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We develop a measure-theoretic framework for dynamic Shapley values in Banach spaces, extending classical cooperative game theory to continuous-time, infinite-dimensional settings. We prove the existence and uniqueness of strong solutions to stochastic differential equations modeling competence evolution in Banach spaces, establishing sample path continuity and moment estimates. The dynamic Shapley value is rigorously defined as a càdlàg stochastic process with an axiomatic characterization. We derive a martingale representation for this process and establish its asymptotic properties, including a strong law of large numbers and a functional central limit theorem under α-mixing conditions. This framework provides a rigorous basis for analyzing dynamic value attribution in abstract spaces, with potential applications to economic and game-theoretic models. [ABSTRACT FROM AUTHOR]

Preparing electrospun fibers by applying a potential difference between a polymeric solution and a contacting substrate is increasingly attracting attention in tissue engineering applications. Among the numerous polymers, polycaprolactone (PCL) bioscaffold has been widely investigated due to its biocompatibility and biodegradability. Bioactive powder can be added to further improve its performance. In the present study, bioactive glass powder modified by adding 0–6 wt.% antibacterial zinc element (coded as ZBG) was prepared through the sol–gel process. Furthermore, PCL bioscaffolds with various ZBG additions were prepared using the electrospinning technique. The zinc-doped bioactive glass powder and electrospun PCL/ZBG bioscaffolds were evaluated using scanning electron microscopy, X-ray diffraction and Fourier-transform infrared spectroscopy to determine their structural properties. Additionally, in vitro bioactivity, biocompatibility and antibacterial performance were investigated. Experimental results showed that sol–gelled ZBG powder possessed superior bioactivity and 0.8 g ZBG was the optimal addition to prepare PCL/ZBG bioscaffolds with. All the electrospun PCL/ZBG bioscaffolds were biocompatible and their antibacterial performance against two S. aureus strains (SA133 and Newman) improved with increasing zinc concentration. Electrospun PCL/ZBG bioscaffolds exhibited excellent bioactivity and have great potential for biomedical application. [ABSTRACT FROM AUTHOR]

Interdependent criteria play a crucial role in complex decision-making across various domains. Traditional methods often struggle to evaluate and prioritize criteria with intricate dependencies. This paper introduces a generalized method integrating the analytic network process (ANP), the decision-making trial and evaluation laboratory (DEMATEL), and the consistent fuzzy analytic hierarchy process (CFAHP) in a fuzzy environment. The Drazin inverse technique is applied to derive a fuzzy total priority matrix, and we normalize the row sum to achieve the steady-state fuzzy priorities. A numerical example in the information systems (IS) industry demonstrates the approach's real-world applications. The proposed method derives narrower fuzzy spreads compared to the past fuzzy analytic network process (FANP) approaches, minimizing objective uncertainty. Total priority interdependent maps provide insights into complex technical and usability criteria relationships. Comparative analysis highlights innovations, including non-iterative convergence of the total priority matrix and the ability to understand interdependencies between criteria. The integration of the FANP's network structure with the fuzzy DEMATEL's influence analysis transcends the capabilities of either method in isolation, marking a significant methodological advancement. By addressing challenges such as parameter selection and mathematical complexity, this research offers new perspectives for future research and application in multi-attribute decision-making (MADM). [ABSTRACT FROM AUTHOR]

Barium zirconate (BaZrO3, BZO), which exhibits superior mechanical, thermal, and chemical stability, has been widely used in many applications. In dentistry, BZO is used as a radiopacifier in mineral trioxide aggregates (MTAs) for endodontic filling applications. In the present study, BZO was prepared using the sol–gel process, followed by calcination at 700–1000 °C. The calcined BZO powders were investigated using X-ray diffraction and scanning electron microscopy. Thereafter, MTA-like cements with the addition of calcined BZO powder were evaluated to determine the optimal composition based on radiopacity, diametral tensile strength (DTS), and setting times. The experimental results showed that calcined BZO exhibited a majority BZO phase with minor zirconia crystals. The crystallinity, the percentage, and the average crystalline size of BZO increased with the increasing calcination temperature. The optimal MTA-like cement was obtained by adding 20% of the 700 °C-calcined BZO powder. The initial and final setting times were 25 and 32 min, respectively. They were significantly shorter than those (70 and 56 min, respectively) prepared with commercial BZO powder. It exhibited a radiopacity of 3.60 ± 0.22 mmAl and a DTS of 3.02 ± 0.18 MPa. After 28 days of simulated oral environment storage, the radiopacity and DTS decreased to 3.36 ± 0.53 mmAl and 2.84 ± 0.27 MPa, respectively. This suggests that 700 °C-calcined BZO powder has potential as a novel radiopacifier for MTAs. [ABSTRACT FROM AUTHOR]

