Search Results (355)

Glycosaminoglycans (GAGs) are part of the extracellular matrix (ECM) and play a major role in maintaining their physiological function. During pathological processes, the ECM is remodeled and its GAG composition changes. Hyaluronic acid (HA) is one of the GAGs that plays an important role in pathological processes such as inflammation and cancer and is therefore an interesting target for imaging. To provide iron oxide nanoparticles (IONP) that bind to hyaluronic acid (HA) as specific probes for molecular imaging, a peptide with high affinity for HA was covalently bound to the surface of commercial IONP (synomag^®-D, NH2) leading to hyaluronic acid-specific iron oxide nanoparticles (HAIONPs). Affinity measurements using a quartz crystal microbalance (QCM) showed a very high affinity of HAIONP to HA, but not to the control chondroitin sulfate (CS). HAIONPs exhibit a very high magnetic particle spectroscopy (MPS) signal amplitude, which predestines them as HA-selective tracers for magnetic particle imaging (MPI). The high relaxivity coefficient r₂ also makes HAIONP suitable for magnetic resonance imaging (MRI) applications. HAIONP therefore offers excellent prerequisites for further development as a probe for the specific quantitative imaging of the HA content of the ECM in pathological areas. Full article

In this paper, we introduce and study a new subclass of bi-univalent functions related to Mittag–Leffler functions associated with Gregory polynomials and satisfy certain subordination conditions defined in the open unit disk. We derive coefficient bounds for the Taylor–Maclaurin coefficients $|{\gamma }_2|$ and $|{\gamma }_3|$, and also explore the Fekete–Szegö functional. Full article

In recent years, special functions have played a significant role in the investigation of different subclasses within the class of bi-univalent functions. In this work, we present and investigate two new subclasses of bi-univalent functions defined in $\mathfrak{U}=$$\{\varsigma \in \mathbb{C}:|\varsigma |<1\}$, characterized by Bernoulli polynomials associated with imaginary error functions. For functions belonging to these subclasses, we establish bounds for their initial coefficients. For these classes, we also tackle the Fekete–Szegö problem. Several new results are also obtained as special cases by specifying certain parameter values in the general findings. Full article

Background/Objectives: Adalimumab and Infliximab are biologics used to treat autoimmune diseases. Monitoring drug and anti-drug antibody (ADA) levels in patients helps optimize treatment. However, current quantitation methodologies for drug and total (free and drug-bound) ADAs often involve multi-step workflows. Automated systems can streamline the process. The i-Tracker chemiluminescent immunoassays (CLIA) are cartridge-based kits for quantifying serum levels of drugs such as Adalimumab, Infliximab, and associated ADAs. Herein, we aimed to establish performance characteristics of the i-Tracker Adalimumab, Infliximab, and total ADAs in serum on the random-access analyzer IDS-iSYS and to compare patient results with an electrochemiluminescent immunoassay (ECLIA)-based reference method. Methods: Remnant serum specimens, calibration material, or spiked serum were used to evaluate assay linearity, precision, functional sensitivity, and accuracy on the IDS-iSYS analyzer and to perform the method comparison. Results: The assays displayed linearity, accuracy, and up to 8% imprecision across clinically relevant analyte ranges. Compared to the reference method, the drug assays exhibited a strong linear fit (correlation coefficient > 0.95) with <±1.0 µg/mL mean bias. The total anti-Adalimumab assay demonstrated over 85% qualitative agreement. The total anti-Infliximab assay, however, showed higher detection rate of ADAs in Infliximab-treated patient specimens, yielding < 60% negative agreement with the reference method. Although i-Tracker total ADA assays exhibited drug sensitivity, they still detected ADAs in supratherapeutic drug concentrations. Conclusions: The i-Tracker assays demonstrated robust analytical performance, suggesting potential for clinical application. The method comparison underscored functional differences with the reference method, an important consideration when transitioning assay formats for monitoring Adalimumab- and Infliximab-treated patients. Full article

