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Insights into the Benzodihydrofuran Derivative-Induced Conformational and Structural Changes in the Alzheimer’s Disease-Associated Amyloid-β Peptide
No full textThe progression of Alzheimer’s disease (AD) is linked to the misfolding and aggregation of amyloid−β (Aβ) monomers into neurotoxic soluble oligomers, protofibrils, and ultimately mature fibrils. The most effective therapeutic approach for treating AD is to inhibit Aβ42 aggregation. Metal complexes and small molecules have been identified as promising inhibitors to combat self–aggregation of Aβ42 monomer. A binuclear metal complex PtRu–1([Ru(bpy)2(dpp)PtCl2]Cl2), containing PtII and RuII metal centers, has been previously reported to inhibit the Aβ42 aggregation in early stages. Thioflavin–T (ThT) assay revealed that incubation of Aβ42 with equimolar or 2−fold molar excess of PtRu–1 led to a 90% decrease in ThT fluorescence, highlighting inhibitory potential against Aβ42 aggregation. Despite comprehensive experimental investigations, the molecular interactions and binding mechanism underlying the inhibitory capacity of Pt−Ru1 on Aβ42 aggregation remain unidentified. Thus, an attempt was made to examine the molecular mechanism by which Pt−Ru1 inhibits the aggregation of Aβ42 monomer. The molecular docking results depict favourable binding (–6.45 kcal/mol) of Pt−Ru1 to Aβ42 monomer influenced by hydrogen bonds, hydrophobic contacts, and π−π stacking interactions.
Sánchez et al. synthesized 15 chalcone derivatives using Claisen–Schmidt condensation by utilizing a natural benzodihydrofuran compound, i.e., fomannoxine. Fluorine substitution was found to significantly enhance cytoprotective activity and reduce the aggregation rate of Aβ, making them promising therapeutic candidates. ThT fluorescence analysis reveals that co-incubation of chalcone−3c with Aβ led to a reduction in fluorescence intensity. Notably, chalcone−3c enhanced cell viability by 50%, thereby reducing cytotoxicity and showing no cytotoxic effect at different concentrations. Thus, molecular docking as well as molecular dynamics (MD) simulations were employed to examine the inhibitory mechanism of chalcone3c against self–aggregation of Aβ42 monomer. The molecular docking results indicated a favorable interaction of chalcone−3c with the Aβ42 monomer, exhibiting a binding energy of −6.7 kcal/mol. The RMSD and RMSF evaluations exhibited a decrease in conformational variations in the Aβ42 monomer following the inclusion of chalcone−3c. An increase in helix content was detected in the Aβ42 monomer, rising from 20.2 ± 1.6 % to 33.8 ± 1.5 %, indicating a reduction in the aggregation tendency of the Aβ42 monomer in the presence of chalcone−3c. Additionally, the intramolecular hydrogen bonds rise from 21.37 ± 0.96 to 22.19 ± 1.05 with the addition of chalcone−3c, supporting the enhancement of the helical conformation of Aβ42 monomer. Contact map analysis revealed reduced aggregation tendency of Aβ42 monomer on the incorporation of chalcone−3c due to reduction in residue interaction in the central hydrophobic core (CHC) and C−terminal region. PCA, FEL, and conformational clustering studies highlight higher conformational homogeneity in Aβ42 monomer in the presence of chalcone−3c, which indicates lower fibrillation propensity in Aβ42 monomer. The illumination of the molecular interactions between Aβ42 monomer and chalcone−3c provides critical insights for the strategic development of more effective aggregation inhibitors as prospective therapeutic candidates against Aβ aggregation in AD
Addressing Thermal Challenges in Rotary-Airlock Valves: An Industrial Perspective
No full textRotary airlocks are pivotal components in a wide range of industrial systems, serving the dual function
of regulating material flow and maintaining pressure differentials between connected environments.
