**4. Conclusions**

There is an abundance of EOQ models based on Wilson's formulation. Although differing in purpose, application type, or calculation principles and providing quite precise predictions for a demand per selected time interval, all these models contain the same drawback. Being based on a logic of calculating costs per one order and multiplying it by number of orders, they all fail to meet the current needs of business environments in order to be applied in practice.

We propose the modification of EOQ based on a different calculation technique which shows significant savings in warehouses costs under particular conditions.

From the proposed models, the most significant savings were observed using the 2nd variation of the first proposed model and accounted for approximately 2% of all inventory costs. The highest potential for application in practice shows the first and second variations of a fourth model due to the ability to cope with the most uncontrolled variables as the retail sector is characterized by constant shifts in demand and supply which are reflected in prices in a nonlinear manner [52]. The savings in this case would amount to 0.4% when the price of stored goods increases under particular conditions (first variation of a fourth model) and to 1.3% when price decreases (second variation of a fourth model) under researched conditions.

The limitations of our proposed models are comprised of delivery costs and price for goods to be described by uniform trend. Thus, in the future, the model could be extended to investigate the inventory management where exogenous parameters do not follow any uniform trend.

**Author Contributions:** Conceptualization, T.N. and J.P.; methodology, T.N. and M.M.; formal analysis, T.N. and A.V.; resources, D.S. and T.B.; writing—original draft preparation, T.N., A.V., and M.M.; writing—review and editing, T.B. and D.S. All authors have read and agreed to the published version of the manuscript.

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

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


**5. Conclusions**

Ag/Ag2O was found to enhance the rate of light-induced bleaching of aqueous methylene blue under both UV/vis and vis illumination, in comparison to the bleaching in homogeneous solution. Even in suspensions containing mixtures and composites of Ag/Ag2O with TiO2 (P25), with varying mass ratios of Ag/Ag2O (20%, 50%, and 80%), the reaction rate was slightly increased under these illumination conditions. However, the bleaching rate of methylene blue was lower in the presence of the composites and mixtures than the rate measured for bare Ag/Ag2O. It is therefore suggested that the bleaching of methylene blue is initiated by an interfacial electron transfer from the excited organic probe compound to Ag2O. TiO2 layers covering the Ag2O seem to inhibit this electron transfer. Since Ag2O can transfer an electron neither to dissolved molecular oxygen nor to a proton for thermodynamic reasons, it is assumed that Ag<sup>+</sup> is reduced to Ag(0) in the processes investigated here. Results of XRD and XPS measurements support this assumption, and indicate that Ag/Ag2O is not stable under the experimental conditions employed in this study. A stabilization of Ag2O by metallic silver, as occasionally claimed, was not observed. Therefore, to address Ag/Ag2O as a (photo)catalytically active material does not seem appropriate.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/2073-4344/8/12/647/s1, Figure S1. EDX diagrams of all prepared photocatalysts. Figure S2. XRD patterns of TM 11 photocatalyst after one cycle of MB bleaching employing UV/vis light. Figure S3. XPS spectra of Ag 3d, O 1s and Ti 2p in the Ag/Ag2O, TM and TC materials. Figure S4. Emission spectrum of the used Xenon lamp. Figure S5. UV/vis spectra of aqueous methylene blue solutions obtained during illumination with visible light in the presence of Ag/Ag2O. Figure S6. Calibration curve for H2 experiment.

**Author Contributions:** Experiments and analysis: S.A.; XPS measurements: J.K.; Redaction of manuscript: S.A., R.D. & R.B.; Review: R.D.; R.B. & N.O.B.; Scientific support: R.D.; Supervision: D.W.B. & M.E.A.

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

**Acknowledgments:** The authors wish to thank Luis Granone for XRD measurements and Stephanie Melchers for SEM/EDAX images.

