Search Results (890)

The volumetric mass transfer coefficient ($k_{L}a$) governs the design, operation, and scale-up of aerobic bioprocesses, yet its dependence on reactor geometry, impeller design, operating conditions, and fluid properties limits prediction by empirical correlations. Machine learning (ML) improves accuracy but faces two barriers in bioprocess practice: selecting the best model among many candidates requires expertise, and small, highly multicollinear data make models chosen based on test error alone prone to overfitting. Using a browser-based, no-code platform, we trained 14 regression algorithms under an identical pipeline on a published $k_{L}a$ dataset, and introduced a composite objective, the generalization-penalized error (GPE), which is the test RMSE plus the absolute train–test RMSE gap. Minimizing GPE rather than test RMSE expanded the top statistically equivalent group to include not only boosting ensembles but also simpler, interpretable models, indicating that black-box models hold no clear advantage once train–test consistency is assessed. Sensitivity analysis showed that tree models produce discontinuous responses, whereas algebraic learning via elastic net (ALVEN) yields smooth surfaces. Shapley additive explanations (SHAP) and an ontology graph, interpreted by a retrieval-augmented language-model agent, identified rotational speed and gas flow rate as dominant, reproducing the established mass transfer mechanism. The framework offers a reproducible, interpretable, expertise-light route to bioprocess model selection. Full article

In this paper, a novel elliptic algebraic model-based positive- and negative-sequence amplitude estimation method is proposed for unbalanced grid voltages. By exploiting the intrinsic elliptic trajectory of unbalanced voltage vectors in the $\alpha \beta$ stationary reference frame, an explicit algebraic relationship between the sequence amplitudes and the elliptic geometric parameters is established. Consequently, the conventional sequence decomposition problem is reformulated as an elliptic parameter identification problem. Based on the proposed elliptic algebraic framework, an online parameter identification scheme is developed to estimate the elliptic parameters and reconstruct the sequence amplitudes. A Lyapunov-based global asymptotic stability analysis is also presented to verify the convergence property of the proposed identification framework. Experimental results further validate the effectiveness of the proposed method. Full article

This paper introduces and investigates a novel two-parameter sequence, termed the biparametric Appell extension (B-App-Ex) and denoted by ${\mathcal{B}}_n(x;\lambda ,\alpha )$. Standard classical Appell sequences often lack sufficient structural parameters, which can limit their operational flexibility in certain advanced spectral schemes. To address this limitation, we construct an enhanced operational framework by integrating a binomial structural kernel ${(1+w)}^{\lambda }$ with a linear exponential scaling $e^{\alpha xw}$ entirely within the Appell class. We provide a rigorous logical deduction of the fundamental properties of this sequence, including its explicit power series representation, a characteristic three-term recurrence relation, and a governing second-order differential equation (DEq.). A significant contribution of this work is the establishment of analytically exact connection and inverse connection formulas between the B-App-Ex basis and various classical orthogonal polynomial (COP) families. Numerical verification via a collocation-based projection framework demonstrates that these algebraic kernels achieve near-machine epsilon precision (≈${10}^{-15}$), remaining stable even for high-order approximations. Furthermore, by isolating the dilation factor $\alpha$, we establish an $O\left(N\right)$ computational complexity that offers a reduction in latency by approximately two orders of magnitude compared to classical matrix-based transformations. The results demonstrate that the proposed biparametric (Bip.) extension offers a versatile and highly optimized analytical template for modeling complex dynamic systems where structural shifting and spatial scaling must be tuned simultaneously. Full article

Econometric estimation of panel data models by feasible generalized least squares (FGLS) provides an example of how conceptually simple problems may run into computational bottlenecks. I address the main computational tasks of FGLS within the R system for statistical computing, comparing different tools from the point of view of computational efficiency. I concentrate on estimating two models: the popular “random effects” with two error components and the less restrictive “general GLS” specification, which does not fit into the standard computational framework usually employed for the former. I compare the standard solution (partial time demeaning) with two alternative strategies, based respectively on algebraic properties and on object-oriented programming. I show how, while naive implementations become infeasible with large datasets, both list operators and object-oriented matrix routines available in the R environment make the problem tractable for most practically relevant sample sizes on any machine. I conclude by briefly discussing the parallelization of critical tasks. Full article

