Search Results (64)

In this study, we introduce two new classes of contractions, namely enriched $(\mathfrak{I},\rho ,\chi )$-contractions and generalized enriched $(\mathfrak{I},\rho ,\chi )$-contractions, within the context of normed spaces. These classes generalize several well-known contraction types, including $\chi$-contractions, Banach contractions, enriched contractions, Kannan contractions, Bianchini contractions, Zamfirescu contractions, non-expansive mappings, and $(\rho ,\chi )$-enriched contractions. We establish related fixed point results for the novel contractions in normed spaces endowed with the binary relations preserving key symmetric properties, ensuring consistency and applicability. The Krasnoselskij iteration method is refined to incorporate symmetric constraints, facilitating fixed point identification within these spaces. By appropriately selecting constants in the definition of enriched $(\mathfrak{I},\rho ,\chi )$-contractions, employing a suitable binary relation, or control function $\chi \in \Theta$, our framework generalizes and extends classical fixed point theorems. Illustrative examples highlight the significance of our findings in reinforcing fixed point conditions and demonstrating their broader applicability. Additionally, this paper explores how these ideas guarantee the stability of the production–consumption markets equilibrium and the economic growth model. Full article

In this paper, we revisit the extension of the classical non-standard cosmological model in which dissipative processes are considered through a bulk viscous term in the new field $\varphi$, which interacts with the radiation component during the early universe. Specifically, we consider an interaction term of the form ${\Gamma }_{\varphi }{\rho }_{\varphi }$, where ${\Gamma }_{\varphi }$ represents the decay rate of the field and ${\rho }_{\varphi }$ denotes its energy density and a bulk viscosity described by $\xi ={\xi }_0{\rho }_{\varphi }^{1/2}$, within the framework of Eckart’s theory. This extended non-standard cosmology is employed to explore the parameter space for the production of Feebly Interacting Massive Particles (FIMPs) as Dark Matter candidates, assuming a constant thermal averaged Dark Matter production cross-section ($⟨\sigma v⟩$), as well as a preliminary analysis of the non-constant case. In particular, for certain combinations of the model and Dark Matter parameters, namely ($T_{\mathrm{end}}$,$\kappa$) and $(m_{\chi },⟨\sigma v⟩)$, where $T_{\mathrm{end}}$ corresponds to the temperature at which $\varphi$ decays, $\kappa$ is the ratio between the initial energy density of $\varphi$ and radiation, and $m_{\chi }$ is the Dark Matter mass, we identify extensive new parameter regions where Dark Matter can be successfully established while reproducing the currently observed relic density, in contrast to the predictions of $\Lambda$CDM and classical non-standard cosmological scenarios. Full article

Spherical structures of dielectric and magnetic materials are studied intensively in basic research and employed widely in applications. The polarization, (P for dielectric and M for magnetic materials), is the parent physical vector of all relevant entities (e.g., moment, , and force, F), which determine the signals recorded by an experimental setup or diagnostic equipment and configure the motion in real space. Here, we use classical electromagnetism to study the polarization, , of spherical structures of linear and isotropic—however, not necessarily homogeneous—materials subjected to an external vector field, (E_ext for dielectric and H_ext for magnetic materials), dc (static), or even ac of low frequency (quasistatic limit). We tackle an integro-differential equation on the polarization, , able to provide closed-form solutions, determined solely from , on the basis of spherical harmonics, ${\mathrm{Y}}_l^m$. These generic equations can be used to calculate analytically the polarization, , directly from an external field, , of any form. The proof of concept is studied in homogeneous dielectric and magnetic spheres. Indeed, the polarization, , can be obtained by universal expressions, directly applicable for any form of the external field, . Notably, we obtain the relation between the extrinsic, , and intrinsic, , susceptibilities (${\chi }_{\mathrm{e}}^{\mathrm{e}\mathrm{x}\mathrm{t}}$ and ${\chi }_{\mathrm{e}}^{\mathrm{i}\mathrm{n}\mathrm{t}}$ for dielectric and ${\chi }_{\mathrm{m}}^{\mathrm{e}\mathrm{x}\mathrm{t}}$ and ${\chi }_{\mathrm{m}}^{\mathrm{i}\mathrm{n}\mathrm{t}}$ for magnetic materials) and clarify the nature of the depolarization factor, , which depends on the degree l—however, not on the order m of the mode $(l,m)$ of the applied . Our universal approach can be useful to understand the physics and to facilitate applications of such spherical structures. Full article

