Croatian Academy of Sciences and Arts

This paper investigates generalizations of the classical Jensen-Steffensen inequality to the operator setting of divided differences. Using Hermite–Genocchi representation and leveraging the fundamental connection between the n-convexity of a function f and the convexity of its n-th derivative f^(n) , we establish a series of new integral and discrete inequalities, including versions of Szegő’s and Mercer’s inequalities for divided differences. Furthermore, we establish a reverse inequality and a refinement theorem, thereby providing a comprehensive treatment of this generalization. A notable application of this framework is obtained by integrating the main inequality over the entire polytope of valid Jensen-Steffensen weights. This procedure yields a novel integral inequality of the Hermite-Hadamard type, providing a tight bound for the averaged operator in terms of the values at the endpoints of the monotonic sequence of nodes.

Background:Previous research has identified that, in individuals with lower folate and/or vitamin B12 levels, homocysteine is associated with specific elements, while amino acids are associated with folate, thereby influencing folate availability during supplementation. This study investigates the impact of the MTHFR 677C/T polymorphism on levels of these compounds in individuals with differing meat consumption preferences, non-vegetarians and vegetarians. Methods:The study was conducted on 162 Croatian subjects. MTHFR gene polymorphism was determined by PCR-RFLP, elements by ICP-QQQ, amino acids by GC-MS, and biochemical parameters by chemiluminescent immunoassay and enzymatic methods. Differences between the groups were tested by ANOVA, while associations between the parameters were examined by multiple regression analyses. Results:The CT + TT genotype had lower folate levels in comparison to the CC genotype. The influence of MTHFR 677C/T polymorphism on element levels was limited to Al and Ca: individuals with the CT + TT genotype exhibited higher plasma Ca levels than the wild-type (CC) genotype, while lower plasma Al values were observed only in vegetarians with the CT + TT genotype. The CT + TT genotype was also associated with higher levels of glutamic acid, proline, glycine (only in vegetarians), and aspartic acid. Conclusion:Although we observed an effect of the MTHFR 677C/T polymorphism on folate, certain elements and amino acid levels, further research is required to validate our findings and establish a more comprehensive understanding of the link between elements, amino acids and the MTHFR gene polymorphism.

The micronucleus assay is a widely used technique for detecting chromosomal damage in human cells, particularly lymphocytes and exfoliated buccal cells. This assay identifies micronuclei, which are small, extranuclear bodies containing chromosomal fragments or whole chromosomes that were not incorporated into the daughter nuclei during cell division. In human lymphocytes, the assay is typically conducted on cells stimulated to divide in culture, whereas in exfoliated buccal cells, it assesses naturally occurring cell samples. The micronucleus assay is valued for its simplicity, cost-effectiveness, and ability to provide insights into genotoxic exposure, genetic instability, and cancer risk. Its application in biomonitoring and epidemiological studies helps in evaluating the effects of environmental, occupational, and lifestyle factors on genetic material, thereby contributing to public health risk assessments and preventive strategies.

The Eastern Adriatic Coast, owing to its karstic nature, features numerous Quaternary cave sites that mostly date to the Pleniglacial - Late Glacial or Holocene (Marine Isotope Stages 2-1). In this paper, we present a wellpreserved small-vertebrate assemblage from the Marlera fossil-cave site (southern Istrian Peninsula), dated to Marine Isotope Stage 3. Taxonomical and paleoecological analyses were conducted on bird and arvicoline assemblages. Further, detailed taphonomic analyses were performed on bird bones and arvicolins subsample. Avifaunal remains were divided into two distinct assemblages: Assemblage I (upper sediment unit), characterized by species preferring open and dry habitats, and Assemblage II (lower sediment unit), that also includes aquatic taxa. The most likely agents of accumulation for bird species not roosting or nesting in the cave were small carnivores and falcons, as reflected in skeletal-part frequencies and gnaw marks. The arvicoline record reveals a productive, karstic mosaic of open grasslands and woodland patches, with Microtus species signaling both dry steppe and locally moist, densely vegetated microhabitats. This faunal structure, combined with the taphonomic evidence and integration of regional paleoclimatic and paleoenvironmental data, shows that the southern Istrian part of the Great Adriatic Plain during MIS 3 was a productive, mostly open landscape with scattered trees and freshwater features. These results significantly contribute to our understanding of the region's paleoecology of this climatically dynamic period.

Air pollution in urban areas originates from multiple interacting sources and is strongly influenced by meteorology, yet direct emission data are often incomplete. This study quantifies how meteorological conditions, station location, and proxy indicators of traffic and residential heating affect PM10-bound polycyclic aromatic hydrocarbons (PAHs) and metals in Zagreb, Croatia. Daily concentrations of PM10, selected PAHs, metals and NO2 from four monitoring stations (2017–2020) were combined with local and ERA5 meteorology, highway traffic counts and gas consumption as emission proxies. Non-negative Matrix Factorization (NMF) was applied separately to PAHs and metals to identify dominant source-related patterns, while Random Forest regression and SHapley Additive Explanations (SHAP) were used to evaluate the influence of temporal, spatial, meteorological, traffic and heating predictors. NMF separated a heating-related PAH component dominated by Pyr and Flu from a traffic-related component characterised by BaA, Chry and BkF, and indicated enrichment of As and Pb at traffic- and industry-affected stations. Random Forest models showed higher predictive skill for PAHs (R2 ≈ 0.60–0.68) than for metals (R2 ≈ 0.24–0.42). Temperature and solar radiation were the main predictors for PAHs, whereas PM10, NO2 and station indicators dominated the prediction of metals. These results demonstrate that integrating proxy emission indicators with explainable machine learning provides an efficient framework for characterising sources and supports season- and location-specific air quality management in data-limited urban environments.