Due to their ability to prevent air leakage while enabling consistent material transfer, which is critical
to the reliable pneumatic conveying of bulk materials in various sectors such as food processing,
chemical manufacturing, cement production, and pharmaceuticals. At the heart of a rotary airlock is a
cylindrical rotor fitted with multiple vanes that create sealed compartments, enabling the controlled
transfer of materials from the inlet to the outlet while maintaining pressure isolation. In industrial
applications—particularly those involving a wide range of powders and varying operating
temperatures—rotary airlocks face several performance challenges. These include air leakage, thermal
expansion, material jamming, and accelerated wear, especially when dealing with abrasive or cohesive
materials. Such challenges can compromise efficiency, reliability, and the overall lifespan of the
equipment, making robust design and regular maintenance essential. In high-temperature
environments, such as cement kilns or chemical reactors, thermal effects further complicate
performance by altering component clearances and weakening sealing integrity, which in turn can
degrade system functionality and increase the risk of failure. Recent research underscores the critical
importance of understanding heat transfer and thermal behavior in rotary systems, emphasizing the
need for accurate thermal modeling to minimize efficiency losses and prevent operational failures. In
this context, the present study investigates the thermal characteristics of rotary airlocks, with a
particular focus on analyzing heat transfer mechanisms, thermal expansion effects, and their influence
on air leakage and rotor-to-casing clearance. By incorporating insights from recent advancements, this
work aims to contribute to the development of improved design strategies and to enhance the reliability
and performance of rotary airlocks operating in thermally challenging industrial environments
Approximation by Certain Linear Convergence Techniques
No full textThe present thesis titled as ``Approximation by Certain Linear Convergence Techniques'' involves the construction of new positive linear operators and examines their approximation properties as well as their applications in multidisciplinary fields. The thesis is divided into eight chapters that majorly covers three important aspects of approximation theory.
Firstly, we give the brief introduction of approximation theory and the basic results that are the inspiration for the development of this theory. We also provide basic definitions as well as approximation tools such as moduli of continuity, modulus of smoothness, Peetre's -functional for the univariate operators, complete and partial modulus of continuities for function of two variables to check the convergence of positive linear operators for the given function. Also, we list the brief account of the related work of various authors for the positive linear operators and found some gaps according which the research work in this thesis has been carried out.
The first direction of the thesis is to focus on the order of approximation of existing positive linear operators. We know the convergence and the order of approximation of the positive linear operators are two important attributes in approximation theory to approximate any function. Using the well-known Korovkin theorem, we can easily verify the convergence of these operators but improving the order of approximation is a critical attribute. We describe a recursive method designed to improve the approximation results of known operators, which results in increased accuracy and efficiency. We presented three modifications of -Bernstein P\u{a}lt\u{a}nea operators with linear, quadratic and cubic order of approximation and study some approximation results concerning the rate of convergence, error estimation and Voronovskaja type formulas for the new modifications.
The next aspect for the thesis is to introduce new positive linear operators that outperform classical operators in terms of approximation properties. These new operators are designed to approximate functions effectively on both finite and infinite domains by using certain parameters to introduce the flexibility in these positive linear operators. It helps to increase the applicability and utility of positive linear operators in various mathematical and engineering contexts.
We define the bivariate operators as well as Generalized Boolean Sum (GBS) operators associated with these operators for the first order modification of -Bernstein P\u{a}lt\u{a}nea operators. In order to approximate Lebesgue integrable functions, we introduce the Durrmeyer-variant of Lupa\c{s} type operators by using Pochhammer -symbol in one as well as two dimensional space. Also, we give the univariate and bivariate versions of the Bernstein-Lototsky operators that are able to preserve any polynomial with some certain conditions by introducing a real parameter \rho>0. We define the new operators to approximate integrable functions by using -Baskakov operators and a non-negative parameter defined on infinite domain. We study the approximation results of these operators by using well-known tools of the approximation theory including convergence and error estimates in terms of moduli of continuity. The results of all these positive linear operators have been verified by graphical illustrations for certain examples. Also, the introduced bivariate versions of the operators can be extended to approximate the functions of several variables. This feature is especially beneficial in real-world situations when functions rely on more than one variable.
