Published Articles Archive

Abstract
This study re-examines the Big Bang model from a Newtonian and empirically oriented perspective and develops Time-Invariant Cosmology (TIC) as an alternative interpretative framework. TIC treats universal space as time-invariant and regards time, understood as the measured duration and numerical ordering of physical change, as an emergent quantity rather than an independently existing physical dimension. Within this framework, the universe is considered eternal, uncreated, and in dynamic equilibrium. Active galactic nuclei (AGNs) are interpreted as rejuvenating systems through which old matter is transformed into energetic outflows that contribute to continuing astrophysical processes. The paper further re-examines conventional interpretations of cosmological redshift and the cosmic microwave background (CMB), and questions whether observations commonly associated with cosmic expansion and an origin in a remote physical past uniquely require the standard Big Bang interpretation. The aim is not merely to criticize the standard model, but to formulate the observational and conceptual basis of TIC and to identify the physical assumptions on which the competing interpretations depend.

Abstract
Magnetic switchbacks contribute significantly to coronal heating and the acceleration of the solar wind. In this study, they are ‎considered a weakly collisional plasma phenomenon influenced by the magnetic-field configuration rather than a process ‎arising solely from electrostatic Coulomb collisions. The proposed mechanism involves magnetic scattering associated with ‎interactions between low-energy Galactic Cosmic Rays (GCRs; 3–30 MeV/nuc) and solar radiation. These interactions are ‎considered to become more pronounced during periods of enhanced solar activity, including the release of Solar Energetic ‎Particles (SEPs). Within this framework, highly modulated GCRs interacting weakly with solar radiation are proposed to ‎generate magnetic switchbacks through a form of anti-Stokes Raman-like scattering. This process transfers energy within the ‎magnetized plasma, thereby contributing to plasma heating and solar-wind acceleration. The interaction is nonlinear and non-‎isotropic, with the external magnetic field modifying charged-particle dynamics and producing characteristic S-shaped ‎trajectories. In the presence of a strong magnetic field, Coulomb scattering can be substantially modified because cyclotron ‎motion (gyromotion) interacts with the Coulomb potential. Consequently, charged particles may follow complex, S-shaped, or ‎non-monotonic trajectories rather than the simple hyperbolic paths associated with conventional unmagnetized Coulomb ‎scattering. The proposed mechanism provides the basis for examining the possible role of magnetized Coulomb scattering in ‎the formation of solar magnetic switchbacks.‎

Abstract
Almost all observations discussed in this work are interpreted as supporting the condensed-matter nature of the Sun. ‎Regrettably, empirical solar data are generally interpreted with the Standard Solar Model (SSM) in mind. Consequently, ‎interpretations of solar features and phenomena are expected to remain compatible with the SSM. For instance, sunspots, ‎granules, and faculae are commonly treated as structures within a gaseous plasma, whereas the present work argues that they ‎are real physical structures formed by condensed crystal lattices. In addition, the Sun's average density (approximately 1.41 ‎g/cm³), which is comparable to that of Earth's oceans and slightly greater than that of water, is often interpreted within a ‎mathematical model rather than considered as possible evidence for a condensed state. The present work argues that the ‎overall density of the Sun is compatible with a condensed liquid state and that a purely gaseous body would not inherently ‎possess the structural properties required for the observed solar dynamo. Moreover, the continuous solar spectrum is ‎examined in relation to the physical state of solar matter. Dense, opaque matter can produce a continuous spectrum ‎approximating blackbody radiation, whereas isolated low-density gases or plasmas characteristically produce discrete ‎emission lines. Most importantly, this work argues that observed solar-dynamic phenomena such as sunspots, solar ‎prominences, coronal rain, sunquakes, and solar tsunamis cannot be adequately explained without a liquid surface and a ‎solid core.‎

