Search Results (177)

Background/Objectives: Relapsing polychondritis (RP) is a rare autoimmune disorder marked by recurrent inflammation of cartilaginous tissues, including the airways. Airway involvement, such as subglottic stenosis and airway malacia, significantly impacts prognosis. Although spirometry is the standard for evaluating respiratory function, it may be unfeasible in patients with severe airway narrowing or tracheostomy. This study evaluated the potential of a smartphone-based application, DepthRecorder, which uses the iPhone’s TrueDepth camera to analyze thoracic motion in real time. Methods: Twelve patients with RP were enrolled. All underwent simultaneous respiratory assessment using spirometry and the DepthRecorder application. Thoracic motion data were corrected for height using previously validated regression formulas. Correlation between DepthRecorder and spirometry values was analyzed using Spearman’s rank correlation for forced vital capacity (FVC), forced expiratory volume in one second (FEV₁), and the FEV₁/FVC ratio. Results: Mean age was 53.8 ± 13.3 years, with equal numbers of males and females. Before correction, DepthRecorder showed moderate correlations for FEV₁ (ρ = 0.48, p = 0.003) and FEV₁/FVC (%) (ρ = 0.57, p < 0.001). After correction, stronger correlations were observed for FVC (ρ = 0.76, p < 0.001), FEV₁ (ρ = 0.72, p < 0.001), and FEV₁/FVC (%) (ρ = 0.60, p < 0.001). Conclusions: The DepthRecorder application demonstrated strong correlations with spirometry following height-based correction. This method may offer a practical, non-invasive tool for respiratory assessment in RP patients who cannot undergo conventional lung function testing. Further studies are needed to validate these findings and establish clinical reference standards. Full article

This paper establishes symmetric inequalities for the reciprocal sums of Fibonacci numbers. By using elementary methods, recurrence properties, Cassini’s identity, and the Fibonacci–Lucas connection, we deduce the precise bounds for these reciprocal sums and an asymptotic formula for the corresponding floor function. This work is novel in two key aspects: it is the first to combine reciprocals of linear recurrence sequences with the tail of the Riemann zeta function, and the first to derive symmetric inequalities for such reciprocal sums. Full article

Objective: Non-contrast computed tomography (CT) remains the gold standard for diagnosing ureteral stones, with excellent sensitivity and specificity. However, reliance on CT alone raises concerns regarding cumulative radiation exposure, particularly in recurrent stone formers. Clinical scoring systems such as CHOKAI, STONE, and modified STONE have been developed to provide practical bedside tools for diagnostic decision-making. This study prospectively compared these three clinical scores for their ability to predict urinary-stone disease in the emergency department. Study Design: Prospective study. Methods and Duration of the Study: Between 6 August 2024 and 15 February 2025, 130 consecutively enrolled adults with flank pain underwent bedside scoring and reference-standard non-contrast CT. Associations were analysed with Chi-Square Tests and multivariable logistic regression. Model calibration was assessed with the Hosmer–Lemeshow test; overall accuracy was calculated. Results: When the variables used in different stone scoring formulas were compared according to the computer tomography results, there was a statistically significant difference (p < 0.01) between patients with and without a history of stone and hydronephrosis. Patients with nausea, history of stone, and hydronephrosis were 11, 4.2, and 5 times more highly to have a stone on computer tomography than those without, respectively. Conclusions: In this Turkish cohort, CHOKAI and modified STONE demonstrated superior predictive performance compared to the original STONE score. These findings suggest that clinical scoring systems, when incorporating predictors such as nausea, prior stone history, and hydronephrosis, may serve as practical alternatives to CT-first diagnostic approaches. Multicenter validation studies are required before routine clinical adoption. Full article

In this paper, the boundary value problem of wave diffraction on a semi-infinite circular pin is solved using the Wiener–Hopf method with compensation of eigenmodes. The solution to the problem is presented as an infinite series defined by a recurrence formula. The reliability and accuracy of the solution are verified numerically in terms of fulfillment of the law of energy conservation. Sufficiently reliable results are obtained at the first iteration. The method used for solving this problem can be applied to solving diffraction problems on axisymmetric volumetric structures. Full article

