The dynamics of a light fermion bound to a heavy one is expected to be described by the Dirac equation with an external potential. The potential breaks translation invariance, whereas the bound state momentum is well defined. Boosting the bound state determines the frame dependence of the light fermion dynamics. I study the Dirac limit of QCD 2 in the limit of N c → ∞ . The light quark wave function turns out to be independent of the frame of the bound state, up to an irrelevant Lorentz contraction. The discrete bound state spectrum determines corresponding discrete energies of the Dirac equation, which for a linear potential allows a continuous spectrum.

Abstract In this paper, we first show that it is possible to establish, by rescaling the proper time axis of inertial reference frames in a space-proper time, a new geometric framework for special relativity – equivalent to the standard framework – allowing the construction of kinetic distortion diagrams which directly visualize time dilation and length contraction for inertial motions. We then show that in the presence of a Newtonian gravitational field, the curvature of spacetime given by the Schwarzschild solution can be translated into the new geometric framework by gravitational distortions, allowing the construction of gravitational distortion diagrams to directly represent Newtonian gravitational field effects on space and time. Finally, we discuss the pedagogical value of this approach, particularly through its diagrammatic representations, for teaching relativity to undergraduate students.

Control competing expansion and contraction of interplanar spacing in layer structured cathode for stable and low-temperature zinc batteries.

The medicinally and ornamentally valuable genus Thunbergia faces taxonomic uncertainty, while certain Acanthaceae species are threatened by habitat loss, underscoring the need for chloroplast genome studies to support conservation efforts. The chloroplast genome of Thunbergia grandiflora was sequenced and assembled. Additionally, 28 Acanthaceae species with significant medicinal value were selected for comparative genomic analysis. Based on the chloroplast genome data of Acanthaceae species, this study conducted phylogenetic and comparative evolutionary analyses. The results preliminarily support a systematic framework that divides Acanthaceae into eight tribes within five subfamilies. Concurrently, the study revealed significant inverted repeat (IR) region structural variations. A clear correspondence was observed between the contraction of IR length and the topological structure of the phylogenetic tree. In particular, species within the genus Strobilanthes exhibited significant contraction in their IR regions, which corresponded consistently with their tendency to cluster into an independent clade in the phylogenetic tree. This suggests that structural variation in the IR regions may be closely associated with the evolutionary divergence of this group. SSR analysis revealed a prevalent mononucleotide A/T repeat dominant pattern across Acanthaceae species. Furthermore, selection pressure analysis detected positive selection acting on multiple key genes, including rbcL, rps3, rps12, cemA, and ycf4, suggesting that these genes may play important roles in the adaptive evolution of Acanthaceae. This study reveals that the chloroplast genomes of Acanthaceae exhibit distinctive characteristics in phylogenetic architecture, dynamic variations in IR regions, and adaptive evolution of key genes, providing important molecular insights for understanding the mechanisms underlying species diversity and for the conservation of medicinal resources within this family.

The inertial frames are the frames moving with a uniform velocity in any direction. The second postulate of Special Relativity speaks of constancy of light speed (in vacuum) in all inertial frames, with no riders. However, it is taken to implicitly mean only those inertial frames that are moving along the line from origin to the event’s location, or of light propagation. For the inertial frames moving otherwise i.e. in directions oblique to the latter, the setup is converted back to the same (i.e. parallel moving observer), by taking up the distance component parallel to observer’s motion for transformation, and ignoring the rest of its components. The Wigner-Thomas rotation arises only on account of this limited interpretation. It disappears when obliquely moving (with respect to direction of event from origin) inertial frames are given recognition. The two non-collinear boosts are equivalent to one boost in the resultant direction that is oblique to the directions of both the boosts. The example presented in the article amply demonstrates it. Therefore, to give sanctity to the Wigner-Thomas rotation, the second postulate needs to be supplemented by specifying the “Inertial Frames” with a rider “that are moving along the Line of its (light’s) motion”. Further, the Lorentz Transformation have not been and also cannot be derived for events other than those of light. However, these are universally applied to such events e.g. those of non-collinearly moving frames in this case. Thus, another (third) postulate is required to be added, and i.e. “The transformation arrived at for light applies to other events also, where the distance-time ratio is not equal to c”. Addition of the postulate will provide the much needed authorization for working out of Wigner-Thomas rotation, along with numerous other cases such as length contraction and time dilation on moving bodies, though with errors. The error would obviously be proportional to the difference between the distance-time ratio of the event and c.

