Search Results (164)

Background/Objectives: Rapid, objective phenotyping of donor kidneys is needed to support peri-implant decisions. Label-free Fourier-transform infrared (FTIR) spectroscopy of static cold-storage Celsior^® perfusion fluid can discriminate kidneys recovered from donation after circulatory death (DCD) versus donation after brain death (DBD). Methods: Preservation solution from isolated kidney allografts (n = 10; 5 DCD/5 DBD) matched on demographics was analyzed in the Amide I and fingerprint regions. Several spectral preprocessing steps were applied, and feature extraction was based on the Fast Correlation-Based Filter. Support vector machines and Naïve Bayes were evaluated. Unsupervised structure was assessed based on cosine distance, multidimensional scaling, and hierarchical clustering. Two-dimensional correlation spectroscopy (2D-COS) was used to examine band co-variation. Results: Donor cohorts were well balanced, except for higher terminal serum creatinine in DCD. Quality metrics were comparable, indicating no systematic technical bias. In Amide I, derivatives improved classification, but performance remained modest (e.g., second derivative with feature selection yielded an area under the curve (AUC) of 0.88 and an accuracy of 0.90 for support vector machines; Naïve Bayes reached an AUC of 0.92 with an accuracy of 0.70). The fingerprint window was most informative. Naïve Bayes with second derivative plus feature selection identified bands at ~1202, ~1203, ~1342, and ~1413 cm⁻¹ and achieved an AUC of 1.00 and an accuracy of 1.00. Unsupervised analyses showed coherent grouping in the fingerprint region, and 2D correlation maps indicated coordinated multi-band changes. Conclusions: Performance in this 10-sample pilot should be interpreted cautiously, as perfect leave-one-out cross-validation (LOOCV) estimates are vulnerable to overfitting. The findings are preliminary and hypothesis-generating, and they require confirmation in larger, multicenter cohorts with a pre-registered analysis pipeline and external validation. Full article

We investigate the geometric and physical properties of the h-almost conformal $\eta$-Ricci–Bourguignon soliton and its gradient form by employing a barotropic equation of state within the framework of $f(\mathcal{R},\mathcal{T})$ gravity. We derive this barotropic equation of state under the assumption that the matter content of $f(\mathcal{R},\mathcal{T})$ gravity is modeled by a barotropic perfect fluid. We also examine the way in which these soliton structures both reveal and limit the underlying symmetries of the spacetime geometry. Furthermore, we obtain modified Poisson and Liouville equations associated with these solitons in such a gravitational setting. Additionally, we explore certain harmonic aspects of the h-almost conformal $\eta$-Ricci–Bourguignon soliton on a spacetime filled with a barotropic perfect fluid, considering a harmonic potential function $\mathrm{\Psi }$. Finally, we present physical interpretations of the conformal pressure $\tilde{p}$ in the context of the h-almost conformal $\eta$-Ricci–Bourguignon soliton within $f(\mathcal{R},\mathcal{T})$ gravity. Full article

This work presents a comprehensive study of weakly B-symmetric warped product manifolds ${\left(WBS\right)}_n$, a natural extension of several classical curvature-restricted geometries including B-flat, B-parallel, and B-recurrent manifolds. We begin by formulating the fundamental properties of the B-tensor $B(X,Y)=aS(X,Y)+brg(X,Y)$, where S is the Ricci tensor, r the scalar curvature, and $a,b$ are smooth non-vanishing functions. The warped product structure is then exploited to obtain explicit curvature identities for base and fiber manifolds under various geometric constraints. Detailed characterizations are established for Einstein conditions, Codazzi-type tensors, cyclic parallel tensors, and the behavior of geodesic vector fields. The weakly B-symmetric condition is analyzed through all possible projections of vector fields, leading to sharp criteria describing the interaction between the warping function and curvature. Several applications are discussed in the context of Lorentzian geometry, including perfect fluid and generalized Robertson–Walker spacetimes in general relativity. These results not only unify different curvature-restricted frameworks but also reveal new geometric and physical implications of warped product manifolds endowed with weak B-symmetry. Full article