In the last part of the thesis, we introduce the applications of positive linear operators in the realm of B\'{e}zier curves. With the widespread use of computers in all industries, these curves have become critical to study. These curves utilize positive linear operators such as Bernstein and their generalizations. We can include some parameters to obtain greater control over these curves. These factors assist in reducing time and expense while improving the curves' accuracy and adaptability.
We generalize the B\'ezier curves by using two parameters to get the better control on shape of the curves. Firstly, we construct the generalized B\'{e}zier curves and B\'{e}zier surfaces depending upon the parameter Secondly, we explore the applications of -calculus in polynomial basis functions and curve modeling. We define the -variant of Bernstein-Chlodowsky basis polynomials and introduce generalization of B\'{e}zier curves by utilizing these basis polynomials. We study the properties of these curves and surfaces and show that the introduced parameter provides us the flexibility to modify the curves as well as surfaces by giving some numerical examples with the help of MATLAB. Also, we provide an exact approach to calculate the control points for the given -B\'{e}zier curve.
In summary, the thesis makes substantial contributions to the field of approximation theory by improving existing approximation techniques, introducing new operators with superior properties, and extending the applications of these operators to the construction and modification of B\'{e}zier curves and surfaces. These advancements hold promise for enhancing various practical applications in computational mathematics, computer graphics, and related areas
Verification of a DFI-Based DDR4 PHY Bridge for DDR PHY Modules
No full textIn this paper we introduce a high-performance DDR4 SDRAM DDR PHY Training Unit design,
this design is independent of the SOC and will only work with the PHY for its training and will
provide a better handshake mechanism between PHY and DDR PHY Training Unit. Our DDR
PHY Training Unit is able to perform DRAM initialization, refresh, and calibration. Its design
is extensible, allowing for further development of other types of DDR4 memory controllers and
adaptation for various DDR4 speed grades. The development process involved creating the
DDR PHY Training Unit’s logic blocks in RTL from the ground up. Standalone verification of
each designed module was conducted, followed by the coverage plane was created to do the
complete validation of the entire integrated product. To evaluate the performance of our DDR
PHY Training Unit, we conducted extensive assessments using both EEMBC benchmarks and
synthetic benchmarks in simulation. These evaluations provide a comprehensive comparison of
their performance across various scenarios, offering valuable insights for further developments
in the field
Factors Influencing Online Impulse Buying Behaviour: An Empirical Study from Northern India
No full textIn the rapidly evolving landscape of digital commerce, online impulse buying behaviour (IBB) has emerged as a critical area of academic inquiry and managerial concern. Despite its growing prevalence, existing research has not fully explored the complex and interconnected factors that influence IBB, particularly how various individual, promotional, website-related, and situational variables interact through consumers' psychological tendencies. Addressing this gap, the present study investigates the multidimensional antecedents of online impulse buying behaviour (IBB), emphasizing the mediating role of impulse buying tendency (IBT).
The research is guided by four key objectives, examining how individual, promotional, website-related, and situational factors affect IBB, and culminates in the development of an integrated conceptual model that places IBT at the core of these relationships.
A proportionate stratified sampling approach was adopted to ensure demographic representation across key Northern Indian regions Punjab, Haryana, Delhi NCR, and Chandigarh. A total of 415 online shoppers, each with a minimum of six online purchases in the past year, participated in the study (165 from Punjab, 140 from Haryana, 90 from Delhi NCR, and 30 from Chandigarh). This sampling strategy enhanced the study’s validity, reliability, and regional representativeness.
