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ABSTRACTThe authors introduce new classes of analytic function with respect [Formula: see text]-symmetric points subordinate to a domain that is not Carathéodory. To use the existing infrastructure or framework, usually, the study of analytic function have been limited to a differential characterization subordinate to functions which are Carathéodory. Here, we try to obtain various interesting properties of functions which are not Carathéodory. Integral representation, interesting conditions for starlikeness and inclusion relations for functions in these classes are obtained.

The main objective of this study was to analyze the deep drawing behavior of sandwich laminate for various blank shapes and lubrications. Commercially available aluminum sandwich laminate with face sheets made of aluminum alloy, AA2219 and a core made of high-density polyethylene was used for the forming behaviour performance. The laminate was characterized by its mass density, porosity and tensile strength for better understanding the physical and mechanical behavior, being essential for analyzing the forming behaviour. Deep drawing, one of the forming techniques on the laminate was performed with a steel spherical punch for three different blank shapes: circular, square and square with round fillets. Furthermore, three different lubricants Vaseline, grease and soap, were used at the contact regions of the die and laminate. This formation occurred under normal atmospheric conditions. Lubrication significantly influenced the drawing performance in addition to the blank shape. Uniform material flow during the drawing process was achieved in the circular specimen, which in turn resulted in better drawing performance of the laminate. The highest drawing force of 1.425 kN was obtained for the circular specimen with the grease lubricant. A higher-order equivalent plastic strain was observed for the lubricant grease, and the least-order strain was observed for the specimens under dry conditions. The higher the effect of lubrication, the lower the friction between the punch and specimen, which in turn resulted in a higher order strain and subsequent reduction in the thickness of the specimen.

In this paper, we defined a new family of meromorphic functions whose analytic characterization was motivated by the definition of the multiplicative derivative. Replacing the ordinary derivative with a multiplicative derivative in the subclass of starlike meromorphic functions made the class redundant; thus, major deviation or adaptation was required in defining a class of meromorphic functions influenced by the multiplicative derivative. In addition, we redefined the subclass of meromorphic functions analogous to the class of the functions with respect to symmetric points. Initial coefficient estimates and Fekete–Szegö inequalities were obtained for the defined function classes. Some examples along with graphs have been used to establish the inclusion and closure properties.

A disco-rectangular volume-fraction-of-fluid (VOF) model tank of a prismatic size is considered here for investigating the severe effect of overhead baffles made of three different materials, nylon, polyamide, and polylactic acid. In this work, the overdamped, undamped, and nominal damped motion of baffles and their effect are studied. In this research, the behaviour of different material baffles based on the sloshing effect and natural frequency of each baffle excited in damped, undamped, and overdamped cases is studied. VOF modelling is carried out in moving Yeoh model mesh with fluid–structure interaction between the water models for various baffle plates. The results of the water volume distribution and baffle displacement operating between a sloshing time of 0 and 1 s are recorded. Also, a strong investigation is carried out for the water volume suspended on overhead baffles by three different material selections.

Motivated by the notion of multiplicative calculus, more precisely multiplicative derivatives, we used the concept of subordination to create a new class of starlike functions. Because we attempted to operate within the existing framework of the design of analytic functions, a number of restrictions, which are in fact strong constraints, have been placed. We redefined our new class of functions using the three-parameter Mittag–Leffler function (Srivastava–Tomovski generalization of the Mittag–Leffler function), in order to increase the study’s adaptability. Coefficient estimates and their Fekete-Szegő inequalities are our main results. We have included a couple of examples to show the closure and inclusion properties of our defined class. Further, interesting bounds of logarithmic coefficients and their corresponding Fekete–Szegő functionals have also been obtained.

In recent times, academicians and scientists have developed many methods for purifying saline water into pure water that is suitable for drinking, as well as other suitable applications. Fortunately, solar desalination has been a very popular technique, which uses eco-friendly solar energy. In this work, a passive-type double-slope solar still was designed and fabricated according to the Global Positioning System (GPS) coordinates of Nizwa city in Oman. Economically and readily available materials, such as acrylic, glass, and foam insulation materials, were used in the construction of the double-slope solar still in addition to the conventional materials used for the supporting structure of the solar still. The climatic factors (such as the solar radiation and ambient temperature), design factors (such as the exposure surface area, inclination, insulation material and thickness, and glazing material), and operating parameters (such as the glass temperature, feed water temperature and yield) obtained were considered in the study to estimate the performance of the solar still. DHT 11 sensors with Arduino programming were used in the experiment to record the temperatures at specific locations on the solar still daily with regular time intervals for a period of 3 to 4 weeks. The solar still was designed to operate from February to March 2023. The temperatures were recorded every two hours daily, whereas the yield was recorded at the end of the day of operation. The quality of the yield was estimated through the measurement of pH and TDS (Total Dissolved Solids) values. The energy and exergy analysis of the desalination unit was carried out to estimate the thermal performance of the system. A significant effect of solar intensity and ambient temperature was observed on the thermal performance of the system and on the quality of the drinking water. An energy efficiency ranging between 30 to 45% and exergy efficiency ranging between 2 to 3.5% was obtained in the system, which was reasonably better for a thermal system involving a renewable source of energy.

