Search Results (128)

This paper explores some frame bundles and physical implications of Killing vector fields on the two-sphere ${\mathbb{S}}^2$, culminating in a novel application to Maxwell’s equations in free space. Initially, we investigate the Killing vector fields on ${\mathbb{S}}^2$ (represented by the unit sphere of ${\mathbb{R}}^3$), which generate the isometries of the sphere under the rotation group $SO\left(3\right)$. These fields, realized as functions $K_v:{\mathbb{S}}^2\to {\mathbb{R}}^3$, defined by $K_v\left(q\right)=v\times q$ for a fixed $v\in {\mathbb{R}}^3$ and any $q\in {\mathbb{S}}^2$, generate a three-dimensional Lie algebra isomorphic to $\mathfrak{so}\left(3\right)$. We establish an isomorphism $K:{\mathbb{R}}^3\to \mathcal{K}\left({\mathbb{S}}^2\right)$, mapping vectors $v=au$ (with $u\in {\mathbb{S}}^2$) to scaled Killing vector fields $a{K}_u$, and analyze its relationship with $SO\left(3\right)$ through the exponential map. Subsequently, at a fixed point $e\in {\mathbb{S}}^2$, we construct a smooth orthonormal right-handed tangent frame $f_e:{\mathbb{S}}^2\backslash \{e,-e\}\to T{\left({\mathbb{S}}^2\right)}^2$, defined as $f_e\left(u\right)=({\widehat{K}}_e\left(u\right),u\times {\widehat{K}}_e\left(u\right))$, where ${\widehat{K}}_e$ is the unit vector field of the Killing field $K_e$. We verify its smoothness, orthonormality, and right-handedness. We further prove that any smooth orthonormal right-handed frame on ${\mathbb{S}}^2\backslash \{e,-e\}$ is either $f_e$ or a rotation thereof by a smooth map $\rho :{\mathbb{S}}^2\backslash \{e,-e\}\to SO\left(3\right)$, reflecting the triviality of the frame bundle over the parallelizable domain. The paper then pivots to an innovative application, constructing solutions to Maxwell’s equations in free space by combining spherical symmetries with quantum mechanical de Broglie waves in tempered distribution wave space. The deeper scientific significance lies in bringing together differential geometry (via $SO\left(3\right)$ symmetries), quantum mechanics (de Broglie waves in Schwartz distribution theory), and electromagnetism (Maxwell’s solutions in Schwartz tempered complex fields on Minkowski space-time), in order to offer a unifying perspective on Maxwell’s electromagnetism and Schrödinger’s picture in relativistic quantum mechanics. Full article

Efficiently identifying subgraphs that match a given query graph within large-scale graphs has become a critical focus in both academic and industrial research. Subgraph matching, a fundamental problem in graph algorithms, facilitates the effective querying of graph data and is fundamentally based on the subgraph isomorphism problem, which is known to be NP-complete. Among the various stages of subgraph matching, the filtering phase is particularly crucial as it directly affects the overall efficiency of the algorithm. A robust filtering mechanism can rapidly identify candidate nodes that satisfy the query criteria, thereby significantly reducing computational costs in the subsequent stages. The analysis of existing subgraph matching techniques reveals several challenges in the filtering stage: (1) redundant enumeration of equivalent nodes; (2) incomplete filtering due to structural limitations; and (3) excessive redundant validations during the verification phase. To overcome these issues, we propose an adaptive subgraph matching (ASM) framework that integrates efficient compressed graph nodes (CGNs) and a novel label count filter (LCF) algorithm. These innovations enhance the filtering process, resulting in significant improvements in query processing performance. Experimental evaluations demonstrate that our approach achieves substantial gains, outperforming state-of-the-art subgraph search and matching algorithms by several orders of magnitude in query processing time. Full article

