Search Results (81)

Starting from the circular aperture diffraction experiment, this paper decomposes the intrinsic interactions underlying wave–particle duality and proposes a specific interaction force: the velocity-perpendicular interaction force. We derive the characterization formula of this force and show that it can induce the phenomenon of circular aperture diffraction of light, with the theoretical results being highly consistent with those calculated by the Huygens–Fresnel principle. The direction of this force is perpendicular to the relative velocity, originating from the coupling effect between the wave nature of light and the particle nature of the circular aperture structure, and it satisfies a modified inverse square law of distance related to the relative velocity. When photons pass through different positions of the circular aperture, the symmetry effect generates a net interaction time. The product of the main component of this force, the net interaction time, and the radius of the circular aperture constitutes a modulation quantity (a ratio of the Planck’s constant), which exerts an on–off modulation effect on the interaction force, thereby inducing the emergence of annular diffraction fringes. This study provides a novel physical interpretation for the circular aperture diffraction of light from the perspective of interaction forces and clarifies the possible existence form of wave–matter interaction forces. This force formula is expected to effectively describe the behavior of microscopic particles, just like the Schrödinger equation, while providing a brand-new perspective on interactions. It holds great application prospects in fields such as single-photon manipulation and quantum precision measurement. Full article

Background: Some widely used wildland fire behavior models, like the Fire Area Simulator (FARSITE), propagate fire fronts by computing the front-normal velocity (spread rate) as a function of local inputs and the front-normal direction. Such models are sometimes observed to cause the collapse of crown fires into sharp wedge shapes that eliminate heading fire behavior. Aims: We set out to document this phenomenon and, more generally, understand the relationships between fire shapes and spread rate functions. Methods: The phenomenon is studied both mathematically and through simulation experiments. Non-smooth fire fronts are theorized mathematically by an Eikonal partial differential equation ($H(x,\tau ,D\tau )=1$), where the unknown $\tau \left(x\right)$ is the time-of-arrival function and the Hamiltonian $H(x,t,p)$ is positively homogeneous and possibly non-convex in p; convex analysis is used to study viscosity solutions in constant conditions. Results: We show that a fire spread model preserves the smoothness of fire fronts if and only if it is equivalent to using the Huygens principle. Nontrivially, this is equivalent to a convexity criterion on the inverse spread rate profile, which is then the polar dual of the Huygens wavelet; this corresponds to Hamiltonian–Lagrangian duality. The relevance of smoothness-destroying models to crown fire is debated. Exact analytical formulas are derived for fire growth in constant conditions. Conclusions: Our understanding of fire spread models is improved by solving the spread equations in more general ways than previously known. In particular, the collapse of heading crown fires into sharp shapes is now explained. Smoothness-destroying spread models cannot be simulated by algorithms based on travel time like cellular automata; their general well-definedness remains an open question. Fire modelers can use these findings to guide their search for improved crown fire models, and more generally to verify the accuracy of numerical implementations. Full article

In this paper, we introduce and formalize the theory of Sheffer stroke hoop algebras, providing a minimal axiomatization for bounded hoop algebras utilizing a single binary operation. We systematically establish the fundamental algebraic properties of this novel structure, beginning with the logical independence of its core axioms. We equip the algebra with an induced partial order, proving it constitutes a well-defined ∧-semilattice, and demonstrate a bidirectional structural translation: bounded hoop algebras satisfying the Double Negation Property (DNP) can be equivalently expressed as Sheffer stroke hoop algebras, and vice versa. Furthermore, we investigate the internal algebraic architecture by introducing sub-algebras, filters, positive implicative filters, and ideals, rigorously establishing the inherent structural duality between filters and ideals. By proving that proper filters naturally induce full algebraic congruences, we successfully construct quotient Sheffer stroke hoop algebras. We characterize prime filters by demonstrating that a quotient algebra forms a chain if and only if its generating filter is prime. Finally, we complete the theoretical framework by establishing the Correspondence Theorem and the First Isomorphism Theorem, seamlessly embedding classical universal algebraic principles into the Sheffer stroke setting. Full article