The possible consequence of an infrared (IR) fixed point in QCD for $N_f=2, 3$ in nuclear matter is discussed. It is shown in terms of d(ilaton)-$\chi$ effective field theory (d$\chi$EFT) incorporated in a generalized effective field theory implemented with hidden local symmetry and hidden scale symmetry that the superallowed Gamow–Teller transition in the doubly magic-shell nucleus ¹⁰⁰Sn recently measured at RIKEN indicates a large anomaly-induced quenching identified as a fundamental renormalization of $g_A$ from the free-space value of 1.276 to ≈0.8. Combined with the quenching expected from strong nuclear correlations “snc”, the effective coupling in nuclei $g_A^{\mathrm{eff}}$ would come to ∼1/2. If this result were reconfirmed, it would impact drastically not only nuclear structure and dense compact-star matter—where $g_A$ figures in $\pi$-N coupling via the Goldberger-Treiman relation—but also in search for physics Beyond the Standard Model (BSM), e.g., $0\nu \beta \beta$ decay, where the fourth power of $g_A$ figures. Full article

In this paper, we extend prominent fixed-point theorems within the framework of symmetry, a structure increasingly relevant in decision-making, optimization, and uncertainty modeling. While previous studies have explored fixed-point theorems in non-Archimedean spaces, the influence of symmetry on the properties of mappings remains underexamined. To address this gap, we introduce and analyze the concepts of $\chi$-contractions and $\chi$-weak contractions, demonstrating how symmetry impacts the conditions for the existence of fixed points. Our methodology integrates these concepts in generalized neutrosophic metric spaces, providing a novel perspective on fixed-point theory. We perform a rigorous analysis, revealing new insights into their practical applications. However, our proposed system may face limitations in complex or dynamic environments, where additional conditions may be necessary to ensure the existence or uniqueness of fixed points. Full article

A binuclear cobalt–radical complex formed by the reaction of Co(hfac)₂·2H₂O (hfac = hexafluoroacetylacetonate) with the 2,2-bis(1-oxyl-3-oxide-4,4,5,5-tetramethylimidazolinyl) biradical (BR) has been synthesized. The complex {(hfac)Co^II(BN)Co^II(hfac)} crystallizes in the triclinic space group P$\overline{1}$ :  C₃₄H₂₈Co₂F₂₄N₄O₁₂, a = 11.1513(5) Å, b = 12.8362(7) Å, c = 18.2903(8) Å, α = 103.061(1)°, β = 100.898(2)°, γ = 102.250(1)°, Z = 2. The compound consists of two non-equivalent pseudo-octahedral Co^II ions, each bearing two hfac ancillary ligands bridged by the tetradentate bis-nitroxide (BN). The temperature dependence of the magnetic susceptibility indicates a strong antiferromagnetic exchange between each of the Co²⁺ ions and the nitroxyl biradical, as well as between the spins within the bridging ligand, forming a spin-frustrated system. Micro-squid investigations, performed on a single crystal of {(hfac)Co^II(BN)Co^II(hfac)}, reveal a peculiarity of the M(H) graph at temperatures below 0.4 K displaying a step that is a result of ground and first excited levels mixing by the applied magnetic field due to a small energy gap between them, as inferred from ab initio calculation. The latter was also carried out for two models of mononuclear Co²⁺ complexes in order to obtain a set of initial parameters for fitting the experimental magnetic curves using the Phi program. Moreover, direct CAS(12,10)/def2-TZVP calculations of the magnetic dependences χT(T) and M(H) were performed, which satisfactorily reproduced the experimental ones. Full article