The binary heterostructured semiconducting visible light photocatalyst of the iron-doped graphitic carbon nitride/bismuth molybdate (Fe-g-C3N4/Bi2MoO6) composite was prepared by coupling with Fe-doped g-C3N4 and Bi2MoO6 particles. In the present study, a comparison of structural characteristics, optical properties, and photocatalytic degradation efficiency and activity between Fe-doped g-C3N4 particles, Bi2MoO6 particles, and Fe-g-C3N4/Bi2MoO6 composite was investigated. The results of X-ray diffraction (XRD) examination indicate that the hydrothermal Bi2MoO6 particles have a single orthorhombic phase and Fourier transform infrared (FTIR) spectroscopy analysis confirms the formation of Fe-doped g-C3N4. The optical bandgaps of the Fe-doped g-C3N4 and Bi2MoO6 particles are 2.74 and 2.73 eV, respectively, as estimated from the Taut plots obtained from UV-Vis diffuse reflectance spectroscopy (DRS) spectra. This characteristic indicates that the two semiconductor materials are suitable for absorbing visible light. The transmission electron microscopy (TEM) micrograph reveals the formation of the heterojunction Fe-g-C3N4/Bi2MoO6 composite. The results of photocatalytic degradation revealed that the developed Fe-g-C3N4/Bi2MoO6 composite photocatalyst exhibited significantly better photodegradation performance than the other two single semiconductor photocatalysts. This property can be attributed to the heterostructured nanostructure, which could effectively prevent the recombination of photogenerated carriers (electron–hole pairs) and enhance photocatalytic activity. Furthermore, cycling test showed that the Fe-g-C3N4/Bi2MoO6 heterostructured photocatalyst exhibited good reproducibility and stability for organic dye photodegradation. [ABSTRACT FROM AUTHOR]

Barium titanate (BaTiO3, BTO), conventionally used for dielectric and ferroelectric applications, has been assessed for biomedical applications, such as its utilization as a radiopacifier in mineral trioxide aggregates (MTA) for endodontic treatment. In the present study, BTO powders were prepared using the sol-gel process, followed by calcination at 400–1100 °C. The X-ray diffraction technique was then used to examine the as-prepared powders to elucidate the effect of calcination on the phase composition and crystalline size of BTO. Calcined BTO powders were then used as radiopacifiers for MTA. MTA-like cements were investigated to determine the optimal calcination temperature based on the radiopacity and diametral tensile strength (DTS). The experimental results showed that the formation of BTO phase was observed after calcination at temperatures of 600 °C and above. The calcined powders were a mixture of BaTiO3 phase with residual BaCO3 and/or Ba2TiO4 phases. The performance of MTA-like cements with BTO addition increased with increasing calcination temperature up to 1000 °C. The radiopacity, however, decreased after 7 days of simulated oral environmental storage, whereas an increase in DTS was observed. Optimal MTA-like cement was obtained by adding 40 wt.% 1000 °C-calcined BTO powder, with its resulting radiopacity and DTS at 4.83 ± 0.61 mmAl and 2.86 ± 0.33 MPa, respectively. After 7 days, the radiopacity decreased slightly to 4.69 ± 0.51 mmAl, accompanied by an increase in DTS to 3.13 ± 0.70 MPa. The optimal cement was biocompatible and verified using MG 63 and L929 cell lines, which exhibited cell viability higher than 95%. [ABSTRACT FROM AUTHOR]

Cooperative alternatives need complex multi-criteria decision-making (MCDM) consideration, especially in resource allocation, where the alternatives exhibit interdependent relationships. Traditional MCDM methods like the Analytic Hierarchy Process (AHP) and Analytic Network Process (ANP) often overlook the synergistic potential of cooperative alternatives. This study introduces a novel method integrating AHP/ANP with Shapley values, specifically designed to address this gap by evaluating alternatives on individual merits and their contributions within coalitions. Our methodology begins with defining problem structures and applying AHP/ANP to determine the criteria weights and alternatives' scores. Subsequently, we compute Shapley values based on coalition values, synthesizing these findings to inform resource allocation decisions more equitably. A numerical example of budget allocation illustrates the method's efficacy, revealing significant insights into resource distribution when cooperative dynamics are considered. Our results demonstrate the proposed method's superiority in capturing the nuanced interplay between criteria and alternatives, leading to more informed urban planning decisions. This approach marks a significant advancement in MCDM, offering a comprehensive framework that incorporates both the analytical rigor of AHP/ANP and the equitable considerations of cooperative game theory through Shapley values. [ABSTRACT FROM AUTHOR]

The Analytic Hierarchy Process (AHP) has been a widely used multi-criteria decision-making (MCDM) method since the 1980s because of its simplicity and rationality. However, the conventional AHP assumes criteria independence, which is not always accurate in realistic scenarios where interdependencies between criteria exist. Several methods have been proposed to relax the postulation of the independent criteria in the AHP, e.g., the Analytic Network Process (ANP). However, these methods usually need a number of pairwise comparison matrices (PCMs) and make it hard to apply to a complicated and large-scale problem. This paper presents a groundbreaking approach to address this issue by incorporating discrete Markov Random Fields (MRFs) into the AHP framework. Our method enhances decision making by effectively and sensibly capturing interdependencies among criteria, reflecting actual weights. Moreover, we showcase a numerical example to illustrate the proposed method and compare the results with the conventional AHP and Fuzzy Cognitive Map (FCM). The findings highlight our method's ability to influence global priority values and the ranking of alternatives when considering interdependencies between criteria. These results suggest that the introduced method provides a flexible and adaptable framework for modeling interdependencies between criteria, ultimately leading to more accurate and reliable decision-making outcomes. [ABSTRACT FROM AUTHOR]