With the increasing content richness of social media platforms, Multimodal Named Entity Recognition (MNER) faces the dual challenges of heterogeneous feature fusion and accurate entity recognition. Aiming at the key problems of inconsistent distribution of textual and visual information, insufficient feature alignment and noise interference fusion, this paper proposes a multimodal named entity recognition model based on dual-stream Transformer: CASF-MNER, which designs cross-modal cross-attention based on visual and textual features, constructs a bidirectional interaction mechanism between single-layer features, forms a higher-order semantic correlation modeling, and realizes the cross relevance alignment of modal features; construct a dynamic perception mechanism of multimodal feature saliency features based on multiscale pooling method, construct an entropy weighting strategy of global feature distribution information to adaptively suppress noise redundancy and enhance key feature expression; establish a deep semantic fusion method based on hybrid isomorphic model, design a progressive cross-modal interaction structure, and combine with contrastive learning to realize global fusion of the deep semantic space and representational consistency optimization. The experimental results show that CASF-MNER achieves excellent performance on both Twitter-2015 and Twitter-2017 public datasets, which verifies the effectiveness and advancement of the method proposed in this paper. Full article

This paper contends that the West’s civic crisis is, at root, a cosmological crisis: civic renewal requires metaphysical repair. It is insufficient to endorse virtue ethics and demand civic virtues without a deeper account of reality that can sustain them. What is needed is a cosmology—one informed by contemporary science—in which nature, personhood, and political community are meaningfully situated within an ordered whole. Drawing on the Platonic isomorphism between soul, city, and cosmos, I outline a hylomorphic framework with the potential to integrate key elements of neo-Aristotelian, Stoic, and Thomist metaphysics with developments in contemporary physics. Against the dominant atomistic and holistic paradigms, I argue that hylomorphism offers a more adequate account of personhood, the polis, and the cosmos itself as an intelligible whole. Full article

This paper focuses on identifying temperature-compensated Y-cuts (using a Cartesian coordinate system) in a piezoelectric α-GeO₂ single crystal, which is isostructural–quartz α-SiO₂. The study aims to minimize the frequency drift of the thickness shear mode by analyzing the resonant frequency’s first- and second-order temperature coefficients T_f⁽¹⁾ and T_f⁽²⁾. To obtain these, the first-order, T_Cij⁽¹⁾, and second-order, T_Cij⁽²⁾, temperature coefficients of the elastic constant, C_ij, previously obtained from room temperature up to 900 °C, were calculated. Upon heating, the thermal behavior of the elastic constants indicated that some, such as C₁₁ and C₃₃, are stable over a range of temperatures, while others, such as C₄₄ and C₆₆, increase with the temperature. This paper also explores a family of singly and doubly rotated Y-cuts of α-GeO₂, revealing cuts with a potential application for temperature compensation and/or linear dependence over the temperature range. The results are compared with those of the well-known piezoelectric isomorph material α-SiO₂. The findings highlight that α-GeO₂ is a promising material for piezoelectric devices in high-temperature environments, outperforming α-SiO₂ (α-quartz), which is limited by a solid–solid phase transition at 573 °C. Full article

The Ramsey number $R\left(F\right)$ of a graph F without isolated vertices is the smallest positive integer n such that every red–blue coloring of $K_n$ produces a subgraph isomorphic to F all of whose edges are colored the same. Let $\mathcal{F}$ be a set of graphs without isolated vertices. For a positive integer t, the vertex-disjoint Ramsey number $V{R}_t\left(\mathcal{F}\right)$ is the smallest positive integer n such that every red–blue coloring of the complete graph $K_n$ of order n results in at least t pairwise vertex-disjoint monochromatic graphs in $\mathcal{F}$; while the edge-disjoint Ramsey number $E{R}_t\left(\mathcal{F}\right)$ is the smallest positive integer n such that every red–blue coloring of $K_n$ produces at least t pairwise edge-disjoint monochromatic graphs in $\mathcal{F}$. If $t=1$ and $\mathcal{F}$ consists of a single graph F, then $V{R}_1\left(\mathcal{F}\right)=E{R}_1\left(\mathcal{F}\right)=R\left(F\right)$ is the Ramsey number of the graph F. Thus, the concepts of vertex-disjoint and edge-disjoint Ramsey numbers provide a generalization of the standard Ramsey number. Upper and lower bounds for $V{R}_t\left(\mathcal{F}\right)$ and $E{R}_t\left(\mathcal{F}\right)$ are established for sets $\mathcal{F}$ of graphs without isolated vertices and the sharpness of these bounds is discussed. The primary goal of this paper is to investigate the values of $V{R}_t\left(\mathcal{F}\right)$ and $E{R}_t\left(\mathcal{F}\right)$ for sets $\mathcal{F}$ of graphs of size 2 or 3 without isolated vertices. The exact values of $V{R}_t\left(\mathcal{F}\right)$ are determined for all such sets $\mathcal{F}$ and all integers $t\ge 2$. The exact values of $E{R}_t\left(\mathcal{F}\right)$ of certain such sets $\mathcal{F}$ with prescribed conditions for all integers $t\ge 2$ are determined. For some special sets $\mathcal{F}$ of graphs of size 2 or 3 without isolated vertices, the exact values of $E{R}_t\left(\mathcal{F}\right)$ are determined for $2\le t\le 4$. Additional results, problems, and conjectures are also presented dealing with these two Ramsey concepts for graphs in general. Full article

