Introduction: Infiltration is found to be the most important process that influences uniformity and efficiency of surface irrigation. Prediction of infiltration rate is a prerequisite for estimating the amount of water entering into the soil and its distribution. Since the infiltration properties are a function of time and space, a relatively large number of field measurements is needed to represent an average of farm conditions (Bautista and Wallender, 1985). In recent years, researchers have proposed methods to reduce the requirement of the regional and field data in order to describe water dynamic in the soil. One of these methods is SCALING which at the first was presented by Miller and Miller (1956) and developed on the similar media theory in the soil and water sciences (Miller and Miller, 1956; Sadeghi et al., 2016). According to similar media theory, soils can be similar, provided that different soils can be placed on a reference curve with ratios of a physical characteristic length, called "SCALING factor". The objective of the present study was SCALING the Philip infiltration EQUATION and analyzing the spatial variability of infiltration characteristics by using minimum field measurements. In this research, a new method was presented for SCALING infiltration EQUATION and compared with previous methods SCALING including: based on sorptivity ( Formula), transmissivity (Formula ), the optimum SCALING factors (Formula ) arithmetic, geometric and harmonic. Materials and Methods: The basic assumption of SCALING through this method was “ the shape of the infiltration characteristics curve is almost constant despite the variations in the rate and depth of infiltration” . The data required for infiltration SCALING were a reference infiltration curve (whose parameters are known) and the depth of water infiltrated within a specified time period in other infiltration curves. In this method, first, EQUATION infiltration parameters are specified for one infiltration curve, called the reference infiltration curve (Formula ). If, for other infiltration EQUATIONs, the depth of water infiltrated is obtained after the specified time(ts) (for example, depth of infiltration water after 4 hours), the scale factor (Fs, dimensionless) is equal to the depth of water infiltrated after ts in the reference infiltration EQUATION to depth of infiltrated water after ts even infiltration EQUATION is as follows: (Formula)(1) where Ii (i=1, 2, … , n) is depth of infiltrated water after a given time (ts) for each infiltration families and is depth of infiltrated water after a given time in reference, and and are parameters of reference curve. In order to assess the proposed SCALING method, root mean square error (RMSE), mean bias error (MBE) and coefficient of determination (R2) were used for a totally 24 infiltration tests. Results and Discussion: The parameters of this model (i. e. sorptivity S and transmissivity factor A) showed a wide variation among the study sites. The variation of these parameters showed no significant difference between sorptivity and transmissivity factors. In addition, Talsama et al. (1969) illustrated that there is a weak relationship between sorptivity and saturated hydraulic conductivity. Results showed that SCALING achieved using α A was better than that obtained using α S. Mean curve was chosen as reference curve and scale curve was obtained by different methods. The results of statistical analysis showed that the proposed method had the best performance (RMSE=0. 006, MBE=0. 0019 and R2=0. 9996). In order to evaluate the effect of the reference curve selection on the results, the scaled cumulative infiltration curve based on different reference curves (different infiltration EQUATION) was evaluated. The results showed that the selection of the reference infiltration curve is optional and each cumulative infiltration families can be selected as the reference curve. For defining the relationship between and, , α S، α A، ، ، data, a statistical analysis was performed. According to our results, had the highest correlation with. Conclusion: In this study, a new method for penetration SCALING was presented. In this method, the infiltration curve can be obtained using the minimum information including a reference curve and the depth of infiltrated water after a given time. The selection of the reference infiltration curve is optional and each cumulative infiltration EQUATION can be selected as the reference curve. In the light of the results of this research, it can be concluded that the proposed method in this study is promising to be used for surface irrigation management.