Functional antibody-dependent enhancement (ADE) represents a fundamental and context-dependent characteristic of antiviral antibody responses, reflecting the dual capacity of antibodies to mediate both the neutralization and Fc receptor-dependent enhancement of infection. In flavivirus research, this duality complicates the interpretation of conventional serological metrics and limits the reliability of single-parameter correlates of immunity, particularly in populations with complex exposure histories. Over the past decade, functional ADE assays have evolved from specialized mechanistic tools into integrated immune assessment platforms supporting translational immunology, vaccine evaluation, and population-level immune surveillance. These platforms incorporate Fcγ receptor-relevant target cell systems, standardized viral inputs, dilution series-based profiling, quantitative enhancement metrics, and structured quality control frameworks to enable reproducible, comparable, and context-aware functional measurements across cohorts and laboratories. A central concept emerging from these developments is that ADE reflects a dynamic functional immune state rather than an intrinsic property of antibodies or a direct indicator of pathological risk. Accordingly, functional ADE platforms support the contextual interpretation of antibody activity across physiologically relevant conditions, facilitating discrimination between transient functional enhancement and clinically meaningful immunological risk. By integrating functional ADE metrics with serological, cellular, and epidemiological data, these platforms provide a structured framework for interpreting immune profiles in vaccine evaluation, booster strategy design, and population-level risk stratification. This review synthesizes the development, standardization, and global dissemination of functional ADE platforms and discusses key principles governing biological relevance, analytical robustness, and inter-site transferability. Emerging directions integrating functional ADE profiling with systems immunology, immunogenomics, and computational modeling are highlighted as pathways toward predictive, decision-support-oriented frameworks. By positioning ADE platforms as immune assessment infrastructures rather than isolated assays, this review underscores their value for mechanistic inquiry, translational interpretation, and preparedness-oriented responses to emerging viral threats in the absence of definitive correlates of protection. Full article

The town of Guano, located in the province of Chimborazo, Ecuador, is a canton renowned for its concentration of cultural expressions related to traditional artisanal techniques, such as the production of garments and leather goods, tanning, textile weaving, products made from cabuya or totora reeds, and knotted rugs. These artisanal practices are embedded in a long-standing historical and symbolic framework, linked to processes of cultural transmission and identity reinterpretation. Furthermore, Guano has been a pivotal site in Ecuadorian archaeological history thanks to the studies of Jacinto Jijón y Caamaño (1927), who identified six cultural phases of the Puruhá culture through ceramic and stratigraphic analysis. The province has earned recognition as the “Cradle of Ecuadorian Nationality” due to its valuable archaeological heritage. However, much of the interpretation of this legacy has been constructed from colonial-era archaeological approaches, which have limited the understanding of the Puruhá worldview and generated interpretive shifts in the cultural attribution of its iconography. This research analyzes, from a semiotic and decolonial perspective, the semiotic codes present in the iconography of the Puruhá culture, observable in archaeological ceramic pieces and their reinterpretation in the Guano rugs, understood as living cultural artifacts. The analysis of the denotative and connotative levels of the graphic motifs integrates the iconographic study, Andean fractal design, and the examination of contemporary artisanal discourses. The results demonstrate the existence of a structured symbolic system, based on principles of duality, complementarity, cyclicality, and the tripartite division of the cosmos, as well as the persistence of patterns such as spirals and zoomorphic figures in current textile production. The study identifies that, despite this symbolic continuity, those who possess this knowledge often attribute these symbols to external cultural frameworks, primarily the Inca culture, which limits their potential as a resource for identity, culture, and tourism. In this sense, the research provides a situated and non-hegemonic interpretive framework that contributes to the cultural reinterpretation of the Guano knotted carpets, offering input for safeguarding intangible cultural heritage, strengthening local identity, and designing sustainable cultural interpretation strategies. Full article

We develop the Sawyer duality principle for non-increasing functions where, in the denominator, the function g is replaced by ${\int }_x^{\infty }{\displaystyle \frac{g\left(t\right)}{t}}dt$. This result complements Stepanov’s result in which g was replaced by ${\displaystyle \frac{1}{x}}{\int }_0^{x}g\left(t\right)dt$. We use our result and obtain Stepanov’s result for non-decreasing functions and similarly use Stepanov’s result in proving our result for non-decreasing functions. These results have also been obtained in ${\mathbb{R}}^n$. Full article

