Let's denote $\mathcal{S}^{\ast}(f_c)$ as a family of analytic functions $f(z)=z+a_2z^2+a_3z^3+\cdots$ in the open unit disk $\mathbb{D}$ that satisfy the following relation for $c\in (0,1)$:$$\frac{zf'(z)}{f(z)}\prec f_c(z)=\frac{1}{\sqrt{1-cz}}, \quad z\in\mathbb{D}.$$First, we introduce the analytic functions $f_c(z)$ and examine their starlike and positivity properties of the real part. Then, we obtain their images in the open unit disk $\mathbb{D}$, which are Cassini Ovals. Cassini Ovals, due to their properties, have applications in solving various problems in fields such as geometry, physics, and mathematics. These curves are used in studying the motion of waves and electromagnetic waves in interstellar spaces, as well as in the design of engineering structures such as telescopes. In this article, with the help of integrals, we investigate the structure of mappings in this family and some properties including maximum and minimum moduli, bounds of the real part of these functions. Moreover, we obtain the relationships between the defined geometric ranks with this family, including the order of starlikeness and order of strong starlikeness.1. IntroductionLet $\mathcal{A}$ be a set of analytic functions of the form $f(z)=z+a2z^2+a3z^3+\cdots$ in the open unit disc $\mathbb{D}:=\left\{z\in\mathbb{C}\colon |z|<1\right\}$. A function $f\in\mathcal{A}$ is called univalent if it is one-to-one. In [5], two classes of starlike and convex functions with order $0\le \beta<1$ are defined as follows:\begin{equation}\label{starlike-convex}\mathcal{S}^{\ast}(\beta):=\left\{f\in\mathcal{A}\colon \Re\left(\frac{zf'(z)}{f(z)}\right)>\beta\right\},\quad \mathcal{K}(\beta):=\left\{f\in\mathcal{A}\colon zf'(z)\in\mathcal{S}^{\ast}(\beta)\right\}.\end{equation}Similarly, in [2], the class of functions called strongly starlike with order $0<\alpha\le 1$ is defined as:\[\mathcal{SS}^{\ast}(\alpha)=\left\{f\in\mathcal{A}\colon \left|\mathrm{Arg}\frac{zf'(z)}{f(z)}\right|<\frac{\alpha \pi}{2}\right\}.\]If $f$ and $g$ are two analytic functions in $\mathbb{D}$, we say that $f$ is subordinate to $g$ \cite{Dur}, denoted by $f\prec g$, if and only if there exists an analytic function $w$ with $w(0)=0$ such that for all $z\in\mathbb{D}$:\[\left|w(z)\right|<1, \quad f(z)=g(w(z)).\]If $g$ is univalent, we have:\[f(z)\prec g(z) \Longleftrightarrow f(0)=g(0),\quad f(\mathbb{D})\subset g(\mathbb{D}).\]Given $c\in(0,1)$, analytic functions $f_c$ are defined as follows:(1.2)$$f_c(z):=\frac{1}{\sqrt{1-cz}}=1+\frac{c}{2}z+\frac{3c^2}{8}z^2+\cdots$$in the principal branch of the complex logarithm, where $\log 1=0$. These functions are univalent in $\mathbb{D}$ and map the open unit disc $\mathbb{D}$ into the interior of the Cassinian Ovals given by the Cartesian equation:\begin{equation}\label{Cassinian-Ovals}(x^2+y^2)^2-\frac{2}{1-c^2}(x^2-y^2)+\frac{1}{1-c^2}=0,\end{equation}or the polar equation:\begin{equation}\label{Cassinian-Ovals1}r^4-\frac{2r^2 }{1-c^2} \cos(2\theta)=\frac{1}{c^2-1}.\end{equation} 2. Main ResultsIn this section, we will first derive the structure of functions in the class $\mathcal{S}^{\ast}(f_c)$, and then using the stated theorems, we will determine the order of starlikeness and strongly starlikeness of functions in the class $\mathcal{S}^{\ast}(f_c)$. Theorem 2.1. A function $f$ belongs to the class $\mathcal{S}^{\ast}(f_c)$ if and only if there exists a function $p \prec f_c$ such that\begin{equation}\label{thm-1-0}f(z)=z\exp\left(\int_{0}^{z}\frac{p(t)-1}{t}dt\right), \quad z\in\mathbb{D}.\end{equation} If we set $p(z)=f_c(z)$ in theorem (2.1), then we get(2.2) $$F_c(z):=z\exp\left(\int_{0}^{z}\frac{f_c(t)-1}{t}dt\right)=\frac{4z}{(1+\sqrt{1-cz})^2}, \quad z\in\mathbb{D}.$$This function $F_c(z)$ is an extreme function for the class $\mathcal{S}^{\ast}(f_c)$. Figure 2 illustrates the image of the open unit disk $\mathbb{D}$ under the mapping $F_c(z)$ for $c=3/4$. Theorem 2.2. Let $f_c$ be the given function described in (1.2). Then $f_c$ is convex and satisfies the following conditions:\begin{equation}\label{max-min0}\max_{|z|=r<1}\left|f_c(z)\right|=f_c(r),\quad \min_{|z|=r<1}\left|f_c(z)\right|=f_c(-r).\end{equation} In the following theorem, we obtain bounds for the real part and strongly starlike mappings of the functions $f_c$. Theorem 2.3. Suppose $c\in(0,1)$. Then we have the following:(1) \[f_c(\mathbb{D})\subset \left\{w\in\mathbb{C}\colon \frac{1}{\sqrt{1+c}}<\Re(w)<\frac{1}{\sqrt{1-c}}\right\},\](2)\[f_c(\mathbb{D})\subset \left\{w\in\mathbb{C}\colon \left|\mathrm{Arg}(w)\right|<\frac12 \arccos\sqrt{1-c^2}\right\}.\] Theorem 2.4. If $f\in \mathcal{S}^{\ast}(fc)$ and $|z|=r<1$, then the following hold:(1) \[\frac{zf'(z)}{f(z)}\prec \frac{zF'_c(z)}{F_c(z)},\quad \frac{f(z)}{z}\prec\frac{F_{c}(z)}{z},\](2) \[F'_c(-r)\le \left|f'(z)\right|\le F'_c(r),\](3) \[-F_c(-r)\le |f(z)|\le F_c(r),\](4) \[\left|\arg{(f(z)/z)}\right|\le \max{|z|=r}\arg\left(\frac{1}{(1+\sqrt{1-cz})^2}\right),\](5) Either $f$ is a rotation of $F_c$ or\[\left\{w\in \mathbb{C} \colon\ |w|\leq-F_c(-1)=\frac{4}{(1+\sqrt{1+c})^2}\right\}\subsetf(\mathbb{D}),\]where in all cases, the function $F_c$ is defined as per equation (2.2).\end{thm}In the following theorem, we determine the subordination order and strong subordination order for the class of functions $\mathcal{S}^{\ast}(f_c)$. Theorem 2.5. The class of functions $\mathcal{S}^{\ast}(f_c)$ has the following properties:(1) For $0\le \beta\le \frac{1}{\sqrt{1+c}}$, we have\[\mathcal{S}^{\ast}(f_c)\subset \mathcal{S}^{\ast}(\beta).\](2) For $\frac{1}{\pi}\arccos\sqrt{1-c^2}\le \alpha\le 1$, we have\[\mathcal{S}^{\ast}(f_c)\subset \mathcal{SS}^{\ast}(\alpha).\] 3. ConclusionsThe class $\mathcal{S}^{\ast}(f_c)$ consists of functions that can be represented in a specific form involving the function $f_c$, which is a special function related to the starlikeness property. The function $F_c(z)$, derived from $f_c(z)$, is an extreme function for the class $\mathcal{S}^{\ast}(f_c)$ and has specific properties, including convexity and bounds on its maximum and minimum modulus on the unit circle. The presented theorems provide bounds for the real part of the functions $f_c$ and establish relationships related to subordination and strong subordination order for the class of functions $\mathcal{S}^{\ast}(f_c)$. Overall, the obtained theorems and their proofs contribute to understanding the structural properties, order of starlikeness and strongly starlikeness, as well as subordination order within the class of functions $\mathcal{S}^{\ast}(f_c)$, for different values of the parameter $c$.

