Search Results (233)

The concept of vector topical functions, which take values in a partially ordered Banach space endowed with a complete lattice structure, was introduced in our preceding study. This structure enabled the development of an abstract convexity theory for vector topical functions, utilizing the notion of vector support. In this paper, applying these abstract convex theories, a DC-type vector optimization is investigated. Using the idea of a slack, the support set of a vector-valued map can be fully characterized by the subdifferential in abstract convex sense. Then, with the aid of this result, a sufficient condition to detect the efficient solutions for the DC-type vector optimization is obtained. In addition, a dual problem for the DC optimization is proposed, for which some strong dual results are established. Full article

We propose a comprehensive rotation-minimizing (RM) Darboux framework for the study of curve theory and relativistic ruled surfaces in Minkowski three-space ${\mathbb{E}}_1^3$. The construction merges the adaptability of the classical Darboux frame to surface geometry with the reduced rotational behavior characteristic of RM frames, yielding a natural geometric description of curves in a Lorentzian environment. For unit speed non-null curves, the governing equations of the RM Darboux frame are derived, and precise connections between the RM curvature functions and the classical Frenet and Darboux invariants are obtained, thereby elucidating the geometric significance of RM curvatures in Lorentzian geometry. Within this setting, multiple classes of ruled surfaces are generated using RM Darboux frame vector fields. Necessary and sufficient conditions for developability, minimality, and flatness are formulated exclusively in terms of RM curvature quantities. The role of the causal character of the generating curve is analyzed in detail, revealing distinct geometric behaviors for space-like and time-like cases. These findings indicate that the RM Darboux framework constitutes a flexible and effective approach for modeling curve-induced surface geometries in Minkowski space, with potential relevance to relativistic kinematics, world sheet constructions, and geometric problems arising in mathematical physics. Full article

This paper studies the existence and construction of bases consisting of tangential and anisotropic vectors in finite-dimensional quadratic spaces over fields of characteristic different from two. While classical theory guarantees the existence of orthogonal bases in regular quadratic spaces, the existence of bases governed by alternative geometric constraints such as tangency or isotropy has remained largely unexplored. We introduce determinant-based constructive methods extending the Gram–Schmidt process to arbitrary quadratic spaces, yielding systematic criteria for generating orthogonal, tangential, and isotropic families of vectors. Our main results establish necessary and sufficient conditions for the existence of tangential bases, including a characterization of regular spaces of positive index and strong algebraic obstructions in the hyperbolic case. In addition, we prove a general constructive existence theorem for isotropic bases in real regular quadratic spaces. Full article

Genetic sequences play a central role in biological and medical research, and mathematics provides powerful means for their representation and analysis. Conventional approaches, such as the fuzzy polynucleotide space ${[0, 1]}^{12}$, model codons as 12-dimensional vectors, but this comes at the cost of high dimensionality. In this study, we introduce two new models, Vector-Fuzzy-I and Vector-Fuzzy-II, that map codons and genetic sequences into the 4-dimensional Euclidean space ℝ⁴ using vector algebra and fuzzy set theory. In the first model, sequence structure is represented by successive vector addition, while in the second, it is represented by positional frequencies normalized by nucleotide locations. These low-dimensional representations are unique, preserve sequence order, and allow effective measurement of similarity and difference via Euclidean metrics. Compared with the fuzzy polynucleotide space, the proposed models achieve dimensionality reduction while enhancing the resolution of sequence differentiation. Our approach offers new mathematical perspectives for sequence analysis in theoretical biology. Full article

This paper presents a robust sensorless control strategy for a dual-inverter doubly fed induction motor (DFIM) designed for high-performance electric vehicle (EV) traction systems. The proposed scheme eliminates the mechanical speed sensor by employing a sliding-mode observer (SMO) for real-time estimation of rotor speed and flux, ensuring accurate feedback under load disturbances and thereby enhancing reliability while reducing implementation cost. The DFIM is powered by two voltage-source inverters that independently control the stator and rotor windings through space vector pulse-width modulation (SVPWM). A power-sharing strategy optimally distributes the electromagnetic power between the two converters, ensuring smooth transitions between sub-synchronous and super-synchronous operating modes. Furthermore, a stator-flux-oriented vector control (SFOC) scheme incorporating a graphical torque optimization algorithm is developed to maximize torque while satisfying inverter and machine constraints across both base-speed and flux-weakening regions. The stability of the SMO-based estimation and closed-loop control is rigorously validated using Lyapunov theory. Comprehensive MATLAB R2024b/Simulink simulations conducted under the WLTC-Class 3 driving cycle confirm high accuracy and robustness, showing fast dynamic response, precise speed estimation, and smooth torque behavior across the full speed range. The results demonstrate that the SMO-based DFIM drive offers a cost-effective and reliable solution for next-generation EV traction applications. Full article

