How flexible are corporate loans after origination? Theory predicts coordination problems should make syndicated loans harder to modify than single-bank loans. We show the opposite. Using comprehensive regulatory data, we document that syndicated loans are modified frequently and respond to borrower distress, while single-lender loans are half as likely to be modified. This gap is not explained by covenants or performance pricing. Instead, syndicated loans are monitored more intensively. We show theoretically and empirically how fixed monitoring costs generate scale economies: larger loans justify continuous monitoring enabling flexible renegotiation, while smaller borrowers receive arm’s-length contracts with limited scope for modifications.

In this work, we establish the conditions for ensuring the existence and uniqueness of common best proximity points for non-self-mappings defined on the general metric spaces. A unified theoretical framework is formulated to cover a broad class of contraction mappings. We describe the required conditions on the real-valued functions (ℵ, Φ) : [0,∞) → R and verify that these secure the existence of common best proximity points for (ℵ, Φ)−interpolative contractions in complete metric spaces. The study further extends this concept by examining multiple forms of interpolative proximal-type contractions, such as proximal, Ćirić —Reich—Rus, Kannan, and Hardy-Rogers variants, through the use of the auxiliary functions (ℵ, Φ). Several illustrated examples are included to demonstrate the applicability of our findings. Finally, we conclude with an application involving a nonlinear fractional differential equation, showing that it fully satisfies the assumption of our main result.

Recent laboratory experimental work has shown that heating and cooling processes exhibit intrinsic asymmetry, with heating occurring more efficiently than cooling. Two decades earlier, nonequilibrium molecular dynamics simulations addressed the topic of heating one side of a computational cell while cooling the other side by applying two different thermostats, producing a sinusoidal temperature profile. We revisit the theory underlying those computer calculations and show how it accurately predicts the laboratory results. Recent realizations of a simple two-dimensional one-particle cell model give surprisingly relevant results, where two Nosé-Hoover thermostats are applied to the two directions (x and y) at two temperatures, Tx ≥ Ty. At equilibrium, the thermostatting rate variables ξx and ξy are identical, while under nonequilibrium temperature differences, the heating variable (ξx) is weaker than the cooling one (ξy), demonstrating the ratio of thermostat effort to thermal bias, just as predicted by theory: ⟨ξx⟩/⟨ξy⟩ = -Ty/Tx. We relate this to the negative rate of change in entropy of the nonequilibrium system that accompanies the contraction of phase space onto a fractal strange attractor of lower dimension. Histograms of the thermostat variables reveal the stark differences between equilibrium and nonequilibrium heat flow. At equilibrium, the cell-model ξ-distributions are both Gaussians centered at zero. We redid much earlier many-body simulations of a Nosé-Hoover thermostatted fluid at equilibrium, which reported that the distribution was biased toward heating; we discovered that the prior work suffered from systematic integration error. In fact, we find that the distribution at equilibrium is a totally symmetric Gaussian for many-body systems, in agreement with the cell model. Under nonequilibrium conditions, when Tx > Ty, the simple 2D cell model clearly demonstrates the microscopic origin of heating-cooling asymmetry, thereby strongly confirming the results of real-world laboratory experiments.

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.

Abstract A clear and self-contained derivation of the Lorentz contraction formula is presented by applying Lorentz spacetime transformations to non-simultaneous events. The usual textbook approach, which involves a stationary observer making simultaneous measurements of the endpoints of a moving object, is avoided. This alternative derivation highlights that Lorentz contraction arises directly from the geometry of spacetime and not from any particular measurement procedure, emphasizing its physical reality as an intrinsic manifestation of relativistic kinematics.

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.

Some properties on large contractions in metric spaces are proven. In particular, such contractions are proven to be asymptotically regular. In addition, if the metric space is complete, then the sequences that they generate are bounded, Cauchy, and convergent to a unique fixed point. Also, cyclic large contractions are an area of focus. It is proven that, if subsets of the cyclic disposal are nonempty closed and they intersect, all the sequences are bounded and Cauchy, and they converge to a unique fixed point located in the intersection of such subsets if the metric space is complete. If the subsets have a pair-wise empty intersection, then the boundedness of such sequences is proven without the need to assume the boundedness of the subsets in the cyclic disposal. The convergence of the sequences to a unique limit cycle of best proximity points, with one per subset in the cyclic disposal, is proven provided that the metric space is complete and that one of such subsets is boundedly compact with a singleton best proximity set. For that property to hold, it is not assumed that the remaining best proximity points are necessarily singletons. It has also been proven that all the subsequences contained within each of the subsets are Cauchy and they converge to a unique best proximity point, even if the corresponding best proximity sets is not a singleton. Furthermore, the hypothesis that one of the best proximity sets between adjacent subsets is a singleton can be weakened for any particular cyclic large contraction. Later on, eventual perturbations of the cyclic large self-mappings in normed spaces are discussed. If the norm of the perturbation additive operator is small enough, it is proven that the perturbed cyclic self-mapping maintains the property of being a cyclic large contraction associated with the unperturbed nominal cyclic large contraction. The maximum upper-bound of the perturbed operator ensures that such a property is given in an explicit manner.