Quantum calculus, which arises in the mathematical fields of combinatorics and special functions as well as in a number of areas, involving the study of fractals and multi−, fractal measures, and expressions for the entropy of chaotic dynamical systems, has attracted the attention of many researchers in recent years. In this paper, by virtue of some useful notations from q−, calculus, we define the q−, Fibonacci dual bicomplex numbers and q−, Lucas dual bicomplex numbers with a different perspective. Afterwards, we give the Binet formulas, binomial sums, exponential generating functions, Catalan identities, Cassini identities, d’, Ocagne identities and some algebraic properties for the q−, Fibonacci dual bicomplex numbers and q−, Lucas dual bicomplex numbers.

Background and Objectives: Water shortage and the need for its optimal use in arid and semi-arid regions, including Iran, has led water officials and farmers to use modern irrigation systems, such as drip irrigation with the aim of making optimal use of water resources. Drip irrigation has been welcomed in most parts of the world due to its high efficiency and the possibility of irrigation in different environmental conditions. The most important reason for the superiority of drip irrigation over other irrigation methods is the controllable amount of water for each plant. Drip irrigation is a method in which water is poured out of the net at low pressure through an orifice or device called an emitter and dripped into the bottom of the plant. This irrigation system, like other methods, requires accurate knowledge of the parameters affecting it to achieve the desired efficiency. One of the most important parameters for the irrigation system is the distribution of moisture in the soil and in fact the shape of the moist bulb. Therefore, knowledge of how to distribute water in the soil is essential for the proper design and management of subsurface drip irrigation systems. Since testing is very difficult and time consuming to detect the shape of moisture distribution in the soil, the use of numerical and analytical simulation can be an effective and efficient way to design these systems. Methodology: In order to determine the progress of the moisture front in drip irrigation, first the soil texture type and physical properties of the soil were determined. It should be noted that the emitter flow rate was measured and adjusted in volume at the beginning of the test to minimize the difference between the emitter flows along the three side tubes. Evaluation experiments were performed with three outflows of 2, 4 and 6 liters per hour. With the start of the system, the progress of the moisture front at different times was measured by digging a trench using a scale. Numerical simulation of moisture front progress was performed using HYDRUS model based on Richard equation and analytical simulation was performed using Moment Analysis. HYDRUS software was used to numerically simulate the progress of the moisture front. The simulation range was considered to be 100 cm by 100 cm on the two-dimensional plane. In these simulations, 3956 nodes are used to represent the entire simulation range and also, relevant equations were used to calculate the two-dimensional spatial Moment of the wetting pattern.Findings: The simulations show that the initial volumetric moisture content is 0.11 and the saturation volumetric moisture content is 0.380 and the water dispersion rate increases over time on the x and z axes. With increasing flow, the maximum dispersion is in the x-axis, which occurs in flow of 6 liters per hour. The result for flow of 6 liters per hour based on the data used is slightly higher than the desired value. The reason why the value of M00 in the flow rate of 6 liters per hour is higher than expected, is that in the simulation flow rate of 6 liters per hour change in the size of the inlet diameter and the amount of flux changes the amount of water entering the soil and moistens a large volume of soil. Due to the different amount of moisture applied to the area at different times, the value of z_c,σ_x^2,σ_z^2 is different and has caused a change in the size of the oval in different flows. The increase in the size of the Ovals indicates the high dispersion of water in that area. The results showed that the Moment analysis was able to express the position of the center of mass of water distributed in the soil with correlation coefficient of 0.986 in linear mode and 0.982 in logarithmic mode. By comparing the values of diameter and depth obtained from the HYDRUS and the drawn Ovals, it can be concluded that both methods provide close results. The accuracy of the Moment analysis method in simulating different types of moisture patterns resulting from drip irrigation under different flows with the use of different volumes of water is similar to the HYDRUS model and therefore it is possible to use this feature to predict the pattern of moisture from a certain flow using a specific volume of water.Conclusion: In this study, the accuracy of Moment analysis in simulating various moisture patterns resulting from drip irrigation under different flows with the use of different volumes of water was investigated and the possibility of using this feature to predict the pattern of moisture from a given flow using a specific volume of water checked. In order to investigate the Moment of the amount of water distributed in the soil by subsurface drip irrigation, simulation was performed by two-dimensional HYDRUS software for three discharges of 2, 4 and 6 liters per hour with an inlet water volume of 12 liters. Then, using the results of simulation of moisture distribution range by a programming language including MATLAB software, and by calculating the Moments, it was determined that the Moments are able to express the position of the center of mass of water distributed in the soil and how it is distributed relative to x and z axes. The increase in the size of the Ovals indicates that more water is distributed in that area. Comparing the diameters and depths of the moisture front between the simulated HYDRUS model and the Moment analysis model, it was found that the Moment analysis is an efficient way to study the distribution of water moisture by drip irrigation and this method can be used as an alternative input to estimate parameters.

