Search Results (929)

Financial time-series data often exhibit statistically significant skewness and heavy tails, and numerous flexible distributions have been proposed to model them. In the context of the Log-linear Realized GARCH model with Skew-t (ST) distributions, our objective is to explore how the choice of prior distributions in the Adaptive Random Walk Metropolis method and initial parameter values in the Generalized Reduced Gradient (GRG) Solver method affect ST parameter and log-likelihood estimates. An empirical study was conducted using the FTSE 100 index to evaluate model performance. We provide a comprehensive step-by-step tutorial demonstrating how to perform estimation and sensitivity analysis using data tables in Microsoft Excel. Among seven ST distributions—namely, the asymmetric, epsilon, exponentiated half-logistic, Hansen, Jones–Faddy, Mittnik–Paolella, and Rosco–Jones–Pewsey distributions—Hansen’s ST distribution is found to be superior. This study also applied the GRG method to estimate new approaches, including Realized Real-Time GARCH, Realized ASHARV, and GARCH@CARR models. An empirical study showed that the GARCH@CARR model with the feedback effect provides the best goodness of fit. Out-of-sample forecasting evaluations further confirm the predictive dominance of models incorporating real-time information, particularly Realized Real-Time GARCH for volatility forecasting and Realized ASHARV for 1% VaR estimation. The findings offer actionable insights for portfolio managers and risk analysts, particularly in improving volatility forecasts and tail-risk assessments during market crises, thereby enhancing risk-adjusted returns and regulatory compliance. Although the GRG method is sensitive to initial values, its presence in the spreadsheet method can be a powerful and promising tool in working with probability density functions that have explicit forms and are unimodal, high-dimensional, and complex, without the need for programming experience. Full article

We consider a multi-species mixture of interacting bosons, $N_1$ bosons of mass $m_1$, $N_2$ bosons of mass $m_2$, and $N_3$ bosons of mass $m_3$, in a harmonic trap with frequency $\omega$. The corresponding intra-species interaction strengths are ${\lambda }_{11}$, ${\lambda }_{22}$, and ${\lambda }_{33}$, and the inter-species interaction strengths are ${\lambda }_{12}$, ${\lambda }_{13}$, and ${\lambda }_{23}$. When the shape of all interactions is harmonic, the system corresponds to the generic multi-species harmonic-interaction model, which is exactly solvable. We start by solving the many-particle Hamiltonian and concisely discussing the ground-state wavefunction and energy in explicit forms as functions of all parameters, the masses, numbers of particles, and the intra-species and inter-species interaction strengths. We then explicitly compute the reduced one-particle density matrices for all the species and diagonalize them, thus generalizing the treatment by the authors earlier. The respective eigenvalues determine the degree of fragmentation of each species. As an application, we focus on phenomena that do not arise in the corresponding single-species or two-species systems. For instance, we consider a mixture of two kinds of bosons in a bath made by a third kind, controlling the fragmentation of the former by coupling to the latter. Another example exploits the possibility of different connectivities (i.e., which species interacts with which species) in the mixture, and demonstrates how the fragmentation of species 3 can be manipulated by the interaction between species 1 and species 2, when species 3 and 1 do not interact with each other. We highlight the properties of fragmentation that only appear in the multi-species mixture. Further applications are briefly discussed. Full article

The matrix transfer function (MTF) is fundamental to the analysis and control of multivariable descriptor systems, especially under zero initial conditions. Its importance lies in its direct relation to input–output behavior and its natural use in frequency-domain methods. Unlike classical approaches that obtain MTF through companion linearizations or indirect Weierstrass–Kronecker reductions, our method derives a closed-form MFD directly from the descriptor pencil (λE − A), avoiding linearizations and preserving descriptor structure. This yields (i) an explicit parameterization of state feedback gains via finite/infinite Jordan pairs, (ii) a normalization law that removes impulsive modes by design, and (iii) improved reproducibility through block-polynomial operations suited to large-scale MIMO systems. The framework further extends eigenstructure assignment to descriptor models, combining clarity of analysis with practical control design. These results establish a systematic basis for scalable methods in MIMO descriptor systems. Full article