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


*Article* **Effect of Confining Conditions on the Hydraulic Conductivity Behavior of Fiber-Reinforced Lime Blended Semiarid Soil**

**Abdullah Ali Shaker 1, Mosleh Ali Al-Shamrani 1,\*, Arif Ali Baig Moghal 2,\* and Kopparthi Venkata Vydehi 2**

**Abstract:** The hydraulic properties of expansive soils are affected due to the formation of visible cracks in the dry state. Chemical stabilization coupled with fiber reinforcement is often considered an effective strategy to improve the geotechnical performance of such soils. In this study, hydraulic conductivity tests have been conducted on expansive clay using two different types of fibers (fiber cast (FC) and fiber mesh (FM)) exhibiting different surface morphological properties. The fiber parameters include their dosage (added at 0.2% to 0.6% by dry weight of soil) and length (6 and 12 mm). Commercially available lime is added to ensure proper bonding between clay particles and fiber materials, and its dosage was fixed at 6% (by dry weight of the soil). Saturated hydraulic conductivity tests were conducted relying on a flexible wall permeameter on lime-treated fiberblended soil specimens cured for 7 and 28 days. The confining pressures were varied from 50 to 400 kPa, and the saturated hydraulic conductivity values (ksat) were determined. For FC fibers, an increase in fiber dosage caused ksat values to increase by 9.5% and 94.3% for the 6 and 12 mm lengths, respectively, at all confining pressures and curing periods. For FM fibers, ksat values for samples mixed with 6 mm fiber increased by 12 and 99.2% for 6 and 12 mm lengths, respectively for all confining pressures at the end of the 28-day curing period. The results obtained from a flexible wall permeameter (FWP) were compared with those of a rigid wall permeameter (RWP) available in the literature, and the fundamental mechanism responsible for such variations is explained.

**Keywords:** confining pressure; expansive clay; fiber; flexible wall permeameter; hydraulic conductivity; lime; rigid wall permeameter


4.3.2. Transition States Probability of Markov Chains 2

The results of the Markovian approach on the 1953–2015 series show that the probability of obtaining a dry year after two successive dry years (D-D-D) is high in the areas of Sassandra (67%) and Gagnoa (59%). As for the stations of Seguéla (51%), Soubré (55%) and Touba (50%) located in an equatorial regime of attenuated transition (Baoulean climate), they recorded average values. At the other stations, this probability is low (<50%) (Table 7). The probability of having a dry year between two wet years (W-D-W), a wet year followed by two successive dry years (W-D-D) and a wet year after two dry years (D-D-W) is very low over the entire basin. The averages recorded are 24%, 20.4% and 16.9%, respectively. Overall, the probability of having three consecutive dry years (D-D-D) is relatively low in the basin (44.8% on average). The most affected regions are those in the southern part of the basin.

**Table 7.** Occurrence of meteorological droughts using Markov Chains 2 over the period 1953–2015.

Note: D: Dry year; W: Humid year.

The results of the occurrence of three successive dry years over the periods 1953–1970 and 1971–2015 are shown in Table 8.

During the period 1953–1970, the probability of having three successive dry years is relatively low at all stations except the Odienné station where this probability is 60%. In the regions of Man, Soubré, Vavoua and Daloa, the probability of having three successive dry years is zero.

During the period 1971–2015, the probability to observe (D-D-D) is high and higher than 50% at Seguéla (60%), Touba (63%) and the maximum is reached at Sassandra (70%). As for the rest of the stations, the probability is low and less than 50%.

**Table 8.** Occurrence of meteorological droughts using Markov Chains 2 over the periods 1953–1970 and 1971–2015.

Note: D: Dry year; W: Humid year.


2.2.7. Juice Panel Test Index (PTI)

Five persons judged random fruit samples from each replicate to give PTI scores according to the following index: Excellent taste = 4; Very good taste = 3; Good taste = 2; Acceptable taste = 1, and Bad taste (unacceptable fruits)=0[63].

### *2.3. Enzymes and Antioxidant Determination*

### 2.3.1. Preparation of the Extract

The mandarin peels were ground after drying in a vacuum oven (45 ◦C), and 10 g of each powder sample was taken and then homogenized in 100 mL of 50% ethanol (1:10, *w*/*v*) stirred for 3 h at room temperature. The samples were filtered to obtain the supernatant. Then the solvent was disposed of with a rotary evaporator [64].

