In psychology there is a plethora of different measures and constructs. However, the literature also shows that many of these measures overlap and may even sometimes be redundant. Recognizing such overlap in measures is essential for consolidation and for moving the field forward. Accordingly, we suggest a role herein of the General Factor of Personality (GFP), which emerges from the correlations between specific personality dimensions and reflects a mix of desirable traits (e.g. being sociable, honest, and emotionally stable). It is argued and shown that the GFP is highly correlated with a wide range of psychological traits. We further postulate that this phenomenon provides a parsimonious way of looking at the overlap between many trait measures. This idea is discussed in light of the ongoing debate on the GFP in which some scholars suggest the general factor is substantive and relevant for understanding personality, whereas others consider it to solely reflect a measurement artifact. Irrespective of whether the substantive, artifact, or a mixed explanation of the GFP is adopted, overlooking the presence of a common general factor in psychological measures may, respectively, either impede the development of unifying theories of human behavior, or otherwise compromise measurement validity.
Splines over triangulations provide a flexible and effcient way to approximate bivariate functions defined over domains, partitioned by triangles. One of the important challenges is the construction of locally supported non-negative basis functions that form a partition of unity, i.e., B-spline-like basis functions. Due to smoothness conditions that depend on the geometry of the triangulation, spline basis functions are typically divided into three groups: triangle, vertex, and edge functions. While the construction of triangle and vertex basis splines is well developed, the computation of non-negative edge basis splines of general degree that form a partition of unity has so far been addressed only for C1 continuous splines, using a completely algebraic approach, with no explicit geometric interpretation ([7]). In this paper a novel approach is presented that extends the control-triangle-based idea known for vertex basis splines and can be geometrically explained and generalized to splines of a higher order of smoothness. The construction is developed on pairs of adjacent triangles forming a strictly convex quadrilateral. Since each smoothness order requires a separate analysis, a detailed study is provided for the C1 and C2 continuous splines of degrees d >= 2 and d >= 4, respectively. Numerical examples are provided to confirm the effectiveness and applicability of the derived construction.
A subgraph of the square lattice with all of its inner faces being 4-cycles is called a square-cell configuration. Prior work has provided explicit expressions for the total and average distances between vertex pairs in symmetric square-cell configurations, including well-structured families such as hexagonal square-cell configurations H(n), trapezium square-cell configurations T(n,k), and bitrapezium square-cell configurations BT(n,k_1,k_2). In this article, we further extend the square-cell configuration from regular boundaries to irregular boundaries, which do not exhibit complete regularity or symmetry in their structure. We find the generalized expressions for the Wiener index and average distance of such irregular configurations, incorporating combinatorial and structural variations. Our results demonstrate how irregularity affects the growth and distribution of pairwise distances and provide a unifying framework that includes both symmetric and asymmetric square-cell graphs as exceptional cases. This generalization provides novel insights into the structural behaviour of square-cell frameworks characterized by complex or perturbed geometries.
Development of bio-based materials with advanced properties is required to replace synthetic and per- and polyfluoroalkyl-based ingredients, particularly for applications involving solid-liquid-gas interfaces. To enable alkaline-resistant materials with tunable aerophobicity, bio-based chitosan/dialdehyde starch hydrogels were prepared through covalent Schiff base crosslinking. Chitosan molecular weight (250-1800 kDa) and concentration (1.5-4.0% w/v) were varied at fixed crosslinker content (1.0% w/v) to investigate the effect on network formation, viscoelasticity and functionality. Rheological analysis shows that systems with low chitosan content require long gelation times (>30 min) to form viscous materials with storage moduli of 1 Pa and internal porous structure (10-100 μm). In contrast, highly concentrated chitosan gels formed rapidly (<4 min) reaching up to 150 Pa, indicating improved structural strength. Swelling experiments on freeze-dried hydrogels at pH 6.8, 10, and 12 showed water absorption with swelling ratios ranging from 5000 to 1300%, depending on composition. Most systems maintained structural stability over the 7-day swelling test, undergoing limited degradation in alkaline conditions (pH 12). Aerophobicity was evaluated by measuring contact angles of bubbles on submersed (in water or pH 12) hydrogels, which range from 130 to 170°, increasing with both chitosan concentration and molecular weight. The material features were demonstrated for electrode development, improving performance at higher overpotentials (−0.67 V) and increasing alkaline water-splitting efficiency by 15%. The prepared materials thus provide alkaline resistance and tunable properties offering potential for various applications, including gas-evolving electrode coatings, alkaline electrolyzer membranes, anti-corrosion coatings, pollutant absorption, environmental remediation, and sensing technologies.
We study subspaces of tensor-product polynomials of bi-degree (n, n) on the unit square whose restrictions to the domain diagonals have degree reduced by an integer k <= n. For maximal reduction k = n, these diagonally-reduced spaces coincide with the B & eacute;zier-Smart surface spaces and have dimension n2 + 2. We derive exact dimension formulas and solve the boundary-diagonal matching problem: when can such a polynomial be replaced by a total-degree polynomial that agrees on the boundary and both diagonals? The answer is a sharp threshold on the degree parameters, with a complete characterisation of existence, uniqueness, and non-uniqueness. For the first non-trivial reduction parameters we provide explicit matching formulas and closed-form error estimates; when the solution is non-unique, the remaining freedom is resolved by L2 optimality. At the endpoint k = n, where matching always fails, we show for n = 3 that the L2-best approximation from the total-degree subspace is also the L infinity-best approximation.