Molecular dynamics (MD) techniques offer significant potential for optimizing mineral extraction processes by simulating economically or physically restrictive conditions at the laboratory level. Lithium, a crucial metal in the electromobility era, exemplifies the need for ongoing re-evaluation of extraction techniques. This research aims to simulate the crystal structures of mineral species present in a polylithionite mineral concentrate [KLi₂Al(Si₄O₁₀)(F,OH)₂] using crystallographic data obtained from X-ray diffraction analysis. This study focuses on optimizing these structures, validating them through density comparisons, and determining the interaction parameter between the identified phases and lithium oxide (Li₂O). The X-ray diffraction analysis revealed five predominant mineral phases: quartz (SiO₂), calcite [Ca(CO₃)], pyrite (FeS₂), cassiterite (SiO₂), and a compound Pb₆O₂(BO₃)₂SO₄. Structural data, including lattice parameters, space groups, and atomic coordinates, were used to construct the crystal structures with Materials Studio 8.0, employing the Crystal Builder module. Optimization was performed using the Forcite module with the Smart optimization algorithm and the Universal force field. The interaction parameter (χ) indicated an affinity between lithium oxide and pyrite, as well as between calcite and quartz. Full article

The Large and Small Magellanic Clouds (LMC and SMC) form the closest interacting galactic system to the Milky Way, therewith providing a laboratory to test cosmological models in the local Universe. We quantify the likelihood for the Magellanic Clouds (MCs) to be observed within the $\mathsf{\Lambda }$CDM model using hydrodynamical simulations of the IllustrisTNG project. The orbits of the MCs are constrained by proper motion measurements taken by the Hubble Space Telescope and Gaia. The MCs have a mutual separation of $d_{\mathrm{MCs}}=24.5\mathrm{kpc}$ and a relative velocity of $v_{\mathrm{MCs}}=90.8\mathrm{km}{\mathrm{s}}^{-1}$, implying a specific phase-space density of $f_{\mathrm{MCs},\mathrm{obs}}\equiv {(d_{\mathrm{MCs}}·v_{\mathrm{MCs}})}^{-3}=9.10\times {10}^{-11}{\mathrm{km}}^{-3}{\mathrm{s}}^3{\mathrm{kpc}}^{-3}$. We select analogues to the MCs based on their stellar masses and distances in MW-like halos. None of the selected LMC analogues have a higher total mass and lower Galactocentric distance than the LMC, resulting in >3.75$\sigma$ tension. We also find that the $f_{\mathrm{MCs}}$ distribution in the highest resolution TNG50 simulation is in $3.95\sigma$ tension with observations. Thus, a hierarchical clustering of two massive satellites like the MCs in a narrow phase-space volume is unlikely in $\mathsf{\Lambda }$CDM, presumably because of short merger timescales due to dynamical friction between the overlapping dark matter halos. We show that group infall led by an LMC analogue cannot populate the Galactic disc of satellites (DoS), implying that the DoS and the MCs formed in physically unrelated ways in $\mathsf{\Lambda }$CDM. Since the ${20}^{\circ }$ alignment of the LMC and DoS orbital poles has a likelihood of $P=0.030$ ($2.17\sigma$), adding this ${\chi }^2$ to that of $f_{\mathrm{MCs}}$ gives a combined likelihood of $P=3.90\times {10}^{-5}$ ($4.11\sigma$). Full article

In the present paper, a sustainable supply chain model is investigated with a variable production rate and remanufacturing for the production of defective items under the effect of learning fuzzy theory, where the lower and upper variations in fuzzy demand rate are affected by learning parameters and backorders are also allowed. Our proposed model reveals a springy manufacturing inventory organization that makes various types of items, and imperfect items can be created through the method of manufacturing things in a fuzzy environment. When the screening process is completed, defective items are remanufactured immediately, and a limited financial plan and space limitations are assumed concerning the product assembly. We minimized the total fuzzy inventory cost with different distributions (beta, triangular, double triangular, uniform, and χ² (chi−square)) concerning the production rate, lot size, and backorder under learning in a fuzzy environment where the costs of screening, manufacturing, carrying, carbon emissions, backorders, and remanufacturing are included. The Kuhn–Tucker optimization technique is applied to solve non-linear equations that are based on some distributions. Numerical examples, sensitivity analysis, managerial insights and observations, limitations, future work, and applications are provided for the validation of our proposed model, and the industrial scope of this proposed work is included. Full article

