This paper investigates the optimal control problem for a class of parabolic equations where the diffusion coefficient is influenced by a control function acting nonlocally. Specifically, we consider the optimization of a cost functional that incorporates a controlled probability density evolving under a Fokker-Planck equation with state-dependent drift and diffusion terms. The control variable is subject to spatial convolution through a kernel, inducing nonlocal interactions in both drift and diffusion terms. We establish the existence of optimal controls under appropriate convexity and regularity conditions, leveraging compactness arguments in function spaces. A maximum principle is derived to characterize the optimal control explicitly, revealing its dependence on the adjoint state and the nonlocal structure of the system. We further provide a rigorous financial application in the context of mean-variance portfolio optimization, where both the asset drift and volatility are controlled nonlocally, leading to an integral representation of the optimal investment strategy. The results offer a mathematically rigorous framework for optimizing diffusion-driven systems with spatially distributed control effects, broadening the applicability of nonlocal control methods to stochastic optimization and financial engineering.
This research aims to investigate the modifications of the structural, dielectric, and sensing properties of CaFeO3-delta ceramics produced by solid-state reaction induced by varying sintering temperatures in the range of 1000-1200 degrees C. A single crystallographic orthorhombic (Pcmn) structure was revealed by X-ray diffraction with Rietveld analysis, both for the powders and sintered ceramics, irrespective of the sintering temperature. The increase in the sintering temperature induces better densification and a larger grain size. Dielectric measurements reveal a pronounced enhancement of the relative permittivity, reaching 2 & times; 10(5) at 1 kHz and 330 degrees C for the sample sintered at 1200 degrees C/4 h. This composition also displays the highest electrical conductivity, 0.4 S/m at 1 MHz. Cole-Cole analysis indicates a clear deviation from ideal Debye behavior, while the relaxational features of the dielectric permittivity suggest a strong correlation between the dielectric response and Fe-related conduction mechanisms. Gas sensing tests show that the ferrite ceramics exhibit consistent ethanol response trends. The ceramic sintered at 1200 degrees C/4 h achieved the highest sensitivity, of 56.28%, which can be attributed to its higher density, larger ceramic grains, and reduced low-frequency conductivity. The CaFeO3-delta ceramic sintered at 1200 degrees C/4 h shows a combination of high permittivity, enhanced conductivity, and strong ethanol sensitivity, making it a promising material for dielectric components, capacitive devices, and gas sensing applications.
Photocatalysts based on TiO2 modified with metals or various oxides are among the most widely used in the photocatalytic conversion of CO2 and H2O to CH4 by using solar energy. However, obtaining photocatalysts with high specific surface area and active sites that provide CO2 adsorption, activation, and hydrogen generation through water oxidation remains a challenge for efficient CH4 production. Here, a series of xRu-modified titanium dioxide (with x = 1, 3, 5 wt %) mesoporous photocatalysts with high surface area were prepared for the reduction of CO2 to CH4 under visible light. Experimental results showed that the properties of the obtained Ti1-xRuxClyO2-y and Ti1-xRuxO2 materials depend on the ruthenium concentration and the heat treatment of the TiO2 support. The evidence of the synergistic action of these parameters on the photocatalytic activity and selectivity in CO2 photoreduction under light irradiation represents a significant result of this study. The selectivity toward CH4 was explained as an effect of the surface basicity. Thus, the highest selectivities to CH4 (90 and 100%) were obtained for the samples with the highest basicity values obtained through the CO2-TDP measurements. High values of activity and selectivity were obtained in the artificial photosynthesis reaction by modifying mesoporous TiO2 by calcination and immobilization of Ru in various concentrations.
Advances in the understanding of exosome biology have led to their recognition as the heart of intercellular communications. Additionally, the new insights into the role of exosomes in neuroinflammation and spreading of characteristic Alzheimer's Disease (AD) pathologies, open the scope for their use as a key target for diagnostic and therapeutic innovation. The immuno-engineering platforms are sensitive for detecting exosomal biomarkers including amyloid-B species, phosphorylated tau, and regulatory microRNAs, in peripheral biofluids with minimal invasion. Hence, these are potential platforms that can facilitate early diagnosis of AD. Although most supporting evidence is presently derived based on preclinical models and limited observational cohorts, these findings support minimally invasive opportunities for early disease monitoring and diagnosis, possibly even before the manifestation of clinical symptoms of AD. Alongside, another advantage of engineered exosomes is their flexible framework for targeted drug delivery. Since engineered exosomes are derived from neuronal or mesenchymal stem cells, they can cross the blood-brain barrier and deliver neuroprotective or immunomodulatory agents with high specificity. Presently, the target precision and off-target biodistribution of engineered exosomes are one of the most active areas of investigation. More encouragingly, incorporating nanotechnology for surface modification and cargo loading strategies can further enhance exosomal signaling, delivery efficiency, and cell-specific uptake by neuronal and glial cells. These applications, however, are presently challenging in terms of scalability and reproducibility. Also, a number of advancements are needed in areas of standardization of exosome isolation, scalable manufacturing, regulatory frameworks, and biological heterogeneity. Overcoming these challenges, however, is feasible with the integration of Artificial Intelligence and multi-omics profiling, and optimisation of exosome-based interventions.
This study explores the genetic diversity of the edible dormouse (Glis glis), a rodent species closely associated with deciduous and mixed woodlands rich in oak and beech trees. The research investigates the phylogeographic patterns and genetic structure of G. glis, particularly focusing on the genetic diversity within Romanian populations and their relationship to other European lineages. Mitochondrial cytochrome b gene sequences have been used to analyze genetic diversity and phylogenetic relationships. We collected 117 samples from various Romanian populations and combined them with the existing GenBank data to provide a broader geographical context. We confirm the existence of distinct phylogenetic lineages within Glis glis, highlighting a pattern of low to moderate genetic diversity within the Romanian populations. Five haplotypes were identified across the analysed Romanian populations. Two of these, Hap_2 and Hap_5, were shared with other European populations, Hap_2 being the most common haplotype in the European lineage. The remaining three haplotypes were unique to Romania, Hap_1 being found in Southern Romania, Piscoiu site, and Hap_3 and Hap_4 from Dobrogea (South-Eastern Romania). The widespread Hap_2 was shared by almost all analysed populations, with the exception of Piscoiu. The findings contribute to the understanding of the genetic structure of this species and have implications for future conservation planning.