This paper introduces a theoretical framework that bridges the conceptual divide between quantum mechanics and relativity by proposing a fundamental building block of the universe: the “Space-Time* quantum.” The theory posits that every object possesses an inherent property, Time* — defined as the reciprocal of its intrinsic frequency. The Space-Time* quantum is a composite entity, consisting of a timeless space energy and a kinetic Time* energy. This framework provides a new perspective on wave-particle duality, the double-slit experiment, and quantum entanglement. It re-examines the principles of Special Relativity, offering a conceptual and visual explanation of phenomena such as time dilation and length contraction as a consequence of changes in the Space-Time quanta. The theory also provides an alternative view on the origin of the universe and the nature of gravity, suggesting that gravitational effects arise from an energy deficiency rather than a curvature of spacetime. This paper establishes a conceptual foundation for further mathematical development to test and validate these new insights.

In this paper, we introduce and investigate two generalized forms of classical contraction mappings, namely the p-Hardy–Rogers and p-Zamfirescu contractions. By incorporating the integer parameter p≥1, these new definitions extend the traditional Hardy–Rogers and Zamfirescu conditions to iterated mappings ħp. We establish fixed-point theorems, ensuring both existence and uniqueness of fixed points for continuous self-maps on complete metric spaces that satisfy these p-contractive conditions. The proofs are constructed via geometric estimates on the iterates and by transferring the fixed point from the p-th iterate ħp to the original mapping ħ. Our results unify and broaden several well-known fixed-point theorems reported in previous studies, including those of Banach, Hardy–Rogers, and Zamfirescu as special cases.

On Pseudo 𝑆𝑏−Menger Space and Rational Type Contraction in 𝑆𝑏−Menger Space with Applications

This paper presents a comprehensive study of fixed point theorems for Reich, Hardy–Rogers, and Ćirić-type contractions in the framework of cone modular spaces. We introduce a novel iteration scheme called [Formula: see text]-iteration, defined by [Formula: see text], with [Formula: see text], both Picard and Mann iterations are generalized. Complete convergence proofs are provided for each contractive condition, establishing the existence and uniqueness of fixed points. These results significantly extend existing work in cone metric spaces and modular metric spaces by considering more general contractive conditions in the unified framework of cone modular spaces. Explicit examples with full numerical computations demonstrate the convergence behavior. The paper concludes with discussions on potential applications and open problems for future research.

A comprehensive computational investigation of a triphenylmethane-acidic dye using Density Functional Theory (DFT) and Time-Dependent DFT (TDDFT) at the B3LYP/6-31G(d) level was conducted. The basic goal was to interpret the properties, i.e., structural, electronic, and spectroscopic properties in several media (gaseous, aqueous, and acetic acid) and to evaluate the suitability for textile applications. The geometric optimization of the acidic dye under observation undergoes solvent induced changes, with the contraction of bond length (e.g., C1–C2 shortened from 1.4039 Å in gas to 1.3872 Å in water) and the angular variation of bonds (e.g., C2–C1–C6 decreased from 120.67° to 120.59° in ethanol), depicting the high conformational stability in polar solvents. The TD-DFT simulations showed a bathochromic shift and a high molar absorptivity (λmax ~245 nm, absorbance ~3200), indicating UV absorption in aqueous environments. The oscillator strength of strong π→π* electronic transitions in the 240–250 nm range further confirms the conjugated system's ability to interact effectively with light, an essential characteristic for dye brilliance and intensity on textile substrates. HOMO–LUMO analysis showed a solvent-dependent narrowing of the energy gap (ΔE), from 3.82 eV in the gas phase to slightly reduced values in ethanol and water, facilitating intramolecular charge transfer and favorable dye–fiber interactions. Mulliken population analysis and molecular electrostatic potential (MEP) mapping highlighted nucleophilic and electrophilic regions, consistent with expected binding behavior to textile fibers in solvents. IR vibrational analysis confirmed structural consistency across 700–3500 cm⁻¹ in interaction with solvents. These findings show that solvent polarity significantly affects the dye's electronic structure and spectroscopic response, providing critical insights for its application in water-based or ethanol-assisted textile processing. The study affirms the value of DFT/TDDFT modeling for pre-screening dye candidates, enabling more efficient, cost-effective, and targeted dye design for optimal textile performance.

The present paper is devoted to the introduction and development of the notions of multivalued graphic contractions and multivalued GF-contractions in the setting of F-metric spaces. By extending the idea of contractions to multivalued mappings associated with an underlying graph structure, we aim to enrich the existing theory of fixed point results in generalized metric frameworks. The main contribution of this study is the establishment of new fixed point theorems for these classes of mappings in F-metric spaces, which provide a natural extension of classical fixed point principles. Furthermore, in order to demonstrate the validity and applicability of our theoretical findings, we construct a non-trivial illustrative example that highlights how the proposed conditions can be effectively utilized. These results not only advance the fixed point theory in abstract metric settings but also open potential avenues for applications in mathematical analysis and applied sciences.