Abstract
Reversible ternary circuit design has attracted considerable attention because ternary logic can reduce interconnection ‎complexity relative to binary logic and is compatible with emerging quantum-computing and nanotechnology platforms. This ‎study proposes a reversible 2-trit ternary parallel adder with a quantum cost of 23, one constant input, and three garbage ‎outputs. Compared with previously reported counterparts, the proposed adder requires lower quantum cost and fewer ‎constant inputs and garbage outputs. Based on this adder, a reversible arithmetic unit is developed for two 2-trit unsigned ‎ternary numbers. The unit performs six arithmetic operations: A+B, A−B, A+1, A−1, A+B+1, and A−B−1. The unsigned inputs ‎and outputs are represented within the decimal range from 0 to 8. A reversible arithmetic unit for two signed 2-trit ternary ‎numbers is also proposed. This circuit has a quantum cost of 32 and requires only one constant input. It performs the same six ‎arithmetic operations using the 3’s-complement representation over the range from −4 to +4. In addition, a new reversible ‎overflow detection module is introduced for signed addition and subtraction. By integrating this module with the proposed ‎signed arithmetic unit, a complete reversible ternary arithmetic circuit with overflow-detection capability is obtained. All ‎proposed circuits are constructed using 1-qutrit shift gates and 2-qutrit Muthukrishnan–Stroud gates, which are primitive ‎ternary gates suitable for implementation in ion-trap quantum-computing technology.‎

Abstract
This paper presents a revised and scientifically cautious formulation of the Fluid-dynamic Morphological Model (FMM), an exploratory computational framework for flux-based analysis of galactic systems using Hubble Space Telescope archival data. The method focuses on raw or minimally processed .flt images retrieved from MAST and extracts reproducible image-level descriptors, including mean flux, peak flux, integrated flux, radial intensity profiles, residual components, nuclear concentration indices, and VDR-like activity indicators. Rather than replacing standard gravitational, photometric, spectroscopic, or cosmological interpretations, FMM is presented as a complementary image-analysis approach inspired by fluid-dynamic terminology. In this formulation, galaxy morphology and nuclear activity are examined through spatial variations in flux concentration, radial structure, and residual asymmetry, with special attention to central regions and wake-like patterns. The framework is demonstrated through a representative HST FITS dataset and compared qualitatively with standard astronomical diagnostics. The results suggest that flux-derived indicators may help organize archival galaxy images, identify regions of morphological asymmetry or enhanced activity, and select targets for deeper astrophysical modeling. The paper defines the model assumptions, diagnostic quantities, processing workflow, limitations, and reproducibility requirements. The revised interpretation emphasizes uncertainty, dimensional consistency, and compatibility with established astrophysical methods, while preserving the author’s original aim of developing an accessible and automated pipeline for exploratory analysis of galactic systems.

Abstract
Building upon our previous studies, we introduce a generalized metric, denoted G, ‎describing the average gravitational field of a homogeneous universe. Starting from the ‎weak-field approximation of the Schwarzschild metric, the local gravitational contribution ‎of an isolated mass is extended to a continuous cosmological matter distribution, leading ‎to a global gravitational potential proportional to ρ_u R_u^2, where ρ_u is the mean cosmic ‎density and R_u is the Hubble radius. The resulting metric naturally defines an effective ‎cosmological refractive index. For a universe at critical density, this index is found to be ‎exactly 2, while departures from perfect homogeneity may increase it toward approximately ‎‎2.4. We further show that incorporating the gravitational potential of the universe into the ‎metric provides a quantitative framework connecting critical density, Mach’s principle, ‎inertia, and the equivalence of inertial and gravitational mass. Within this approach, ‎cosmic flatness is interpreted as a natural consequence of the global gravitational structure ‎rather than as a property requiring finely tuned initial conditions. The proposed framework ‎offers an alternative perspective on several outstanding problems in cosmology while ‎remaining within the weak-field approximation of general relativity. Its broader ‎cosmological implications, including possible reinterpretations of phenomena commonly ‎attributed to dark matter and dark energy, are discussed cautiously and presented as ‎directions for further investigation.‎