With the growing need for long-term secure communications in Internet-of-Things (IoT) and sensor-network environments, practical and robust post-quantum key-establishment mechanisms have become increasingly important. In this work, we revisit the ephemeral-only Ding key exchange (DKE) proposed at ACNS 2019, which is based on one-sample Ring Learning With Errors (Ring-LWE) with rounding, and the original analysis of which covers only passive security. Building on the DKE framework, we propose MoRo-KEM, a Module Learning With Errors (Module-LWE)-based key-encapsulation mechanism using rounding. First, we lift the construction from the Ring-LWE setting to the Module-LWE setting, retaining ring-level efficiency while enabling more flexible parameter choices and reducing reliance on rigid algebraic structure. Second, we replace discrete Gaussian sampling for secrets and errors with centered binomial sampling, thereby simplifying constant-time vectorized implementations while preserving the required noise behavior. Third, we extend the resulting key-exchange core to an IND-CPA-secure public-key encryption scheme and further obtain an IND-CCA-secure KEM via the Fujisaki–Okamoto transform. Finally, at security level $\mathrm{I}$, MoRo-KEM achieves a decryption failure rate of $2^{-166}$, lower than the $2^{-139}$ reported for CRYSTALS-Kyber, thus improving robustness against decryption-failure attacks. These properties make the proposed design attractive for secure key establishment among sensor nodes, edge devices, and gateways operating under constrained computation, memory, and communication budgets. Overall, our construction provides a concrete path from ephemeral key exchange to a practical IND-CCA-secure KEM instantiated over Module-LWE. Full article

This study introduces a novel matrix defined over the nonzero natural numbers, whose entries are governed by a rigorous closed-form expression. The matrix architecture replicates the topological properties of the Ulam spiral, mapping the integer sequence onto a structured lattice with a well-defined formulation. We investigate the interplay between the matrix’s linear algebraic properties and its number-theoretic implications. A primary focus is the established connection between the matrix’s lines, rows, diagonals, and antidiagonals, and the Hardy–Littlewood F-conjecture. By analyzing the matrix’s internal structure, this work provides a new analytical framework for further study of the conjecture. The matrix links its visual characteristics to quadratic polynomials, offering fresh insights into the distribution of prime numbers. Full article

In this paper, we introduce and study a Szász-type family of positive linear operators generated by Euler polynomials of negative order on $[0,\infty )$. The construction is based on an explicit finite representation of these polynomials with non-negative terms, which ensures the positivity of the corresponding kernel. We prove the basic properties of the operators and show that they can be represented as finite convex combinations of shifted classical Szász operators. We also provide a probabilistic representation of the kernel as a finite mixture of Poisson distributions, which clarifies the role of the parameter k and the resulting moment structure. The corresponding algebraic and central moment identities are derived and used to establish convergence on compact intervals and to obtain quantitative estimates in terms of the modulus of continuity, Lipschitz-type classes, and Peetre’s K-functional. Furthermore, Voronovskaya-type asymptotic results are obtained, including a quantitative form and a second-order asymptotic formula. Numerical tables and a graphical illustration are presented for selected test functions and parameter values, and the results are consistent with the theoretical convergence behaviour. The paper shows that Euler polynomials of negative order provide a positive and structurally tractable framework for constructing Szász-type approximation operators on the positive real axis. Full article