The Directed Energy Deposition (DED) process has demonstrated high efficiency in manufacturing steel parts with complex geometries and superior capabilities. Understanding the complex interplays of alloy compositions, cooling rates, grain sizes, thermal histories, and mechanical properties remains a significant challenge during DED processing. Interpretable and data-driven modeling has proven effective in tackling this challenge, as machine learning (ML) algorithms continue to advance in capturing complex property structural relationships. However, accurately predicting the prime mechanical properties, including ultimate tensile strength (UTS), yield strength (YS), and hardness value (HV), remains a challenging task due to the complex and non-linear relationships among process parameters, material constituents, grain size, cooling rates, and thermal history. This study introduces an ML model capable of accurately predicting the UTS, YS, and HV of a material dataset comprising 4900 simulation analyses generated using the “JMatPro” software, with input parameters including material compositions, grain size, cooling rates, and temperature, all of which are relevant to DED-processed low-alloy steels. Subsequently, an ML model is developed using the generated dataset. The proposed framework incorporates a physics-based DED-specific feature that leverages “JMatPro” simulations to extract key input parameters such as material composition, grain size, cooling rate, and thermal properties relevant to mechanical behavior. This approach integrates a suite of flexible ML algorithms along with customized evaluation metrics to form a robust foundation to predict mechanical properties. In parallel, explicit data-driven models are constructed using Multivariable Linear Regression (MVLR), Polynomial Regression (PR), Multi-Layer Perceptron Regressor (MLPR), XGBoost, and classification models to provide transparent and analytical insight into the mechanical property predictions of DED-processed low-alloy steels. 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 study, a semi-analytical solution to the inhomogeneous Whittaker equation is developed for both initial and boundary value problems. A new class of special integral functions ${}^f\mathrm{Zi}_{\kappa ,\mu }\left(x\right)$, along with their derivatives, is introduced to facilitate the construction of the solution. The analytical properties of ${}^f\mathrm{Zi}_{\kappa ,\mu }\left(x\right)$ are rigorously investigated, and explicit closed-form expressions for ${}^f\mathrm{Zi}_{\kappa ,\mu }\left(x\right)$ and its derivatives are derived in terms of Whittaker functions ${\mathrm{M}}_{\kappa ,\mu }\left(z\right)$ and ${\mathrm{W}}_{\kappa ,\mu }\left(z\right)$, confluent hypergeometric functions, and other special functions including Bessel functions, modified Bessel functions, and the incomplete gamma functions, along with their respective derivatives. These expressions are obtained for specific parameter values using symbolic computation in Maple. The results contribute to the broader analytical framework for solving inhomogeneous linear differential equations with applications in engineering, mathematical physics, and biological modeling. Full article

This study investigates the impact of structured input, referential activities, and affective activities on English simple past tense acquisition in a second language (L2). Thirty-three participants from a senior high school were divided into four groups based on the pretest–posttest design: referential only, affective only, a combination of both, and a control group. A self-paced reading (SPR) test was used to measure accuracy and response times to evaluate the effectiveness of these instructional strategies. Structured input and referential tasks enhance grammatical acquisition more rapidly and accurately than affective-only treatments or controls, showing the beneficial effects of structured input on grammar acquisition. The results emphasized the importance of designing instructional strategies that address specific processing challenges in L2 learning by focusing on form–meaning connections. By demonstrating differential impacts of structured input activities on grammatical learning and processing efficiency, the research contributes to the field of second language acquisition. The SPR method was selected for its ability to capture subtle, immediate differences in processing at the word level, its suitability for controlled classroom-based online administration, and its established validity in L2 processing research. Unlike other methods, SPR allows precise measurement of reaction times for specific sentence components, isolating processing effects of the target grammatical form while minimizing the influence of explicit knowledge. Full article