Radio mean labeling of a connected graph G is an assignment of distinct positive integers to the vertices of G satisfying a mathematical constraint called radio mean condition. The maximum label assigned to any vertex of G is called the $span$ of the radio mean labeling. The minimum $span$ of all feasible radio mean labelings of G is the radio mean number of G, denoted by $rmn\left(G\right)$. In our previous study, we proved that if G has order n, then $rmn\left(G\right)\in [n,rmn\left(P_n\right)]$ where $P_n$ is a path of order n. All graphs of diameters 1, 2 and 3 have the radio mean number equal to order n. However, they are not the only graphs on n vertices with radio mean number n. Graphs isomorphic to path $P_n$ are the graphs having the maximum diameter among the set of all graphs of order n and they possess the maximum feasible radio mean number. In this paper, we show that, for any integer in the range of achievable radio mean numbers, there always exists a graph of order n with the given integer as its radio mean number. This is approached by introducing a special type of tree whose construction is detailed in the article. The task of assigning radio mean labels to a graph can be considered as an optimization problem. This paper critiques the limitations of existing Integer Linear Programming (ILP) models for assigning radio mean labeling to graphs and proposes a new ILP model. The existing ILP model does not guarantee that the vertex labels are distinct, positive and satisfy the radio mean condition, prompting the need for an improved approach. We propose a new ILP model which involves $n^2$ constraints is the input graph’s order is n. We obtain a radio mean labeling of cycle of order 10 using the new ILP. In our previous study, we showed that, for any graph G, we can extend the radio mean labelings of its diametral paths to the vertex set of G and obtain radio mean labelings of G. This insight forms the basis for an algorithm presented in this paper to obtain radio mean labels for a given graph G with n vertices and diameter d. The correctness and complexity of this algorithm are analyzed in detail. Radio mean labelings have been proposed for cryptographic key generation in previous works, and the algorithm presented in this paper is general enough to support similar applications across various graph structures. Full article

The spectrum of a graph $\mathrm{\Gamma }$, denoted by $Spec\left(\mathrm{\Gamma }\right)$, is the multiset of eigenvalues of its adjacency matrix. A Cayley graph $Cay(G,S)$ of a finite group G is called Cay-DS (Cayley graph determined by its spectrum) if, for any other Cayley graph $Cay(G,T)$, $Spec\left(Cay\right(G,S\left)\right)=Spec\left(Cay\right(G,T\left)\right)$ implies $Cay(G,S)\cong Cay(G,T)$. A group G is said to be Cay-DS if all Cayley graphs of G are Cay-DS. An interesting open problem in the area of algebraic graph theory involves characterizing finite Cay-DS groups or constructing non-isomorphic Cayley graphs of a non-Cay-DS group that share the same spectrum. The present paper contributes to parts of this problem of metacyclic groups $M_{8p}$ of order $8p$ (with center of order 4), where p is an odd prime, in terms of irreducible characters, which are first presented. Then some new families of pairwise non-isomorphic Cayley graph pairs of $M_{8p}$ ($p\ge 5$) with the same spectrum are found. As a conclusion, this paper concludes that $M_{8p}$ is Cay-DS if and only if $p=3$. Full article