Logos are not merely graphic symbols designed to distinguish brands; they are deeply embedded in the cultural, historical, and social frameworks of the societies that produce them. As visual representations, logos provide insight into the values, beliefs, and collective identities of nations. This study investigates the industrial logos of Mercedes-Benz, Renault, Toyota, and Saipa through the theoretical lens of Pierre Bourdieu's concept of habitus. By analysing the design and cultural context of these logos, the research explores how social structures influence industrial design and how logos function as visual reflections of cultural identities. The research adopts a qualitative, descriptive-analytical approach, employing visual content analysis to examine the design features and cultural meanings behind these logos. The methodology aims to uncover the underlying connections between cultural norms, societal values, and the design decisions that shape logos. The findings demonstrate that logos are far more than tools for brand recognition; they are expressions of the cultural, historical, and social values of their origin nations. The Mercedes-Benz logo, featuring a distinctive three-pointed star, exemplifies Germany's industrial habitus, which emphasises precision, order, and power. The three points of the star represent dominance in three realms: land, sea, and air. This symbolic representation is not coincidental; it reflects Germany's cultural values of engineering excellence, meticulous attention to detail, and a commitment to technological advancement. The minimalist and geometric design of the logo aligns with Germany's reputation for functional yet sophisticated industrial aesthetics. The logo transcends its visual simplicity, embodying the country's industrial strength, technological dominance, and cultural ethos of perfectionism.Renault’s logo, a geometric diamond inspired by the Art Deco movement, captures France’s cultural habitus, which celebrates creativity, individuality, and artistic innovation. The logo has evolved over time, but its core design elements have consistently reflected France’s historical and cultural identity. The diamond’s clean lines and symmetry symbolise both stability and innovation, characteristics deeply rooted in France's industrial history. Moreover, the aesthetic choices in Renault’s logo align with France’s legacy as a leader in art and design, showcasing the interplay between functional utility and artistic expression. Through its design, Renault reflects the cultural emphasis on ingenuity, craftsmanship, and the pursuit of beauty, traits that define the French cultural identity. Toyota’s logo, characterised by its overlapping Ovals, represents Japan’s habitus of harmony, balance, and interconnection. The design’s simplicity and elegance are rooted in Japanese cultural principles, including Zen philosophy and the aesthetic of "ma" (the concept of space and balance). The three Ovals in the logo symbolise the union of customer, company, and the broader world, reflecting a deeply ingrained cultural value of interconnectedness and mutual respect. The use of rounded forms and harmonious proportions further highlights the importance of balance and fluidity, both key aspects of Japanese design philosophy. Additionally, the logo conveys a commitment to quality, sustainability, and innovation, which are central to Japan's industrial and cultural identity. Toyota’s design not only represents a global brand but also serves as a cultural ambassador, showcasing the integration of traditional Japanese values into a modern industrial context.Saipa’s logo, designed by the renowned Iranian graphic designer Morteza Momayez, draws inspiration from traditional Iranian architectural motifs, particularly geometric patterns found in Persian tilework. The design reflects Iran’s habitus, which blends historical pride with a forward-looking vision. The logo’s symmetrical and structured form represents stability, unity, and continuity, qualities that resonate with Iran’s cultural and historical identity. By incorporating elements of Iranian heritage into a modern industrial design, Saipa’s logo bridges the gap between past and future, presenting itself as a symbol of national pride and innovation. The use of traditional patterns highlights the importance of cultural authenticity in the design process while also emphasising Iran’s ambition to assert itself on the global stage as a technologically advanced and independent nation. Saipa’s logo is not just a visual identifier but a testament to the resilience, creativity, and cultural richness of Iran.The findings of this study reveal that logos are far more than visual markers of brand identity; they are deeply rooted in the cultural and social fabric of the societies from which they originate. Each logo analysed in this research embodies the unique cultural characteristics of its home nation, serving as a visual narrative that reflects the beliefs, values, and traditions of its creators. By examining these logos through the framework of Bourdieu’s habitus, the study highlights the profound influence of cultural structures on design decisions. The concept of habitus, as defined by Pierre Bourdieu, refers to the system of dispositions, habits, and practices that are ingrained within individuals and groups through their social and cultural environments. Habitus shapes perceptions, preferences, and actions, providing a lens through which individuals and communities interpret the world. When applied to industrial design, habitus reveals how cultural norms and societal values are embedded in the creative process, shaping the form and function of design artefacts like logos. In this context, logos become more than visual symbols; they are cultural artefacts that embody the shared practices and ideologies of their societies.The Mercedes-Benz logo, for instance, is a direct manifestation of Germany’s cultural emphasis on precision and engineering excellence. The three-pointed star, with its geometric simplicity and clean lines, captures the essence of German industrialism, where functionality and efficiency are paramount. The logo’s historical evolution further illustrates Germany’s commitment to technological progress and its leadership in the global automotive industry. By aligning its visual identity with the cultural values of order, power, and perfection, Mercedes-Benz has created a logo that resonates with its audience on both an aesthetic and cultural level. Renault’s logo, on the other hand, reflects France’s rich artistic heritage and its cultural valorisation of creativity and individuality. The diamond shape, inspired by Art Deco, is both modern and timeless, symbolising innovation and artistic refinement. The evolution of Renault’s logo demonstrates a consistent effort to balance aesthetic appeal with functional clarity, a hallmark of French design. By incorporating elements of French artistic tradition into its branding, Renault has created a logo that not only represents its industrial achievements but also pays homage to the cultural legacy of France.Toyota’s logo exemplifies Japan’s cultural values of harmony, interconnectedness, and continuous improvement. The overlapping Ovals symbolise the unity of customer, company, and the global