### 2.3.2. DPPH Radical Scavenging Assay

The total antioxidant activities in the mandarin peel extracts with different treatments at a concentration of (500 μg/mL) were examined according to [65]. We mixed 100 μL of each solution with 1 μL of ethanolic DPPH in the microtiter plate wells and incubated it at room temperature in the dark for 30 min. A microtiter plate reader (BioTek Elx808, USA) was used to measure the absorbance at 517 nm b and then applied Equation (2).

$$\text{Radical savinging activity} \left( \% \right) = \frac{(\text{Abs. control} - \text{Abs. sample})}{(\text{Abs. control})} \times 100 \tag{2}$$

### 2.3.3. Catalase Activity (CAT)

CAT activity was assayed by using Biodiagnostic, Kit No. CA 25 17, Egypt, according to the method described by [66,67]. The formed chromophore absorbance was inversely proportional to the amount of catalase in the experimented sample [68]. Briefly, we mixed 0.05 mL of the sample, 0.5 mL of phosphate buffer (pH = 7), and 0.1 mL of chromogeninhibitor and incubated for one min at room temperature, added 0.50 mL H2O2 and 0.20 mL chromogen-inhibitor to the mixture then incubated for 10 min at 37 ◦C. The decrease in absorbance was recorded at 510 nm.

### *2.4. Statistical Analysis*

Before running a one-way ANOVA, pretests were conducted. We tested the normality assumption on sample distributions and obtained *p*-values of 0.0001. for homogeneity; we used the Levene test with *p*-value = 0.01598. The triplicate data means were analyzed for statistical differences by one-way ANOVA at a confidence level of 95% [69], using Costat program version 6.4 (Costat 2008). The sample size was calculated using the following Equation (3)

$$m = \left(\frac{ZSD}{E}\right)^2\tag{3}$$

Means were compared with the least significant difference (LSD) as a post hoc test at a probability level of 5%.

### **3. Results**

### *3.1. Discarded Fruit %*

After harvest, citrus fruits are considered perishable and vulnerable to quality decline due to rot and water loss from transpiration and respiration [6]. The data referred to the influence of various postharvest treatments on discarded fruit percentage of Murcott mandarins, regardless of the cold storage period, as illustrated in (Table 1).

**Table 1.** Effect of postharvest treatments on discarded fruit percentage (DFP%) of Murcott mandarin fruits during 1, 2, 3, and 4 months of cold storage and after 6 days of shelf life during 2018 and 2019 seasons.

IMZ = imazalil, lowercase letters in the same column indicate significant difference, while uppercase letters in the rows and columns indicate significant difference between means by LSD at a 0.05 level.

This data indicated that, compared with other treatments, coating with wax plus 100 ppm nanosilver and packaging in perforated polyethylene (PPE) was the best treatment for reducing the percentage of discarded fruit during the two seasons of a study in 2018 (Table 1) and 2019 (Table 1). Moreover, coating wax and nano silver at 50 or 100 ppm reduced discarded fruit percentage relative to the control, which gave the highest ratio. Coating with nano silver at 50 or 100 ppm significantly affected the discarded fruit percentage.

The control treatment could be seen, regardless of shelf-life period, to have the highest discarded fruit percentage compared to the combination of wax mixed with 100 ppm nanosilver and packaged in PPE, which recorded the lowest percentage. Moreover, all other treatments were more effective in reducing the discarded fruit percentage relative to the control. Coating with wax and 50 ppm nanosilver and packaging in PPE treatments had a similar effect on discarded fruit percentage (Table 1).

Concerning the influence of the cold storage period on the discarded fruit percentage of Murcott mandarins, it was evident that after the second month of cold storage, the rate of discarded fruit increased as the cold storage period progressed, reaching the highest percentage after four months of cold storage (Table 1). The previous trend was typically repeated as the shelf-life period progressed in the two seasons of study.

