Search Results (184)

This paper introduces a new class of periodic volatility models, namely, the Stochastic Volatility Periodic Logarithmic Asymmetric GARCH (PlogAG-SV) model. The proposed framework extends periodic logGARCH models by incorporating a stochastic volatility component combined with a distinctive threshold mechanism, thereby significantly enhancing their ability to capture asymmetric and time-varying volatility dynamics. Sufficient conditions for strict stationarity, second-order stationarity, and the existence of higher-order moments are rigorously established, providing a comprehensive characterization of the model’s probabilistic properties. Parameter estimation is conducted via extensive Monte Carlo simulations, demonstrating the robustness and reliability of the proposed estimation procedure across a wide range of scenarios. Furthermore, the empirical relevance of the PlogAG-SV model is illustrated through an application to the Algerian dinar–euro exchange rate, highlighting its effectiveness in modeling real-world financial volatility. Full article

Recall that in On a general second order derivative, Sci. Rep. Tokyo Kyoiku Daigaku A, 5(124–127)(1956), 111–114, Ozaki, Ono and Umezawa proved a result that if $f\left(z\right)$ is analytic and satisfies $|f^{″}\left(z\right)|<1$ in the unit disc $\mathbb{D}=\left\{z:\left|z\right|<1\right\}$, then $|f^{\prime }\left(z\right)-1|<1$ and so, $f\left(z\right)$ is univalent in $\mathbb{D}$, because $\mathfrak{Re}\left\{f^{\prime }\left(z\right)\right\}>0$ in $\mathbb{D}$ implies univalence by the Noshiro–Warschawski Theorem. In this paper, we obtain another sufficient condition for univalence of $f\left(z\right)$ by applying a hypothesis for modulus of $arg\left\{f^{″}\left(z\right)\right\}$. Full article

The Church of St. Francis in Pula, Croatia, is a well-preserved example of Franciscan gothic sacral architecture from the late 13th century. As preaching was highly valued by the Franciscan order as a way of communicating with the faithful, the study is focused on determining whether speech intelligibility in the church would have been adequate for successful communication between priests and their audience. The archaeoacoustic analysis of the church was performed in four stages: (1) in situ acoustic measurements in the present state, (2) development and calibration of the model of the present state based on measurement results, (3) development of the two models of the presumed historical state based on the calibrated model and historical data, and (4) prediction of acoustic conditions in the present and the historical states in terms of reverberation time T₃₀ and of speech intelligibility in terms of speech transmission index STI. The factors considered in the study were (1) acoustics of the church, (2) profile of the audience (friars and the faithful), (3) layout of the audience areas (choir area in the front of the nave for the friars, back area of the nave for the faithful), (4) positions of the speech sources (altar for addressing the friars, pulpit for addressing the faithful), (5) occupancy (unoccupied and fully occupied church), (6) language used in liturgical ceremonies (Latin and native language), and (7) language proficiency of the audience (native speakers, users of a second language). The results show that (1) fair speech intelligibility (STI ≥ 0.45 for the faithful as native speakers, STI ≥ 0.50 for friars as non-native speakers of Latin) can be achieved for 50% of the audience in the choir area and for the entire audience in the back area in favourable conditions (fully occupied church, audience addressed from dedicated speaker positions), (2) the position of the pulpit (close to the audience and considerably elevated above it) is more favourable than the position of the altar (remote, barely elevated above the audience), and (3) in unoccupied conditions, fair speech intelligibility can still be achieved in at least 50% of the back audience area with the faithful gathered close to the pulpit, while it is not possible for the front audience area addressed from the altar. The summary conclusion is that the church of St. Francis in its presumed historical layout(s) would fulfil its primary function in a limited capacity. Fair speech intelligibility would likely have been sufficient for the audience to follow liturgical ceremonies conducted in the church, but not without difficulty. Full article

The present study focuses on scientific and experimental research on corrosion damage to the bodies of subway cars. The main purpose of the research is to assess the degree of corrosive wear on the main load-bearing metal structures of the subway cars after the end of their service life in order to determine the possibility of their further operation. Scientific and experimental research was conducted under the conditions of the municipal enterprise “Kyiv Metro” on subway cars of the series (models) Yezh, 81-714/717 and 81-714.5/717.5, which had reached the end of their service life. The main methodological approach of the research consisted of conducting technical diagnostics of the subway cars using standardized non-destructive testing methods. The goal of the research was achieved by solving two main tasks. The first task was to determine mathematical expressions describing the dynamics of changes in the thickness and degree of corrosive wear of the metal structures of the studied subway cars, depending on number of years in operation. The second task was to determine the possibility of extending the service of the subway cars after reaching the end of their service life. The scientific novelty of this study lies in determining the degree of thinning and the development of corrosive wear of the metal structures of the studied subway cars depending on the type of structure and service life. The practical significance of the obtained results lies in the possibility to predict the residual strength resources of the individual elements of the metal structures of the studied cars using the corrosive wear criterion. It was established that the 092GS material of the main metal structures of the subway car bodies is sufficiently resistant to corrosion processes. The results of the research show that the metal structures of the subway cars studied had a margin of safety and, therefore, their service life could be extended. Full article