The Zeta-Minimizer Theorem establishes that the Riemann zeta function $\zeta \left(s\right)$ and the primes arise variationally as unique minimizers of a phase functional defined on a symmetric measure space $\left(X,\mu ,G\right)$ equipped with helical operators. Three fundamental axioms—strict concave entropy maximization (Axiom 1), spectral Gibbs minima with non-vanishing ground states (Axiom 2), and irreducible bounded oscillations with flux conservation (Axiom 3)—allow for the selection of the non-proper Archimedean conical helix as the sole topology satisfying all constraints. Primes emerge as indivisible minimal cycles in the associated representation graph $\Gamma$ (via Hilbert irreducibility and Maschke’s theorem), while the Euler product is recovered through the spectral Dirichlet mapping of the helical eigenvalues. The partial zeta product, $Z\left(s\right)=\prod _j{\displaystyle \frac{1}{1-p_j^{-s}}},s\in \mathbb{R}\left\{0\right\},$ constitutes the exact grand partition function of any finite subsystem. Numerical inversion of this product directly recovers the mixture frequency $s$ from any experimental compressibility factor $Z_{\mathrm{m}\mathrm{i}\mathrm{x}}$. Mole fractions $x_i\left(s\right)$, interaction parameters $\Delta \left(x_i\right)$, and the Lyapunov spectrum $\lambda \left(x_i\right)$ then follow deductively via the helical transfer matrix and the closed-form linear ODE for $\Delta$. Occupation numbers $N\left(x_i\right)$ attain sharp maxima precisely at Fibonacci ratios $F_r/F_{r+1}$, leading to the molecular prime-ID rule. For twelve representative purely binary (irreducible) systems spanning atomic noble gases, simple diatomics, polar molecules, and an aromatic ring, the residuals satisfy $|Z\left(s\right)-Z_{\mathrm{m}\mathrm{i}\mathrm{x}}|<1.5\times {10}^{-8}$. The resulting $\lambda \left(x_i\right)$ curves accurately reproduce critical points, liquid ranges, and thermodynamic anomalies with zero adjustable parameters. The Riemann Hypothesis follows rigorously as a theorem: the unique fixed point of the duality functor $s\mapsto 1-s$ that preserves the orthogonality condition $\sum {\mathrm{c}\mathrm{o}\mathrm{s}}^2{\theta }^k=1$ is $\mathrm{R}\mathrm{e}\left(s\right)=1/2$, enforced by Axiom 1 concavity and Axiom 3 irreducibility. The framework is fully deductive and parameter-free and extends naturally to arbitrary mixtures and multiplicities through the helical representation graph. It provides a variational unification of analytic number theory, spectral geometry, thermodynamic phase behavior, and the Riemann Hypothesis from first principles. Full article

The equilibrium shape of a crystal is a fundamental problem in materials science and condensed matter physics. The Wulff construction, a cornerstone of crystal morphology prediction, is traditionally presented and utilized as a powerful geometric algorithm to derive equilibrium shapes from anisotropic surface energy $\gamma \left(\mathbf{n}\right)$. While its application across materials science is vast, the profound mathematical physics underpinning it, specifically its intrinsic identity as a manifestation of the Legendre transform, is often relegated to a passing remark. This work recenters the focus on this fundamental duality. We present a comprehensive, step-by-step derivation of the Wulff shape from the variational principle of surface energy minimization under a constant volume, employing the language of support functions and differential geometry. We then rigorously demonstrate that the equilibrium shape, defined by the support function $h\left(\mathbf{n}\right)$, and the surface energy density $\gamma \left(\mathbf{n}\right)$ are conjugate variables linked by a Legendre transformation; the Wulff shape $\mathcal{W}$ is precisely the zero-sublevel set of the dual function ${\gamma }^{*}\left(\mathbf{x}\right)={sup}_{\mathbf{n}}[\mathbf{x}·\mathbf{n}-\gamma \left(\mathbf{n}\right)]$. This perspective elevates the Wulff construction from a mere graphical tool to a canonical example of convex duality in thermodynamic systems, connecting it to deeper principles in convex analysis and statistical mechanics. To bridge theory and computation, we provide a robust computational algorithm implemented in pseudocode capable of generating Wulff shapes for two-dimensional (2D) crystals with arbitrary N-fold symmetry. Finally, we discuss the relevance and extensions of the classical theory in contemporary research, including non-equilibrium growth, nanoscale effects, and the coupling of crystal shapes with elastic membrane environments. Full article