Mn(III)– and Co(III)–salen complexes (Mn-1 and Co-2) have been synthesized by a simple one-pot procedure through oxidation of Mn(II) and Co(II) precursors in air. X-ray structural analysis reveals that both complexes adopt similar coordination modes, including a typical square planar metal/salen coordination sphere, which is further occupied by two axial ligands, i.e., an acetate anion and a water molecule. Despite their structural similarity, they are not isomorphous given their distinct cell parameters. In the solid-state structures, both complexes exist as hydrogen-bonded dimers through hydrogen bonding interactions between the axially coordinating water molecules and outer O₄ cavity from another molecule of the complex. The reductive activity of both complexes has been explored. While the reaction of Mn-1 with potassium triethylborohydride was unsuccessful, leading to a complicated mixture, the use of Co-2 furnished the formation of a novel product (CoK-3) that was isolated as red crystals in reasonable yield. CoK-3 was characterized as a heterometallic dimer involving the coordination of a K⁺ ion within the O₄ cavity of a semi-hydrogenated salen/cobalt complex while the cobalt center has been reduced from Co(III) to Co(II). In addition, an attempt at reducing Co-2 with pinacolborane resulted in the isolation of crystals of Co-4, whose structure was determined as a simple square planar Co^II–salen complex. Finally, three complexes (Mn-1, Co-2 and CoK-3) have been investigated for their cytotoxic activities against two human breast cancer cell lines (MCF-7 and MDA-MB 468) and a normal breast epitheliel cell line (MCF-10A), with cisplatin used as a reference in order to discover potential drug candidates that may compete with cisplatin. The results reveal that Co-2 can be a promising drug candidate, specifically for the MCF-7 cancer cells, with minimal damage to healthy cells. Full article

The most promising method for the purification of concentrated technical sulfuric acid is the purification sorption method, which is the most effective and innovative, using a natural sorbent. Study of the process of sorption of iron and copper cations from concentrated technical sulfuric acid by a natural zeolite. The specific surface area of the zeolite isolated from reactive sulfuric acid is 4.781 m²/g. The true absorption volume in the zeolite after the purification of sulfuric acid decreases to a value of 147.0068 mL/g for a zeolite sample. The adsorption pore volume for the zeolite after the acid purification calculated from the obtained results is 0.229 mL/g. The physicochemical methods of analysis (NGR, IR, X-ray diffraction, DTA, porosimetry, electron microscopy) and chemical methods revealed that in concentrated sulfuric acid the Fe–O bonds of octahedrons and SiO bonds of tetrahedrons of the zeolite framework are stable. The sorption process was carried out under conditions of a room temperature of T = 25 °C, the ratio “zeolite: H₂SO₄” of 10:100, and a process time of 5–50 min. The specified concentration of the Fe and Cu cations was created by introducing the calculated amount of FeSO₄·7H₂O and CuSO₄·5H₂O, in order to identify the patterns of the sorption process of copper and iron in their joint presence (C_Fe > C_Cu; C_Fe = C_Cu). The regularities of sorption of iron and copper cations by zeolite in their joint presence on the model system “H₂SO₄–zeolite–Fe–Cu” were studied and selective sorption capacity of zeolite with respect to iron cations was revealed. The maximum degree of sorption of iron cations in concentrated sulfuric acid is achieved in 10–15 min and makes up 95% and that of copper 30.6%. The process of iron sorption from sulfuric acid occurs according to the types of ion isomorphism and ion exchange, as indicated by a very high number of sorbed Fe ions and the absence of their release (desorption) from the zeolite into the solution. The Cu cations are sorbed by zeolite from acid by the ion exchange method, which is confirmed by the physicochemical analysis methods. Full article

Metal cations are often used to regulate montmorillonite, but the mechanism is still unclear. In this paper, the regulation of different cations in montmorillonite was studied, and it was found that the regulation of different cations had significant effects on the structure of montmorillonite. Firstly, the viscosity is negatively correlated with particle size, and the order of particle size is trivalent > divalent > monovalent cation. Secondly, the swelling capacity is positively correlated with the absolute value of zeta potential, and the order of the zeta potential is monovalent > trivalent > divalent cation. Thirdly, the smaller hydrated ion radius and static electricity of monovalent cations significantly reduce the layer spacing. Meanwhile, isomorphism displacement results in a significant increase in the proportion of cis-vacant configuration due to changing the electronegativity of the octahedron. The comprehensive performance is that the particle size is significantly reduced and the absolute value of zeta potential is significantly increased. It is easy to peel off and expand in water to form a uniform and stable colloidal substance, which has the best gel performance. The research results can provide theoretical support for the regulation of montmorillonite structure and gel properties by different valence metal cations. Full article