community, reflecting Japan’s collectivist ethos and its focus on building meaningful relationships. The design’s simplicity and balance are deeply rooted in Japanese aesthetic principles, emphasising the importance of cohesion and sustainability. Toyota’s logo serves as a visual representation of the country’s commitment to quality, innovation, and the integration of traditional values into modern industrial practices. Saipa’s logo, with its incorporation of traditional Iranian motifs, stands as a testament to the cultural pride and historical depth of Iran. The geometric patterns in the logo evoke the intricate artistry of Persian tilework, while its symmetrical design conveys stability and unity. Saipa’s logo reflects Iran’s ambition to maintain its cultural identity while embracing technological advancement. By integrating elements of Iranian heritage into a modern industrial context, Saipa has created a logo that serves as both a symbol of national identity and a representation of the country’s aspirations for global recognition. The study concludes that logos are not merely functional tools for brand recognition; they are deeply symbolic artefacts that encapsulate the cultural, historical, and social identities of their creators. Through the lens of habitus, this research underscores the interconnectedness of culture and design, revealing how logos serve as visual embodiments of the values and traditions of the societies they represent. The analysis of Mercedes-Benz, Renault, Toyota, and Saipa highlights the diverse ways in which cultural frameworks influence industrial design, offering valuable insights into the role of habitus in shaping visual identities.By understanding logos as reflections of habitus, designers and researchers can gain a deeper appreciation for the cultural narratives embedded within these visual symbols. This perspective not only enriches our understanding of industrial design but also emphasises the importance of cultural context in creating meaningful and resonant visual identities. Logos, as this study demonstrates, are powerful tools for storytelling, connecting the past, present, and future of the societies they represent. Through their designs, logos offer a glimpse into the collective identities of nations, serving as enduring symbols of cultural and industrial heritage.   

Introduction Water scarcity and the need for optimal water utilization in arid and semi-arid regions, including Iran, have encouraged water authorities and farmers to adapt modern irrigation systems likedrip irrigation, to make optimal use of water resources. The most important advantage of drip irrigation over other irrigation methods is its ability to control the amount of water applied to each plant. New irrigation methods focus on plant irrigation and not on land irrigation. In arid and semi-arid regions, a drip irrigation system is used to use water optimally and prevent wastage and evaporation. Factors such as soil texture, type of cultivated plant, amount of available water, distance of drippers and laterals, the wetted surface, and the dimensions of the moisture bulb under the soil surface are involved in the design of the drip irrigation system. Due to the variety of soil textures in the earth, the movement of water under the soil surface is different in all kinds of textures, therefore, knowing exactly how water moves in the soil and how the moisture bulb is distributed under the soil surface is of particular importance. The purpose of this study is to investigate the movement of moisture bulbs, check their dimensions under the soil surface in different soil textures and flow rates, and evaluate the capability of the Moment analysis method to simulate this process under various conditions. Materials and Methods To simulate the moisture bulb in different soil textures, detailed information on the physical properties of the soil, including the percentage of particles that make up the soil texture, bulk and real density, porosity, and saturated hydraulic conductivity, is required. In this research, the simulation of the moisture front in different soil texture was conducted using Rosetta software, which defines 12 types of soil textures. In these tests, the source of soil power was considered as surface and point. The total feeding volume of each type of soil texture is 24 L, and this volume was used with different flow rates of two, four, six, and eight L s-1. To numerically simulate the progress of the moisture front, Hydrus software was used. Then the analytical simulation of the moisture front was done using the equations of the Moment analysis method. In this study, an ellipse was drawn to represent the moisture bulb simulated by Hydrus software at different times for the applied flow rates. Coefficient k was used to draw the ellipse, and its appropriate value was determined by minimizing the difference between the model and Hydrus results. Results and Discussion To calculate the moments, the first step is to obtain the values of M00 According to the applied flow rates of two, four, six, and eight L s-1 and the amount of volume intended to feed all types of soil texture, i.e., 24 L, the duration of irrigation is 12, 6, 4, and 3 hr, respectively. The comparison of moisture distribution over all periods and soil textures showed acceptable results, and the distributed subsurface moisture values were similar. In the study of clay texture, with time from the start of irrigation, the difference in the total amount of distributed moisture increased, and the reason for this result is the decrease in the permeability of the clay due to the filling of fine pores. The results indicated that σx2 values changed with the increase in irrigation duration. The highest variance was found in sandy clay with a flow rate of 8 L s-1 (1503.3 cm2), while the lowest variance was observed in clay texture with a flow rate of 4 L s-1 (368.6 cm2). By increasing the amount of applied discharge, σz2 increases and the slope of this increase is different in each soil texture, according to the characteristics of that texture. Also, the effect of irrigation duration on the value of σz2 is evident. In other words, the longer the duration of irrigation, the more the amount of variance changes. Conclusion In this research, the accuracy of the Moment analysis method in predicting moisture distribution from drip irrigation was evaluated using results from Hydrus and Moment analysis. The Hydrus results demonstrated that the moisture bulb expanded over time in both the horizontal and vertical directions. The results also indicated higher flow rates increased the horizontal expansion of the moisture bulb, while the duration of irrigation affected both horizontal and depth expansions. Using the moment analysis method, the center of mass of water distribution in the soil and the changes in the moisture front along the x and z axes were determined. By examining and comparing the dimensions of the moisture front resulting from Hydrus and Ovals, it was observed that there is a suitable compatibility between the two methods. Therefore, the Moment analysis method can be relied upon to estimate the dimensions of the moisture bulb in drip irrigation. It also provides an efficient and accurate approach to reducing the time and cost of field experiments.