Currently, the energy dissipation efficiency of intermediate column dampers is extremely low, and traditional lever amplification damping systems occupy a large space in buildings. Aiming at solving these problems, this paper puts forward a new intermediate column–lever negative stiffness viscous damper (CLNVD), which has the characteristics of small impact on building space and significant amplification of the damper displacement. The CLNVD consists of the following four parts: the viscous damper, the negative stiffness device, the lever, and the intermediate column. This paper introduces the displacement amplification coefficient (f_d) to assess the CLNVD’s displacement amplification effect and introduces the energy dissipation coefficient (f_E) to assess the CLNVD’s energy dissipation effect. The expressions for f_d and f_E are derived according to the geometric magnification coefficient and effective displacement factor. Moreover, the impacts of multiple factors including the CLNVD’s position, the lever’s amplification coefficient, the bending line stiffness of beam, the negative stiffness, the damping coefficient, the damping index, and the inter-story displacement on the CLNVD’s f_d and f_E are elaborated. The analysis results reveal the following: when the CLNVD is located in the middle of the span, the f_d and f_E of the CLNVD will be maximized, and f_E will increase first and then decrease as the beam’s bending line stiffness increases. Meanwhile, the amplification capability of the CLNVD increases as the lever’s amplification coefficient χ rises. When the negative stiffness does not exist, there exists an optimum lever’s amplification coefficient χ that maximizes f_E. When the combination of damping coefficient c and index α satisfies a specific relationship, f_E of the CLNVD reaches its largest value. When the negative stiffness and the loss stiffness of VD are within the region proposed in this paper, the CLNVD will achieve a higher f_d and avoid providing significant negative stiffness. Subsequently, this paper proposes an optimization design method of the CLNVD. Finally, the amplification effect of CLNVD as well as the effectiveness of its optimization design method are verified through examples. In the case study, the CLNVD offers a larger damping ratio under the circumstance of fortification earthquakes. Under fortification and rare earthquakes, the inter-story displacement of Scheme 1 has been decreased by half roughly. According to the above-mentioned results, the CLNVD provides a brand-new approach for designers in the seismic design of buildings. Furthermore, this paper will provide beneficial reference for the damping design of other amplification devices equipped with negative stiffness dampers. Full article

Located in Dali, Yunnan, the Zhaozhou basin is home to many precious architectural heritages, particularly the historical horse caravan architecture. These buildings face the challenge of renewal and transformation. It is of great significance to explore the local population’s awareness of the architectural heritage of the horse caravan in order to protect the architectural heritage and facilitate rural revitalization. This study reviews the related research on “space perception”, establishes a theoretical framework of space perception under the architectural dimension, and develops hypotheses. The social cluster of typical settlements in the Zhaozhou basin is selected as the research object, and empirical analyses are carried out using SPSS and AMOS software. An analytical framework model of empirical research is constructed to evaluate the space perception of the current social population. The results of the reliability and validity tests of the questionnaire show that the CR is greater than 0.7 and that the AVE is greater than 0.5. The value of the structural equation model fitting index χ2/df is 1.863, which is less than 3. The model test results show that research hypotheses H1–H5 are supported; that is, space perception has a significant positive impact on cognition and local identity, cognition has a significant positive impact on local identity and space function, and place identity has a significant positive impact on space appeal. This study demonstrates the relationship between space perception and the architectural remains of the horse caravan, and it analyzes the human psychological perception behind the material space. The findings support the need for further conservation of the horse caravan architecture. This study further deepens the theory of space perception and its application in the study of vernacular architecture, which can provide a research path for the protection and development of vernacular architectural heritage. Full article