In this paper, explicit exact representations of the Unit Step Function and Ramp Function are obtained. These important functions constitute fundamental concepts of operational calculus together with digital signal processing theory and are also involved in many other areas of applied sciences and engineering practices. In particular, according to a rigorous process from the viewpoint of Mathematical Analysis, the Unit Step Function and the Ramp Function are equivalently performed as bi-parametric single-valued functions with only one constraint imposed on each parameter. The novelty of this work, when compared with other investigations concerning accurate and/or approximate forms of Unit Step Function and/or Ramp Function, is that the proposed exact formulae are not exhibited in terms of miscellaneous special functions, e.g., Gamma Function, Biexponential Function, or any other special functions, such as Error Function, Complementary Error Function, Hyperbolic Function, or Orthogonal Polynomials. In this framework, one may deduce that these formulae may be much more practical, flexible, and useful in the computational procedures that are inserted into operational calculus and digital signal processing techniques as well as other engineering practices. Full article

Stabilization of the resonance frequency in thin-film acoustic devices to variations in environmental conditions is commonly reduced to the passive or active compensation of a single factor (usually temperature) and the isolation or addition of a separate correction circuit for every other factor (e.g., pressure and mass loading). In this work, the possibility of dual-factor compensation is proposed, where the response of a multi-layered thin structure to both temperature and ambient pressure variation vanishes due to the choice of intrinsic parameters (materials and thickness ratios). The response functions are derived for the $S_0$ Lamb mode at long wavelengths in an explicit analytical form in terms of bulk material characteristics. It is demonstrated that the dual-factor intrinsic stabilization requires at least a three-layered structure and can be achieved for materials commonly used in temperature-compensated devices (aluminum nitride, fused silica, and aluminum). Identification of the key material characteristics governing the existence of a stability solution can serve for a targeted search of such composites and implementation of new thin-film dual devices. Full article

The continuous-wave (CW) illuminator, whose fundamentals are related to the theoretical understanding of loop antennas loaded with ferrite materials, is a device which plays an important role in electromagnetic pulse (EMP) susceptibility assessment. However, existing theoretical formulas do not consider cases where ferrite materials are loaded into the loop antenna. This paper provides a new explicit theoretical formula for the impedance of a circular loop antenna loaded with ferrite materials for CW illuminator design, and explores the variation regularity of its input impedance. Loading ferrite materials affects the internal impedance of the loop antenna and forces some modifications to the classical calculation procedure, resulting in an asymptotic numerical calculation method and a closed-form solution. The full-wave simulation results from CST Studio Suite show a maximum error of less than 0.99%, compared to the classical theory. With ferrite material loaded, the input impedance of the loop antenna is significantly reduced and smoothed in a wide range of normalized radii. For a loop antenna with a fixed circumference, the input impedance indicates that the Q-factor decreases as the thickness of the ferrite material increases. Conversely, for a ferrite-loaded loop antenna with a constant material thickness, a larger loop circumference results in a higher Q-factor. In summary, this study provides a fast and accurate computational method for the input impedance design of CW illuminators, while also offering an effective tool for further research on the performance of ferrite-loaded loop antennas. Full article

In this paper, we introduce and analyze a novel two-dimensional Moran random walk model, where each component evolves by either increasing by one unit or resetting to zero at each time step, with transition probabilities dependent on time. The primary contribution of this work is the derivation of an explicit closed-form expression for the probability distribution of the final maximum altitude, $U_n=max(U_n^{\left(1\right)},U_n^{\left(2\right)})$. Additionally, we provide a detailed analysis of the height statistics and cumulative distribution associated with the model. Using probabilistic techniques, we establish the exact distribution of the final altitude and its moments. Furthermore, we conduct numerical simulations to illustrate the behavior of the model for various parameter values. These results offer new insights into the statistical properties of two-dimensional Moran processes and have potential applications in population genetics, nuclear physics, and related fields. Full article