The study employed a quantitative design, using Partial Least Squares Structural Equation Modeling (PLS-SEM) to analyze the proposed hypotheses. Results indicate that individual factors such as hedonic motivation and mood states significantly influence IBT but do not directly impact IBB. Promotional factors including discount offers, online reviews, online campaigns, product recommendations, and limited-time deals exert a significant influence on both IBT and IBB. Among website-related features, website aesthetics emerged as a key predictor of both IBT and IBB, while security/privacy and convenience showed partial effects. Regarding situational factors, money availability and credit card usage positively influenced IBB, while time availability showed no significant effect. Mediation analysis confirmed the central role of IBT in linking these factors to IBB.
Theoretically, this study advances the application of the Stimulus-Organism-Response (S-O-R) framework and Self-Determination Theory (SDT), while integrating perspectives from the Competitive Arousal Model and the Consumption Impulse Formation and Enactment Model. This multi-theoretical approach provides a deeper understanding of the psychological mechanisms driving OIB. Practically, the research offers actionable insights for digital marketers, e-commerce firms, and policymakers by suggesting targeted strategies to stimulate impulse purchases, enhance user experience, and uphold ethical marketing standards.
Despite certain limitations such as geographical scope, cross-sectional design, and reliance on self-reported data the study provides a robust foundation for future research. It encourages further investigation into the evolving nature of consumer behaviour, particularly in response to emerging technologies such as AI, AR/VR, and voice commerce
Photocatalytic Oxidation of Nitrogenous Fertilizers Using Cyclodextrin and Reduced Graphene Oxide Modified Metal-TiO2 Nanocomposites
No full textChapter-1
This comprehensive introduction provides a solid foundation for understanding the role of nitroge- nous fertilizers, the challenges of nitrogen loss, and the potential of advanced nanocomposites in im- proving nitrogen utilization in agriculture is systematically explained in this chapter. However, sig- nificant nitrogen loss through volatilization, leaching, and emissions leads to environmental concerns and reduced crop efficiency. The research gap emphasizes the need for advanced nanocomposites like M-TiO2, reduced graphene oxide (RGO), and cyclodextrin (CD) to enhance nitrate production and minimize nitrogen loss. The proposed approach suggests that combining these materials could lead to more efficient photocatalytic oxidation of urea, improving nitrate conversion and reducing nitrogen-related environmental issues.
Chapter-2 Nowadays, fertilizers are used to boost crop production. Nitrogenous fertilizers are assimilated as nitrate. Unfortunately, 60-70% of nitrogen is lost due to different leaching processes. Photocatalytic urea oxidation is now emerging as a new methodology. Nitrate conversion is favorable under alka- line ph. However, it can subsequently cause deprotonation of ammonium ions to result ammonia leaching. In this report, efficiencies of bare and RGO loaded TiO2 were examined. In the presence of NaF, the nanocomposite possesses a 9.8(1) % nitrate yield, significantly greater than the other analo- gous reactions. Such observation will be helpful in developing new methodologies to afford sustain- able agriculture.
Chapter-3 Photocatalytic oxidation of urea is an essential area of study for converting urea to nitrate. As crops absorb nitrogen in the form of NO3− but due to incomplete oxidation, a substantial fraction of it es- capes into the atmosphere as N2. Hence, an effective photocatalyst is urgently needed to improve ni- trate conversion. This study focuses on the influence of β-cyclodextrin and Ag deposition on TiO2 towards the photocatalytic oxidation of urea. β-cyclodextrin (15-25 wt.%) and Ag (1-3 wt.%) loaded binary and ternary nanocomposites have been prepared using hydrothermal and photo deposition iv methods, respectively. The binary and ternary hybrids were characterized using FESEM, EDX, HR- TEM, XRD, XPS, DRS, PL, DLS, and FT-IR analysis. Photocatalytic urea degradation activity was evaluated under solar irradiation. The β-CD25/TiO2@Ag1 ternary nanocomposites show 78% degra- dation efficiency with 17.8% nitrate yield after 180 minutes reaction time which is the highest. This observation can be ascribed to the higher affinity of β-CD towards N2 due to the hydrophobic effect and the surface plasmon effect of Ag, which amplifies its visible light response. Such observations will attract much interest from a large section of material and agricultural chemists to design new catalysts for photochemical urea oxidation to afford sustainable agriculture.
