Search Results (479)

We investigate whether the geometric parameters of a three-dimensional domain can be recovered from the Dirichlet spectrum of the Laplacian. As a controlled benchmark, we consider rectangular boxes, about which the eigenvalues are explicitly known and the Weyl coefficients can be computed in closed form. Exploiting the short-time asymptotics of the heat trace, we extract the leading Weyl coefficients from finite spectral data and show how they encode volume, surface area, and the third spectral Weyl term. These coefficients uniquely determine the side lengths of the box via an explicit cubic reconstruction formula. Numerical experiments based on several thousand eigenvalues demonstrate that the method is stable, accurate, and robust with respect to spectral truncation. The box setting thus provides a stringent validation of the proposed inverse spectral methodology and serves as a foundation for its extension to smooth curved domains, such as triaxial ellipsoids, where explicit spectral formulas are no longer available. Full article

We study a generalized class of Jacobsthal–Lucas polynomials that depends on two parameters. First, we introduce essential formulas for these polynomials, involving their series representation, inverse formula, and moment formula. These formulas allow us to investigate this generalized class of polynomials further and to develop novel formulations. The essential standard linearization problem of these polynomials is solved, and the linearization coefficients are given in simple forms. In addition, some mixed linearization formulas with other classes of polynomials are presented. The derivative formulas of these polynomials, expressed as combinations of different polynomials, are given. By employing symbolic algebra methods—most notably Zeilberger’s algorithm and other well-known identities from the literature—many hypergeometric functions appearing in the coefficients can be reduced, resulting in simpler expressions. In addition, some definite integrals are evaluated using the newly introduced formulas. Full article

The aim of this paper is to establish an inversion and Calderón formulas for the generalized Gabor transform associated with a class of Sturm–Liouville operators. We also investigate several problems related to reproducing kernel theory for this transform. In particular, we study the concept of Tikhonov regularization and the extremal functions associated with the new generalized Gabor transform. Full article

This work presents the first systematic development of the inverse scattering transform for matrix nonlinear Schrödinger equations in the case where the discrete spectrum has triple poles, under nonzero boundary conditions at infinity. These systems arise physically as reductions modeling spinor Bose-Einstein condensates with hyperfine spin $F=1$ and find applications in nonlinear optics. A uniformization variable is employed to map the underlying Riemann surface to the complex plane, enabling a complete characterization of the analyticity, symmetries, and asymptotic behaviors of the Jost functions and scattering data. Extending the established framework for simple and double poles, we show that $\mathrm{rank} P(x,t,z_n)=3$ requires a third-order zero of $\det a\left(z\right)$ at $z=z_n$, while $\mathrm{rank} P(x,t,z_n)=2$ necessitates a fourth-order zero—a nontrivial feature absent in lower-order cases. The discrete spectrum for both rank configurations is fully characterized, and the full singular behavior near a triple pole is derived, respecting the quartet symmetry $z_n$, $z_n^{*}$, $v{k}_0^2/z_n$, $v{k}_0^2/z_n^{*}$ imposed by the nonzero boundary conditions. Solving the resulting matrix Riemann-Hilbert problem with triple poles yields the potential reconstruction formula and, in the reflectionless case, explicit expressions for general N-triple-pole soliton solutions, with a detailed example for $N=1$ presented to illustrate the construction. Full article

A symbolic method is presented for examining the solvability and constructing the exact solution to boundary value problems for systems of linear ordinary loaded differential equations and loaded integro-differential equations with nonlocal boundary conditions. The method uses the inverse of the differential operator involved in the system of loaded differential or integro-differential equations. A solvability criterion based on the determinant of a matrix and an exact analytical matrix-form solution formula are presented. For the implementation of the method into computer algebra system software, two algorithms are provided. The effectiveness of the method is demonstrated by solving several problems. The theoretical and practical results obtained complement the existing literature on the subject. Full article