To consolidate or adapt to many studies on meromorphic functions, we define a new subclass of meromorphic functions of complex order involving a differential operator. The defined function class combines the concept of spiral-like functions with other studies pertaining to subclasses of multivalent meromorphic functions. Inclusion relations, integral representation, geometrical interpretation, coefficient estimates and solution to the Fekete-Szegö problem of the defined classes are the highlights of this present study. Further to keep up with the present direction of research, we extend the study using quantum calculus. Applications of our main results are given as corollaries.

In this paper, we introduce a new class of analytic functions subordinated by functions which is not Carathéodory. We have obtained some interesting subordination properties, inclusion and integral representation of the defined function class. Several corollaries are presented to highlight the applications of our main results.

We introduce a new class of Bazilevič functions involving the Srivastava–Tomovski generalization of the Mittag-Leffler function. The family of functions introduced here is superordinated by a conic domain, which is impacted by the Janowski function. We obtain coefficient estimates and subordination conditions for starlikeness and Fekete–Szegö functional for functions belonging to the class.

We define a function to unify the well-known class of Janowski functions with a class of spirallike functions of reciprocal order. We focus on the impact of defined function on various conic regions which are symmetric with respect to the real axis. Further, we have defined a new subclass of multivalent functions of complex order subordinate to the extended Janowski function. This work bridges the studies of various subclasses of spirallike functions and extends well-known results. Interesting properties have been obtained for the defined function class. Several consequences of our main results have been pointed out.

In this paper, we familiarize a class of multivalent functions with respect to symmetric points related to the differential operator and discuss the impact of Janowski functions on conic regions. Inclusion results, the subordination property, and coefficient inequalities are obtained. Further, the applications of our results that are extensions of those given in earlier works are presented as corollaries.

In this paper, we introduce and study a new subclass of multivalent functions with respect to symmetric points involving higher order derivatives. In order to unify and extend various well-known results, we have defined the class subordinate to a conic region impacted by Janowski functions. We focused on conic regions when it pertained to applications of our main results. Inclusion results, subordination property and coefficient inequality of the defined class are the main results of this paper. The applications of our results which are extensions of those given in earlier works are presented here as corollaries.

In this paper, we carry out a systematic study to discover the properties of a subclass of meromorphic starlike functions defined using the Mittag–Leffler three-parameter function. Differential operators involving special functions have been very useful in extracting information about the various properties of functions belonging to geometrically defined function classes. Here, we choose the Prabhakar function (or a three parameter Mittag–Leffler function) for our study, since it has several applications in science and engineering problems. To provide our study with more versatility, we define our class by employing a certain pseudo-starlike type analytic characterization quasi-subordinate to a more general function. We provide the conditions to obtain sufficient conditions for meromorphic starlikeness involving quasi-subordination. Our other main results include the solution to the Fekete–Szegő problem and inclusion relationships for functions belonging to the defined function classes. Several consequences of our main results are pointed out.

A class of p-valent functions of complex order is defined with the primary motive of unifying the concept of prestarlike functions with various other classes of multivalent functions. Interesting properties such as inclusion relations, integral representation, coefficient estimates and the solution to the Fekete–Szegő problem are obtained for the defined function class. Further, we extended the results using quantum calculus. Several consequences of our main results are pointed out.

In this paper, we defined a new class of λ-pseudo-Bazilevič functions of complex order using subordination. Various classes of analytic functions that map unit discs onto a conic domain and some classes of special functions were studied in dual. Some subordination results, inequalities for the initial Taylor–Maclaurin coefficients and the unified solution of the Fekete–Szegő problem for subclasses of analytic functions related to various conic regions, are our main results. Our main results have many applications which are presented in the form of corollaries.