Chapter-4 Urea oxidation is important to increase agricultural growth, which can meet the food requirements across the world. It is pivotal for converting nitrogen to nitrate that is usable by crops, thus prevent- ing nitrogen loss to the atmosphere. This study focuses on improving the photodegradation efficiency of TiO2 by incorporating β-CD (beta-cyclodextrin), RGO (reduced graphene oxide), and Ag to en- hance nitrate conversion. FT-IR, DRS, PL, EDX, XRD, XPS, HR-TEM DLS, and FESEM were conducted to characterize these materials. Among all the catalysts, the quaternary composite, β- CD/ TiO2/Ag/RGO, exhibited superior performance, achieving an 86.2% degradation efficiency with a 27.8% nitrate yield under sunlight irradiation within 150 minutes of reaction time. Several factors contribute to the enhanced photoactivity of β-CD/TiO2/Ag/RGO, including the high surface area and absorptive power of β-CD, the high electron mobility of RGO, and the LSPR effect of Ag, extending the catalyst's response to visible light. An intriguing aspect of this study is the encapsulation of gase- ous nitrogen into the hydrophobic interior cavity of β-CD, contributing to the enhancement of urea oxidation. These findings can be very substantial for both agriculturists and chemists, providing val- uable insights into designing novel photocatalysts for improved urea oxidation, thereby enhancing agricultural,productivity
Effect of Internal and External Dynamics on Galaxy Properties and Their Evolution
No full textThe current work is an account of few aspects of galaxy evolution, where the galaxies dy-
namic plays a crucial role. The thesis has been split into five chapters, the first of which
includes an introduction to the subject matter and a review of the literature, followed
by a summary of the thesis’s contents. In the second chapter, we study simple analytic
model of nearly Keplerian modes for co-rotating gravitationally coupled gaseous and
stellar discs. We present a simple analysis for large-scale, long-wavelength slow modes
for m = 1 for co-rotating gravitationally coupled gaseous and stellar discs. We derived
the dispersion relation using the Wentzel-Kramers-Brillouin (WKB) approximation and
explored the stability of modes. Such modes are useful to address the problem of asym-
metric light distribution observed in galaxies like M31. In the third chapter, we analyze
stellar orbits at the galaxy’s central region that are disturbed by an asymmetric dark
matter halo potential which are observed in observations as well as numerical simulations
recently. We used first-order epicyclic theory to solve the orbits and obtained a central
region’s azimuthal variation in the effective stellar orbits. We discuss the kinematical
lopsidedness of the stellar orbits within a 3 kpc radius of the galaxies. The fourth &
fifth chapter discusses the gas-removing mechanism (Ram pressure stripping) when the
galaxy passes through the cluster medium. In the fourth chapter, we analyze the effect
of spiral arms on the ram pressure in the galaxy; for this, we have considered different
types of mass galaxies with different numbers of arms and widths. We analyze how the
gravitationally bound force affects the ram pressure on removing gas from the disc, these
parameters help us to study this phenomena In the fifth chapter, we analyze the impact
of the magnetic field on the ram pressure. The magnetic field is an intrinsic part of the
galaxy, and it acts as a restoring force against ram pressure stripping in the galaxies.
The resulting in gas retention when a galaxy passes through the cluster medium
Impact of Foreign Direct Investment on Economic Growth: A Comparative Empirical Analysis of BRICS Countries
No full textThe increasing globalization of economies has led to a significant rise in cross-border capital
flows, with Foreign Direct Investment (FDI) emerging as a crucial driver of economic growth.