Abstract
The characterization of compact multiplanetary systems provides important insights into ‎planetary structure, orbital architecture, irradiation environments, and long-term ‎dynamical stability. In this work, the newly confirmed TOI-5624 system is investigated as a ‎five-planet system composed of TOI-5624 b, c, d, e, and f. The analysis is based on ‎observational data from the NASA Exoplanet Archive, combined with a reproducible ‎Python-based computational framework. A set of physical, orbital, thermal, and first-order ‎dynamical parameters is examined, including semi-major axis, orbital period, planetary ‎mass and radius, bulk density, equilibrium temperature, stellar flux, surface gravity, escape ‎velocity, period ratios between successive planets, and mutual Hill separations. Semi-‎major axes are independently calculated using Kepler’s third law and compared with ‎archive values, showing excellent agreement with differences below approximately 0.11 ‎percent. The results indicate that TOI-5624 is a compact multiplanetary system with ‎planets distributed between approximately 0.042 AU and 0.237 AU. The orbital period ‎ratios between successive planets are approximately 2.326, 1.741, 1.565, and 2.111, ‎suggesting a non-resonant but dynamically ordered architecture with near-‎commensurabilities. The mutual Hill separation analysis shows that all adjacent planet ‎pairs exceed both the classical two-planet Hill-stability limit of 2√3 and the conservative ‎empirical spacing threshold of Δ=10, indicating that the nominal system architecture is ‎well separated against immediate close encounters at the first-order level. The equilibrium ‎temperatures range from about 478.5 K to 1136 K, while the incident stellar flux spans from ‎approximately 8.7 to more than 275 times the Earth’s flux, indicating a strongly irradiated ‎system with no planet in an Earth-like habitable environment. This study provides a ‎consistent computational characterization of the TOI-5624 system and demonstrates a ‎reproducible first-order framework for examining the physical properties, irradiation ‎environment, orbital architecture, and dynamical spacing of newly confirmed compact ‎multiplanetary systems.‎

Abstract
This work proposes a structural–informational model of space–time in which a global low-frequency background oscillation ‎‎(~0.06 Hz) plays a fundamental role in the dynamics and stability of physical systems across all scales. Based on pendulum ‎experiments and a re-examination of Brownian motion, it is argued that purely stochastic molecular impacts are insufficient ‎to explain sustained particle motion. Instead, both macroscopic oscillators (such as Foucault and torsion pendula) and ‎microscopic particles are interpreted as responding to a universal space–time pulsation. The model further reveals a structural ‎correspondence between this space–time pulsation and the cosmic microwave background, suggesting a common underlying ‎physical origin. Within the proposed framework, gravity emerges from a fundamental vacuum pressure acting on a cellular ‎background structure of space–time, while Newton’s gravitational constant is interpreted as an effective parameter arising ‎from the balance between this pressure and a newly introduced surface mass–energy density (SMED). Modified de Broglie ‎relations explicitly incorporate background space–time cells, providing a unified description of orbital dynamics for both ‎micro- and macro-objects. Elementary particles are interpreted as localized soliton-like excitations of space–time energy, with ‎proton structure described by a Gaussian standing-wave configuration whose internal nodal patterns are associated with ‎quark confinement. Mass generation is treated as a geometric–energetic property of space–time rather than as a consequence ‎of interaction with a scalar Higgs field. The approach links gravitation, electromagnetism, and strong interactions to a single ‎underlying physical mechanism associated with vacuum pressure and predicts that dark matter may correspond to stabilized ‎background space–time cells. Overall, the results suggest that matter, fields, and interactions arise from a common structural ‎dynamic of space–time, accessible in principle through low-frequency oscillatory phenomena.‎

Abstract
A low-frequency pulsation of the metric structure of space–time with a characteristic frequency of approximately 0.06 Hz is ‎theoretically examined within a structural–informational framework. This oscillatory mode is considered as a global ‎background feature consistent with experimental data within the proposed framework, which may influence the dynamics of ‎particles and macroscopic objects. The phenomenon is treated as having a gravitational origin and is associated, in the ‎proposed model, with variations in the energy density of space–time. The characteristic frequency emerges from the dynamics ‎of a background space–time lattice, representing a deeper structural level governing gravitational interaction. Potential ‎signatures are explored using data of different pendulums, whose oscillation periods and energetic relations are found to be ‎consistent with excitation by such a global mode within the limits of the model. The approach provides a conceptual ‎structural–informational perspective on inertia, mass, and gravitational dynamics.‎