In this article, the mechanism of relaxation polarization currents occurring at a constant temperature (isothermal process) in crystals with ionic-molecular chemical bonds (CIMBs) in an alternating electric field was investigated. Methods of the quasi-classical kinetic theory of dielectric relaxation, based on solutions of the nonlinear system of Fokker–Planck and Poisson equations (for the blocking electrode model) and perturbation theory (by expanding into an infinite series in powers of a dimensionless small parameter) were used. Generalized nonlinear mathematical expressions for calculating the complex amplitudes of relaxation modes of the volume-charge distribution of the main charge carriers (ions, protons, water molecules, etc.) were obtained. On this basis, formulas for the current density of relaxation polarization (for transient processes in a dielectric) in the k-th approximation of perturbation theory were constructed. The isothermal polarization currents are investigated in detail in the first four approximations (k = 1, 2, 3, 4) of perturbation theory. These expressions will be applied in the future to compare the results of theory and experiment, in analytical studies of the kinetics of isothermal ion-relaxation (in crystals with hydrogen bonds (HBC), proton-relaxation) polarization and in calculating the parameters of relaxers (molecular characteristics of charge carriers and crystal lattice parameters) in a wide range of field parameters (0.1–1000 MV/m) and temperatures (1–1550 K). Asymptotic (far from transient processes) recurrent formulas are constructed for complex amplitudes of relaxation modes and for the polarization current density in an arbitrary approximation k of perturbation theory with a multiplicity r by the polarizing field (a multiple of the fundamental frequency of the field). The high degree of reliability of the theoretical results obtained is justified by the complete agreement of the equations of the mathematical model for transient and stationary processes in the system with a harmonic external disturbance. This work is of a theoretical nature and is focused on the construction and analysis of nonlinear properties of a physical and mathematical model of isothermal ion-relaxation polarization in CIMB crystals under various parameters of electrical and temperature effects. The theoretical foundations for research (construction of equations and working formulas, algorithms, and computer programs for numerical calculations) of nonlinear kinetic phenomena during thermally stimulated relaxation polarization have been laid. This allows, with a higher degree of resolution of measuring instruments, to reveal the physical mechanisms of dielectric relaxation and conductivity and to calculate the parameters of a wide class of relaxators in dielectrics in a wide experimental temperature range (25–550 K). Full article

Padé approximants are computational tools customarily employed for resumming divergent Stieltjes series. However, they become ineffective or even fail when applied to Stieltjes series whose moments do not satisfy the Carleman condition. Differently from Padé, Levin-type transformations incorporate important structural information on the converging factors of a typical Stieltjes series. For example, the computational superiority of Weniger’s $\delta$-transformation over Wynn’s epsilon algorithm is ultimately based on the fact that Stieltjes series converging factors can always be represented as inverse factorial series. In the present paper, the converging factors of an important class of superfactorially divergent Stieltjes series are investigated via an algorithm developed one year ago from the first-order difference equation satisfied by the Stieltjes series converging factors. Our analysis includes the analytical derivation of the inverse factorial representation of the moment ratio sequence of the series under investigation, and demonstrates the numerical effectiveness of our algorithm, together with its implementation ease. Moreover, a new perspective on the converging factor representation problem is also proposed by reducing the recurrence relation to a linear Cauchy problem whose explicit solution is provided via Faà di Bruno’s formula and Bell’s polynomials. Full article

Introduction: Shaofu Zhuyu Decoction (SZD) is a traditional Chinese herbal formula commonly used for gynecological disorders involving “blood stasis” and lower abdominal pain. Although applied clinically for endometriosis, evidence regarding its efficacy and safety remains fragmented. This systematic review and meta-analysis aimed to evaluate the clinical efficacy and safety of SZD combined with conventional medication (CM) for the treatment of endometriosis. Methods: Databases including PubMed, EMBASE, CNKI, and Web of Science were searched from inception to May 2024 for randomized controlled trials (RCTs) comparing SZD + CM versus CM alone. Risk of bias was assessed using the risk of bias 2.0 tool. The primary outcome was total effective rate (TER); secondary outcomes included serum CA-125 levels, pain scores (VAS), recurrence rate, and adverse events. Results: Eleven RCTs (n = 1186 patients) were included. Meta-analysis showed that SZD plus CM significantly improved TER compared to CM alone (OR 1.15; 95% CI: 1.09–1.22; p < 0.00001). Reductions in CA-125 levels (OR −1.57; 95% CI: −2.18 to −0.95; p < 0.00001) and pain (VAS) scores (OR −4.90; 95% CI: −6.82 to −2.98; p < 0.00001) were also significant. Three studies reported lower recurrence in the SZD group. Adverse events were generally mild and comparable between groups. Conclusions: SZD combined with CM appears more effective than CM alone in improving endometriosis symptoms, reducing biochemical markers, and decreasing pain intensity, with acceptable safety. However, the findings are limited by methodological heterogeneity and geographic concentration of studies. Rigorous multicenter trials are warranted to support integration of SZD into global endometriosis care. Full article