In the present research note, we explore the nature of the conformal Ricci solitons on the energy–momentum squared gravity model $\mathcal{F}(\mathcal{R},{\mathcal{T}}^2)$ that is a modification of general relativity. Furthermore, we deal with a subcase of the $\mathcal{F}(\mathcal{R},{\mathcal{T}}^2)=\mathcal{R}+\lambda {\mathcal{T}}^2$-gravity model coupled with a perfect fluid, which admits conformal Ricci solitons with a time-like concircular vector field. Using the steady conformal Ricci soliton, we derive the equation of state for the perfect fluid in the $\mathcal{F}(\mathcal{R},{\mathcal{T}}^2)$-gravity model. In this series, we convey an indication of the pressure and density in the phantom barrier period and the stiff matter era, respectively. Finally, using a conformal Ricci soliton with a concircular vector field, we study the various energy constraints, black holes, and singularity circumstances for a perfect fluid coupled to $\mathcal{F}(\mathcal{R},{\mathcal{T}}^2)$-gravity. Lastly, employing conformal Ricci solitons, we formulate the first law of thermodynamics, enthalpy, and the particle production rate in $\mathcal{F}(\mathcal{R},{\mathcal{T}}^2)$-gravity and orthodox gravity. Full article

Background/Objectives: Spontaneous intracranial hypotension (SIH), caused by spinal cerebrospinal fluid (CSF) leakage, commonly presents with orthostatic headache and CSF hypovolemia. While CSF dynamics in the cerebral aqueduct are well studied, alterations in spinal CSF flow remain less defined. We aimed to quantitatively assess spinal CSF flow at C2 using phase-contrast (PC) MRI enhanced by artificial intelligence (AI) and to evaluate its utility for diagnosing SIH and predicting responses to epidural blood patch (EBP). Methods: We enrolled 31 patients with MRI-confirmed SIH and 26 age- and sex-matched healthy volunteers (HVs). All participants underwent ECG-gated cine PC-MRI at the C2 level and whole-spine MR myelography. AI-based segmentation using YOLOv4 and a pulsatility-based algorithm was used to extract quantitative CSF flow metrics. Between-group comparisons were analyzed using Mann–Whitney U tests, and receiver operating characteristic (ROC) analysis was used to evaluate diagnostic and predictive performance. Results: Compared to HVs, SIH patients showed significantly reduced CSF flow parameters across all metrics, including upward/downward mean flow, peak flow, total flow per cycle, and absolute stroke volume (all p < 0.001). ROC analysis revealed excellent diagnostic accuracy for multiple parameters, particularly downward peak flow (AUC = 0.844) and summation of peak flow (AUC = 0.841). Importantly, baseline CSF flow metrics significantly distinguished patients who required one versus multiple epidural blood patches (EBPs) (all p < 0.001). ROC analysis demonstrated that several parameters achieved near-perfect to perfect accuracy in predicting EBP success, with AUCs up to 1.0 and 100% sensitivity/specificity. Conclusions: AI-enhanced PC-MRI enables the robust, quantitative evaluation of spinal CSF dynamics in SIH. These flow metrics not only differentiate SIH patients from healthy individuals but also predict response to EBP treatment with high accuracy. Quantitative CSF flow analysis may support both diagnosis and personalized treatment planning in SIH. Full article

The present work discusses the birth of the Universe via quantum tunneling through a potential barrier, based on quantum cosmology, taking a running cosmological constant into account. We consider the Friedmann–Lemaître–Robertson–Walker (FLRW) metric with positively curved spatial sections ($k=1$) and the matter’s content is a dust perfect fluid. The model was quantized by the Dirac formalism, leading to a Wheeler–DeWitt equation. We solve that equation both numerically and using a WKB approximation. We study the behavior of tunneling probabilities $T{P}_{WKB}$ and $T{P}_{int}$ by varying the energy E of the dust perfect fluid, the phenomenological parameter $\nu$, the present value of the Hubble function $H_0$, and the constant energy density ${\rho }_{\Lambda }^0$, with the last three parameters all being associated with the running cosmological constant. We observe that both tunneling probabilities, $T{P}_{WKB}$ and $T{P}_{int}$, decrease as one increases $\nu$. We also note that $T{P}_{WKB}$ and $T{P}_{int}$ grow as E increases, indicating that the Universe is more likely to be born with higher dust energy E values. The same is observed for the parameter ${\rho }_{\Lambda }^0$, that is, $T{P}_{WKB}$ and $T{P}_{int}$ are larger for higher values of ${\rho }_{\Lambda }^0$. Finally, the tunneling probabilities decrease as one increases the value of $H_0$. Therefore, the best conditions for the Universe to be born, in the present model, would be to have the highest possible values for E and $\Lambda$ and the lowest possible values for $\nu$ and $H_0$. Full article