Abstract
This article establishes the theoretical foundations of a structural–informational model of space–time in which the vacuum is treated as a ‎physically real, material–informational medium rather than an empty geometric background. Space–time is proposed to possess an intrinsic ‎cellular organization governed by a universal fundamental pressure, which acts as the primary stabilizing quantity for localized energy ‎configurations. Within this framework, energy localization is identified with finite space–time volumes, and mass emerges as a structural ‎manifestation of space–time deformation maintained by pressure equilibrium. Two distinct but interconnected structural levels are developed. ‎The normal space–time lattice forms locally in association with matter and underlies electromagnetic interactions, providing geometric ‎interpretations of electric charge and electromagnetic constants as response parameters of the structured vacuum. At a deeper level, a background ‎space–time lattice is introduced as a global, matter-independent structural state of the metric, responsible for gravitational dynamics. Collective ‎oscillations of this background lattice lead naturally to the prediction of a global low-frequency pulsation of space–time with a characteristic ‎frequency near 0.06 Hz, identified as an intrinsic eigenmode of the structured vacuum. The model bridges classical mechanics, general relativity, ‎and quantum behavior by extending the de Broglie relation to include cellular participation of space–time and by interpreting wave–particle ‎duality as a scale-dependent manifestation of cellular dynamics. Experimentally relevant consequences are examined, most notably neutron β-‎decay, where the observed neutron lifetime emerges as a geometric delay associated with electron propagation through the normal space–time ‎lattice. The close agreement between theoretical predictions and experimental measurements supports the physical reality of the proposed ‎structural parameters. Overall, the framework shifts the foundations of physics from material entities to the organization and dynamics of space–‎time itself.‎

Abstract
Transient pressure disturbances in spacecraft pumped-fluid loops are commonly represented by linearized one-dimensional models, yet the error introduced by linearization is rarely quantified against a nonlinear formulation derived from the same conservation laws. This study develops a Navier-Stokes-based validity framework for single-phase spacecraft pumped-fluid loops. Mass conservation and axial momentum balance for a slightly compressible Newtonian liquid are reduced to coupled pressure-velocity equations that retain convective inertia and flow-regime-dependent wall friction. A consistent linear model is obtained by perturbation about a nonzero steady circulation state. The equations are solved with fourth-order spatial differencing and classical fourth-order Runge-Kutta integration. Verification against an exact smooth nonlinear characteristic solution gives the designed fourth-order convergence, with relative error decreasing to 2.72×10⁻¹⁰ at 800 grid points, and the nonlinear solution recovers the moving-base linear limit as the acoustic Mach number tends to zero. Two spacecraft-informed applications are examined: a turbulent HFE-7200 external thermal-control loop and a laminar 50/50 propylene-glycol/water internal loop. For a 20% smooth pump disturbance, the global linear-versus-nonlinear pressure discrepancies are 0.0667% and 0.0116%, respectively, with peak transient pressure excursions of approximately 74.8 and 13.6 kPa. Even at the largest tested disturbance amplitude (45%), the discrepancies remain 0.1481% and 0.0260%. A broader dimensionless map shows that errors above 1% require simultaneously larger acoustic Mach number and disturbance amplitude, while the 5% threshold in the tested turbulent family appears only near M ≳ 0.08 with strong forcing. The results show that the consistent linear model is quantitatively sufficient for the representative low-Mach spacecraft loops studied, while the nonlinear formulation provides a verified criterion for identifying conditions under which that simplification ceases to be adequate.

Abstract
This paper examines the proposed roles of the Higgs boson and the Reverse Higgs boson in relation to metallic lattice states and gravitational aether. The Higgs boson is treated as producing protons from positrons, whereas the Reverse Higgs boson is associated with conversions between massive fermions and photons. Three possible metallic-lattice configurations are considered: the spherical metallic photon, the Bohr atom, and the Thomson atom. These states are then related to a proposed duality between Newtonian gravitational force and Einsteinian space-time curvature. Within the model, gravitational force is associated with nuclei and with gravitons propagating along tensioned electromagnetic field lines. When a nucleus is absent at the field point, residual space-time curvature remains and acts on non-nuclear entities. Spherical metallic photons and Thomson atoms are therefore assigned a “phantom nucleus” so that they can function as gravitational sources. The Krueger-Farmer gravitational-aether interpretation is developed by relating gravitational interaction to nuclear motion and to two closely spaced characteristic frequencies. The paper also compares four states of matter, including the Schrödinger atom, and examines de Broglie relations, fermionic-wave amplitude, multiple-electron Bohr atoms, and non-orthogonality of Bohr orbits. Finally, the proposed graviton mass-speed relation is compared with the uncertainty principle in an attempt to connect quantum mechanics with gravity within the author’s M-theory framework.