In most cases, advance data is used for evaluating border irrigation. Due to soil variability, as well as initial and boundary conditions in border irrigation, water advance rate varies considerably in different borders. SCALING techniques helped to reduce the required measurements in soil and water issues. The aim of this study was to scale the volume balance EQUATION and provide a simple EQUATION to determine water advance in border irrigation. For this purpose, 21 borders, including cultivated and uncultivated borders with slope of 0. 001 to 0. 005, roughness of 0. 017 to 0. 211, length of 91. 4 to 100 m, and discharge rate of 0. 08 to 0. 16 m 3 /m/min were used. Scale factors were defined such that the volume balance EQUATION remained independent from soil and initial conditions. The scaled advance curves showed certain patterns. As a result, empirical EQUATIONs were fitted to the scaled solutions. The empirical EQUATION was evaluated for prediction of water advance in the border. The root mean square error obtained from the observed and calculated values by the experimental EQUATION for the different borders, in most cases, was less than 5 minutes, and the mean absolute error value was less than 10%. The determination coefficient of the final advance from observed and calculated values by the experimental EQUATION was 0. 93. In general, simple form and independent to the soil type EQUATIONs presented are advantages of this method.

After introducing similar media theory, many SCALING methods were developed and have been widely used to cope with soil variability problem as well as to achieve invariant solutions of Richards’ EQUATION. Recently, a method was developed for SCALING Richards’ EQUATION (RE) for dissimilar soils such that the scaled RE is independent of soil hydraulic properties for a wide range of soils. This method uses exponential-power hydraulic functions which are restricted to a limited range of soil-water content and matric potential. Hence, this method does not apply to the phenomena in which soil-water content and matric potential exceeds this range. Therefore, this research was performed to extend the method for a wider range of soil-water content and matric potential. This objective was achieved by modifying the exponential-power hydraulic functions and the SCALING method was extended to the entire range of soil wetness (from saturated to dry). This study was followed to solve RE for soil-water infiltration using SCALING. To do so, numerical solutions of the scaled RE was approximated by a scaled form of Philip three-term EQUATION with soil-independent coefficients. The obtained approximate solution was tested using literature data of infiltration experiments on a sandy and two clayey soils. Results indicated that the solution can reasonably estimate (with the average relative error at most 9% for the cases studied here) measured infiltrated water. Also, it was shown that this solution can accurately approximate (with the average relative error at most 4% for the cases studied here) the numerical solutions of RE (for the same conditions and hydraulic functions). Hence, because of its simplicity, the solution is proposed as an alternative for numerical solutions of RE or other empirical EQUATIONs for soil-water infiltration. Additionally, this solution can be easily applied to determine soil hydraulic functions by inverse solutions.

In this paper, we obtain a new conservation law for the Harry Dym EQUATION by using the SCALING method. This method is algorithmic and based on variational calculus and linear algebra. In this method, the density of the conservation law is constructed by considering the SCALING symmetry of the EQUATION and the associated flux is obtained by the homotopy operator. This density-flux pair gives a conservation law for the EQUATION. A conservation law of rank 7 is constructed for the Harry Dym EQUATION.

Spatial variability of soils makes difficult analysis of soil water flow phenomena especially in a large area such as a watershed. Using SCALING methods is a solution in variability problems. The objective of this study was to investigate the effect of the non-linear variability on performance of the SCALING methods of Richards’EQUATION for modeling infiltration in a watershed. The method of Warrick et al. by adopting van Genuchten hydraulic functions was used and variability of n values (power of van Genuchten hydraulic functions) was considered as the nonlinear variability. Marghmalek watershed, a sub watershed of Zayanderoud, with 97 Sq. kilometers was studied. In addition, ten virtual watersheds with various degrees of variability of n were evaluated which were generated by stochastic method of Monte Carlo. Using HYDRUS-1D model, original and scaled Richards’ EQUATIONs were solved for infiltration condition with constant hydraulic head and uniform initial soil water content. The results indicated that coefficient of variations of n values in the Marghmalek watershed (equal to 2.57%) is small enough that the SCALING method can be used efficiently in modeling infiltration.Therefore, in this watershed, generalized solutions of Richards’ EQUATION can be adequately used instead of individual solutions for every points of the watershed. Evaluations in the virtual watersheds indicated that variability of n values considerably affect the error between the generalized and individual solutions. Based on the result of this study, it can be concluded that SCALING methods of Richards’ EQUATION can be adequately applied in the watersheds in which coefficient of variations of n values does not exceed 3%.