In this paper, we introduce a new difference operator, called the $\left(p,q\right)$-Hahn difference operator, which extends both the classical Hahn operator and the $\left(p,q\right)$-difference operator by incorporating an additional shift parameter, $\omega$. This extension allows the operator to reflect translation effects together with scaling behavior within a common framework. We investigate the basic algebraic properties of the operator, including linearity, product and quotient rules, and explicit formulas for power functions. A generalized Leibniz rule is established using $\left(p,q\right)$-binomial coefficients. In addition, a corresponding $\left(p,q\right)$-Hahn integral is defined, and a fundamental relation between the operator and the integral is obtained under suitable assumptions. Furthermore, several special and limiting cases are analyzed in order to clarify the connection between the proposed operator and existing difference operators. In particular, it is shown that the operator reduces to the classical derivative, the $q$-difference operator, and the standard $\left(p,q\right)$-difference operator under appropriate parameter choices. Finally, applications to $\left(p,q\right)$-Hahn Sturm–Liouville-type problems and hypergeometric-type difference equations are discussed. These results suggest that the proposed operator provides a consistent extension of existing difference-calculus structures. Full article

Extreme cyclic temperature fluctuations (−200 °C to 200 °C) and inherent clearance nonlinearity in deployment hinges severely threaten the on-orbit deployment accuracy and dynamic stability of large variable-geometry spacecraft antennas for geosynchronous Earth orbit applications. However, current modeling approaches suffer from three critical limitations: single-configuration models requiring manual switching, there are inherent geometric nonlinear errors from conventional floating frame formulations, and incomplete thermo-mechanical coupling neglects the temperature effects on contact stiffness and friction. To address these gaps, we propose a unified high-fidelity dynamic model based on the Absolute Nodal Coordinate Formulation (ANCF). This model eliminates geometric errors and mesh mismatch, enables seamless multi-configuration deployment without switching, and fully incorporates temperature-dependent material properties and nonlinear contact forces. An improved Hilber–Hughes–Taylor-$\alpha$ implicit integration algorithm with second-order accuracy and unconditional stability is adopted to solve the strongly nonlinear differential-algebraic equations. Numerical results demonstrate that the proposed model achieves a calculation error below 3% against experimental data, significantly outperforming the traditional floating frame of reference formulation with an error of 15–22%. Non-uniform temperature fields increase thermally induced vibration amplitudes by 32–45%, and every 0.1 increase in the friction coefficient raises the impact force at the clearance hinge by 15–20%. The proposed unified modeling framework provides a solid theoretical basis for deployment stability prediction and the on-orbit control optimization of large variable-geometry spacecraft antennas. Full article

In this study, we propose a matrix-based transformation framework constructed from special integer sequences, including Fibonacci, Lucas, Pell, and Jacobsthal numbers. The approach is based on block-wise $2\times 2$ matrix transformations that preserve key structural invariants, particularly the determinant, ensuring explicit invertibility of the scheme. By combining multiple recurrence-based matrices within a unified framework, the method provides flexible forward and inverse transformations without increasing matrix dimensions or introducing additional redundancy. The determinant-preserving property enables intrinsic consistency checking and supports an analytic error-detection and correction mechanism at the block level. Several illustrative examples are presented to demonstrate the applicability of the proposed scheme and its computational characteristics. The framework is purely algebraic and can be extended to other matrix families generated by linear recurrence relations, making it suitable for a wide range of applications in applied and computational mathematics. Full article

This paper investigates the problem of exponential synchronization for a class of quaternion-valued inertial neural networks with mixed time delays under aperiodic intermittent control. First, a neural network model incorporating both discrete and distributed delays is established. To overcome the limitations of conventional approaches, a novel quaternion-based controller is proposed, which operates without relying on model order reduction or quaternion decomposition techniques, thereby achieving global exponential synchronization of the system. Furthermore, by constructing an appropriate Lyapunov function and combining the algebraic properties of quaternions with inequality techniques, sufficient conditions for synchronization are rigorously derived within the Lyapunov stability framework. Numerical simulations are conducted to demonstrate the effectiveness of the proposed control strategy and validate the theoretical results. Finally, an image encryption application is developed to further corroborate the practical viability of the proposed scheme, wherein the original image is encrypted into a noise-like pattern without information leakage and perfectly recovered upon synchronization, with quantitative error analysis confirming high-precision exponential synchronization. Full article