Introduction: Machine learning algorithms usually do not consider spatial autocorrelation in soil data, unless it is perspicuity specified. Machine learning algorithms that compute autocorrelated observations have been recently formulated, such as geographic random forest (Georganos et al., 2019), or spatial ensemble techniques (Jiang et al., 2017). In theory, if we include all relevant environmental variables to model a soil property or class, there should be no spatial autocorrelation in the residuals of the fitted models. If this happens, some important predictors are likely to be missed. Despite the availability of the data set and the care taken during modeling, residual autocorrelation is still likely to occur. Several researchers have suggested the use of spatial alternative covariates as an indicator of spatial location in the SCORPAN model. The most common alternative is to use geographic coordinates (east and north) as covariates in the model, which leads to synthetic maps, especially when used in combination with tree-based algorithms. On the other hand, distance maps from observation locations are proposed by Hengl et al. (2018). Distance maps to observation locations usually do not have a clear meaning in terms of soil processes in an area (e.g., distance from a river). In the field of digital soil mapping, the current use of distance maps is not satisfactory for several reasons. The presence of pseudo-covariates with a set of covariates related to pedology is not very useful because it prevents the analysis of residuals and the creation of new hypotheses from these residuals. It also hinders the interpretation of the most important key predictors. Finally, pseudo-distance covariates may be well integrated into multiple pedology-related covariates, making them better predictors or masking the effect of pedology-related covariates. In spatial ecology, spatial eigen-vector maps, spatial filters or trend level regression replace distance maps in reducing or eliminating spatial autocorrelation (Kuhn et al., 2009). The purpose of this study is first to detect and calculate the spatial autocorrelation in the soil data. In the second step, it is going to develop a non-spatial model without considering the spatial autocorrelation, then to extract the spatial eigenvectors as an index of the spatial autocorrelation, and finally to use them as independent variables in spatial modeling.Methods and Materials: In this study, the soil salinity data utilized of 297 soil samples from a section of the Qazvin plain. The first and second derivatives of a digital elevation model as topography factors, remote sensing indices, parent material map, geoform map, and annual average temperature and rainfall maps were used to select the most important auxiliary variables. Finally, in order to select the best and most relevant environmental variables for modeling, the correlation between these variables and the dependent variable i.e. soil salinity in 297 study points was used using FSelector package of R software. Moran's I and Jerry's C indices were used to evaluate the spatial autocorrelation of soil data. First, the non-spatial ordinary least square (OLS) model was fitted to predict the spatial distribution of soil salinity. At this stage, spatial autocorrelation was not considered. Then spatial regression was fitted by calculating spatial filters through spatial eigenvectors as independent variables. Finally, the comparison of the outputs of the non-spatial OLS model and the spatial regression model was done with criteria such as R2, Akaike information criteria (AIC), autocorrelation of residuals and root mean of square error (RMSE).Results and Discussion: Statistical analysis indicated the high variability of soil salinity in the study area (coefficient of variation or CV more than 35%). Also, soil salinity shows high skewness and kurtosis, indicating its abnormal distribution. The high variability of this soil characteristic emphasizes the interaction of complex and numerous factors, including soil forming processes and different management strategies. The most important variables selected based on the correlation analysis include elevation, Multi-resolution Valley Bottom Flatness (MrVBF), wetness index, drainage basin, greenness index, normalized differential vegetation index (NDVI) and the corrected and transformed vegetation index (CTVI). A total of 7 variables were selected, which include four topography variables and three remote sensing variables. Among the topographical variables, the MrVBF had the most importance (correlation: 0.70). The spatial distribution map of soil salinity shows that the soil salinity is low in the northern, northeastern and northwestern parts towards the center of the studied area. The highest amount of salinity is found in the southern and southeastern regions. Moran's I and Jerry's C indices were 0.57 and 0.4, respectively. Based on both indices, soil salinity in the study area exhibits spatial autocorrelation. In the spatial regression model, by considering spatial autocorrelation, compared to the non-spatial model, the results are improved. By considering the spatial autocorrelation, the value of R2 increased, while the values of AIC, spatial autocorrelation of the residuals and RMSE decreased. The distribution maps of residuals from the non-spatial OLS model and the spatial regression model differ in terms of the spatial sign of the residuals and the spatial autocorrelation distribution that can be recognized in the form of clusters. Clusters (red or blue) indicate the presence of spatial autocorrelation in the residuals. In the distribution map of the residuals of the non-spatial model, more and larger clusters (marked with green Ovals) are identified, indicating the existence of spatial autocorrelation in the residuals of the model. The presence of spatial autocorrelation in the residuals of a model shows that the model is not able to remove the spatial dependence, which may be due to not considering an important auxiliary variable in the modeling.Conclusion: This study was conducted in order to investigate the effect of spatial autocorrelation on the results of soil salinity modeling. Soil salinity prediction was done by non-spatial OLS model (without considering spatial autocorrelation) and spatial regression model (with spatial autocorrelation considered). The results indicated the improvement of the performance of the spatial regression model compared to the non-spatial ordinary least squares model. In the spatial model, considering the spatial autocorrelation as a covariate, the value of R2 increased, while the values of AIC, spatial autocorrelation of the residuals, and RMSE decreased.