Clostridioides difficile is a leading pathogen involved in healthcare-associated diarrhea. With its increasing incidence, mortality, and antibiotic resistance, there is an urgent need for novel therapeutic strategies to address the infection and prevent its recurrence. Gegen Qinlian Decoction (GQD) is a traditional Chinese medicine for the treatment of diarrhea, but its main active ingredient is not known. Therefore, in this study, we evaluated the biological activity of berberine (BER) and baicalein (BAI), key components of GQD, against C. difficile. Time–kill curves and scanning electron microscopy were employed to assess their effects on C. difficile growth, while Enzyme-Linked Immunosorbnent Assay (ELISA) and cytotoxicity assays were used to examine their impact on toxin production. We also employed Quantitative Reverse Transcription PCR (qRT-PCR) to examine how BER and BAI influenced the expression of toxin-associated genes. At sub-inhibitory concentrations, these compounds exerted antibacterial activity against C. difficile by disrupting the integrity of the cell membrane and cell wall. Furthermore, BER and BAI also suppressed toxin production, demonstrating effects comparable to those of vancomycin. This suppression likely resulted from their bactericidal activity and the inhibition of toxin gene expression. This study not only highlights the potential application of GQD in treating C. difficile infections but also offers promising options for developing drugs targeting the growth and virulence of this pathogen. C. difficile infection (CDI) is a leading cause of severe diarrhea, and its treatment remains challenging due to limited drug options and its high recurrence rate. BAI and BER, the main active components of the traditional Chinese medicinal formula GQD, inhibited the growth of C. difficile by disrupting its cellular structure and significantly reduced the production of toxins associated with disease severity. Furthermore, the effects of BAI and BER on C. difficile were comparable to those of conventional antibiotics, suggesting that these compounds could be potential alternative therapies for CDI. This study not only highlights the therapeutic potential of GQD in treating CDI but also provides a replicable research strategy for the development of novel anti-CDI agents. Full article

In this study, we define a new family of Gaussian polynomials, called Gaussian Chebyshev polynomials, by extending classical Chebyshev polynomials into the complex domain. These polynomials are characterized by second-order linear recurrence relations, and their connections with the Chebyshev polynomials are established. We also examine properties such as Binet-type formulas and generating functions. Moreover, we characterize some relationships between Gaussian and classical Chebyshev polynomials for the first and second kinds. We obtain some well-known theorems, such as Cassini, Catalan, and d’Ocagne’s theorems, for the first and second kinds. Furthermore, we present important connections among four types of these new polynomials. In the proofs of our results, we utilize the symmetric and antisymmetric properties of the Chebyshev polynomials. Finally, it is shown that Gaussian Chebyshev polynomials are closely related to well-known special sequences such as the Fibonacci, Lucas, Gaussian Fibonacci, and Gaussian Lucas numbers for some specific values of variables. Full article

In this study, we aim to construct a finite set of orthogonal matrix polynomials for the first time, along with their finite orthogonality, matrix differential equation, Rodrigues’ formula, several recurrence relations including three-term relation, forward and backward shift operators, generating functions, integral representation and their relation with Jacobi matrix polynomials. Thus, the concept of “finite”, which is used to impose parametric constraints for orthogonal polynomials, is transferred to the theory of matrix polynomials for the first time in the literature. Moreover, this family reduces to the finite orthogonal M polynomials in the scalar case when the degree is 1, thereby providing a matrix generalization of finite orthogonal M polynomials in one variable. Full article

This paper investigates a class of nonlinear rational difference equations with delayed terms, which often arise in various mathematical models. We analyze the iterative behavior of these rational functions and show how their iterations can be represented through second-order linear recurrence relations. By establishing a connection with generalized Balancing sequences, we derive explicit formulas that describe the system’s asymptotic behavior. Our main contribution is proving the existence of a unique globally asymptotically stable equilibrium point for all trajectories, regardless of initial conditions. We also provide analytical expressions for the solutions and support our findings with numerical examples. These results offer valuable insights into the dynamics of nonlinear rational systems and form a theoretical basis for further exploration in this area. Full article

Six well-known sequences (Fibonacci and Lucas numbers, Pell and Pell–Lucas polynomials, and Chebyshev polynomials) are characterized by quadratic linear recurrence relations. They are unified and reviewed under a common framework. Several useful properties (such as Binet-form expressions, Cassini identities, and Catalan formulae) and remarkable results concerning power sums, ordinary convolutions, and binomial convolutions are presented by employing the symmetric feature, series rearrangements, and the generating function approach. Most of the classical results concerning these six number/polynomial sequences are recorded as consequences. Full article

