginning of the required procedure. This was followed by 2g of ascorbic acid or placebo the night and the morning post-procedure. Intravenous hydration with normal saline at a rate of 50–125mL/h was started in every patient till at least 6 h post-procedure. Incidence of CIN was less in ascorbic acid group (9%) and 20% in control group (p = 0.02). A considerable change in the antioxidant state was noticed in the group treated with ascorbic acid. Since then various RCTs have been performed [126, 127]. Pooled analysis of these trials assumed that patients who receive ascorbic acid have 33% less risk of CIN in comparison with patients receiving placebo or alternative pharmacological therapy (RR: 0.67 (95% CI: 0.46–0.96), p = 0.03) [100]. This indicates that ascorbic acid provides effective nephron protection in the face of CIN and may form a part of efficient prophylactic pharmacological regimens. However, the utilization of ascorbic acid has not yet been recommended

Statins maintain nitric oxide formation, lower oxidative stress, and beneficially affect the endothelial function [101]. In one retrospective study of more than 1,000 patients with renal impairment undergoing coronary angiography, the risk of CIN was markedly decreased in patients who are receiving a statin before the procedure [128]. Another study of more than 29,000 patient recorded in a percutaneous cardiac intervention registry demonstrated that patients who received statins before the procedure had both a lower CIN incidence (p < 0.0001) and nephropathy that required dialysis (p < 0.03) [181]. Further studies looking into the benefit from

High-dose statin therapy may be theoretically more efficacious regarding CIN prevention as a result of acute suppression of inflammatory chemokines [130]. Xie and his colleagues investigated the potency of high-dose statins (simvastatin 80mg, atorvastatin 40 and 80 mg) compared with low-dose statins (simvastatin 20 mg, atorvastatin 10 and 20mg) and revealed that high-dose statins lowered the incidence of CIN [131]. These results were backed up by a recent meta-analysis which showed that high-dose statins (atorvastatin 80 mg, simvastatin 80 mg) in comparison with low-dose statins (atorvastatin 10 and 20 mg, simvastatin 20 mg) in patients having acute coronary syndromes resulted in a relative risk ratio for CIN of 0.46 (4.5 vs 10.2%, p = 0.004); however, it was not of considerable significance among patients performing elective procedures [132]. However, high-dose statins

are guideline recommended medications to lower the risk of CIN.

Adenosine has been implicated to be a responsible factor for mediating CM-enhanced renal vasoconstriction [133–135]: hence the use of adenosine antagonists appears logical [136]. Theophylline and aminophylline have been often used to measure their efficacy as adenosine receptor antagonists in guarding against contrast-induced acute kidney injury (CI-AKI). Various randomized trials have used theophylline [20, 137, 138]. A meta-analysis of those studies guided to the fact that theophylline considerably lowers the risk of CIN (RR: 0.48; 95% CI: 0.26–0.89;

#### *Contrast-Induced Nephropathy DOI: http://dx.doi.org/10.5772/intechopen.90457*

acid for CIN prevention was reported by Spargias and his colleagues [116]. Two hundred and thirty-one patients were summoned and randomized to obtain either 3g of ascorbic acid supplied in chewable tablets or placebo at least 2h prior to the beginning of the required procedure. This was followed by 2g of ascorbic acid or placebo the night and the morning post-procedure. Intravenous hydration with normal saline at a rate of 50–125mL/h was started in every patient till at least 6 h post-procedure. Incidence of CIN was less in ascorbic acid group (9%) and 20% in control group (p = 0.02). A considerable change in the antioxidant state was noticed in the group treated with ascorbic acid. Since then various RCTs have been performed [126, 127]. Pooled analysis of these trials assumed that patients who receive ascorbic acid have 33% less risk of CIN in comparison with patients receiving placebo or alternative pharmacological therapy (RR: 0.67 (95% CI: 0.46–0.96), p = 0.03) [100]. This indicates that ascorbic acid provides effective nephron protection in the face of CIN and may form a part of efficient prophylactic pharmacological regimens. However, the utilization of ascorbic acid has not yet been recommended by the contrast media safety committee.


**3.2 QoS applied to multimedia TCP flows (no min/max bandwidth set)**

The second campaign aimed at verifying the efficiency of the QoS management server. The Iperf was moved in the (C) node, so as to check Link 3.

An ethernet cable subsituted the wireless connection during a PPP connection. Delays and packet loss, in fact, are not particularly relevant in this kind of control, attention being mainly focused on flow management.