Land availability constraints limit the installation of conventional ground-mounted solar installations. As a result, Floating Photovoltaic (FPV) systems are gaining popularity as an alternative to renewable energy generation. FPV consist of individual solar panels that are commonly symmetrical and modular. However, the hydrodynamic behaviour of FPVs in water surface waves is understudied to ensure their stability and optimal performance under varying environmental conditions. This literature review examines various modelling techniques applied in studying FPV hydrodynamics. Specifically, the application of Computational Fluid Dynamics (CFD) solvers and potential flow theory solvers is investigated for their effectiveness in capturing the behaviour of FPVs and mooring dynamics under the impact of wind and waves. The review highlights the advantages and limitations of each approach. Findings suggest that a combined CFD-potential flow approach offers a perfect balance between accuracy and computational efficiency, offering valuable insights into the performance of FPVs. However, extensive research is notably absent in hydrodynamic modelling for large-scale FPVs. This lack of research represents a significant gap in our current study on multiscale FPV systems. Full article

In the present article, we study a nonlinear mathematical model for the steady-state non-isothermal flow of a dilute solution of flexible polymer chains between two infinite horizontal plates. Both plates are assumed to be at rest and impermeable, while the flow is driven by a constant pressure gradient. The fluid rheology model used is FENE-P type. The flow energy dissipation (mechanical-to-thermal energy conversion) is taken into account by using the Rayleigh function in the heat transfer equation. On the channel walls, we use one-parameter Navier’s conditions, which include a wide class of flow regimes at solid boundaries: from no-slip to perfect slip. Moreover, we consider the case of threshold-type slip boundary conditions, which state the slipping occurs only when the magnitude of the shear stresses overcomes a certain threshold value. Closed-form exact solutions to the corresponding boundary value problems are obtained. These solutions represent explicit formulas for the calculation of the velocity field, the temperature distribution, the pressure, the extra stresses, and the configuration tensor. The results of the work favor better understanding and more accurate description of complex dynamics and energy transfer processes in FENE-P fluid flows. Full article

In this paper, we study the conformal symmetry for locally rotationally symmetric Bianchi type I space-time. New exact conformal solutions of Einstein’s field equations for this space-time were obtained. The space-time geometry of these solutions is found to be non-vacuum, conformally flat, and shear-free. We show that in order for LRS Bianchi type I space-time to admit a conformal vector field it must reduce to the FRW space-time. Some physical and kinematic properties of the obtained conformal solutions are also discussed. Full article

The Seven Masters of the Quanzhen 全真七子 sect served as central figures during the founding phase of Quanzhen Daoism and played key roles in the sect’s early development. Originally positioned as the “Northern Seven Perfected Ones” (Bei Qi Zhen 北七真), they were instrumental in propelling the prosperity and expansion of Quanzhen Daoism. Over time, their images subsequently proliferated across various media—including portrayals in stone inscription, painting, biography, and novel, undergoing transformations through inscriptions, paintings, biographies, and novels—transforming transmission channels from Daoist temples to stage performances and from street corners to modern screens. In the Jin and Yuan 金元 periods, Daoist biographies and inscriptions portrayed the Seven Masters as exemplary figures of Daoist practice. In folk novels and precious scrolls (Baojuan 宝卷) in the Ming 明 and Qing 清 dynasties, they were presented as legendary, divine immortals and distant ancestors available for narrative appropriation. In modern times—particularly due to the popularity of Jin Yong 金庸’s martial art novels—they completed their universalization as Daoist cultural resources blending chivalric ethos and entertainment value. Examining the evolution of the Seven Masters’ imagery, two fundamental implications emerge: First, this transformation was jointly shaped by the power structures, functional needs, and media forms of each era. Second, beneath the fluid representations from sacred patriarchs of the Jin–Yuan period to modern entertainment symbols, there is an enduring thread of Daoist transcendental consciousness. Full article

Conventional diagnostic methods (CDMs) for lower respiratory infections (LRIs) have limitations in detecting causative pathogens. This study evaluates the utility of shotgun metagenomic sequencing (SMS) as a complementary diagnostic tool using bronchoalveolar lavage (BAL) fluid. Sixteen BAL fluid samples from pneumonia patients with positive CDM results—including bacterial/fungal cultures; PCR for Mycobacterium tuberculosis or cytomegalovirus; and the BioFire^® FilmArray^® Pneumonia Panel (BioFire Diagnostics LLC, Salt Lake City, UT, USA)—underwent 10 Gb SMS on the Illumina NovaSeq 6000 platform (Illumina, San Diego, CA, USA). Reads were aligned to the NCBI RefSeq database; with fungal identification further supported by internal transcribed spacer (ITS) analysis. Antibiotic resistance genes (ARGs) were annotated using the Comprehensive Antibiotic Resistance Database. Microbial reads accounted for 0.00002–0.04971% per sample. SMS detected corresponding bacteria in 63% of cases, increasing to 69% when subdominant taxa were included. Fungal reads were low; however, Candida species were identified in four samples via ITS. No viral reads were detected. ARGs meeting perfect match criteria were found in two cases. This is the first real-world study comparing SMS with CDMs, including semiquantitative PCR, in BAL fluid for LRI. SMS shows promise as a supplementary diagnostic method, with further research needed to optimize its performance and cost-effectiveness. Full article