The interaction between postharvest treatments and cold storage also affected the discarded fruit percentage. There was a significant increase in the discarded fruit percentage in the control treatment compared with other used treatments after the fourth month of cold Storage. On the other hand, coating treatments with nano silver—at both unmixed concentrations or at 100 ppm mixed with wax—were more effective in reducing the percentage of discarded fruit (similar in their effect) compared to using a wax coating alone or the control by the end of cold storage. This trend of results was nearly similar to that obtained with the interaction effect between postharvest treatments and shelf-life period, with one exception being that coating with nanosilver (100 ppm) alone before packaging in PPE had the greatest ability to reduce the percentage of discarded fruit relative to other treatments after the last period of shelf life in both seasons (Table 1).

### *3.2. Weight Loss %*

Fruit weight loss is primarily connected to water loss, mainly because transpiration, which is responsible for 90% of overall weight reduction, initially originates from the peel [70–72]. The data in Table 2 demonstrate that during the 2018 and 2019 seasons, the percentage of weight lost generally rose with longer storage times in both the cold storage and shelf-life periods.

**Table 2.** Effect of postharvest treatments on fresh weight loss percentage (FWL%) of Murcott mandarin fruits during 1, 2, 3, and 4 months of cold storage and after 6 days of shelf life during the 2018 and 2019 seasons.

IMZ = imazalil, lowercase letters in the same column indicate significant difference, while uppercase letters in the rows and columns indicate significant difference between means by LSD at a 0.05 level.

Furthermore, the results showed that all applications significantly decreased weight loss compared to the control during both the cold storage period (Table 2) and days of shelf life (Table 2), and the applied treatments nanosilver (100 ppm) and wax with nanosilver (100 ppm) with packaging in perforated polyethylene (PPE) were more effective.at reducing weight loss.

Furthermore, the most pronounced effect in reducing the weight loss percentage was recorded by combining a wax coating and 100 ppm nanosilver, and packaging the sample in PPE. Moreover, coating with wax and nanosilver at either 50 or 100 ppm reduced the fresh weight loss percentage of mandarins relative to the control.

In this respect, the data in Table 2 indicates the effect of the postharvest treatments, cold storage period, and their interaction with the fresh weight loss percentage of Murcott mandarins. This data showed that after the first month of cold storage (Table 2), all applied treatments were capable of reducing weight loss compared with the control. The differences among these treatments were not big enough to be significant except for "coated with 100 ppm nanosilver"—alone or mixed with wax and packaged in PPE. The weight loss percentage for all applied treatments tended to increase significantly with the advancement of cold storage.

Similar results were nearly found when discussing the interaction effect between used postharvest treatments and shelf-life (Table 2) duration, except for the combination consisting of wax plus 100 ppm nanosilver and packaging in PPE, which was able to record the lowest weight loss percentage as compared with other treatments after the last period of shelf life, especially in the second season (Table 2).

### *3.3. Pulp Firmness*

The strength and fruit hardness of coated mandarins were significantly improved. In comparison, uncoated fruit undergoes tissue suppleness with time while being stored [53,73]. For both coated and uncoated fruits, there is no discernible change in fruit firmness during the first few days of low-temperature storage; rather, variations emerge over time [74].

The effect of postharvest treatments during the cold storage period on pulp firmness during the 2018 and 2019 seasons is displayed in Table 3. The data revealed that the combination consisting of coating with wax plus 100 ppm nanosilver and packaging in perforated polyethylene (PPE) was the most effective treatment for reducing the loss of pulp firmness, and it gave the greatest value of firmness as compared with other used treatments. In addition, all applied treatments recorded a higher firmness value than the control treatment, which showed the lowest value. This trend was stable in the two seasons of study (Table 3).

During the shelf-life period, it could be noticed that coating with wax mixed with 100 ppm nanosilver and packaging in PPE had a more elevated value for pulp firmness. Moreover, other treatments also caused a higher firmness value relative to the control treatment in both seasons (Table 3). On the contrary, mandarins treated with imazalil and packaged in PPE had the lowest firmness value.