Abstract
Absolutivity theory introduces an objective reality of time within a true four-dimensional spacetime model built on universal ‎simultaneity and an expanding three-dimensional space continuum. The theory unifies asymptotic modified Newtonian ‎gravity with quantum theory within an orthogonal four-dimensional framework that opposes intrinsic spacetime curvature ‎and eliminates gravitational singularities. This paper presents three physical applications of Absolutivity theory: black holes ‎and Hawking radiation, four-dimensional harmonics wave theory, and the mass-gravity property. For black holes and ‎Hawking radiation, Absolutivity predicts a hidden vacuum area located between the massive core and the Schwarzschild ‎radius. Within this region, both photons and mass particles can orbit according to Lagrange's principle of stationary action. ‎Photons experience curvature in a gravitational field without requiring an attractive force, as they possess no mass-gravity ‎property. The theory supports the existence of Hawking radiation from a classical continuum perspective but does not predict ‎complete evaporation of the black hole core. In four-dimensional harmonics wave theory, the true spacetime topology allows ‎energy to ingress from three independent spatial directions toward a single spacetime point. This yields a theoretical energy ‎concentration higher by a factor of the square root of three compared to the one-dimensional Mizohata-Takeuchi conjecture. ‎The treatment emphasizes that dimensional density of energy must be properly accounted for in harmonic analysis. ‎Regarding the mass-gravity property, the gravitational potential field of a particle is shown to be velocity-dependent. As a ‎particle approaches the speed of light, its gravity field becomes confined within the particle structure and cannot radiate ‎outward. Consequently, measurements of gravitational potential fields cannot provide an accurate estimate of the total mass ‎present in the universe. These applications demonstrate that Absolutivity offers a deterministic, causality-embedded, non-‎curved spacetime framework capable of addressing both quantum and astrophysical phenomena.‎

Abstract
The inverse function occupies a special position in elementary calculus because the standard power-law rule for integration ‎fails for a particular exponent. This exceptional behavior motivates a broader investigation into the mathematical structure of ‎logarithmic and hyperbolic functions. In this article we examine the asymptotic behavior of logarithmic and inverse functions, ‎with particular emphasis on singularities, asymptotes, and intersection structure. We investigate how logarithmic behavior ‎naturally emerges from inverse power relationships and discuss the geometric significance of the transition between these two ‎classes of functions. The discussion is then extended toward conceptual analogies in physics, especially in relation to ‎asymptotic behavior appearing in special relativity and gravitational theory. Rather than proposing modifications to ‎established physical theories, the article explores mathematical parallels between divergent structures, limiting processes, and ‎physical interpretation.‎ The aim of this work is therefore not to replace existing physical theories, but to highlight mathematical patterns that recur in ‎both analysis and theoretical physics.‎

Abstract
This work extends previous investigations into the relationship between the Einsteinian ‎Hamiltonian formulation and the Musakhail aether-based Lagrangian description of ‎dynamics. While earlier studies established their simultaneous role in the Newtonian-‎Einsteinian framework, the present paper focuses specifically on a formal Lagrangian ‎dynamical analysis in order to derive the corresponding equation of motion. Within the ‎proposed framework, the resulting dynamics suggest a correspondence in which the ‎classical relation F=ma transitions naturally toward the relativistic energy expression E=‎mc^2, interpreted here through the restoration of Newtonian behavior during the so-called ‎Reverse Higgs process. In this regime, the effective mass remains constant (m=m_e ) ‎rather than velocity-dependent, permitting a force-based description of particle-wave ‎interaction. The analysis further introduces a rotating Einstein energy vector derived from ‎the invariant relation E^2=(pc)^2+(m_0 c^2 )^2, which is employed to describe the ‎cyclic interaction between fermionic constituents and electromagnetic wave structure. This ‎approach yields a dual interpretative framework in which either photon energy extraction or ‎spin measurement may occur, depending on the observational configuration. The ‎formalism also explores a complex representation in which the orthogonal axis is treated as ‎imaginary, producing a geometrical interpretation associated with oscillatory spin states of ‎fermions (±1/2) and photons (0,±1). The resulting model suggests an underlying ‎symmetry between fermionic and bosonic spin states within the proposed aether-‎dynamical environment, providing a phenomenological bridge between classical force ‎dynamics and relativistic energy relations.‎