Accurate correction of radial lens distortion is a fundamental requirement in computer vision and photogrammetry, as geometric inaccuracies directly affect 3D reconstruction, mapping, and geospatial measurements, particularly in high-precision imaging systems. In this study, we propose a fully analytical, non-iterative method for truncated inverse modeling of radial lens distortion, applicable to general radial distortion polynomials that contain constant terms. Unlike classical truncated Lagrange series reversion, which relies on recursive expansion and combinatorial series construction, the proposed formulation determines inverse distortion coefficients directly through a system of constrained algebraic inverse polynomials. This enables deterministic computation of inverse parameters without iterative refinement, numerical root finding, or combinatorial complexity. The method was evaluated using ultra-wide-angle smartphone camera imagery exhibiting severe barrel distortion modeled by an eighth-degree depressed radial distortion polynomial. Its performance was compared with a commonly used iterative inverse modeling approach. The analytical formulation demonstrated improved numerical stability and substantially reduced reprojection errors when correcting highly nonlinear distortion profiles, achieving sub-pixel accuracy in image rectification. In contrast, the iterative approach exhibited instability and significantly larger reprojection errors under identical conditions. These results demonstrate that the proposed framework provides a general, robust, and repeatable solution for inverse radial distortion modeling, particularly for high-order polynomial models. The method offers clear practical advantages for camera calibration pipelines in photogrammetry, remote sensing, robotics, and other applications requiring high-fidelity imaging. Full article

Motivated by the fact that the Fibonacci sequence is the simplest nontrivial second-order recurrence with a rational generating function, we develop a Fibonacci-weighted Hardy theory for bicomplex holomorphic functions. Starting from the coefficient norm ${\sum }_{n\ge 0}{\left|a_n\right|}^2/F_{n+1}$, we obtain a bicomplex Hilbert module whose reproducing kernel is governed by ${(1-t-t^2)}^{-1}$ and whose maximal disk of holomorphy is determined sharply by the nearest kernel singularity, giving the radius ${\rho }_F={\phi }^{-1/2}$ (the square-root inverse of the golden ratio $\phi$). The arithmetic recurrence makes several objects fully explicit: we derive closed formulas for the kernels through the idempotent decomposition of $\mathbb{BC}$, compute exact norms of the shift powers and a golden-ratio spectral radius, and package the local theory into a sheaf of Fibonacci-holomorphic germs that are compatible with the bicomplex idempotent splitting. We also treat $(p,q)$-Fibonacci weights, obtaining a one-parameter family of rational kernels ${(1-pt-q{t}^2)}^{-1}$ and corresponding operator bounds. In addition to providing a concrete bicomplex model within weighted Hardy theory, the resulting explicit kernels furnish benchmark examples for kernel-based interpolation and for the operator theory of unilateral weighted shifts. Full article

Employing ab initio electronic structure methods, in this study, I examine the effect of order on the spin gapless semiconducting behavior of the Mn₂CoAl Heusler compound. The occurrence of atomic disorder in general destroys the spin gapless semiconductivity observed in the inverse XA lattice structure; however, in some cases, novel magnetic configurations emerge. In the case of structures derived from the XA structure, where only Mn-Co or Mn-Al atoms are mixed, Mn₂CoAl alloy presents a half-metallic magnetic character. In the case of full disorder (A2 lattice structure), where atoms occupy all sites with the same probability, the ground state is an antiferromagnetic metallic one. The L2₁ and B2 lattice structures, where Mn atoms occupy both sites of a similar local environment, correspond to a ferromagnetic state of very high spin magnetic moment per formula unit. The present study encompasses a much larger variety of disordered structures in comparison with other studies in the literature. It concludes that the control and minimization of the concentration of impurities at anti-sites is imperative to achieving optimal performance in spintronic devices based on spin gapless semiconducting Mn₂CoAl. Full article

SSRMS refers to a Space Station Remote Manipulator System. The robotic arm of the Wentian module can complete tasks such as supporting astronauts’ extravehicular activities, installing and maintaining payloads, and inspecting the space station. The seven-joint SSRMS manipulator is critical for space missions. This study aims to build its kinematic model via screw theory. It simplifies SSRMS to right-angle rods, defines joint screw axes, twist coordinates, and initial pose matrix. Using the PoE (Product of Exponentials) formula, the 7-DOF forward kinematics equation is derived. In addition, it derives fixed joint angle for inverse kinematics, including analytical solutions and numerical solutions. It elaborates analytical solutions for fixing joints 1/7 and 2/6 and numerical solutions for fixing joints 3/4/5, solves all joint angles via kinematic decoupling, and addresses special cases. Experiments with China’s space station small arm parameters show the probability of meeting the accuracy threshold ${10}^{-4}$ is 99.79%, verifying model effectiveness, while noting singularity-related weak solving areas. This provides a reliable basis for subsequent inverse kinematics optimization. Full article