FDI not only provides financial resources but also facilitates technology transfer, enhances
human capital development, and integrates host countries into global value chains. Developing
economies, in particular, seek FDI to bridge investment gaps, boost industrialization, and
stimulate economic modernization. The present study investigates the dynamic relationship
between FDI inflows, economic growth, and key macroeconomic determinants in the BRICS
nations: Brazil, Russia, India, China, and South Africa, over the period 1991 to 2020. The
BRICS economies represent some of the world’s most dynamic emerging markets, collectively
contributing significantly to global GDP and trade. The primary objectives are to examine the
impact of FDI on economic growth, identify and evaluate the factors influencing FDI inflows,
and analyse the short- and long-term coupling effects between FDI and economic growth. The
research aims to fill a significant gap in the literature by focusing on this crucial group of
emerging economies, given their economic importance in the world economy in the coming
decades. Using an extensive dataset sourced from World Bank Indicators, OECD Statistics, and
the Penn World Table (Version 10.0), the study employs Method of Moments Quantile
Regression (MMQR) and Wavelet Coherence (WTC) analysis to uncover nuanced insights.
The study explicitly accounts for the heterogeneity among BRICS nations by employing the
Method of Moments Quantile Regression (MMQR) with fixed effects, a technique recently
introduced by Machado and Silva (2019) that effectively addresses cross-sectional dependence
and unobserved heterogeneity. It further incorporates wavelet coherence analysis, an
innovative approach in the field of economics, to explore short-term and long-term dynamics
between FDI inflows and its determinants by mapping the patterns of temporal intersections of
their relationship.
The results of cointegration highlight that there is a long-term relationship between FDI inflows
and economic growth in BRICS economies. The MMQR results further reveal that GDP, Trade
Openness (TO), Institutional Quality (INSQ), and Information and Communication
Technology (ICT) positively and significantly influence FDI inflows, underscoring their
importance as critical drivers. Conversely, Exchange Rate (EXR) volatility and Total Factor
Productivity (TFP) exhibit a negative impact, indicating the necessity of stable exchange rate
regimes and efficient resource utilization for attracting foreign investment. Wavelet Coherence
v
analysis further highlights the dynamic, time-frequency relationships between FDI and its
determinants, revealing short-term coherence (4-8 years) is most pronounced across variables,
particularly for GDP, TFP, TO, and ICT, indicating strong immediate interactions with FDI
inflows. Medium-term coherence (8-16 years) shows varied relationships, with trade openness
and institutional quality displaying intermittent associations. Long-term coherence (16-32
years) is generally weaker across variables, though GDP and TFP exhibit slightly more stable
long-term impacts compared to exchange rate, human capital, institutional quality, trade
openness, and ICT. This suggests that these factors’ influence is more pronounced in the short
run.
The findings emphasize the need for BRICS nations to sustain economic growth through
structural reforms, enhance trade openness, improve institutional quality, stabilize exchange
rates, and invest in ICT and human capital to foster sustainable FDI inflows. Policymakers
should adopt measures to stabilize currency fluctuations and provide a conducive investment
climate for foreign investors. Although this study focuses on the original BRICS nations, future
research could expand the scope to include the recently added BRICS members, examine
sector-specific FDI inflows, and explore industry-level dynamics to provide more targeted
policy recommendations
Optimality and Duality for Variational & Bilevel Optimization Problems
No full textOptimization is a fundamental aspect of mathematical modeling and decision-making, playing a crucial role in several areas such as economics, engineering, and operations research. In many practical situations, decisions must be made to optimize multiple conflicting objectives simultaneously, leading to the field of multiobjective optimization. Multiobjective optimization seeks to find solutions that balance these competing objectives, providing a set of optimal trade-offs rather than a single optimal solution. The study of various models in optimization and multiobjective optimization is essential because it allows researchers and practitioners to explore different mathematical formulations and algorithms tailored to specific problem characteristics. By studying these models, we gain insights into how different optimization approaches perform under varying conditions, enabling us to choose the most suitable methods for addressing complex decision-making challenges in diverse application domains.
The main objective of this thesis is to address three significant problems in the field of optimization. One major focus is achieving higher-order duality results for fractional variational problems under generalized convexity conditions. This involves developing and proving advanced duality theorems that can handle complex fractional and variational formulations. Secondly, the thesis aims to derive optimality conditions and duality results for interval-valued variational programming problems, where uncertainty in parameters is represented as intervals. Lastly, using a reformulation approach, the thesis concentrates on obtaining optimality conditions and duality results for bilevel optimization problems.