Conventional thermospheric density models are limited in their ability to capture solar-geomagnetic coupling dynamics and lack probabilistic uncertainty estimates. We present MSIS-UN (NRLMSISE-00 with Uncertainty Quantification), an innovative framework integrating sparse principal component analysis (sPCA) with heteroscedastic neural networks. Our methodology leverages multi-satellite density measurements from the CHAMP, GRACE, and SWARM missions, coupled with MSIS-00-derived exospheric temperature (tinf) data. The technical approach features three key innovations: (1) spherical harmonic decomposition of T∞ using spatiotemporally orthogonal basis functions, (2) sPCA-based extraction of dominant modes from sparse orbital sampling data, and (3) neural network prediction of temporal coefficients with built-in uncertainty quantification. This integrated framework significantly enhances the temperature calculation module in MSIS-00 while providing probabilistic density estimates. Validation against SWARM-C measurements demonstrates superior performance, reducing mean absolute error (MAE) during quiet periods from MSIS-00’s 44.1% to 23.7%, with uncertainty bounds (1σ) achieving an MAE of 8.4%. The model’s dynamic confidence intervals enable rigorous probabilistic risk assessment for LEO satellite collision avoidance systems, representing a paradigm shift from deterministic to probabilistic modeling of thermospheric density. Full article

This paper introduces a novel generalized q-symmetric differential operator for studying a certain subclass of univalent functions with negative coefficients. We establish several significant theoretical results for this class, including sharp coefficient bounds and characterization theorems based on the generalized Hadamard product. Two significant applications demonstrate the theoretical framework’s practical utility. First, in the context of geometric modeling, we demonstrate how the function class and operator can be utilized to create and control complex, non-overlapping transformations. Second, in digital signal processing, we show that these functions serve as stable digital filter prototypes and that our operator is an effective tool for fine-tuning the filter’s frequency response. These applications bridge the gap between abstract geometric function theory and practical system design by demonstrating the operator’s versatility as a tool for analysis and synthesis. Full article

Biunivalent holomorphic functions form an interesting class in geometric function theory and are associated with special functions and solutions of complex differential equations. This paper provides a complete distortion theory for such functions, in particular, the sharp coefficient estimates. Another interesting feature is that (in contrast to general collections of univalent functions) one obtains in the same fashion the sharp bounds for coefficients of biunivalent functions with k-quasiconformal extension for any $k<1$. Full article

In the present work, we define certain families, ${\mathbb{M}}_{\Sigma }\left(\mu ,{\rm Y},\gimel ,q; x\right)$ and ${\mathbb{N}}_{\Sigma }\left(\mu ,{\rm Y},\gimel ,q; x\right)$, of normalized holomorphic and bi-univalent functions associated with Bazilevič functions and $\gimel$-pseudo functions involving the $q$-Bernoulli polynomial, which is defined by the symmetric nature of quantum calculus in the open unit disk $U$. We determine the upper bounds for the initial symmetry Taylor–Maclaurin coefficients and the Fekete–Szegö-type inequalities of functions in the families we have introduced here. In addition, we indicate certain special cases and consequences for our results. Full article

This paper investigates a new subclass of bi-univalent analytic functions defined on the open unit disk in the complex plane, associated with the subordination to $1+\mathrm{s}\mathrm{i}\mathrm{n}z$. Coefficient bounds are obtained for the initial Taylor–Maclaurin coefficients, with a particular focus on the second- and third-order Hankel determinants. To illustrate the non-emptiness of the proposed class, we consider the function $\sqrt{1+tanhz}$, which maps the unit disk onto a bean-shaped domain. This function satisfies the required subordination condition and hence serves as an explicit member of the class. A graphical depiction of the image domain is provided to highlight its geometric characteristics. The results obtained in this work confirm that the class under study is non-trivial and possesses rich geometric structure, making it suitable for further development in the theory of geometric function classes and coefficient estimation problems. Full article

We propose a new strategy for constructing Runge–Kutta (RK) methods using evolutionary computation techniques, with the goal of directly minimising global error rather than relying on traditional local properties. This approach is general and applicable to a wide range of differential equations. To highlight its effectiveness, we apply it to two benchmark problems with oscillatory behaviour: the (2+1)-dimensional nonlinear Schrödinger equation and the N-Body problem (the latter over a long interval), which are central in quantum physics and astronomy, respectively. The method optimises four free coefficients of a sixth-order, eight-stage parametric RK scheme using a novel objective function that compares global error against a benchmark method over a range of step lengths. It overcomes challenges such as local minima in the free coefficient search space and the absence of derivative information of the objective function. Notably, the optimisation relaxes standard RK node bounds ($c_i\in [0,1]$), leading to improved local stability, lower truncation error, and superior global accuracy. The results also reveal structural patterns in coefficient values when targeting high eccentricity and non-sinusoidal problems, offering insight for future RK method design. Full article