Tunneling nanotubes (TNTs) are dynamic cell surface conduits that enable direct transfer of ions, signaling molecules, and organelles. They have emerged as a key mechanism of intercellular communication, complementing classical pathways such as synapses and paracrine signaling. In the central nervous system (CNS), TNTs exhibit a functional duality, particularly under aging and stress, where TNT-mediated exchange may shift from protective to maladaptive. On one hand, TNTs support homeostatic functions, ranging from mitochondrial transfer to stem cell-mediated rescue and astrocyte–neuron metabolic support. On the other hand, they facilitate the spread of prions and neurodegenerative protein aggregates, such as Tau and α-synuclein, with astrocytes playing a regulatory role. Despite rapid advances, TNT research faces challenges from conceptual heterogeneity and experimental standardization, especially in complex tissues such as the CNS. Recent mechanobiological and bio-inspired approaches, including force-based assays and three-dimensional culture models, provide new insights into TNT formation, stability, and cargo transport, extending beyond neural systems. This review offers an integrative synthesis of molecular, structural, and mechanobiological principles underlying TNT-mediated communication, emphasizing astrocyte–neuron crosstalk, while proposing validation criteria to support rigor, reproducibility, and cross-study comparability. TNTs thus emerge as dynamic, context-dependent interfaces with broad relevance to neurodegeneration, cancer, and biomedical applications. Full article

Transformer modeling is a crucial method for analyzing transient phenomena such as inrush currents. The primary characteristic of a transformer transient model is its ability to reflect how the transformer’s structure and material properties influence the magnetic and electric fields. In high-voltage direct current (HVDC), the single-phase converter adopts a double-core-limb and double-side-limb configuration, whose core structure, magnetic flux distribution, and ferromagnetic materials differ from conventional power transformers. This paper conducts research on low-frequency transient modeling of single-phase four-limb converter transformers. This study first determines the magnetic field distribution of the single-phase converter transformer with the inclusion of leakage flux. Subsequently, a corresponding model is derived from the principle of duality. Due to the laminated structure, the iron core exhibits different excitation characteristics from those of a single silicon steel sheet. For the excitation branch, AC-DC hybrid excitation is used to measure incremental excitation inductance and the nonlinear excitation curve is calculated based on this inductance. Furthermore, the allocation method of this curve in the core limb, side limb, and yoke is proposed to establish the converter transformer model. The results of no-load and inrush current tests based on the scaled model validate the effectiveness of this model, which can accurately calculate the inrush current under different remanence and closing conditions. Full article

This paper proves a new lemma that characterizes controllability for linear Volterra control systems and shows that the usual controllability assumption for the variational linearized system near an optimal pair is superfluous. Building on this, it establishes a Pontryagin-type maximum principle for Volterra optimal control with general control and state constraints (fixed terminal constraints and time-dependent state bounds), where the cost combines a terminal term with a state-dependent and integral term. Using the Dubovitskii–Milyutin framework, we construct conic approximations for the cost, dynamics, and constraints and derive necessary optimality conditions under mild regularity: (i) a classical adjoint system when only terminal constraints are present and (ii) a Stieltjes-type adjoint with a non-negative Borel measure when pathwise state constraints are active. Furthermore, under convexity of the cost functional and linear Volterra dynamics, the maximum principle becomes a sufficient criterion for global optimality (recovering the classical sufficiency in the differential case). The differential case recovers the classical PMP, and an SIR example illustrates the results. A key theme is symmetry/duality: the adjoint differentiates in the state while the maximum condition differentiates in the control, reflecting operator transposition and the primal–dual geometry of Dubovitskii–Milyutin cones. Full article