Statement of Problem: In most cases of periodontal therapy, antibiotics are suggested as an adjuvant. It is necessary to evaluate the effect of systemic administration of antibiotics in treatment of periodontal diseases and introduce a cost-effective method for management of periodontal infections in individuals who have no access to periodontal therapy.Purpose: This study aimed to compare the effect of antibiotics alone, SCALING and root planing (SRP) alone or SRP combined with antibiotics as gold standard approach in improvement of PPD of patients with chronic periodontitis.Materials and Method: This was an experimental study conducted on 44 patients with chronic peridontitis. They were randomly assigned to three groups as follows: 1- SRP Group receiving SCALING and root planing alone. 2- AB Group that received antibiotic. 3- Combination Group that received SRP and antibiotic. Clinical measurements including probing depth (PPD), gingival bleeding index (GBI) and plaque index (PI) were performed at base line and 3 months after the treatment. Statistical analyses were performed using covariance analysis kolmogrove- smimov test and ANOYA test.Results: All 3 groups showed a significant reduction in PPD, GBI and PI 3 months after treatment (p <0.05 in all 3 groups) Improvement in PPD measures in the combination group was statistically significant (p =0.0001). The difference between the groups was not significant with respect to GBI reduction (p >0.05).Conclusion: In chronic periodontitis, systemic antibiotic therapy alone was as effective as mechanical therapy alone in reduction of PPD, but systemic administration of antibiotic in combination with SCALING and root planning showed the most improvement in PPD measures.

BACKGROUND AND OBJECTIVE: In recent years, using of local antibiotic as an adjunctive treatment in periodontitis has been considered. The aim of this study was to survey the local effects of doxycycline with SCALING/ root planning in treatment of adult periodontitis. METHODS: This experimental study was accomplished on five patients with adult periodontitis. The patients were chosen with at least three pockets with depth of approximately ≥4 mm and bleeding in each quadrant. After initial preparation and SCALING, the jaws were divided into 3 parts; upper right: receiving doxycycline gel (case group), upper left: receiving base gel (control group) and lower right: do not received any gel (Sham group). One, three and six months after beginning the study, all the indices were measured again; and finally all data were analyzed by statistical tests. FINDINGS: In this study after 6 months, reduction of pocket depth and clinical attachment level (CAL) in case, control and sham groups were difference. Mean of pocket depth in case group was reduced from 2.3±0.5 mm to 1.5±0.6 mm after three months, and 1.9±0.6 mm after six months, and in control group from 2.2±0.8 mm to 1.6±0.6 mm after three months, and 1.8±0.7 mm after six months, these differences for clinical attachment level in buccal side of the teeth in three groups were significant (p<0.05). Also, there were differences in bleeding index in three groups. As for mobility and plaque index there was not any significant difference between the groups. CONCLUSION: Totally, the outcome of doxcycline gel and SPR treatment group was satisfied than the other groups during 6 months, although the effects were not too long.

In hydrologic regional frequency analysis, information of one or more stations is generalized for a region. In this case, the variation of this information is assumed to have a defined coefficient called scale. In this study, SCALING properties of 7-day low flow of 19 basins in Mazandaran province in northern Iran were investigated. SCALING implies the relationship between probabilistic features and the area of the basin. If this exponent (called SCALING exponent) has a linear relationship with drainage area and does not include a significant relationship with probability weighted moments, low flow is called “simple SCALING”. The study showed that the logarithm of the drainage area and the logarithm of the probability weighted moments of order 1 to 10 are linear and the SCALING exponent did not have a significant relationship with probability weighted moments. Acordingly the 7-day low flows of Mazandaran province are simple SCALING.