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This paper aims to develop a novel grey Bernoulli model with memory characteristics, which is designed to dynamically choose the optimal memory kernel function and the length of memory dependence period, ultimately enhancing the model's predictive accuracy.

This paper enhances the traditional grey Bernoulli model by introducing memory-dependent derivatives, resulting in a novel memory-dependent derivative grey model. Additionally, fractional-order accumulation is employed for preprocessing the original data. The length of the memory dependence period for memory-dependent derivatives is determined through grey correlation analysis. Furthermore, the whale optimization algorithm is utilized to optimize the cumulative order, power index and memory kernel function index of the model, enabling adaptability to diverse scenarios.

The selection of appropriate memory kernel functions and memory dependency lengths will improve model prediction performance. The model can adaptively select the memory kernel function and memory dependence length, and the performance of the model is better than other comparison models.

The model presented in this article has some limitations. The grey model is itself suitable for small sample data, and memory-dependent derivatives mainly consider the memory effect on a fixed length. Therefore, this model is mainly applicable to data prediction with short-term memory effect and has certain limitations on time series of long-term memory.

In practical systems, memory effects typically exhibit a decaying pattern, which is effectively characterized by the memory kernel function. The model in this study skillfully determines the appropriate kernel functions and memory dependency lengths to capture these memory effects, enhancing its alignment with real-world scenarios.

Based on the memory-dependent derivative method, a memory-dependent derivative grey Bernoulli model that more accurately reflects the actual memory effect is constructed and applied to power generation forecasting in China, South Korea and India.

Topology optimization of structures under self-weight loading is a challenging problem which has received increasing attention in the past years. The use of standard formulations based on compliance minimization under volume constraint suffers from numerous difficulties for self-weight dominant scenarios, such as non-monotonic behaviour of the compliance, possible unconstrained character of the optimum and parasitic effects for low densities in density-based approaches. This paper aims to propose an alternative approach for dealing with topology design optimization of structures into three spatial dimensions subject to self-weight loading.

In order to overcome the above first two issues, a regularized formulation of the classical compliance minimization problem under volume constraint is adopted, which enjoys two important features: (a) it allows for imposing any feasible volume constraint and (b) the standard (original) formulation is recovered once the regularizing parameter vanishes. The resulting topology optimization problem is solved with the help of the topological derivative method, which naturally overcomes the above last issue since no intermediate densities (grey-scale) approach is necessary.

A novel and simple approach for dealing with topology design optimization of structures into three spatial dimensions subject to self-weight loading is proposed. A set of benchmark examples is presented, showing not only the effectiveness of the proposed approach but also highlighting the role of the self-weight loading in the final design, which are: (1) a bridge structure is subject to pure self-weight loading; (2) a truss-like structure is submitted to an external horizontal force (free of self-weight loading) and also to the combination of self-weight and the external horizontal loading; and (3) a tower structure is under dominant self-weight loading.

An alternative regularized formulation of the compliance minimization problem that naturally overcomes the difficulties of dealing with self-weight dominant scenarios; a rigorous derivation of the associated topological derivative; computational aspects of a simple FreeFEM implementation; and three-dimensional numerical benchmarks of bridge, truss-like and tower structures.

This study aims to analyze the impact of fractional derivatives on heat transfer and entropy generation during transient free convection inside various complex porous enclosures, such as triangle, L-shape and square-containing wavy surfaces. These porous enclosures are saturated with Cu-water nanofluid and subjected to the influence of a uniform magnetic field.

In the present study, Darcy’s model is used for the momentum transport equation in the porous matrix. Additionally, the Caputo time fractional derivative is introduced in the energy equation to assess the heat transfer phenomenon. Furthermore, the total entropy generation has been computed by combining the entropy generation due to fluid friction (S_ff), heat transfer (S_ht) and magnetic field (S_mf). The complete mathematical model is further simulated using the penalty finite element method, and the Caputo time derivative term is approximated using the L1 scheme. The study is conducted for various ranges of the Rayleigh number (102≤Ra≤104), Hartmann number (0≤Ha≤20) and fractional order parameter (0<α<1) with respect to time.

It has been observed that the fractional order parameter α governs the characteristics of entropy generation and heat transfer within the selected range of parameters. The Bejan number associated with heat transfer (Be_ht), fluid friction (Be_ff) and magnetic field (Be_mf) further demonstrate the dominance of flow irreversibilities. It becomes evident that the initial evolution state of streamlines, isotherms and local entropy varies according to the choice of α. Additionally, increasing Ra values from 10² to 10⁴ shows that the heat transfer rate increases by 123.8% for a square wavy enclosure, 7.4% for a triangle enclosure and 69.6% for an L-shape enclosure. Moreover, an increase in the value of Ha leads to a reduction in heat transfer rates and entropy generation. In this case, Bemf→1 shows the dominance of the magnetic field irreversibility in the total entropy generation.