In the present work, we suggest a new approach for studying the equilibrium states of an hydrodynamic isothermal turbulent self-gravitating system as a statistical model for a molecular cloud. The main hypothesis is that the local turbulent motion of the fluid elements is purely chaotic and can be regarded as a perfect gas. Then, the turbulent kinetic energy per fluid element can be substituted for the temperature of the chaotic motion of the fluid elements. Using this, we write down effective formulae for the internal and total the energy and for the first principal of thermodynamics. Then, we obtain expressions for the entropy, the free energy, and the Gibbs potential. Searching for equilibrium states, we explore two possible systems: the canonical ensemble and the grand canonical ensemble. Studying the former, we conclude that there is no extrema for the free energy. Through the latter system, we obtain a minimum of the Gibbs potential when the macro-temperature and pressure of the cloud are equal to those of the surrounding medium. This minimum corresponds to a possible stable local equilibrium state of our system. Full article

Centrifugal pumps are known to efficiently transport water from a certain point. However, they developed great concerns in water supply and distribution applications regarding their operating efficiency, which were caused by the accumulated losses and sudden power consumption growth. Thus, mitigating these concerns is important to improve the performance of the centrifugal pump. This study used ANSYS 2022 R2 for the optimization design process, combining the strengths of Computational Fluid Dynamics (CFD) and Response Surface Method (RSM), to come up with an optimal design for a centrifugal water pump. Splitter blades, with a length of 80% of the main blade, were included in the design to assess their effects on the performance of the pump. Design parameters such as the placement of the splitter blades, their ellipse ratios, and the volute tongue, were also investigated for further improvement. Results indicate that finding a perfect balance between the placement of the splitter blades, the design of the volute tongue clearance and thickness, and configuring the ellipse ratio of the splitter blades improves the pump’s performance. The optimal design results in 27.35%, 15.70%, 28.18%, 16.67%, and 8.36% improvement in total efficiency, total head, static efficiency, static head, and power consumption, respectively. Full article

This editorial presents 24 research articles published in the Special Issue entitled Geometry of Manifolds and Applications of the MDPI Mathematics journal, which covers a wide range of topics from the geometry of (pseudo-)Riemannian manifolds and their submanifolds, providing some of the latest achievements in many branches of theoretical and applied mathematical studies, among which is counted: the geometry of differentiable manifolds with curvature restrictions such as complex space forms, metallic Riemannian space forms, Hessian manifolds of constant Hessian curvature; optimal inequalities for submanifolds, such as generalized Wintgen inequality, inequalities involving $\delta$-invariants; homogeneous spaces and Poisson–Lie groups; the geometry of biharmonic maps; solitons (Ricci solitons, Yamabe solitons, Einstein solitons) in different geometries such as contact and paracontact geometry, complex and metallic Riemannian geometry, statistical and Weyl geometry; perfect fluid spacetimes [...] Full article

ARDS is a challenging syndrome in which the hallmark is alveolar epithelium damage, with the consequent extravasation of fluids into the interstitium and alveolar space. Patients with severe ARDS almost always require mechanical ventilation and aggressive fluid resuscitation, at least in the initial phases. The increased intrathoracic pressure during positive pressure ventilation reduces cardiac output, worsening the circulatory status of these patients even more. In this pathological context, fluid therapies serve as a means to restore intravascular volume but can simultaneously play a detrimental role, increasing the amount of liquid in the lungs and worsening gas exchange and lung mechanics. Indeed, clinical research suggests that fluid overload leads to worsening outcomes, mostly in terms of gas exchange, days of mechanical ventilation, and ICU stay duration. For these reasons, this review aims to provide basic information about ARDS pathophysiology and heart–lung interactions, the understanding of which is essential to guide fluid therapy, together with the close monitoring of hemodynamics and fluid responsiveness. Full article