Abstract
This paper presents an exploratory, force-based framework for gravitation and ‎electrodynamics, motivated by a correspondence between Musakhail's aether dynamics ‎and Einsteinian special relativity. These two perspectives are interpreted through the lens of ‎Lagrangian-Hamiltonian duality, wherein force-based formulations (Lagrangian) and ‎energy-based formulations (Hamiltonian) are treated as complementary descriptions of ‎underlying physical dynamics. The aims of this work are threefold. First, to develop a force-‎based interpretation of gravitational interactions by examining Musakhail's force relation, ‎F=c^2 (m-m_0 ) in parallel with the relativistic energy expression, E^2=(pc)^2+‎‎(m_0 c^2 )^2 highlighting their dual structure. Second, to introduce and analyze two ‎exploratory electromagnetic four-vectors (J·E,E×B) and (ħω,v×B) employing an ‎extremization principle as a heuristic tool for investigating structural analogies between ‎dissipation, Poynting flux, and Lorentz-force dynamics. Third, to explore a minimal-scale ‎electro-gravitational correspondence through helical flux-tube geometries and a constant-‎mass acceleration mechanism, suggesting possible shared features between fermionic ‎transport and electromagnetic field configurations. The extremization procedure, in which ‎the scalar component of a four-vector is set equal to the magnitude of its vector ‎component, is applied heuristically to reveal formal parallels rather than to derive rigorous ‎field equations. Within this phenomenological model, gravitational interactions are ‎considered as collective nuclear-scale force processes, while electromagnetic energy ‎transport is examined through Lorentz-force cancellation and Poynting-flow relations. The ‎helical flux-tube structures provide a unifying geometric motif, with effective tension ‎identified with Newtonian gravitational force. This work is intended as a conceptual and ‎phenomenological exploration rather than a replacement for established relativistic field ‎theories. Its physical relevance depends on further mathematical development and ‎empirical validation. Several qualitative, testable consequences are outlined to motivate ‎future theoretical refinement and experimental assessment.‎

Abstract
Chemotherapy can generate substantial anticipatory anxiety because patients may expect nausea, vomiting, fatigue, pain, ‎loss of control, and disruption of family or occupational roles. These reactions are shaped not only by treatment-related ‎physical effects but also by cognitive appraisal, previous experiences, information obtained from others, and the perceived ‎ability to cope. This article presents an expanded brief counselling framework that integrates cognitive-behavioral methods ‎with structured problem solving, self-practice, mindfulness, and acceptance-based strategies. The framework is designed for ‎use before and during chemotherapy and emphasizes realistic cognitive reappraisal rather than simple positive thinking. It ‎also incorporates distress screening, collaborative goal setting, practical coping plans, and referral when symptoms exceed the ‎scope of brief counselling. Contemporary psycho-oncology guidance supports routine assessment of psychological distress ‎and the use of evidence-based psychosocial interventions, including cognitive-behavioral and mindfulness-based approaches. ‎The proposed framework is intended as a clinically practical model rather than as evidence of a newly tested intervention. ‎Future research should evaluate its feasibility, cultural adaptability, and effects on anxiety, psychological flexibility, treatment ‎engagement, and quality of life.‎