The reinforcement effect of single-reinforced soil support under external loading has limitations, and it is difficult for it to meet engineering stability requirements. Therefore, the stability analysis of slopes supported by a combination of anti-slip piles and reinforced soil under the seismic loading effect needs an in-depth study. Based on the upper-bound theorem of limit analysis and the strength-reduction technique, this study establishes an upper-bound stability model for high–steep slopes that simultaneously considers seismic action and the combined reinforcement of anti-slide piles and reinforced soil. A closed-form safety factor is derived. The theoretical results are validated against published data, demonstrating satisfactory agreement. Finally, the MATLAB R2022a sequential quadratic programming method is used to optimize the objective function, and the Optum G2 2023 software is employed to analyze the factors influencing slope stability due to the interaction between anti-slide piles and geogrids. The research indicates that the horizontal seismic acceleration coefficient k_h exhibits a significant negative correlation with the safety factor F_s. Increases in the tensile strength T of the reinforcing materials, the number of layers n, and the length l all significantly improve the safety factor F_s of the reinforced-soil slope. Additionally, as l increases, the potential slip plane of the slope shifts backward. For slope support systems combining anti-slide piles and reinforced soil, when the length of the geogrid is the same, adding anti-slide piles can significantly improve the slope’s safety factor. As anti-slide piles move from the toe to the crest of the slope, the safety factor first decreases and then increases, indicating that the optimal reinforcement position for anti-slide piles should be in the middle to lower part of the slope body. The length of the anti-slip piles should exceed the lowest layer of the geogrid to more effectively utilize the blocking effect of the pile ends on the slip surface. The research findings can provide a theoretical basis and practical guidance for parameter optimization in high–steep slope support engineering. Full article

This work investigates the behavior of the coefficients of analytic functions within certain subclasses characterized by inherent symmetric structures. By leveraging deep connections with functions exhibiting positive real part properties, the approach introduces a modern analytical framework that links the studied coefficients to those of auxiliary functions with regulated behavior. This connection allows for the derivation of sharp estimates and facilitates computational treatment. The proposed method builds upon certain classical and modern coefficient inequalities. The study focuses on obtaining precise bounds for specific determinant expressions associated with initial, inverse, and inverse logarithmic coefficients, all within a subclass of starlike functions exhibiting internal symmetry aligned with a recently introduced canonical structure. This symmetric perspective reveals how geometric properties can lead to refined quantitative outcomes that enhance contemporary analytic theory. Full article

The concept of coefficient estimates on univalent functions is one of the interesting aspects explored recently by many researchers. Motivated by this direction, in this present work, we obtain the upper bounds of initial inverse coefficients and logarithmic coefficients and the upper bounds of differences between these successive coefficients related to concave univalent functions. Further, we also calculate the upper bounds of third-order Hankel, Toeplitz, and Vandermonde determinants in terms of specified coefficients connected to concave univalent functions. Full article

We establish a theory whose structure is based on a fixed variable and an algebraic inequality and which improves the well-known least squares theory. The mentioned fixed variable plays a basic role in creating such a theory. In this direction, some new concepts, such as p-covariances with respect to a fixed variable, p-correlation coefficients with respect to a fixed variable, and p-uncorrelatedness with respect to a fixed variable, are defined in order to establish least p-variance approximations. We then obtain a specific system, called the p-covariances linear system, and apply the p-uncorrelatedness condition on its elements to find a general representation for p-uncorrelated variables. Afterwards, we apply the concept of p-uncorrelatedness for continuous functions, particularly for polynomial sequences, and we find some new sequences, such as a generic two-parameter hypergeometric polynomial of the ${}_{4}F_3$ type that satisfies a p-uncorrelatedness property. In the sequel, we obtain an upper bound for 1-covariances, an improvement to the approximate solutions of over-determined systems and an improvement to the Bessel inequality and Parseval identity. Finally, we generalize the concept of least p-variance approximations based on several fixed orthogonal variables. Full article

In this article, through the application of the q-Sălăgean operator associated with functions characterized by bounded boundary rotation, we propose a few new subclasses of bi-univalent functions that utilize the q-Sălăgean operator with bounded boundary rotation in the open unit disk $\mathbb{E}$. For these classes, we establish the initial bounds for the coefficients $|a_2|$ and $|a_3|$. Additionally, we have derived the well-known Fekete–Szegö inequality for this newly defined subclasses. Full article