This study investigates the synchronization of coupled fractional-order Markovian reaction-diffusion neural networks (MRDNNs) with partially unknown transition rates. The novelty of this work is mainly reflected in three aspects: First, this study incorporates the Markovian switching model and reaction-diffusion term into a fractional-order system, which is a challenging and under-explored issue in existing literature, and effectively addresses the synchronization problem of fractional-order MRDNNs by introducing a continuous frequency distribution model of the fractional integrator. Second, it derives a new set of sufficient synchronization conditions with reduced conservatism; by utilizing the (extended) Wirtinger inequality and delay-partitioning techniques, abundant free parameters are introduced to significantly broaden the solution range. Third, it proposes an LMI-based optimal synchronization design by establishing an efficient offline optimization framework with semidefinite constraints, and achieves the precise solution of control gains. Finally, numerical simulations are conducted to validate the effectiveness of the proposed method. Full article

This study introduces a new integral operator $I_{p,\mu }^{\delta }$ that extends the traditional Rafid operator to meromorphic p-valent functions. Using this operator, we define and investigate two new subclasses: ${\Sigma }_p^{+}\left(\delta ,\mu ,\alpha \right)$, consisting of functions with nonnegative coefficients, and ${\Sigma }_p^{+}\left(\delta ,\mu ,\alpha ,c\right)$, which further fixes the second positive coefficient. For these classes, we establish a necessary and sufficient coefficient condition, which serves as the foundation for deriving a set of sharp results. These include accurate coefficient bounds, distortion theorems for functions and derivatives, and radii of starlikeness and convexity of a specific order. Furthermore, we demonstrate the closure property of the class ${\Sigma }_p^{+}\left(\delta ,\mu ,\alpha ,c\right)$, identify its extreme points, and then construct a neighborhood theorem. All the findings presented in this paper are sharp. To demonstrate the practical utility of our symmetric operator paradigm, we apply it to a canonical fractional electrodynamics problem. We demonstrate how sharp distortion theorems establish rigorous, time-invariant upper bounds for a solitary electrostatic potential and its accompanying electric field, resulting in a mathematically guaranteed safety buffer against dielectric breakdown. This study develops a symmetric and consistent approach to investigating the geometric characteristics of meromorphic multivalent functions and their applications in physical models. Full article

This paper presents a reformulation of classical existence and uniqueness results for second-order boundary value problems (BVPs) using the Kannan fixed point theorem, extending beyond the Banach contraction principle. We shift focus from the nonlinearity j to the solution operator T defined via Green’s function and establish a sufficient condition under which T satisfies the Kannan contraction criterion. Specifically, if the derivative of j is bounded by K and $K·{(\eta -\zeta )}^2/8<1/3$, then T is a Kannan contraction, ensuring a unique solution. This condition applies even when the Banach contraction principle fails. We also explore the plausibility of applying the Chatterjea contraction, though rigorous verification remains open. Examples illustrate the applicability of the results. This work highlights the utility of generalized contractions in differential equations. Full article

Periodic solutions of high-order nonlinear differential equations are fundamental in dynamical systems, yet they remain challenging to establish with traditional methods. This paper addresses the existence of periodic solutions in general $2n$-order autonomous and nonautonomous ordinary differential equations. By extending Carathéodory’s variational technique from the calculus of variations, we reformulate the original periodic solution problem as an equivalent higher-order variational problem. The approach constructs a convex function and introduces an auxiliary transformation to enforce convexity in the highest-order term, enabling a tractable operator-theoretic analysis. Within this framework, we prove two main theorems that provide sufficient conditions for periodic solutions in both autonomous and nonautonomous cases. These results generalize the known theory for second-order equations to arbitrary higher-order systems and highlight a connection to the Hamilton–Jacobi theory, offering new insights into the underlying variational structure. Finally, numerical examples validate our theoretical results by confirming the periodic solutions predicted by the theory and demonstrating the approach’s practical applicability. Full article

This paper presents some oscillation criteria for second-order half-linear dynamic equations defined on unbounded above arbitrary time scales. These criteria offer sufficient conditions for all solutions of the equations to display oscillatory behavior. We investigate both delay and advanced cases of these equations, and our approach encompasses a broader class of dynamic equations than previously considered in the literature. The results of this study not only generalize well-known oscillation criteria used in differential equations but also significantly broaden their applicability to arbitrary time scales. Additionally, we provide illustrative examples to demonstrate the relevance and accuracy of our findings. Full article