This paper establishes a rigorous theoretical framework for analyzing the existence and uniqueness of solutions to Cohen–Grossberg bidirectional associative memory neural networks (CGBAMNNs) incorporating four distinct types of time-varying delays: leakage, neutral, distributed, and transmission delays. This study makes three key contributions to the field: First, it overcomes the fundamental challenge posed by the system’s inherent inability to be expressed in vector–matrix form, which previously limited the application of standard analytical techniques. Second, the work develops a novel and generalizable methodology that not only proves sufficient conditions for solution existence and uniqueness but also, for the first time in the literature, provides an explicit representation of the unique solution. Third, the proposed framework demonstrates remarkable extensibility, requiring only minor modifications to be applicable to a wide range of delayed system models. Theoretical findings are conclusively validated through numerical simulations, confirming both the robustness of the proposed approach and its practical relevance for complex neural network analysis. Full article

Let $\mathfrak{R}$ be a commutative ring with identity $1\ne 0$. The weakly zero-divisor graph of $\mathfrak{R}$, denoted $W_{\Gamma }(\mathfrak{R})$, is the simple undirected graph whose vertex set consists of the nonzero zero-divisors of $\mathfrak{R}$, where two distinct vertices $\mathfrak{a}$ and $\mathfrak{b}$ are adjacent if and only if there exist $r\in \mathrm{ann}(\mathfrak{a})$ and $s\in \mathrm{ann}(\mathfrak{b})$ such that $rs=0$. In this paper, we study the signless Laplacian spectrum of $W_{\Gamma }({\mathbb{Z}}_n)$ for several composite forms of n, including $n=p^2{q}^2$, $n=p^{2}qr$, $n=p^m{q}^m$ and $n=p^{m}qr$, where $p, q, r$ are distinct primes and $m\ge 2$. By using generalized join decomposition and quotient matrix methods, we obtain explicit eigenvalue formulas for each case, along with structural bounds, spectral integrality conditions and Nordhaus–Gaddum-type inequalities. Illustrative examples with computed spectra are provided to validate the theoretical results, demonstrating the interplay between the algebraic structure of ${\mathbb{Z}}_n$ and the spectral properties of its weakly zero-divisor graph. Full article

We study the quantum state discrimination problem under the minimum error (ME) strategy for a set of N pure equidistant states. These states are characterized by the property that the inner product between any pair of states is given by a unique complex number S. We provide the explicit form of the states and analyze their main structural properties. The optimal success probability for ME discrimination is evaluated as a function of the number of states, as well as the modulus and phase of the inner product S. Furthermore, we propose an experimental scheme for implementing the ME discrimination of equidistant states. We also investigate the quantum coherence consumed in the implementation of the minimum error discrimination of the equidistant states, which has an established operational interpretation as cryptographic randomness gain. As an application, we propose a quantum communication protocol in which Alice prepares and sends one of the equidistant states, while Bob applies the minimum error discrimination to extract the classical information encoded in the state. Finally, we discuss the optimal conditions under which the protocol achieves an optimal balance of classical correlations and quantum coherence, thereby ensuring effective information transfer and cryptographic security. Full article

Mineral resource classification plays a critical role in communicating confidence levels, yet supporting methodologies such as drill-hole spacing analysis and geostatistical simulations are not consistently applied in routine updates of deterministic resource models. As a result, both local and global uncertainty quantification remain underutilized, and drilling requirements are often defined without a clear link to uncertainty reduction. This paper introduces a mineral resource uncertainty and drilling policy framework developed and applied at Compañía Minera Doña Inés de Collahuasi (CMDIC). The framework quantifies the uncertainty of each mineral resource model update when new data are available and provides an initial approach to determining drilling requirements based on CMDIC’s risk acceptance policies for different project stages. The proposed approach is a stochastic workflow that uses the current deterministic mineral resource model and database to generate geostatistical simulations. These simulations account for data quality, quantity, geological variability, and copper-grade variability. They form the basis for mineral resource classification with an explicit uncertainty quantification and provide an optimized drilling campaign to achieve desired risk levels subject to budget constraints. Because stochastic modeling updates faster than deterministic modeling, it provides timely insights from new drilling campaigns and delivers valuable insights for subsequent deterministic geological and grade modeling updates. The implementation of this workflow demonstrates its feasibility as a standard step following deterministic modeling, leading to cost-effective mineral resource development and management by aligning technical practices with the organization’s strategic objectives and risk preferences. Full article