The purpose of this research was to investigate whether music empirically associated with therapeutic effects contains intrinsic informational structures that differentiate it from other sound sequences. Drawing on ontology, phenomenology, nonlinear dynamics, and complex systems theory, we hypothesize that therapeutic relevance may be linked to persistent structural patterns embedded in musical signals rather than to stylistic or genre-related attributes. This paper introduces the Discriminating Music Sequences (DiMuSes) method, an unsupervised, structure-oriented analytical framework designed to detect such patterns. The method applies 24 scalar evaluators derived from statistics, fractal geometry, nonlinear physics, and complex systems, transforming sound sequences into multidimensional vectors that characterize their global temporal organization. Principal Component Analysis (PCA) reduces this feature space to three dominant components (PC1–PC3), enabling visualization and comparison in a reduced informational space. Unsupervised k-Means clustering is subsequently applied in the PCA space to identify groups of structurally similar sound sequences, with cluster quality evaluated using Silhouette and Davies–Bouldin indices. Beyond clustering, DiMuSe implements ranking procedures based on relative positions in the PCA space, including distance to cluster centroids, inter-item proximity, and stability across clustering configurations, allowing melodies to be ordered according to their structural proximity to the therapeutic cluster. The method was first validated using synthetically generated nonlinear signals with known properties, confirming its capacity to discriminate structured time series. It was then applied to a dataset of 39 music and sound sequences spanning therapeutic, classical, folk, religious, vocal, natural, and noise categories. The results show that therapeutic music consistently forms a compact and well-separated cluster and ranks highly in structural proximity measures, suggesting shared informational characteristics. Notably, pink noise and ocean sounds also cluster near therapeutic music, aligning with independent evidence of their regulatory and relaxation effects. DiMuSe-derived rankings were consistent with two independent studies that identified the same musical pieces as highly therapeutic.The present research remains at a theoretical stage. Our method has not yet been tested in clinical or experimental therapeutic settings and does not account for individual preference, cultural background, or personal music history, all of which strongly influence therapeutic outcomes. Consequently, DiMuSe does not claim to predict individual efficacy but rather to identify structural potential at the signal level. Future work will focus on clinical validation, integration of biometric feedback, and the development of personalized extensions that combine intrinsic informational structure with listener-specific response data. Full article

Two-dimensional (2D) powders constitute an important class of molecular thin films where a specific close-packed plane forms parallel to the substrate surface, while there is no preferred lateral ordering. Using results from classic lattice reduction theory, a systematic scheme is proposed in order to determine the 3D surface unit cell for 2D powders in reciprocal space. The approach is based on a sorted set of lengths $q_1,q_2,q_3,\dots$ of the in-plane components of the scattering vector, which is directly obtained from the scattering pattern. After a first match is established, a refinement procedure is presented that makes full use of the complete set of scattering vectors and, as such, corrects for small experimental errors and ensures a good overall match with the observed reflections. After identifying the in-plane components, the full 3D surface unit cell can be found in a straightforward way. Full article

Numerous attempts to define art have been made from antiquity to the present, yet historical overviews often adopt a Eurocentric (and American-centric) perspective focused mainly on culturally dependent aesthetic approaches. As a universal social and cultural phenomenon, art resists center-periphery models. The cognitive turn reshaped art theory by reconsidering art as a cognitive dimension of humanity. Art has no limits on who can create or enjoy it. The ability to use and understand metaphor, for instance, demonstrates everyday human artistic cognition. The analysis relies on both field research (case studies) and academic literature; it argues for a revised theoretical frame for defining art and organizes it into a dynamic model of three main vectors: (1) art as communication (including art as agency); (2) art as creation; and (3) art as experience (involving both audience and artist). The model can incorporate the study of emotions into the third criterion while remaining open to both materialist and non-materialist approaches. Rather than offering a new definition, the study integrates the perspective of cognitive anthropology, cognitive semantics, and the anthropology of art in order to broaden understanding. Instead of searching for special aesthetic or economic values, these three dimensions of art appear more universal. A pragmatic analysis of how art “works” in individuals and groups provides a useful model for cognitive sciences. Instead of binary codes, it is a vectorial model, a 3D space for expressing family resemblance, since there is no common denominator (prototype) for all kinds of art. Full article