During the process of damage identification and safety-state evaluation of cable-stayed bridges, the cable tension should also be incorporated into common monitoring, which usually includes displacement and strain. However, the testing process of cable tension is complicated, and the disassembly, installation and maintenance of the cable tension meter are higher priced and difficult. To improve the efficiency of damage evaluation regarding cable-stayed bridges, information-entropy theory is introduced and the curvature entropy index of the difference in the influence line of displacement is proposed. To obtain effective data parameters for damage evaluation, first, the dynamic disturbance in the displacement time-history response is removed through variational modal decomposition, and the multi-axle effect of vehicles is regularized, so as to identify the measured influence line of displacement of cable-stayed bridges. Second, the peak value of the curvature entropy index of the difference in the influence line of displacement under varied damage degrees of stay cables is extracted to construct the inverse fitting formula of damage degree. The entropy value of the measured influence line of displacement is then substituted into a PSO-BP neural network, so as to obtain the damage degree of the corresponding position of the measured data regarding the influence line of displacement of bridges. Finally, the health status of stay cables is evaluated using the information-entropy parameters of the influence line of displacement. The theoretical model and actual data are used for testing, and the research results show that: (1) the location and degree of cable damage can be effectively located and quantified by using the curvature entropy index of the difference in the influence line of displacement, and (2) the cable health index of the cable-stayed bridge tested by actual data is 96.73%, consistent with the conclusion of on-site technical evaluation. Full article

This paper develops a unified analytical framework for pricing discretely sampled volatility-average swaps under the 4/2 stochastic volatility model. The model accommodates a broad range of volatility dynamics by combining affine and inverse-affine components in the instantaneous volatility specification, thereby unifying and extending the structural features of the classical Heston and 3/2 stochastic volatility models. Closed-form expressions for the conditional complex moments of the asset price are derived and serve as the fundamental building blocks for obtaining explicit analytical pricing formulas for volatility-average swaps under discrete sampling. The validity of the proposed pricing formulas is rigorously established within the admissible parameter space of the model. Extensive numerical experiments verify the accuracy and computational efficiency of the analytical results when compared with Monte Carlo simulations. The numerical analysis further reveals that discretely sampled volatility swap prices converge to their continuous-time counterparts in a manner that may be monotonic or non-monotonic, depending on the interaction between the volatility and inverse-volatility components of the 4/2 model, thereby emphasizing the importance of sampling effects in volatility derivative valuation. A detailed sensitivity analysis demonstrates how variations in the parameters governing the volatility and inverse-volatility components influence the fair strike prices, underscoring the structural flexibility of the 4/2 stochastic volatility model. Overall, the proposed framework provides an analytically tractable and computationally efficient approach for pricing volatility-linked derivatives under discrete sampling, offering valuable insights for both theoretical research and practical applications in volatility markets. Full article

Background: Early diagnosis of familial hypercholesterolemia (FH) is crucial to improve long-term outcomes. FH diagnosis relies on elevated low-density lipoprotein cholesterol (LDL-C) levels, familial clinical characteristics, and identification of pathogenic variants in FH-related genes. Secondary factors, such as overweight and obesity, are known to influence lipid profiles in the general population. More recently, polygenic risk scores based on single-nucleotide polymorphisms (SNPs) have been proposed as additional determinants of LDL-C levels. Methods: We enrolled 214 pediatric subjects with LDL-C levels ≥95th percentile (after 6 months of dietary intervention) and with at least one parent with LDL-C levels ≥ 95th percentile. All participants underwent biochemical and auxological assessment and genetic testing for FH. In a subgroup of 60 subjects, LDL-C polygenic scores based on 6- and 12-SNPs were calculated. Results: Pathogenic variants confirming heterozygous FH were identified in 190 subjects (variant-positive, V+); 17 were variant-negative (V−), yielding a mutation detection rate of 91.8%. An additional seven patients carrying variants of uncertain significance were excluded from the primary analysis. LDL-C was modestly higher in V+ than V− subjects using both Friedewald (212 vs. 188 mg/dL; p = 0.035) and Martin–Hopkins formulas (208 vs. 187 mg/dL; p = 0.041), while the other main clinical and laboratory parameters were similar. In V+, LDL-C was higher in subjects with null variants, compared to those with defective variants. Body mass index (BMI SDS) was inversely correlated with HDL-C (p < 0.001), and obesity (BMI z-score > 2 SDS) was associated with lower HDL-C and higher LDL-C, non-HDL-C, and ApoB. With regard to the polygenic scores, 12- and 6-SNP scores showed overlap between V+ and V−, and published cut-offs did not discriminate lipid severity in our population; however, in V+ subjects, the 12-SNP score acted as a phenotype modifier, being independently associated with higher LDL-C and non-HDL-C levels after adjustment for age, sex, and BMI SDS. Conclusions: In children selected by LDL-C ≥ 95th percentile, together with autosomal dominant familial hypercholesterolemia, genetic confirmation of FH is achieved in the vast majority of cases. Variant type (null vs. defective), BMI, and polygenic background contribute to phenotypic heterogeneity, supporting the need to address other factors alongside genetic diagnosis. Further validation is needed before polygenic scores can be implemented in routine clinical practice. Full article