Introduction The lines of turquoise carving and engraving on turquoise stone is one of the traditional and ornamental arts. This art is one of the sub-branches of gem carving, which is a part of Iranian artificial arts in terms of practicality and tools.  Turquoise carving has been popular in the city of Mashhad since the distant past. The city of Mashhad has been chosen as the international city of precious and semi-precious stones by the World Industries Council. The art of carving is one of the subsets of the art of turquoise carving; turquoise carving artists have succeeded in making beautiful paintings from this blue gem by carving in the form of letters using the art of calligraphy. The presence of valuable mines, including the Turquoise Mine in "Ten Mines" from the villages of Neyshabur city, and the transfer of this mineral to the city of Mashhad from the distant past have collected engravers and turquoise carvers in this city. Research Method The engravers engrave inscriptions, images, and lines on the seals with the most complete splendor. The purpose of the research, based on the analysis and description of the cutting shapes, is to introduce the types of lines, motifs, and images carved on the turquoise gem, based on the essence of the subject. The questions that this research aims to answer are: how are the cutting shapes, types of lines, and motifs used in contemporary Mashhad turquoise carving art classified from a qualitative perspective? What tools and methods are used in the art of engraving? How to make turquoise panels? The research method in this study is descriptive-analytical. The method of collecting data is library information and field research, including photography (observation and interviews). The statistical population includes (15) prominent engravers and turquoise engraving professors as well as knowledgeable and well-informed people. The interviews were saved as audio files and analyzed as texts. In the following, interviews were carried out with turquoise carving and engraving artists who were mostly working in the upper floor of Bazaar Reza in Mashhad, using the materials that are used to expand the art. These hardworking artists proposed turquoise carving and engraving; this art was examined in terms of the subject of the study. Research Findings In the meantime, engraving and carving on seals and gems are worth attention. Ferdowsi, a high-ranking poet of Iran, writes about the carving and engraving of lines on turquoise in the story of Bijan and Manijeh: "One victorious seal of Rostam Baroi-- written with iron by the action of hair". In this verse, Ferdowsi calls the turquoise stone with the name of “Pirouze”. Rostam's name is engraved on the turquoise stone and this ring was in the hand of Iranian warrior Rostam as a seal. In that period, they used tools like iron for carving. The art of engraving is done very delicately and Rostam's name is written as thin as a hair on the gem of the ring. Khwaja Nasir al-Din Tusi writes in his book Tensukh Namah Ilkhani about turquoise’s change of color: "Engravers consider any turquoise that turns green to be dead. They turned this green turquoise and polished it again, and it was correctable. Artists and art masters have proposed different solutions for the development and prosperity of engraving art, the most important of which include: first, the cooperation of designers with engraving artists to present new designs in the design of motifs, to create new and innovative designs, and to combine designs and lines in calligraphy and its integration into each other. They can create harmony between motifs and lines in engraving and calligraphy with the poems of great poets of Iran in the form of motifs taken from Iranian literature, the icons of famous Iranian artists and poets. Second, the government and related organizations can encourage and support artists. Third, certification of high-quality turquoise gems and exquisite carvings, specifying the name of the engraver, the type of gem, can give credibility to the gem and jewel. Fourth, the introduction of advertising of this art in mass media and virtual space. Fifth, the creation of workshops within the trade union, to increase employment and entrepreneurship, can result in the employment of graduates. At last, holding domestic and foreign exhibitions can introduce this art to the world. By making certified turquoise jewelry with new designs and proper marketing, it is possible to export this product, a type of non-oil export, by connecting to global markets. Conclusion The art of engraving on turquoise stone is an ancient art, so that in the Metropolitan Museum there are rings belonging to the 11th century AD. It was made from Neyshabur turquoise gem with a "dome" (dome) cut with a circular and oval shapes. Today, the shapes of thrash include circles, Ovals, cylinders, hearts, hexagons, and polygonals with angled cutting, known as "Trush Fest". Of course, sometimes it is used by young people in its natural form, after polishing. Today, tools and working methods have developed, and artists in this profession try to create original works using new tools and methods while using past experiences. These engraved images include those of Imams, the inscriptions of names, supplications, famous surahs of the Quran with naskh, thulh, nastaliq and broken nastaliq script in the form of a raised edge and togud along with the engraving of the golden dome of Imam Reza and motifs of daffodils, eight leaves. The chrysanthemum is done inside the bergamot frame on the turquoise gem. One of the innovations of the art of turquoise carving is to make a tableau by carving letters from turquoise stone. Due to new methods and new tools, the quality of lathe has increased. The art of engraving has declined in terms of quantity due to the limitation in the number of artists and the lack of coherence of the carving workshops in Mashhad.