The following tools were adopted: (1) QoS Server; (2) Server-side Vlc for MMS over http video flow transmission (www.videolan.org/vlc); (3) Client-side Vlc for flow reception; (4) WireShark.

Fig. 7, diagrammed through WireShark, represents the scenario and the first measurements of this campaign. It refers to the following profile: no QoS applied, symmetric upload and dowmlod of 1Mbit/s, no bandwidth guaranteed. The client receives the first video (red line) until second 230, then the second video (green line) starts and the firts one is interrupted at second 280.

As expected, in the concurrent period (sec. 230 to 280) both TCP videos are blocked, the bandwidth being inadequate to support both of them.

Fig. 8 represents the second test and involves three videos on three distinct ports; in this case, a QoS profile was enabled which guarantees an increasing priority from the first to the third flow.

First starts the video on the lowest priority port (blue curve); the intermediate priority video starts 20 seconds later (green curve) and, in consequence, the first data flow declines. In the period between sec. 40 to 80 the maximum throughput was increased, so as to emphasize the effect of dark and still scenes in the second video. In this way, the total throughput is constant and bandwidth waste is kept under control.

A Testbed About Priority-Based Dynamic

priority flow starts (red curve).

such method and Fig. 10 reports the results.

Fig. 9. TCP concurrent flows with QoS (bit/s).

totally flattened, but only slowed down.

can not reach the maximum speed.

**Class Priority level Min. bandwidth %**

1 Highest priority 0% 100% 2 Intermediate 30% 30% 3 Lowest priority 20% 100%

ones.

flows.

Connection Profiles in QoS Wireless Multimedia Networks 87

Nevertheless, this kind of priority management among traffic classes implies the almost complete cancellation of the less important services for the benefit of the most important

In the initial QoS profile, an increasing priority was assigned to the three TCP flows on distinct ports. Fig. 9 shows the measures obtained. The less priority flow (blue curve) is strongly limited by the second one (green curve). They are both flattened when the highest

In order to improve such results, each traffic class was then assigned a minimum and a maximum throughput (Tab. 3). The third campaign tries to demonstrate the effectiveness of

**guaranteed**

Table 3. minimum throughput guaranteed and maximum available, as assigned to single

Note that an upper bound having been imposed to the intermediate flow, the lowest is not

The most priority flow starts at second 50 and, in consequence, the less priority traffic becomes slower, but not more than the 20% guaranteed. The same applies to the intermediate flow, for which a 30% at least is available. The highest priority flow, of course,

**Max. bandwidth % at disposal**

Fig. 7. two concurrent video flows without QoS (bit/s): scenario and results.

The same observations apply to the third and highest priority flow (red curve): the three videos share the bandwidth and, thanks to QoS, the lowest priority one is flattened, the medium is assigned less bandwidth and the highest has the best quality.

Fig. 8. three concurrent videos with QoS (bit/s).

#### **3.3 Bandwidth control in QoS management**

As the previous measurements showed, the QoS policy adopted helps to avoid bandwidth waste and guarantees a better service, especially for VoIP, IPTV support etc.

Fig. 7. two concurrent video flows without QoS (bit/s): scenario and results.

medium is assigned less bandwidth and the highest has the best quality.

Fig. 8. three concurrent videos with QoS (bit/s).

**3.3 Bandwidth control in QoS management**

The same observations apply to the third and highest priority flow (red curve): the three videos share the bandwidth and, thanks to QoS, the lowest priority one is flattened, the

As the previous measurements showed, the QoS policy adopted helps to avoid bandwidth

waste and guarantees a better service, especially for VoIP, IPTV support etc.

Nevertheless, this kind of priority management among traffic classes implies the almost complete cancellation of the less important services for the benefit of the most important ones.

In the initial QoS profile, an increasing priority was assigned to the three TCP flows on distinct ports. Fig. 9 shows the measures obtained. The less priority flow (blue curve) is strongly limited by the second one (green curve). They are both flattened when the highest priority flow starts (red curve).

In order to improve such results, each traffic class was then assigned a minimum and a maximum throughput (Tab. 3). The third campaign tries to demonstrate the effectiveness of such method and Fig. 10 reports the results.

Fig. 9. TCP concurrent flows with QoS (bit/s).

Table 3. minimum throughput guaranteed and maximum available, as assigned to single flows.

Note that an upper bound having been imposed to the intermediate flow, the lowest is not totally flattened, but only slowed down.