Background/Objectives: Vector-borne diseases like malaria remain a major global health concern, worsened by insecticide resistance in mosquito populations. Quinoline-based compounds have been extensively studied for their pharmacological effects, including antimalarial and larvicidal properties. Modifying quinoline structures with hydrazone groups may enhance their biological activity and physicochemical properties. This study reports the synthesis, structural characterization, and larvicidal testing of a new series of aryl hydrazones (6a–i) derived from 8-trifluoromethyl quinoline. Methods: Compounds 6a–i were prepared via condensation reactions and characterized using ¹H NMR, ¹⁹F-NMR, ¹³C NMR, and HRMS techniques. Their larvicidal activity was tested against Anopheles arabiensis. Single-crystal X-ray diffraction (XRD) was performed on compound 6d to determine its three-dimensional structure. Hirshfeld surface analysis, fingerprint plots, and interaction energy calculations (HF/3-21G) were used to examine intermolecular interactions. Quantum chemical parameters were computed using density functional theory (DFT). Molecular docking studies were performed for the synthesized compounds 6a–i against the target acetylcholinesterase from the malaria vector (6ARY). In silico ADMET properties were also calculated to evaluate the drug-likeness of all the tested compounds. Results: Compound 6a showed the highest larvicidal activity, causing significant mortality in Anopheles arabiensis larvae. Single-crystal XRD analysis of 6d revealed a monoclinic crystal system with space group P2₁/c, stabilized by N–H···N intermolecular hydrogen bonds. Hirshfeld analysis identified H···H (22.0%) and C···H (12.1%) interactions as key contributors to molecular packing. Density functional theory results indicated a favorable HOMO–LUMO energy gap, supporting molecular stability and good electronic distribution. The most active compounds, 6a and 6d, also showed strong binding interactions with the target protein 6ARY and satisfactory ADMET properties. The BOILED-Egg model is a powerful tool for predicting both blood–brain barrier (BBB) and gastrointestinal permeation by calculating the lipophilicity and polarity of the reported compounds 6a–i. Conclusions: The synthesized arylhydrazone derivatives demonstrated promising larvicidal activity. Combined crystallographic and computational studies support their structural stability and suitability for further development as eco-friendly bioactive agents in malaria vector control. Full article

The MHD (magnetic hydrodynamics) boundary problem in three-dimensional domains of certain types is considered within the framework of discrete potential theory. The discrete character of the information obtained from remote sensing of the Earth and planets of the Solar System can be taken into account when using the basic principles of this theory. This approach makes it possible to reconstruct the spatial distribution of magnetic fields and the velocity field with relatively high accuracy using the heterogeneous data in some network points. In order to restore the magnetic image of a planet with a so-called dynamo, the subsequent approximations approach is implemented. The unknown physical field is represented as a sum of terms of different magnitudes. Such an approach allows us to simplify the nonlinear partial differential equation system of magnetic hydrodynamics and extend it to discrete magnetic field and velocity vectors. The solution of the simplified MHD equation system is constructed for some classes of bounded domains in Cartesian coordinates in three-dimensional space. Full article

Topological field theories (TFTs) have captured the attention of mathematicians due to their various applications. In categorical terms, an nTFT is defined as a monoidal functor that maps the category of n-dimensional cobordisms to the category of vector spaces. In this paper, we introduce the category of two-dimensional closed–open cobordisms, denoted as $2Co{b}_{CO}$. We demonstrate that the generating morphisms in this category total 35. Furthermore, we establish that the category $2Co{b}_{CO}$ is a monoidal category. We define a triple $(B,\epsilon ,{\epsilon }^{\prime })$ as a doubly Frobenius algebra if both $(B,\epsilon )$ and $(B,{\epsilon }^{\prime })$ are Frobenius algebras. We then introduce the category of doubly Frobenius algebras, wherein the objects are doubly Frobenius algebras and the morphisms are homomorphisms of Frobenius algebras that satisfy specific compatibility conditions. Additionally, we present a new type of 2TFT, which we refer to as the two-dimensional closed–open TFT (denoted as $2TF{T}_{CO}$). We demonstrate that the category of all $2TF{T}_{CO}$, referred to as $2\mathcal{T}\mathcal{F}{\mathcal{T}}_{CO}$, is equivalent to the category of all commutative doubly Frobenius algebras, denoted as $\mathcal{C}\mathcal{F}$. Full article