The circle form has always fascinated artists throughout history and has played an important role in the creation of works of art. This form is often used to depict nature and still life, and at the same time, it is the main element of abstract compositions. Beyond its aesthetic appeal, the circle embodies deep meanings that help interpret the content of works of art. This study initially examines the representation of the circle form in the works of painters of early modernism. Subsequently, it traces the evolution of this form in abstract paintings. To address these goals, this research seeks to answer several key questions: What role does the circle play in the works of artists of early modernism? How do these works compare in terms of similarities and differences with abstract art? What are the underlying factors affecting the emergence of the role of the circle in the works of artists of the two periods?The spiritual developments that paved the way for modernism in the fine arts, occurred in the closing decades of the 19th century. The significant advances made by leading figures of modernism, including Monet, Cézanne, and Van Gogh, led to a revival of visual aesthetics and a profound shift in the interpretation of the artistic process (Bocola, 2014, p. 100). Over time, and with the emergence of different styles of painting, the term abstraction emerged. This concept, introduced within the context of modern Western art, marked a fundamental departure from the representational aspects that had defined naturalistic art in various styles and movements. As a result, this shift initiated a transformative movement in the 20th century in which artists who championed abstract art claimed to be able to convey a range of human experiences, such as mental processes, emotions, and unique thoughts, without relying on the depiction of recognisable external subjects (Ravanju & Pedram, 2021).The present study was conducted using a descriptive-analytical method, with library data collection and purposive sampling. The statistical sample of this study includes eight paintings by artists such as Claude Monet, Vincent Van Gogh, Paul Cézanne, Wassily Kandinsky, and Hilma af Klint. The early stage of modernism, characterised by movements such as Impressionism and Post-Impressionism, represents a progressive integration of scientific perspective and contemporary philosophical thought. The aim of Impressionist artists was to convey to their audience the concept of forms immersed in a luminous space, which required extensive exploration of light as a fundamental element affecting our perception of colour. Thus, in the twentieth century, building on the advances of visual artists in the nineteenth century, a significant transformation in the realm of art called "abstract art" took place.In contemporary art movements, the "circle" serves as a fundamental element for the development and valorisation of abstract art, cubism, and movements such as structuralism and Orphism, and is even the foundation of the Impressionist movement (Dobokor, 1994, p. 110). Monet is known as a pioneering figure of Impressionism, who used natural outdoor light to express the instantaneous changes of landscapes as they were illuminated by sunlight (Wang , 2022). In his “Sunrise”, he used the complementary colours of blue and orange, placing the sun as an orange circle on a blue background. Despite its small size, the circle acts as the focal point of the composition due to the striking contrast it creates with the surrounding blue. It should be noted that in the Impressionist movement, the accurate depiction of the physical qualities of light was considered a fundamental principle of painting. As a result, it is not surprising that the circular shape of the sun, representing light and radiance, often appears in the landscapes of Impressionist painters. Claude Monet, in line with his contemporaries, praised the beauty of sunlight and transformed the sun into a luminous ring (Dobokor, 1994, p. 111).Another early modernist artist who used the circle to depict the sun in his works was the Post-Impressionist painter Vincent van Gogh. The circular disk of the sun was one of Van Gogh's favourite subjects. Van Gogh's "The Extravagant" is bathed in light that shines from a huge halo that the painter's pen has drawn in the form of concentric circles. This luminous circle illuminates the cultivated land, indicating that the wheat ears are bearing fruit. Van Gogh seems to have shown in his paintings the presence of the Christian sun in the lives of the weakest social classes (Villas Boas, 2024, p. 20). In this way, it demonstrates the bond and friendship between religion and people. Van Gogh states: "If light is a symbol of goodness and truth, then the sun, which is the most important source of light, must be one with God." (Dobokor, 1994, p. 111). This analysis suggests that the importance of light, especially the sun, which is depicted as a luminous circle, is deeply rooted in Van Gogh's religious upbringing. He saw the source of light as a divine being, which influenced the brightness of his artwork.Cézanne was another artist whose goal was to strengthen the foundations of Impressionism, which led him to explore the theory of colour and form and integrate theoretical concepts with practical application (Pakbaz, 2017, p. 313). The sphere or circle is one of the three forms that Paul Cézanne envisioned as the fundamental shapes that make up the universe. He recreates nature using cylinders, cones, and spheres, ensuring that in three-dimensional space, the edges of every object and every view tend toward a central point. As a result, after prolonged observation and exploration, the viewer's gaze is focused. Cézanne believed that within every orange, apple, marble, and container, there is a focal point (Dobokor, 1994, p. 111).Klint was a prominent artist known for his landscapes and portraits in the late 19th and early 20th centuries. Klimt's fame among American audiences was further enhanced by his appearance in an exhibition titled "The Spiritual in Art: Abstract Painting" held in 1986 (Ohrner, 2019). Unlike Kandinsky, Mondrian, and Malevich, whose artworks were influenced by spirituality, Klint considered spirituality to be the core essence of her artistic practice (Isenberg, 2020). She created a series of paintings consisting of forms of circles, Ovals, and spirals that depicted supernatural force (Furio, 2014). One of these series was based on the discovery of the atom and its impact on the artist. All of these developments and changes had a direct impact on the creation of works by artists such as Klimt. He frequently organised his abstract works into series, each with recognisable titles that reflected his deep interests in both science and spirituality, such as Atom and Parsifal (Friedman, 2020).The results of this study show that analysing works of art from two distinct periods reveals a noticeable evolution in the expressive techniques employed by artists, which can be attributed to changes in lifestyle, personal and religious beliefs, culture, and scientific discoveries. In early modernist works, the circle form was mainly used to depict tangible and observable shapes, while abstract works, influenced by cultural influences and inspired by pioneering discoveries such as the discovery of the atom, began to explore unfamiliar territories.  