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.

This paper introduces new generalized forms of contractive mappings in the framework of complete metric spaces. By extending the classical Reich and Sehgal contractions to their iterated counterparts in Singh’s sense, we establish unified fixed-point theorems that ensure both existence and uniqueness under constant and variable contractive parameters. The proposed p-Reich and p-Sehgal contractions encompass several well-known results, including those of Banach, Kannan, Chatterjea, Reich, and Sehgal, as special cases. Convergence of the associated Picard iterative process is rigorously analyzed, revealing deeper insights into the iterative stability and asymptotic behavior of nonlinear mappings in metric spaces. The practical utility of our unified fixed-point theorems is illustrated through concrete applications in fractal and fractional calculus.

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

In this study, the subject of the multivalued $ \rho _{\ast } $-interpolative Ćirić-Reich-Rus-type fuzzy contractions is introduced and investigated in which the $ \vartheta $-comparison functions and the property of the $ \rho _{\ast } $-admissibility play an important role. In the first step, the existence of fixed point theorems is proven for such a type of contractions in the context of the complete fuzzy metric spaces. Then, some of the results are extended in the framework of the fuzzy metric spaces equipped with a partial order. In this direction, we give some examples to clarify the obtained results and definitions. Additionally, we demonstrate an application about the solutions of non-linear matrix equations on the basis of fixed points of these new contractions.

We establish sufficient criteria for the existence and uniqueness of fixed points for α-β-FG-Khan contractions in b-metric spaces. Examples are provided to illustrate these ideas. Additionally, we apply these theoretical results to solving an initial value problem (IVP).

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.

The rapid development of portal sites represented by Naver has brought about a fundamental transformation in the way news enters the public sphere. In this context, issues such as the influence of algorithmic recommendation systems on news dissemination, media organizations' strategic choices within platform environments, content homogenization, and the resulting crisis of publicness have emerged as some of the most prominent research topics in journalism and media studies. This study adopts a mixed research approach combining literature review and case analysis. The research sample consists of 30 news articles published on the Naver platform between February and August 2025 concerning the issue of “raising the age threshold for free subway rides for older adults.” Using content analysis, the study empirically examines media content homogenization through indicators such as keyword repetition rates, temporal distribution of coverage, and the number of content frames. The findings indicate that, in order to secure greater platform visibility, media organizations strategically adjust news headlines, content frames, and publication timing, which in turn intensifies news homogenization and leads to a marked contraction of news diversity and deliberative space within the public sphere. Based on these results, the study constructs a theoretical analytical framework of ‘algorithmic recommendation-media strategies-content homogenization-crisis of publicness.’ The study argues that the ecrisis of publicness is not the result of media organizations voluntarily abandoning their social responsibility, but rather an inevitable outcome of an algorithmically driven media environment. Accordingly, it proposes that the publicness and diversity of digital journalism should be reconstructed through the coordinated advancement of platform governance, adjustments in media strategies, and institutional regulation,

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.

In the present paper, we define a pseudo 𝑆𝑏 −Menger space with counterexamples and prove a decomposition theorem for a pseudo 𝑆𝑏 −Menger space. Also, we prove fixed-point theorems for rational-type contraction in a newly defined 𝑆𝑏−Menger space. Our results extend the results of Gupta V et al [8] in 𝑆𝑏 −Menger spaces. Applications are also given to prove the effectiveness of our results.

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.

Interfacial forces and nanoconfined environments play crucial roles in transport phenomena within low-dimensional materials. In this study, we propose a photothermally regulated surface-tension mechanism for hydrogen-isotope fractionation, in which light-induced changes in the surface tension of gallium ( Ga ) dynamically modulate the confined environment between graphene oxide ( GO ) layers. Under near-infrared irradiation, the surface tension of Ga decreases, altering its wettability within the interlayer galleries and inducing a reversible contraction of the GO interlayer spacing. temperature-dependent transmission electron microscopy confirmed this dynamic modulation, showing that confined Ga nanoparticles undergo fully reversible expansion-contraction and display surface-energy-driven extension behavior analogous to macroscopic particles. Such confinement-induced structural responsiveness regulates the local arrangement of water molecules, leading to distinct molecular aggregation states for H 2 O and D 2 O . Due to stronger intermolecular attraction, D 2 O diffusion is more restricted in confinement, leading to pronounced isotope selectivity. Experimentally, the membrane achieved a separation factor of 70.53 for H 2 O : D 2 O and demonstrated selective removal of tritium water ( T 2 O ). Our study elucidates the interplay between photothermally driven interfacial energy modulation and confined molecular transport, offering new insights into tunable separation processes and interfacial physics.

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.