Keeping these objectives in mind, we will address the optimality and duality of developed mathematical models.
In what follows, the whole work has been examined by dividing it into six chapters.
Chapter 1 provides a brief overview of the theory of variational problems, interval-valued optimization problems, and bilevel optimization problems, tracing their evolution and significance. It presents essential definitions, notations and a comprehensive review of the foundational concepts necessary to understand these areas. This chapter also includes a concise survey of relevant work conducted by other researchers, highlighting key findings and advancements that have contributed to the current body of knowledge. Thus, it provides readers with the necessary background to comprehend the contributions of the subsequent chapters to these fields.
Chapter 2 explores the multiobjective fractional variational problems, emphasizing support functions. It introduces the definitions of higher-order pseudoinvex, higher-order (F,α,ρ,d)-convex, and higher-order (F,α,ρ,d)-pseudoconvex functions, enriching the theoretical framework for optimization problems. Further, Mond-Weir-type primal-dual pairs are formulated under both inequality and cone constraints. A rigorous theoretical analysis is then conducted to establish the relationship between the values of the dual pairs, providing insights into the underlying structure and connections between these models. Finally, the chapter concludes by validating the weak duality theorems, reinforcing the theoretical findings and demonstrating their practical implications for optimization problems.
Chapter 3 investigates multiobjective fractional variational problems involving support functions over cones, introducing the concept of higher-order K-η convexity. Within this context, the study explored duality results that relate to the values of primal and dual problems. To enhance understanding, a numerical example of a functional that is higher-order K-η convex but not first-order K-η convex is included. Various models are further shown to be special cases of our proposed framework under certain parametric values. Additionally, a real-world example is presented to validate the findings of the weak duality theorem, demonstrating the practical relevance of the theoretical framework developed in this work.
Chapter 4 deals with the interval-valued variational problems for both second-order and higher-order objective functions. The chapter introduces definitions of η -bonvexity and higher-order invexity, providing illustrative examples that satisfy these definitions while not conforming to existing ones. Thus, this necessitates a theoretical analysis of interval-valued problems. Furthermore, primal-dual pairs for both second-order and higher-order interval-valued variational objective functions are formulated, along with the governing optimality conditions for the models. The exploration of duality theorems elucidates the relationship between primal and dual problem values, offering insights into the underlying structure and connections between these models. We further discuss under what environment and how the existing model can be derived from the presented model. Numerical examples are presented to demonstrate the effectiveness and applicability of the proposed model. Moreover, an example is employed to validate the weak duality theorem, showcasing the practical relevance of the theoretical framework developed in this research.
Chapter 5 aims to study the robust bilevel programming problems with interval-valued objective functions and constraint-wise uncertainty at the upper-level. By utilizing an optimal value reformulation, the bilevel problem is remodified into a single-level problem, which allows for the application of robust counterpart optimization techniques to handle uncertainty effectively. The study establishes necessary optimality conditions for robust LU-optimal solutions, employing an extended robust nonsmooth Abadie constraint qualification (EACQ) based on convexificators. Furthermore, an example is provided with a detailed explanation to enhance understanding of the theoretical optimality conditions. Additionally, the chapter discusses duality results for the original problem and its Mond-Weir dual.
Chapter 6 focuses on the class of multiobjective interval-valued bilevel optimization problem. Initially, we state a nonsmooth constraint qualification for this class. Following this, necessary and sufficient optimality conditions for the optimization model are developed. Further, the Mond–Weir-type dual model is formulated for considered bilevel interval-valued multiobjective optimization problems, and weak, strong, and converse duality results are established under generalized ∂^*-convexity assumptions. To understand the established necessary and sufficient conditions proposed in the theorem, a detailed discussion is provided through numerical examples