The most priority flow starts at second 50 and, in consequence, the less priority traffic becomes slower, but not more than the 20% guaranteed. The same applies to the intermediate flow, for which a 30% at least is available. The highest priority flow, of course, can not reach the maximum speed.

A Testbed About Priority-Based Dynamic

redistributed.

years.

of the most relevant ones.

Connection Profiles in QoS Wireless Multimedia Networks 89

The two clients share the same profile, so the bandwidth is equally divided and

At second 150 the third client (red curve) connects to the system; the minimum throughput of his or her profile is four times the others', so clients 1 and 2 are limited accordingly.

When client 1 disconnects, bandwidth is distributed among clients 2 and 3 in a ratio of 1 to 4.

Finally, client 3 logs out and the whole bandwidth is at client's 2 disposal.

Fig. 11. bandwidth proportional reassignment among connected users.

Smart Navigation and the braoader field of Infomobility.

**4. The PEGASUS project: Real time support in infomobility services**

2050, nearly 70% of the global population will be living in larger cities [23].

One of the most important applications to which QoS techniques have been applied are

Transportation is one of the main fields where advanced technological systems can improve human life in a significant way: risks due to accidents, time wasted travelling and pollution could be highly reduced by applications for vehicle localization, behaviour prediction, etc. These considerations are at the basis of the increasing interest that ITS are gaining in these

Furthermore, the latest study on global urbanization conducted by the Population Division of the Department of Economic and Social Affairs of the United Nations predicts that, in

This immense aggregation of people will surely pose great challenges to the sustainability of modern lifestyle, and the problem of an efficient management of mobility stands out as one

As this measure shows, if guaranteed bandwidth percentages are properly managed, a high QoS can be obtained in an easy and immediate way.

Fig. 10. TCP concurrent flows with bounded bandwidth QoS (bit/s).

### **3.4 Proportional reassignment of bandwidth**

An important feature that must be handled in this kind of QoS management is bandwidth reassignment proportionally to each user's minimum guaranteed.

In this case, three PCs and the usual tools were adopted and two kinds of profiles were defined (Tab. 4).

Table 4. Minimum and maximum throughput for each client.

Clients were connected to the server through the PPPoE protocol; the maximum throughput between clients and server was set to 3Mbit/s, so as to simulate a set of wireless relays.

In this case, the upper bandwidth was to be shared among concurrent users and, in consequence, none was to reach the maximum.

Results are shown in Fig. 11: initially, the only connected client 1 (green curve) gets the whole bandwidth available according to his profile (3 Mbit/s).

After 100 seconds approximately, client 2 is also connected, throughput is assigned according to the minimum guaranteed and exceeding bandwitdh is reassigned according to such value.

As this measure shows, if guaranteed bandwidth percentages are properly managed, a high

QoS can be obtained in an easy and immediate way.

Fig. 10. TCP concurrent flows with bounded bandwidth QoS (bit/s).

reassignment proportionally to each user's minimum guaranteed.

Clients 1 and 2 128 Kbit/s 3 Mbit/s Client 3 600 Kbit/s 3 Mbit/s

Table 4. Minimum and maximum throughput for each client.

whole bandwidth available according to his profile (3 Mbit/s).

An important feature that must be handled in this kind of QoS management is bandwidth

In this case, three PCs and the usual tools were adopted and two kinds of profiles were

**Clients Min. guaranteed Max. at disposal**

Clients were connected to the server through the PPPoE protocol; the maximum throughput between clients and server was set to 3Mbit/s, so as to simulate a set of wireless relays.

In this case, the upper bandwidth was to be shared among concurrent users and, in

Results are shown in Fig. 11: initially, the only connected client 1 (green curve) gets the

After 100 seconds approximately, client 2 is also connected, throughput is assigned according to the minimum guaranteed and exceeding bandwitdh is reassigned according to

**3.4 Proportional reassignment of bandwidth**

consequence, none was to reach the maximum.

defined (Tab. 4).

such value.

The two clients share the same profile, so the bandwidth is equally divided and redistributed.

At second 150 the third client (red curve) connects to the system; the minimum throughput of his or her profile is four times the others', so clients 1 and 2 are limited accordingly.

When client 1 disconnects, bandwidth is distributed among clients 2 and 3 in a ratio of 1 to 4.

Finally, client 3 logs out and the whole bandwidth is at client's 2 disposal.

Fig. 11. bandwidth proportional reassignment among connected users.