This paper analyzes the Bagley–Torvik fractional-order equation with generalized fractional Hilfer derivatives of two orders for functions in Banach spaces under conditions expressed in the language of weak topology. We develop a comprehensive theory of fractional-order differential equations of various orders. Our focus is on the equivalence results (or the lack thereof) of this new class of fractional-order Hilfer operators and on maximizing the regularity of the solution. To this end, we examine the equivalence of differential problems involving pseudo-derivatives and integral problems involving Pettis integrals. Our results are novel, even within the context of integer-order differential equations. Another objective is to incorporate fractional-order problems into the growing research field that uses weak topology and function spaces to study vector-valued functions. The auxiliary results obtained in this article are general and applicable beyond its scope. Full article

Most machine learning algorithms operate on vectorized data with Euclidean structures because of the significant mathematical advantages offered by Hilbert space, but improved representational efficiency may offset more involved learning on non-Euclidean structures. Recently, a method that integrates the marginalized graph kernel into the Gaussian process regression framework was used to learn directly on molecular graphs. Here, we describe an implementation of this method for crystalline materials based on effective crystal graph representations: the molecular graphs of 128-atom supercells of body-centered cubic (BCC) iron with periodic boundary conditions. Regressors trained on hundreds of time steps of a density functional theory molecular dynamics (DFT-MD) simulation achieved root mean square errors of less than 5 meV/atom. The mechanical stability of BCC iron was investigated at high pressure and elevated temperature using regressors trained on short DFT-MD runs, including at conditions found in the inner core of the earth. Phonon dispersions obtained from the short runs show that BCC iron is mechanically stable at 360 GPa when the temperature is above 2500 K. Atoms in the super cell were displaced in the direction of the first, second, and third nearest-neighbors from selected configurations that included thermal atomic displacements, and forces exerted on the displaced atoms were computed by numerical differentiation of the regressors. Full article

Integration in non-integer-dimensional spaces (NIDS) is actively used in quantum field theory, statistical physics, and fractal media physics. The integration over the entire momentum space with non-integer dimensions was first proposed by Wilson in 1973 for dimensional regularization in quantum field theory. However, self-consistent calculus of integrals and derivatives in NIDS and the vector calculus in NIDS, including the fundamental theorems of these calculi, have not yet been explicitly formulated. The construction of precisely such self-consistent calculus is the purpose of this article. The integral and differential operators in NIDS are defined by using the generalization of the Wilson approach, product measure, and metric approaches. To derive the self-consistent formulation of the NIDS calculus, we proposed some principles of correspondence and self-consistency of NIDS integration and differentiation. In this paper, the basic properties of these operators are described and proved. It is proved that the proposed operators satisfy the NIDS generalizations of the first and second fundamental theorems of standard calculus; therefore, these NIDS operators form a calculus. The NIDS derivative satisfies the standard Leibniz rule; therefore, these derivatives are integer-order operators. The calculation of the NIDS integral over the ball region in NIDS gives the well-known equation of the volume of a non-integer dimension ball with arbitrary positive dimension. The volume, surface, and line integrals in D-dimensional spaces are defined, and basic properties are described. The NIDS generalization of the standard vector differential operators (gradient, divergence, and curl) and integral operators (the line and surface integrals of vector fields) are proposed. The NIDS generalizations of the standard gradient theorem, the divergence theorem (the Gauss–Ostrogradsky theorem), and the Stokes theorem are proved. Some basic elements of the calculus of differential forms in NIDS are also proposed. The proposed NIDS calculus can be used, for example, to describe fractal media and the fractal distribution of matter in the framework of continuum models by using the concept of the density of states. Full article

In this review, we present a general framework for the construction of Kac–Moody (KM) algebras associated to higher-dimensional manifolds. Starting from the classical case of loop algebras on a circle ${\mathbb{S}}^1$, we extend the approach to compact and non-compact group manifolds, coset spaces, and soft deformations thereof. After recalling the necessary geometric background on Riemannian manifolds, Hilbert bases, and Killing vectors, we present the construction of generalized current algebras $\mathfrak{g}\left(\mathcal{M}\right)$, their semidirect extensions with isometry algebras, and their central extensions. We show how the resulting algebras are controlled by the structure of the underlying manifold, and we illustrate the framework through explicit realizations on $SU\left(2\right)$, $SU\left(2\right)/U\left(1\right)$, and higher-dimensional spheres, highlighting their relation to Virasoro-like algebras. We also discuss the compatibility conditions for cocycles, the role of harmonic analysis, and some applications in higher-dimensional field theory and supergravity compactifications. This provides a unifying perspective on KM algebras beyond one-dimensional settings, paving the way for further exploration of their mathematical and physical implications. Full article