Special relativity is often introduced through algebraic formalism, yet many of its core ideastime dilation, length contraction, and the relativity of simultaneityare inherently geometric and can feel counterintuitive to beginners. This paper develops a visualization-first pathway that pairs spacetime diagrams with concise animations to make the kinematics of inertial frames perceptible and internally consistent. After motivating the role of diagrams in scientific reasoning, we construct frame-aware figures for three classic thought experiments: the light clock, the ladderbarn paradox, and the train-and-lightning scenario. Each case is presented with coordinated axes [x, ct] and [x, ct], light-cone guides, and simultaneity slices to reveal how invariant light speed and Lorentz structure constrain what observers in relative motion can agree upon. The light-clock diagram shows why moving clocks tick slower by tracing longer null-bounded paths between mirror strikes; the ladderbarn construction demonstrates length contraction as a frame-specific slice through a worldsheet; and the trainlightning example renders frame-dependent simultaneity without contradiction. We discuss affordances [conceptual scaffolding, error diagnosis, and transfer to algebra] and limitations [idealization, static figures for accelerated motion] and outline a design space for interactive tools that link diagrams, algebra, and simulation. The result is a compact, teachable sequence that helps novices see relativistic effects while preserving mathematical rigor.

One of the most fundamental hypotheses proposed to explain the electron acceleration in astrophysical and space plasmas is that the magnetic rope can contract and expand during a short period. However, such contraction and expansion of magnetic rope have never been directly evidenced hitherto. Targeting this longstanding problem, here we provide direct evidence for the magnetic rope contraction and expansion by utilizing the first-order Taylor expansion method and the magnetospheric multiscale measurements. The contraction and expansion of magnetic ropes happen during a few seconds in high-speed plasma flows, with the contraction related to an increase of pressure inside the rope and the expansion related to a decrease of pressure. Excitingly, during the magnetic rope contraction we observe electron acceleration, whereas during the magnetic rope expansion we observe electron deceleration. These findings have robustly validated the fundamental hypothesis in astrophysics, i.e., electrons can be accelerated by contracting magnetic ropes.

Achieving carbon neutrality requires not only cutting CO₂ emissions but also converting captured CO₂ into useful functions. This work tests whether carbonate ions produced by chemical-absorption direct air capture in alkaline media can act as charge carriers for electrochemical energy storage. Layered double hydroxides (LDHs) served as hosts for CO₃²⁻, and the influence of the metal-cation combination on carbonate intercalation and deintercalation was examined systematically. In a model electrolyte of 1 mol kg⁻¹ K₂CO₃, cyclic voltammetry showed no faradaic response for MgAl-LDH, while MnAl- and NiAl-LDH exhibited anion-coupled redox features. For NiAl-LDH the relevant couples lie outside the stability window of this electrolyte and therefore were not accessed. Comparisons with HCO₃⁻ and OH⁻ indicate that CO₃²⁻ is the predominant intercalating species. Galvanostatic charge and discharge measurements on a structurally optimized MnAl-LDH with abundant anion storage sites delivered initial capacities of 288 and 248 mAh g⁻¹, respectively. X-ray diffraction and X-ray photoelectron spectroscopy verified reversible expansion and contraction of the interlayer spacing together with a Mn³⁺/²⁺ redox process during carbonate intercalation and deintercalation. Although the capacity declined to 90 mAh g⁻¹ by cycle 20, composition tuning and morphology control are plausible routes to mitigate this loss. Electrochemical impedance spectroscopy indicated similar activation energies for insertion of CO₃²⁻ and OH⁻. The ability to trigger CO₃²⁻ release electrochemically, despite the strong stabilization of carbonate within LDH interlayers and its limited exchange under open-circuit conditions, points to electrochemically driven ion-exchange applications, including removal of hazardous anions.

We establish new fixed point theorems in cone Banach spaces using a tri-Inertial split-averaged λ-iteration process. Our results focus on Berinde-type weak contractions and common fixed points for compatible mappings. The new iteration generates three auxiliary sequences and improves convergence speed and stability compared to classical schemes. We provide error estimates and convergence rates, extending classical results. Applications to nonlinear integral and differential equations demonstrate the effectiveness of the proposed approach, which we denote as TISA-λ-iteration. Keywords: Cone Banach Space, Fixed Point, Berinde-type Contraction, Common Fixed Point, TISA-λ-iteration