Abstract
This article develops a theoretical and conceptual mathematical framework for representing marriage, family structure, and ‎divorce. The framework combines set-theoretic representation, normalized similarity measures, active-bond dynamics, ‎probability trees, and ideas from complex systems. Each person is modeled as a time-dependent attribute structure embedded ‎in a universal attribute space. The central modeling assumption is a non-identity principle: within a sufficiently rich ‎description, two distinct persons are represented by non-identical identity structures. Interpersonal closeness is therefore not ‎defined by complete equality, but by normalized overlap measures such as the Jaccard index and, in a more general ‎formulation, by weighted or fuzzy similarity measures. Marriage is modeled not merely as the intersection of two person-sets, ‎but as an active marital-bond structure supported by shared values, emotional attachment, cooperation, legal or symbolic ‎commitment, residence, children, shared responsibilities, and common goals. Love is represented as a time-dependent ‎reinforcement variable that may increase, decrease, stabilize, or recover according to interaction history, conflict, repair ‎capacity, and deliberate maintenance. Because relationship outcomes are high-dimensional, context-sensitive, and path-‎dependent, the article does not propose a universal deterministic equation for marriage or divorce. Instead, it formulates a ‎probability-tree representation in which branch probabilities may depend on personality, culture, socioeconomic pressure, ‎family interference, previous reactions, and timing. Divorce is defined as the collapse of the active marital-bond measure ‎rather than the disappearance of all shared attributes. The framework is extended to nuclear and extended family structures ‎and is connected to family systems theory, mathematical sociology, agent-based modeling, and complex-systems reasoning. ‎The numerical examples and Monte Carlo simulation included in the article are illustrative and are not presented as empirical ‎divorce predictions. No empirical validation is reported in the present paper. Rather, the model is proposed as a formal ‎theoretical scaffold designed for near-future empirical testing, in which the marital-bond measure and probability-tree branch ‎probabilities may be operationalized, estimated, and evaluated using longitudinal couple data.‎

Abstract
This article presents a conceptual framework for innovative therapeutic interventions for neurodivergent couples through the integration of the neurodiversity approach and the double empathy model. Utilizing an analytical-review methodology, this article systematically examines and synthesizes contemporary interdisciplinary literature on neurodiversity, intimate relationships, autism, ADHD, and couples therapy. The analysis indicates that many relational difficulties in neurodivergent partnerships arise not from unilateral empathic deficits but from reciprocal differences in cognitive processing, communication styles, and sensory experiences. The proposed framework emphasizes four interrelated clinical domains: psychoeducation grounded in neurodiversity principles, explicit communication structuring, sensory environment modulation, and conflict reframing through the lens of the double empathy model. Integrating these perspectives shifts therapeutic focus from correcting individual “deficits” to fostering mutual understanding between differing perceptual and social systems. By promoting reciprocal empathy, relational adaptation, and acceptance of neurological differences, this integrative model offers a transformative direction for couples therapy. The article concludes by outlining implications for therapist training and future empirical research aimed at developing evidence-based protocols tailored to neurodivergent couples.

Abstract
Marital conflict is among the most common issues faced by couples, and unresolved conflicts can lead to numerous familial problems. This study aimed to examine the effectiveness of Imago therapy training on emotional acceptance and spirituality among married female students experiencing marital conflicts. Imago Therapy is a relational and integrative approach based on attachment and developmental theories, which helps partners explore unconscious childhood patterns that influence their adult relationships. By fostering mutual empathy, emotional awareness, and dialogue, it facilitates greater acceptance of emotions and nurtures a deeper sense of spirituality and connection within relationships. The statistical population included all married female students who referred to the counseling center of Islamic Azad University, Central Tehran Branch, during the 2024-2025 academic year. The sample consisted of 30 participants, selected through convenience sampling, who were randomly assigned to experimental and control groups (15 in each). After a pretest, participants in the experimental group received Imago therapy training based on the standard ten-session protocol (each session 90 minutes). A posttest and a two-month follow-up were conducted thereafter. Data were collected using the Marital Conflicts Questionnaire (MKCS) and the relevant subscales of the Connor-Davidson Resilience Scale (CD-RISC) assessing emotional acceptance and spirituality. Data analysis was performed using mixed repeated measures ANOVA in SPSS 26. The results showed that Imago therapy significantly increased emotional acceptance and spirituality among married female students with marital conflicts (p