This paper presents a fully implicit finite difference scheme for the numerical approximation of a wave equation featuring strong damping and a distributed delay term. The discretization employs second-order accurate approximations in both time and space. Although implicit, the scheme does not ensure unconditional stability due to the nonlocal nature of the delayed damping. To address this, we perform a stability analysis based on Rouché’s theorem from complex analysis and derive a sufficient condition for asymptotic stability of the discrete system. The resulting criterion highlights the interplay among the discretization parameters, the damping coefficient, and the delay kernel. Two quadrature techniques, the composite trapezoidal rule (CTR) and the Gaussian quadrature rule (GQR), are employed to approximate the convolution integral. Numerical experiments validate the theoretical predictions and illustrate both stable and unstable dynamics across different parameter regimes. Full article

A second-order linear differential operator A is defined on a tree of arbitrary topology. Any internal vertex P of the tree divides the tree into $m_p$ branches. The restrictions $A_i,i=1,\dots ,m_p$ of the operator A on each of these branches, where the vertex P is considered the root of the branch and the Dirichlet boundary condition is specified at the root. These restrictions must be, in a sense, asymmetric (not similar) to each other. Thus, the distinguished class of differential operators A turns out to have only simple eigenvalues. Moreover, the matching conditions at the internal vertices of the graph contain a set of parameters. These parameters are interpreted as stiffness coefficients. This paper proves that a finite set of eigenvalues allows one to uniquely restore the set of stiffness coefficients. The novelty of the work is the fact that it is sufficient to know a finite set of eigenvalues of intermediate Weinstein problems for uniquely restoring the required stiffness coefficients. We not only describe the results of selected studies but also compare them with each other and establish interconnections. Full article

It is well-known that the necessary and sufficient condition for a connected graph to be unicyclic is that its omega invariant, a recently introduced graph invariant useful in combinatorial and topological calculations, is zero. This condition could be stated as the condition that the order and the size of the graph are equal. Using a recent result saying that the length of the unique cycle could be any integer between 1 and n − a₁ where a₁ is the number of pendant vertices in the graph, two explicit labeling algorithms are provided that attain these extremal values of the first and second Zagreb indices by means of an application of the well-known rearrangement inequality. When the cycle has the maximum length, we obtain the situation where all the pendant vertices are adjacent to the support vertices, the neighbors of the pendant vertices, which are placed only on the unique cycle. This makes it easy to calculate the second Zagreb index, as the contribution of the pendant edges to such indices is fixed, implying that we can only calculate these indices for the edges on the cycle. Full article

This paper investigates the existence and uniqueness of bounded nonoscillatory solutions for two classes of m-th-order nonlinear neutral differential equations that incorporate both discrete and distributed delays. By applying Banach’s fixed-point theorem, we establish sufficient conditions under which such solutions exist. The results extend and generalize previous works by relaxing assumptions on the nonlinear terms and accommodating a wider range of feedback structures, including positive, negative, bounded, and unbounded cases. The mathematical framework is unified and applicable to a broad class of problems, providing a comprehensive treatment of neutral equations beyond the first or second order. To demonstrate the practical relevance of the theoretical findings, we analyze a delayed temperature control system as an application and provide numerical simulations to illustrate nonoscillatory behavior. This paper concludes with a discussion of analytical challenges, limitations of the numerical scope, and possible future directions involving stochastic effects and more complex delay structures. Full article

In this paper, we study a geometric framework for second-order differential systems arising in classical and relativistic mechanics. For this class of systems, we derive necessary and sufficient conditions for their Lagrangian description. The main objectives of this work are to construct efficient structure-preserving variational integrators in a variational framework. To achieve this, we develop new variational integrators through Lagrangian splitting and prove their equivalence to composition methods. We display the superiority of the newly derived numerical methods for the Kepler problem and provide rigorous error estimates by analysing the Laplace–Runge–Lenz vector. The framework provides tools applicable to geometric numerical integration of both ordinary and partial differential equations. Full article

In this paper, we propose an implicit finite difference scheme for a wave equation with strong damping and a discrete delay term. Although the scheme is implicit, the use of second-order finite difference approximations for the strong damping term in both space and time prevents it from being unconditionally stable. A sufficient condition for the asymptotic stability of the scheme is established by applying the Jury stability criterion to show that all roots of the characteristic polynomial associated with the resulting linear recurrence lie strictly inside the unit disk. This stability condition is derived under an appropriate constraint that links the time and space discretization steps with the damping and delay parameters. A numerical example is provided to illustrate the decay behavior of the scheme and confirm the theoretical findings. Full article