Elliptical contraction vs FitzGerald-Lorentz contraction

One of the important research directions of fixed point theory is the generalization of metric spaces. An interesting generalization of metric space is the modification of triangular inequality. In the last few decades, many generalizations of metric space have been introduced in the field of fixed point theory by changing triangle inequality using multiplication of constants or functions. Recently, a new generalization of metric space with changing triangle inequality using the composition of two functions, namely, a double-composed metric space, has been introduced. A double-composed metric space is a new concept using the composition of functions, unlike the previous generalizations of metric space that modify the triangular inequality using the multiplication of functions. And, Banach-type fixed point result and Kanan-type fixed point result are established under certain assumptions in the setting of double-composed metric spaces. In this paper, we reconsider the Banach-type fixed point result in the setting of double-composed metric spaces under new and simple conditions. We have proved the fixed point theorem by using a new proof method and, consequently, we have demonstrated that Banach’s contractions in double-composed metric spaces have a unique fixed point under different assumptions from the previous one. We also present an example showing the validity of our fixed point result. Finally, we apply our fixed point result to show the existence of solution of Fredholm integral equations.

In order to investigate the coupling mechanism between tailwater vortex and cavitation bubbles (CB) during the operation of a low-head pump-as-turbine (PAT), the method of combining experiment and numerical simulation is used to quantify the vortex dynamics characteristics in combination with the vorticity transport equation under high flow conditions for PAT mode. The results show that the decrease in Thoma number significantly regulates the symbiotic evolution of tailwater vortex and CB: prolonging the residence time of CB in the draft tube (DT) and changing its evolution mode, resulting in the extension of vortex rope (VR) generation period, length contraction, and the increase in breaking vortex in DT. The peak volume of CB is 7 times that in the rotor region, squeezing the channel vortex and the wake vortex, weakening its contribution to VR. Vortex dynamics shows that the relative vortex stretching term is the core driving force of vorticity, which causes velocity gradient distortion and VR high-frequency oscillation synchronously with vertical vorticity. The baroclinic torque term (BT) only generates pulse contribution in the early stage of CB collapse. Under critical cavitation, BT converts the cavity collapse energy into vortex energy through density-pressure gradient coupling, which expands the vortex core radius to 0.03 m, increases the circulation peak to 2.3 m2/s, and shifts outward by 27.3%, resulting in vortex energy diffusion and high-frequency oscillation of the flow field. This study provides a theoretical basis for cavitation suppression and operational optimization of low-head PAT.

The genocide in Gaza has led to the complete collapse of the humanitarian system. The capacities of international actors have been crippled by direct targeting, coupled with systematic and large–scale prevention of aid entry. As a result, no functioning humanitarian system remains, and the overall response has collapsed. Localization of humanitarian action has thus become an imposed necessity shaped by the realities on the ground, rather than the outcome of a deliberate strategic vision. In this context, local organizations have emerged as virtually the only active responders. This study examines the structural constraints faced by local actors amid the extreme contraction of humanitarian space. The findings reveal that the core of the crisis lies in Israelʼs use of humanitarian action as a weapon of control, alongside severe shortages of resources and equipment, threats to the safety of aid workers, breakdowns in coordination channels, scarcity of funding, and the outright looting of humanitarian aid.

Global warming has been altering the East Asian climate at an unprecedented rate since the 20th century. In order to evaluate the changes in the East Asian winter climate (EAWC) and support policy-making for climate mitigation and adaptation strategies, this paper utilizes the multimodel ensemble from the Couple Model Intercomparison Project 6 and a temperature threshold method to investigate the EAWC changes during the period 1979–2100. The results show that the EAWC has been undergoing widespread and robust changes in response to global warming. The winter length in East Asia has shortened and will continue shortening owing to later onsets and earlier withdrawals, leading to a drastic contraction in length from 100 days in 1979 to 43 days (27 days) in 2100 under SSP2-4.5 (SSP5-8.5). While most regions of the East Asian continent are projected to become warmer in winter, the Japan and marginal seas of northeastern Asia will face the risks from colder winters with more frequent extreme cold events, accompanied by less precipitation. Meanwhile, the Tibetan Plateau is very likely to have colder winters in the future, though its surface snow amounts will significantly decline. Greenhouse gas (GHG) emissions are found to be responsible for the EAWC changes. GHG traps heat inside the Earth’s atmosphere and notably increases the air temperature; moreover, its force modulates large-scale atmospheric circulation, facilitating an enhanced and northward-positioned Aleutian low together with a weakened Siberian high, East Asian trough, and East Asian jet stream. These two effects work together, resulting in a contracted winter with robust and uneven regional changes in the EAWC. This finding highlights the urgency of curbing GHG emissions and improving forecasts of the EAWC, which are crucial for mitigating their major ecological and social impacts.