In the process of using the freezing method to uncover coal from stone gates, the thermal evolution profiles of the coal body during the freezing process tend to be complex due to the presence of gas and moisture. To investigate the temperature response of coal containing gas under different freezing temperature conditions, a self-developed low-temperature freezing test system for coal containing water and gas was used to conduct freezing and cooling tests at different freezing temperatures (−5 °C to −30 °C). The temperature changes at various measuring points inside the coal over time were monitored in real time, and the temperature distribution, cooling law, and strain evolution process of the coal in the axial and radial directions were analyzed. The experimental results show that the cooling process of the center point of the coal can be divided into four stages: rapid cooling, extremely slow temperature drop, relatively slow cooling, and stable constant temperature. The time required to reach the stable constant temperature stage is inversely proportional to the freezing temperature, and corresponding prediction formulas have been established based on this. The standardized coal briquettes exhibit a gradient distribution characteristic of gradually increasing temperature from outside to inside in both axial and radial directions, with the radial temperature distribution being well matched by an exponential decay model. The strain of coal is affected by both thermal shrinkage and ice-induced expansion. The occurrence time of frost heave is positively correlated with freezing temperature, while the strain of frost heave is negatively correlated with freezing temperature. The axial frost heave effect is significantly stronger than the radial effect, but the radial frost heave occurs slightly earlier than the axial effect. This study reveals the thermal-mechanical coupling response mechanism of gas-containing coal during the low-temperature freezing process, and the research results can provide theoretical support for parameter optimization and engineering application of low-temperature freezing anti-outburst technology. Full article

Closed-form analytic inverses allow explicit tracking of parameter effects, facilitate interpretation of experimental signals, and support solving inverse problems. Here, we derive a rigorous closed-form expression for the inverse Laplace transform of a class of shifted quasi-rational spectral functions with a square-root radical and a power-law decaying factor. These functions appear in coupled diffusion processes in physics and in the analysis of electromagnetic signal propagation through electrically cascaded networks, signal processing, and related areas. The transform is expressed as a finite sum of three generalized hypergeometric functions—two Kummer functions and one five-parameter Kampé de Fériet function—each multiplied by a monomial depending on the decay parameter. The validity of the result is confirmed by direct Laplace transformation, which recovers the original spectral function. Several known inverse transforms appear as limiting cases, illustrating the generality of the solution. Additionally, reduction formulas for a subclass of Kampé de Fériet functions demonstrate how the general solution encompasses previously known results and highlight the generality of the method. Full article

We develop a function theory on a three-dimensional reduced quaternionic model endowed with a projected (and, therefore, non-associative) product, together with its natural dual extension generated by a nilpotent infinitesimal unit. After introducing the associated first-order Dirac-type system, we construct explicit Cauchy kernels and prove a Cauchy–Pompeiu representation for sufficiently smooth functions with values in the dual algebra. We derive a Teodorescu-type right inverse, Liouville- and uniqueness-type principles, and residue formulas for isolated singularities. For smooth hypersurfaces, we establish Plemelj–Sokhotski boundary limits for the Cauchy transform and its dual lift. Worked examples illustrate how the reduced product interacts with boundary geometry and provide a practical route to computation. Full article