Recently, fractional-order models have been widely used to express numerous physical phenomena, such as anomalous diffusion and dispersion in complex viscoelastic porous media. These models offer a more accurate representation of physical reality that classical models fail to capture; this is why they find a broad range of applications in science and engineering.

The fractional derivative model is used to illustrate the flow pattern, heat transfer and entropy-generating characteristics under the influence of a magnetic field. Furthermore, to the best of the author’s knowledge, a fractional-derivative-based mathematical model for the entropy generation phenomenon in complex porous enclosures has not been previously developed or studied.

Interest rate derivatives (IRDs) are the essential components of financial risk management and are used across various industry sectors. The objective is to analyze the differences in approach to managing interest rate risks between the Indian corporates that execute IRDs and the ones that do not.

Interest rate fluctuations require Indian corporates to hedge their exposures in foreign currency interest rates. This is all the more true for mid-sized corporates because of their balance sheet exposures. Additionally, they may not have the resources to formulate risk management policies. This paper analyzes data collected from financial statements of a diverse set of companies that use IRD and helps in formulating such a strategy.

The results indicate significant differences for some of the parameters like information asymmetry and agency cost between users and non-users of IRDs. The study further suggests causality between users of derivatives and parameters like size, growth and debt.

The study compares users and non-users of IRDs, thereby identifying factors unique to users of IRDs. It also studies causality relations which explain the motivation to do IRDs. Thus, it enables risk managers to use this as a reference point to decide on their strategies.

While there are multiple studies across geographies and sectors including commercial banks in India on the usage of interest rate swaps, this study focuses on Indian mid-tier corporates. Furthermore, the study distinguishes between users and non-users based on financial parameters, which in turn would provide a framework for decision-hedging strategies.

After completion of the case study, the students will be able to understand the different risks associated with a business, focusing on price risk and the importance of price risk management in business; understand and evaluate the products available for hedging price risk through exchange-traded derivatives in the Indian scenario; and understand and evaluate the different strategies for price risk management through exchange-traded derivatives in the Indian scenario.

The case study pertains to a small business, M/s Sethi Jewellers. The enterprise is being run by Shri Charan Jeet Sethi and his son Tejinder Sethi. The business is located in Jain Bazar, Jammu, UT, in Northern India. The business was started in 1972 by Charan Jeet’s father. They deal in a wide range of jewelry products and are well-established jewelers known for selling quality ornaments. Tejinder (MBA in marketing) was instrumental in revamping his business recently. Under his leadership, the business has experienced rapid transformation. The business has grown from a one-room shop fully managed by Tejinder’s grandfather to a multistory showroom with several artisans, sales staff and security persons. Through his e-store, Tejinder has a bulk order from a client where the client requires him to accept the order with a small token at the current price and deliver the final product three months from now. Tejinder is in a dilemma about accepting or rejecting the large order. Second, if he accepts, should he buy the entire gold now or wait to buy it later at a lower price? He is also considering hedging the price risk through exchange-traded derivatives. However, he is not entirely sure, as he has a few apprehensions regarding the same, and he is also not fully aware of the process and the instruments he has to use for hedging the price risk on the exchange.

The case study is aimed to cater to undergraduate, postgraduate and MBA students in the field of finance. This case study can be used for students interested in commodity derivatives, risk management and market microstructure.

Teaching notes are available for educators only.

CSS 1: Accounting and finance.

This paper aims to synthesize new screen-printing ink formula based on new derivatives of azo thiadiazol disperse dyes and evaluate their characteristics after being printed on polyester fabric substrates.

New dispersed dyes based on 1, 3, 4-Thiadiazole derivatives (dyes 1 and 2) were prepared and confirmed by different analyses, infrared (IR), mass and nuclear magnetic resonance (NMR) spectroscopy, and then formulated as colored materials in the screen-printing ink formulations. Printing pastes containing the prepared dyestuffs and other ingredients were used for printing polyester using screen-printing or traditional printing. The characteristics of printed polyester fabric substrates were measured by color measurements such as a*, b*, L*, C*, E, Ho, R% and color strength, as well as light, washing, crock and alkali perspiration fastness, and finally, the depth of penetration was evaluated.

The prepared 1, 3, 4-Thiadiazole derivatives (dyes 1 and 2) were obtained from the reaction of 5,5’-(1,4-phenylene)bis(1,3,4-Thiadiazole-2-amine) with resorcinol and m-toluidine as a coupling component. The suitability of the prepared dyestuffs for silk screen-printing on polyester fabrics has been investigated. The prints obtained from a formulation containing dye 1 possess high color strength as well as good overall fastness properties if compared to those obtained using dye 2.