The origin of life remains one of the most profound and enduring enigmas in the biological sciences. Despite substantial advances in prebiotic chemistry, fundamental uncertainties persist regarding the precise mechanisms that enabled the emergence of the first cellular entity and, subsequently, the foundational branches of the tree of life. After examining the core principles that define living systems, we propose that life emerged as a novel property of a prebiotically assembled system—formed through the integration of distinct molecular worlds, defined as sets of structurally and functionally related molecular entities that interact via catalytic, autocatalytic, and/or self-assembly processes. This emergence established a permanent system–process duality, wherein the system’s organization and its dynamic processes became inseparable. Upon acquiring the capacity to replicate and mutate its genetic program, this primordial organism initiated the evolutionary process, ultimately driving the diversification of life under the influence of evolutionary forces and leading to the formation of ecosystems. The challenge of uncovering the origin of life and the emergence of biodiversity is not solely scientific, it requires the integration of empirical evidence, theoretical insight, and critical reflection. This work does not claim certainty but proposes a perspective on how life and biodiversity may have arisen on Earth. Ultimately, time and scientific inquiry will determine the validity of this view. Full article

Schrödinger’s operator relations combined with Einstein’s special relativistic energy-momentum equation produce the linear Klein–Gordon partial differential equation. Here, we extend both the operator relations and the energy-momentum relation to determine new families of nonlinear partial differential relations. The Planck–de Broglie duality principle arises from Planck’s energy expression $e=h\nu$, de Broglie’s equation for momentum $p=h/\lambda$, and Einstein’s special relativity energy, where h is the Planck constant, $\nu$ and $\lambda$ are the frequency and wavelength, respectively, of an associated wave having a wave speed $w=\nu \lambda$. The author has extended these relations to a family that is characterised by a second fundamental constant $h^{\prime }$ and underpinned by Lorentz invariant power-law particle energy-momentum expressions. In this note, we apply generalized Schrödinger operator relations and the power-law relations to generate a new family of nonlinear partial differential equations that are characterised by the constant $\kappa =h^{\prime }/h$ such that $\kappa =0$ corresponds to the Klein–Gordon equation. The resulting partial differential equation is unusual in the sense that it admits a stretching symmetry giving rise to both similarity solutions and simple harmonic travelling waves. Three simple solutions of the partial differential equation are examined including a separable solution, a travelling wave solution, and a similarity solution. A special case of the similarity solution admits zeroth-order Bessel functions as solutions while generally, it reduces to solving a nonlinear first-order ordinary differential equation. Full article

With the development of uncertain finance, uncertain stock models have become increasingly popular for modeling stock prices. This paper explores the symmetric properties inherent in the uncertain mean-reverting stock model, particularly in the structure of its differential equations and the resulting pricing formulas. The primary findings comprise the derivation of explicit pricing formulas, via uncertain differential equations, for European, American, Asian, and geometric average Asian options under the uncertain mean-reverting stock model. The symmetry in the inverse uncertainty distributions and the duality between call and put options are highlighted, demonstrating the model’s alignment with symmetric financial principles. Furthermore, several numerical examples are provided to illustrate the applicability and the symmetry-related characteristics of the derived formulas. Full article

This paper deals with J. A. Wheeler’s proposal that each piece of reality owes its existence to observation—an approach to physics, which implies that all physical entities at their bottom are informational in character. Focusing on the double-slit experiment with photons, which is the key evidence for the wave–particle dualism of photons, this paper follows Wheeler’s observational approach and interprets this experiment as a question posed to nature. Considering how the enquiry regarding the wave–particle duality of photons is answered by nature, it is shown that experimental questions are being answered by nature in the form of spatiotemporal patterns of elementary observations (EOs) which are binary pieces of information, produced by the dissipation of energy. Working through this line of thought, Wheeler’s statements of “binary information gain”, “observer participance” and the “impossibility of continuum idealizations of physical laws” are elucidated and connections to the Landauer Principle are made. Full article