In this paper, we introduce and formalize the theory of Sheffer stroke hoop algebras, providing a minimal axiomatization for bounded hoop algebras utilizing a single binary operation. We systematically establish the fundamental algebraic properties of this novel structure, beginning with the logical independence of its core axioms. We equip the algebra with an induced partial order, proving it constitutes a well-defined ∧-semilattice, and demonstrate a bidirectional structural translation: bounded hoop algebras satisfying the Double Negation Property (DNP) can be equivalently expressed as Sheffer stroke hoop algebras, and vice versa. Furthermore, we investigate the internal algebraic architecture by introducing sub-algebras, filters, positive implicative filters, and ideals, rigorously establishing the inherent structural duality between filters and ideals. By proving that proper filters naturally induce full algebraic congruences, we successfully construct quotient Sheffer stroke hoop algebras. We characterize prime filters by demonstrating that a quotient algebra forms a chain if and only if its generating filter is prime. Finally, we complete the theoretical framework by establishing the Correspondence Theorem and the First Isomorphism Theorem, seamlessly embedding classical universal algebraic principles into the Sheffer stroke setting. Full article

Compact finite difference schemes approximate spatial derivatives through implicit relations between neighboring grid points. Despite using compact stencils and relatively simple algebraic structures, these schemes achieve high-order accuracy and spectral-like resolution, reducing dispersion errors while maintaining low numerical dissipation. These properties make them particularly attractive for problems requiring accurate spatial derivatives and computational efficiency, such as wave propagation, aeroacoustics, and turbulent flow simulations. This review presents the main ideas behind compact finite difference schemes, including their derivation from Taylor expansions and Padé approximations, their accuracy properties, and their resolution characteristics through modified wavenumber analysis. The manuscript is intended as a review and practical synthesis, rather than as the proposal of a new numerical scheme, and aims to connect the theoretical construction of compact schemes with their numerical behavior, practical implementation, and representative applications. To support reproducibility, we provide a fully documented open-source Python 3.11 notebook with a reference implementation of the schemes discussed in the paper. The examples include first- and second-order derivative calculations and representative one- and two-dimensional boundary-value problems, including Helmholtz-type equations. Finally, we survey applications across computational fluid dynamics, acoustics, geophysical flows, structural mechanics, biology, electromagnetism, and quantitative finance. Full article

This paper proposes a two-dimensional orthogonal pattern division multiple access (OPDMA) technique to address key challenges in massive MIMO systems, including complex channel estimation, multipath interference, Doppler effects, and inter-antenna interference. Byleveraging optimal frequency hopping patterns with ideal autocorrelation and cross-correlation properties, constructed using a two-dimensional cyclic shift method, OPDMA eliminates the need for equalizers and channel estimation, thereby simplifying receiver design and mitigating pilot contamination. A method for constructing these patterns is introduced, based on an algebraic Costas array with a two-dimensional cyclic shift approach. The simulation results show that OPDMA significantly reduces the bit error rate (BER), simplifies system architecture, and enhances communication quality. These findings highlight OPDMA’s potential to improve performance and streamline the design of massive MIMO systems compared to traditional methods, which implies that OPDMA can be a promising low-complexity interference-suppression strategy when the optimal frequency hopping patterns design parameters match the expected Doppler shift and multipath delay. Full article

In this paper, we introduce and investigate a new class of special polynomials called degenerate Peter–Genocchi polynomials. We define these polynomials and their associated numbers via an explicit generating function and explore a variety of their fundamental algebraic and analytic properties. In particular, we derive summation formulas (expressing polynomials via their associated numbers), addition formulas (splitting the polynomial argument), an implicit summation formula (a bivariate convolution identity), and symmetric identities. We also establish connections with degenerate Stirling numbers of both kinds, higher-order degenerate Genocchi polynomials, and higher-order degenerate Daehee polynomials. Furthermore, we investigate derivative properties and present a differential operator formula. Finally, we provide tables of approximate zeros and graphical representations of the zeros in the complex plane. Full article