We find that the whole set of known baryons of spin parity $J^P={{\displaystyle \frac{1}{2}}}^{+}$ (the ground state) and $J^P={{\displaystyle \frac{3}{2}}}^{+}$ (the first excited state) is organized in multiplets which may efficiently be encoded by the multiplets of conjugacy classes in the small finite group $G=(192, 187)$. A subset of the theory is the small group $(48, 29)\cong GL(2, 3)$ whose conjugacy classes are in correspondence with the baryon families of Gell-Mann’s octet and decuplet. G has many of its irreducible characters that are minimal and informationally complete quantum measurements that we assign to the baryon families. Since G is isomorphic to the group of braiding matrices of $SU{\left(2\right)}_2$ Ising anyons, we explore the view that baryonic matter has a topological origin. We are interested in the holographic gravity dual $Ad{S}_3/QF{T}_2$ of the Ising model. This dual corresponds to a strongly coupled pure Einstein gravity with central charge $c=1/2$ and AdS radius of the order of the Planck scale. Some physical issues related to our approach are discussed. Full article

Drug–target affinity (DTA) prediction is a critical step in virtual screening and significantly accelerates drug development. However, existing deep learning-based methods relying on single-modal representations (e.g., text or graphs) struggle to fully capture the complex interactions between drugs and targets. This study proposes CM-DTA, a cross-modal feature fusion model that integrates drug textual representations and molecular graphs with target protein amino acid sequences and structural graphs, enhancing feature diversity and expressiveness. The model employs the multi-perceptive neighborhood self-attention aggregation strategy to capture first- and second-order neighborhood information, overcoming limitations in graph isomorphism networks (GIN) for structural representation. The experimental results on the Davis and KIBA datasets show that CM-DTA significantly improves the performance of drug–target affinity prediction, achieving higher accuracy and better prediction metrics compared to state-of-the-art (SOTA) models. Full article

In this study, we comparatively analyzed the variable-temperature crystal structures for two isomorphous salts, [1-benzyl-4-aminopyridinium][M(mnt)₂] (M = Ni or Cu; mnt²⁻ = maleonitriledithiolate; labeled as APy-Ni or APy-Cu). Both salts crystallize in the triclinic P–1 space group at 296 K, comprising linear [M(mnt)₂]⁻ (M = Ni or Cu) tetramers. A magnetostructural phase transition occurs at T_C~190 K in S = ½ APy-Ni at ambient pressure, with a conversion of paramagnetic tetramers into nonmagnetic spin-paired dimers. The discontinuous alteration of cell parameters at T_C signifies the characteristic of first-order phase transition in APy-Ni. No such transition appears in the nonmagnetic APy-Cu within the same temperature vicinity, demonstrating the magnetic interactions promoting the structural phase transition in APy-Ni, which is further reinforced through a comparison of the lattice formation energy between APy-Ni and APy-Cu. The phase transition may bear a resemblance to the mechanisms typically observed in spin-Peierls systems. We further explored the magnetic and phase transition properties of APy-Ni under varying pressures. Significantly, T_C shows a linear increase with rising pressure within the range of 0.003–0.88 GPa, with a rate of 90 K GPa⁻¹, manifesting that the applied pressure promotes the transition from tetramer to dimer. Full article

This paper presents a comprehensive characterization of finite local rings of length 4 and with residue field ${\mathbb{F}}_{p^m},$ where p is a prime number. Such rings have an order of $p^{4m}$ elements. The current paper provides the structure and classification, up to isomorphism, of local rings consisting of $p^{4m}$ elements. We also give the exact number of non-isomorphic classes of these rings with fixed invariants $p,n,m,k.$ In particular, we have listed all finite local rings of 4-length and of order $p^8$ and $256.$ Full article