Integral equations, which are defined as “the equation containing an unknown function under the integral sign”, have many applications of real-world problems. The second type of Fredholm integral equations is generally used in radiation transfer theory, kinetic theory of gases, and neutron transfer theory. A special case of these equations, known as the quadratic Chandrasekhar integral equation, given by $x\left(s\right)=1+\lambda x\left(s\right){\int }_0^1\frac{s}{t+s}x\left(t\right)dt,$ can be very often encountered in many applications, where x is the function to be determined, $\lambda$ is a parameter, and $t,s\in [0,1]$. In this paper, using a fixed-point theorem, the existence conditions for the solution of Fredholm integral equations of the form $\chi \left(l\right)=\varrho \left(l\right)+\chi \left(l\right){\int }_p^{q}k(l,z)\left(V\chi \right)\left(z\right)dz$ are investigated in the space $C_{\omega }\left[p,q\right],$ where $\chi$ is the unknown function to be determined, V is a given operator, and $\varrho ,k$ are two given functions. Moreover, certain important applications demonstrating the applicability of the existence theorem presented in this paper are provided. Full article

COVID-19 has severely affected almost every aspect of our everyday lives, especially the use of open greenspace (OGS) in urban settings, which has proven to have a significant role in increasing overall public health and well-being. Hence, the restricted usage of these spaces should be reconsidered. This research aims to analyze the sensitive nature of OGS usage (1) during the pandemic from the perspective of users’ perceived safety and (2) after the pandemic to assess the possible long-term effects. Additionally, this research proposed that location-tracking mobile applications could lead to an increased frequency of OGS visits. The methodology contains detailed background research and two surveys. One survey was conducted during the pandemic in 2020 (sample size n = 412) and was repeated post-pandemic in 2024 (sample n = 451). The 2020 questionnaire A includes questions about the duration, frequency, and activities of OGS usage while focusing on the perceived safety and possibilities of monitoring OGS visits using mobile apps. The 2024 survey represents the continuation of the 2020 survey, focusing on the post-pandemic state of OGS. The statistical analysis is separated into a descriptive data analysis, various χ² independence tests and a machine learning safety prediction. The results indicate how COVID-19 could affect OGS usage and how app-related physical safety enhancements during the pandemic cannot be statistically distinguished from those in the post-pandemic period. Although the interest in location-tracking mobile applications has statistically decreased in 2024, the majority of the total 863 participants stated that applications could increase their feeling of perceived safety. The added value of this research is that it considers age and gender roles in analyzing OGS usage in the context of a pandemic. Full article

In this article, we study the Cauchy problem of the chemotaxis-Navier–Stokes system with the consumption and production of chemosignals with a logistic source. The parameters $\chi \ne 0, \xi \ne 0, \lambda >0$ and $\mu >0$. The system is a model that involves double chemosignals; one is an attractant consumed by the cells themselves, and the other is an attractant or a repellent produced by the cells themselves. We prove the global-in-time existence and uniqueness of the weak solution to the system for a large class of initial data on the whole space ${\mathbb{R}}^2$. Full article

The study of isotopic ratios in planetary atmospheres gives an insight into the formation history and evolution of these objects. The more we can constrain these ratios, the better we can understand the history and future of our solar system. To help in this endeavour, we used Infrared Space Observatory Short Wavelength Spectrometer (ISO/SWS) Jupiter observations in the 793–1500 cm${}^{-1}$ region together with the Nonlinear Optimal Estimator for MultivariatE Spectral analySIS (NEMESIS) radiative transfer suite to retrieve the temperature–pressure profile and the chemical abundances for various chemical species. We also used the 1500–2499 cm${}^{-1}$ region to determine the cloud and aerosol structure of the upper troposphere. We obtained a best-fit simulated spectrum with ${\chi }^2/N=0.47$ for the 793–1500 cm${}^{-1}$ region and ${\chi }^2/N=0.71$ for the 1500–2499 cm${}^{-1}$ region. From the retrieved methane abundances, we obtained, within a 1$\sigma$ uncertainty, a ${}^{12}$C/${}^{13}$C ratio of 84 ± 27 and a D/H ratio of (3.5 ± 0.6) × 10${}^{-5}$, and these ratios are consistent with other published results from the literature. Full article