    Statement of The Problem: Autism Spectrum Disorder is a neurodevelopmental disorder that affects the development of certain parts of the brain, affecting the perception and communication skills of a developing child. The symptoms of Autism appear before the age of three, its main cause is still unknown and it’s not curable; but education plays an effective and significant role in improving the living conditions of children with Autism.Today, one of the effective ways to communicate with children is by using the visual method. Considering that some of the autistic children do not have the ability to speak, images can be a substitute for words for them. In addition, some of these children who have good visual memory and visual understanding pay more attention to images as a means of communication. Therefore, illustrations are used efficiently in the compilation of the content of books and other educational tools.Due to the prevalence of Autism, taking effective measures is necessary to educate and help the mental and social development of these children according to their characteristics. Since these children encounter images with their unique visual perception and neurological characteristics, they do not perceive them the same way as non-autistic children do. Knowing about the characteristics of their perception and also the type of illustrations that are compatible with their perception should be helpful and effective in improving the production of visual content for this group of children.The main question: The main question is what features should be included in visual content for children with Autism according to their visual perception. The main goal of this research is to introduce the visual characteristics that are suitable for the unique visual perception of autistic children; which is useful in the production of visual content for this group of children. Also, getting to know the way of visual perception in these children is also important as a secondary goal.Research Method: The research is applied and the type of data is qualitative. Regarding physical and mental characteristics, visual perception and identification of visual characteristics suitable for autistic children, due to the lack of Persian sources in this field, the focus was on non-Persian sources, and the research was done based on online searches in reliable scientific databases.  Interdisciplinary studies have been done focusing on the visual perception of autistic children of the visual elements and qualities such as: line, shape, volume, texture, color, writing, type of composition, form and color contrasts, symmetry and balance. It should be mentioned that in the image analysis section, the perception of autistic children from all the mentioned cases is based on the visual analysis of the samples. In the analysis section, in order to match the scientific findings with the real examples available in the educational system, these examples are targeted and based on criteria such as the amount of use, the age of the audience, the quality of the images and the ability to access them for free. Platforms and specialized websites in this field were collected and sampled. Due to the lack of native and Iranian educational resources in this field, non-Iranian sources have inevitably been referred to.The number of samples is 40 illustrated educational cards (printed and digital) suitable for the first and second grades of elementary school age group, with the topic of daily activities, which are precisely examined and analyzed based on the quality of the presence of visual indicators in the images such as: line, shape, volume, texture, color, writing, The type of composition, form and color contrasts, symmetry and balance. At the end, the results of theoretical studies and visual analyzes are suggested and introduced as visual indicators corresponding to the visual perception of autistic children. It is obvious that in image analysis, the main reference of the authors is on theoretical studies and the examples are not the basis of the final conclusion (it should be noted that due to the lack of space in the article, the analysis of 10 images is presented in the text).Results:Point: It is used both geometrically and non-geometrically, this element is also used for the purpose of creating texture.Line: The provided images do not have any contour lines. A variety of straight and curved lines have been used, but curved lines are used more than lines with sharp angles. The use of curved lines in the images is consistent with the data obtained about the principles of graphic design for Autism.Shape: Geometric shapes such as circles, rectangles, squares, triangles, Ovals and combined shapes, as well as repeating shapes that form a kind of texture in parts of the image can be seen. Shapes with many rounded corners were used in the images, which is consistent with findings of a preference for rounded, curved edges over sharp edges in graphic design for Autism (Satpathy, 2020).Volume: The images are mainly two-dimensional and flat, however, in a small number of images, the shadows, and the darkness and brightness in the colors have added a kind of bulge and volume to parts of the image.Texture: Texture was used less than the rest of the elements and is mostly created from the repetition of elements such as points, lines and forms such as spots. In the discussions related to the visual perception of autistic children, it was pointed out that they show a lower understanding of texture than other children, because the understanding of texture requires more complex neural networks in the visual pathway in the brain. Considering this issue, it can be said that the brief use of texture in the presented images can be consistent with this research finding.Color: In most of the images, the main and secondary colors are used with low saturation and purity, and are combined with neutral colors such as white, black, and gray. Warm colors like orange, cool colors like blue, and colors like green, brown, and pink are seen in a large number of images. Colors with low saturation can be more suitable for autistic children due to their high sensitivity to sensory stimuli. Children with Autism are more sensitive to changes in color saturation compared to other children (Holtzclaw, 2011, 12).According to the findings, some of these children show different and unusual visual processing ability due to their high sensitivity to sensory stimuli; in such a way that they perceive bright visual stimuli with a very high sensory load and as a result avoid it. (Simmons et al., 2009, 2707) For this reason, autistic children show less interest in the color yellow than other children, and prefer green, brown, and earth tones more than other children (Grandgeorge and Masataka, 2016, 1-4).According to the studies, cool colors like blue can have a calming effect on these children. (Bahamin et al., 2015, 5) Dull, whitish and gray colors such as pink are often liked by these children and have relaxing effects. (Effect of colors, undated) In addition, the color pink is the most effective color in calming aggressive behavior in these children (Bahamin et al., 2015, 5).Warm colors cause negative psychological effects such as causing anger, or even negative physical effects such as causing pain in parts of the body. (The effect of colors, undated) Therefore, the use of colors such as orange in the presented images is contrary to the needs of these children.Rhythm: The rhythm in the images is often monotonous and consists of repeating lines, dots, and shapes. Also, the progressive rhythm can be seen in one of the images, which consists of repeated and nested oval forms.Movement and direction: The composition of the elements in the images is such that the movement of the eye and the audience’s gaze is focused towards the center and top of the frame, on the main subject. The content of the images are designed in a concise and simple way, and the background elements are not seen in large numbers. Studies have shown that people with Autism are easily distracted by information they don’t like; Therefore, it is better to use simple graphics and avoid using images in the background. It is also important to avoid using abstract images and remove elements that are too prominent. (Satpathy, 2020) Autistic children’s understanding of visual stimuli is more focused on the local details, and global understanding of visual stimuli is less seen in these children. (Kurtz, 2006, 12).Text: The typeface used is sans serif, geometric and monoline. Which is consistent with the principles proposed for graphic design for autistic children.Symmetry: In most of the images, the presence of complete symmetry or asymmetrical symmetry is visible.Balance and equilibrium: Images have balance due to their symmetry. The overall images have balance and equilibrium, sometimes with a bit of weight in the right or left part of the image.Proportion: In most of the images, the proportion and size of the image components are close to reality.In general, it can be said that almost all visual elements and qualities can be used in creating visual content for autistic children with some restrictions. Autistic children’s visual perception of simpler elements with less details, less bright colors and lights, shapes with less sharpness, softer and simpler textures, composition with less elements is better, which we explained in detail for each element in the section “the results of the analysis”. Paying attention to these factors is effective in creating peace in daily teaching and communication with these children and even in improving their physical health.The results of the analysis show that the visual perception of autistic children has not been paid much attention to by the designers in the design of illustrated educational cards for them, so it is hoped that with the expansion of interdisciplinary research, we will see the improvement of appropriate designs for this audience community.