### *3.4. Vitamin C Content*

Due to acid consumption as respiration substrates, ascorbic acid degrades over time when stored [75]. Nevertheless, the data shown in Table 4 indicated that the highest content of vitamin C in the juice of Murcott mandarin was obtained by coating with either wax, 50 ppm nanosilver, or the combination of wax and 100 ppm nanosilver treatments with packaging in perforated polyethylene (PPE) during cold storage period effect in the two seasons of study (Table 4). The highest impact was demonstrated by the last treatment (the combination of wax and 100 ppm nanosilver), which maintained the highest content of vitamin C. In contrast, both seasons found the least vitamin C content in the control treatment (imazalil followed by packaging in PPE).

The same trend was noticed throughout the shelf-life periods (Table 4) consistently during the two seasons of study. All used treatments recorded higher vitamin C content than the control. Moreover, samples coated in all treatments with wax and others before packaging in PPE were similar in their vitamin C content in the 2019 season (Table 4).

**Table 3.** Effect of some postharvest applied treatments on pulp firmness (g/cm2) of Murcott mandarin fruits during 1, 2, 3, and 4 months of cold storage and after 6 days of shelf life during 2018 and 2019 seasons.

IMZ = imazalil, lowercase letters in the same column indicate significant difference, while uppercase letters in the rows and columns indicate significant difference between means by LSD at a 0.05 level.

**Table 4.** Effect of some postharvest applied treatments on vitamin C content (mg/100 mL juice) of Murcott mandarin fruits during 1, 2, 3, and 4 months of cold storage and after 6 days of shelf life during 2018 and 2019 seasons.

IMZ = imazalil, lowercase letters in the same column indicate significant difference, while uppercase letters in the rows and columns indicate significant difference between means by LSD at a 0.05 level.

### *3.5. Panel Taste Index*

In recent studies, 46 different mandarin varieties belonging to several natural subgroups were examined for wide genetic variability in numerous fruit-quality features, including physical, physiological (ripening period), nutritional composition, and sensory attributes [76].

Nevertheless, the effects of some postharvest treatments in the cold storage period are shown in Table 5. The data indicated that all used treatments gave an excellent taste index for Murcott mandarins, with significant differences relative to the control treatment in both seasons. The same trend was observed with the effect of used postharvest treatments throughout the shelf-life period in both study seasons (Table 5).

**Table 5.** Effect of some postharvest applied treatments on taste panel index (PTI) of Murcott mandarin fruits during 1, 2, 3, and 4 months of cold storage and after 6 days of shelf life during 2018 and 2019 seasons.

IMZ = imazalil, lowercase letters in the same column indicate significant difference, while uppercase letters in the rows and columns indicate significant difference between means by LSD at a 0.05 level.

Concerning the influence of the cold storage period and shelf-life period on the taste panel index, the results introduced in Table 5 showed that the "excellent" taste panel index was noted after the first month of cold storage. Subsequently, the taste panel index decreased gradually by the end of cold storage in both seasons.


**7. Conclusion**

The analysis of the represented data shows that for the age period 4–6 there is a process of dynamic maturation of the right-brain structures of the ventral visual system and their connections to the structures of the prefrontal cortex, leading to gradual improvement of the children's abilities for visual discrimination of objects in difficult circumstances (incomplete images). Impact on the development of complex forms of non-verbal visual gnosis has the combination of age, demographic and gender factors, among which a special place is the age of 5 years. The positive dynamics of the mechanisms of holistic processing of complex non-verbal stimuli started in the pre-school period, but their formation continued in the next stages. Particular attention is paid to the fact that over the 6-year period most of the children with typical development continue to show great difficulty in recognizing incomplete images. They enroll at school with underdeveloped perceptual and control functions, which is why the group should be considered as risky for the development of dyslexic symptoms.

The neuropsychological probe "Recognition of incomplete images" is a sensitized option for the diagnosis of non-verbal visual gnosis in childhood. It has a high prognostic value and allows an early detection of cases of delayed development within the broad childhood norm. The application of the task (in isolation or in combination with others) supplemented by a competent quantitative and qualitative analysis responds to the leading tendencies in modern child neuropsychology and allows the timely identification of children at risk of learning difficulties.