The method of synthesis of the new dyestuffs and screen-printing ink provides a simple and practical solution to prepare some new heterocyclic disperse azo dyes, and they are formulated in the screen-printing inks for printing on a polyester fabric substrate.

The prepared disperse dyes based on 1,3,4-Thiadiazole derivatives (dyes 1 and 2) could be used in textile printing of polyester on an industrial scale.

The purpose of this study is to analyse and compile the literature on various option pricing models (OPM) or methodologies. The report highlights the gaps in the existing literature review and builds recommendations for potential scholars interested in the subject area.

In this study, the researchers used a systematic literature review procedure to collect data from Scopus. Bibliometric and structured network analyses were used to examine the bibliometric properties of 864 research documents.

As per the findings of the study, publication in the field has been increasing at a rate of 6% on average. This study also includes a list of the most influential and productive researchers, frequently used keywords and primary publications in this subject area. In particular, Thematic map and Sankey’s diagram for conceptual structure and for intellectual structure co-citation analysis and bibliographic coupling were used.

Based on the conclusion presented in this paper, there are several potential implications for research, practice and society.

This study provides useful insights for future research in the area of OPM in financial derivatives. Researchers can focus on impactful authors, significant work and productive countries and identify potential collaborators. The study also highlights the commonly used OPMs and emerging themes like machine learning and deep neural network models, which can inform practitioners about new developments in the field and guide the development of new models to address existing limitations.

The accurate pricing of financial derivatives has significant implications for society, as it can impact the stability of financial markets and the wider economy. The findings of this study, which identify the most commonly used OPMs and emerging themes, can help improve the accuracy of pricing and risk management in the financial derivatives sector, which can ultimately benefit society as a whole.

It is possibly the initial effort to consolidate the literature on calibration on option price by evaluating and analysing alternative OPM applied by researchers to guide future research in the right direction.

The purpose of this paper is to improve autonomous flight performance of a fixed-wing unmanned aerial vehicle (UAV) via simultaneous morphing wingtip and control system design conducted with optimization, computational fluid dynamics (CFD) and machine learning approaches.

The main wing of the UAV is redesigned with morphing wingtips capable of dihedral angle alteration by means of folding. Aircraft dynamic model is derived as equations depending only on wingtip dihedral angle via Nonlinear Least Squares regression machine learning algorithm. Data for the regression analyses are obtained by numerical (i.e. CFD) and analytical approaches. Simultaneous perturbation stochastic approximation (SPSA) is incorporated into the design process to determine the optimal wingtip dihedral angle and proportional-integral-derivative (PID) coefficients of the control system that maximizes autonomous flight performance. The performance is defined in terms of trajectory tracking quality parameters of rise time, settling time and overshoot. Obtained optimal design parameters are applied in flight simulations to test both longitudinal and lateral reference trajectory tracking.

Longitudinal and lateral autonomous flight performances of the UAV are improved by redesigning the main wing with morphing wingtips and simultaneous estimation of PID coefficients and wingtip dihedral angle with SPSA optimization.

This paper originally discusses the simultaneous design of innovative morphing wingtip and UAV flight control system for autonomous flight performance improvement. The proposed simultaneous design idea is conducted with the SPSA optimization and a machine learning algorithm as a novel approach.

In this paper we talk about complex matrix quaternions (biquaternions) and we deal with some abstract methods in mathematical complex matrix analysis.

We introduce and investigate the complex space HC consisting of all 2 × 2 complex matrices of the form ξ=z1+iw1z2+iw2−z‾2−iw‾2z‾1+iw‾1, (z1,w1,z2,w2)∈C4.

We develop on HC a new matrix holomorphic structure for which we provide the fundamental operational calculus properties.

We give sufficient and necessary conditions in terms of Cauchy–Riemann type quaternionic differential equations for holomorphicity of a function of one complex matrix variable ξ∈HC. In particular, we show that we have a lot of holomorphic functions of one matrix quaternion variable.

This study aims to propose and numerically assess different ways of discretising a very weak formulation of the Poisson problem.

We use integration by parts twice to shift smoothness requirements to the test functions, thereby allowing low-regularity data and solutions.

Various conforming discretisations are presented and tested, with numerical results indicating good accuracy and stability in different types of problems.

This is one of the first articles to propose and test concrete discretisations for very weak variational formulations in primal form. The numerical results, which include a problem based on real MRI data, indicate the potential of very weak finite element methods for tackling problems with low regularity.