Objectives: The hospital organizational model can have an impact on people’s health. A critical lesson can be drawn from the pandemic. The possible negative sequelae of the practice of separation of maternal–infant dyads adopted during an infant’s first SARS-CoV-2 pandemic infection on infants have not been considered. Our purpose was to investigate the short- and long-term effects on neonates born to SARS-CoV-2 infected mothers of two different mother–infant dyad management strategies after birth (Separation vs. Rooming-In). Methods: This prospective cohort study enrolled 60 pregnant women who tested positive for SARS-CoV-2 infection and their newborns. We identified two cohorts of study based on mother–infant dyad management after delivery: Cohort A (Separation) and Cohort B (Rooming-In). Inclusion criteria were neonates born from mothers infected with SARS-CoV-2 during the pregnancy undergoing or not undergoing separation. Main Outcome: Rate of exclusive breastfeeding at 6 months of age was the primary outcome. The rate of mother–infant transmission of SARS-CoV-2 infection, growth, incidence of acute infections and neurodevelopment up to 12 months of life were also evaluated. Results: In total, 60 mother–infant dyads (maternal age 30.6 vs. 33.8 years, p = 0.335; gestational age 39.0 vs. 38.9 weeks, p = 0.451) were enrolled at delivery, and 53 dyads completed the study at the 6-month follow-up. Baseline clinical characteristics were similar between the two cohorts. At 6-month follow-up, the rate of breastfeeding was significantly decreased in Cohort A compared with Cohort B (4% vs. 46%, p < 0.001). The rate of SARS-CoV-2 infection was similar between the two cohorts of the study. Weight gain at 6 months of life was significantly higher in Cohort A compared to Cohort B (8129 g, 95% CI, 7562 to 8695; vs. 7393 g, 95% CI, 6912 to 7874; p = 0.005). No differences were detected in terms of rate of acute neonatal infections and neurodevelopment outcomes. Conclusions: The separation practice led to a reduction in the rate of breastfeeding after discharge and to a consequently increased implementation of formula milk, which might justify the alarming increased weight gain of newborns who did not undergo the Rooming-In practice. Given the potential of recurrent outbreaks of other viral pandemics, our results suggest more caution early in life towards the disruption of consolidated procedures that may have long-term consequences. However, the COVID-19 pandemic offered a unique context to observe the effects of temporary mother–infant separation; clinicians should be reassured that the temporary separation practice did not affect neurodevelopment and be aware that it could be considered an option, at least if Rooming-In cannot be carried out due to severe reasons such as lack of staff or adequate space. Full article

This study investigates the computation of fractional and higher integer-order moments for a stochastic process governed by a one-dimensional, non-homogeneous linear stochastic differential equation (SDE) driven by fractional Brownian motion (fBm). Unlike conventional approaches relying on moment-generating functions or Fokker–Planck equations, which often yield intractable expressions, we derive explicit closed-form formulas for these moments. Our methodology leverages the Wick–Itô calculus (fractional Itô formula) and the properties of Hermite polynomials to express moments efficiently. Additionally, we establish a recurrence relation for moment computation and propose an alternative approach based on generalized binomial expansions. To validate our findings, Monte Carlo simulations are performed, demonstrating a high degree of accuracy between theoretical and empirical results. The proposed framework provides novel insights into stochastic processes with long-memory properties, with potential applications in statistical inference, mathematical finance, and physical modeling of anomalous diffusion. Full article

This study investigates the sediment transport characteristics in the lower reservoir area of a pure pumped-storage power station (Pure-PSPS) to address the sediment abrasion issue under high sediment-laden conditions. By establishing a physical model and employing multivariate statistical analysis methods, we systematically reveal the multifactorial coupled influence mechanism of key parameters in the lower reservoir area on turbine sediment concentration (TSC), while developing a predictive TSC formula applicable to high-sediment Pure-PSPS based on sediment-carrying capacity theory and sediment mass conservation principles. The study indicates the following: (1) Under consistent basic parameters such as reservoir length, the decay rate of sediment concentration along the path from the reservoir inlet to the power station’s intake and outlet decreases to 30~80% under high inflow conditions, while under medium and low inflow conditions, the decay rate exceeds 80%. (2) The lower boundary of the median particle size adjustment range for suspended sediment gradually increases from 0.006 mm for 30- and 40-year flood recurrence intervals to 0.009 mm for an 80-year recurrence interval, and under the 80-year recurrence interval, the particle size fluctuation range converges to a high and narrow distribution of 0.009~0.011 mm. (3) The constructed linear regression model has an R² value of 0.8. The inflow sediment concentration (standardized coefficient β = 0.36) exhibits the strongest explanatory power for the dependent variable, followed by inflow discharge (β = 0.345) and the height difference between the intake/outlet and the silted bed surface (β = 0.319). (4) By optimizing the Adomian decomposition method, dimensional analysis, and multiple regression techniques, and based on sediment-carrying capacity theory and sediment mass conservation principles, this study derived and fitted a predictive formula for TSC in high-sediment-laden Pure-PSPS environments with favorable validation results. The research not only clarifies the interactive relationship between high-sediment-laden flow and turbine sediment concentration in Pure-PSPS but also fills the methodological gap in predicting operational conditions for pure pumped-storage power stations under extreme sediment scenarios. The established regular patterns provide a scientific foundation for the design and feasibility assessment of similar Pure-PSPS projects in sediment-rich rivers. Full article