Search Results (117)

We present a comprehensive mathematical analysis of a within-host dual-target HIV dynamics model, which explicitly incorporates the virus’s interactions with its two primary cellular targets: CD4⁺ T cells and macrophages. The model is formulated as a system of five nonlinear delay differential equations, integrating three distinct discrete time delays to account for critical intracellular processes such as the development of productively infected cells and the maturation of new virions. We first establish the model’s biological well-posedness by proving the non-negativity and boundedness of solutions, ensuring all trajectories remain within a feasible region. The basic reproduction number, ${\mathcal{R}}_0^d$, is derived using the next-generation matrix method and serves as a sharp threshold for disease dynamics. Analytical results demonstrate that the infection-free equilibrium is globally asymptotically stable (GAS) when ${\mathcal{R}}_0^d\le 1$, guaranteeing viral eradication from any initial state. Conversely, when ${\mathcal{R}}_0^d>1$, a unique endemic equilibrium emerges and is proven to be GAS, representing a state of chronic infection. These global stability properties are rigorously established for both the non-delayed and delayed systems using carefully constructed Lyapunov functions and functionals, coupled with LaSalle’s invariance principle. A sensitivity analysis identifies viral production rates ($p_1,p_2$) and infection rates (${\beta }_1,{\beta }_2$) as the most influential parameters on ${\mathcal{R}}_0^d$, while the viral clearance rate (m) and maturation delay (${\tau }_3$) have a suppressive effect. The model is extended to evaluate antiretroviral therapy (ART), revealing a critical treatment efficacy threshold ${ϵ}^{cr}$ required to suppress the virus. Numerical simulations validate all theoretical findings and further investigate the dynamics under varying treatment efficacies and maturation delays, highlighting how these factors can shift the system from persistence to clearance. This study provides a rigorous mathematical framework for understanding HIV dynamics, with actionable insights for designing targeted treatment protocols aimed at achieving viral suppression. Full article

This paper develops several new generalizations of Gronwall–Bellman–Bihari-type integral inequalities. We establish three novel integral inequalities that extend classical results to more complex settings, including integrals with mixed linear and nonlinear terms, delayed (retarded) arguments, and general integral kernels. In the preliminaries, we review known Gronwall–Bellman–Bihari inequalities and useful lemmas. In the main results, we present at least three new theorems. The first theorem provides an explicit bound for solutions of an integral inequality involving a separable kernel function and a nonlinear (Bihari-type) term, significantly extending the classical Bihari inequality. The second theorem addresses integral inequalities with delayed arguments, showing that the delay does not enlarge the growth bound compared to the non-delay case. The third theorem handles inequalities with combined linear and nonlinear terms; using a monotone iterative technique, we prove the existence of a maximal solution that bounds any solution of the inequality. Rigorous proofs are given for all main results. In the Applications section, we illustrate how these inequalities can be applied to deduce qualitative properties of differential equations. As an example, we prove a uniqueness result for an initial value problem with a non-Lipschitz nonlinear term using our new inequalities. The paper concludes with a summary of results and a brief discussion of potential further generalizations. Our results provide powerful tools for researchers to obtain a priori bounds and uniqueness criteria for various differential, integral, and functional equations. It is important to note that the integral inequalities established in this work provide bounds on the solution under the assumption of its existence on the considered interval $[t_0,T]$. For nonlinear differential or integral equations where the nonlinearity $F$ fails to be Lipschitz continuous, solutions may develop movable singularities (blow-up) in finite time. The bounds derived from our Gronwall–Bellman–Bihari-type inequalities are valid only on the maximal interval of existence of the solution. Determining the region where solutions are guaranteed to be free of such singularities is a separate and profound problem, often requiring additional techniques such as the construction of Lyapunov functions or the use of differential comparison principles. The primary contribution of this paper is to provide sharp estimates and uniqueness criteria within the domain where a solution is known to exist a priori. Full article

This paper develops a robust portfolio optimization framework that integrates Weighted Shannon Entropy (WSE) into the classical mean–variance paradigm, offering a distribution-free approach to diversification suited for volatile and heavy-tailed markets. While traditional variance-based models are highly sensitive to estimation errors and instability in covariance structures—issues that are particularly acute in cryptocurrency markets—entropy provides a structural mechanism for mitigating concentration risk and enhancing resilience under uncertainty. By incorporating informational weights that reflect asset-specific characteristics such as volatility, market capitalization, and liquidity, the WSE model generalizes classical Shannon entropy and allows for more realistic, data-driven diversification profiles. Analytical solutions derived from the maximum entropy principle and Lagrange multipliers yield exponential-form portfolio weights that balance expected return, variance, and diversification. The empirical analysis examines two case studies: a four-asset cryptocurrency portfolio (BTC, ETH, SOL, and BNB) over January–March 2025, and an extended twelve-asset portfolio over April 2024–March 2025 with rolling rebalancing and proportional transaction costs. The results show that WSE portfolios achieve systematically higher entropy scores, more balanced allocations, and improved downside protection relative to both equal-weight and classical mean–variance portfolios. Risk-adjusted metrics confirm these improvements: WSE delivers higher Sharpe ratios and less negative Conditional Value-at-Risk (CVaR), together with reduced overexposure to highly volatile assets. Overall, the findings demonstrate that Weighted Shannon Entropy offers a transparent, flexible, and robust framework for portfolio construction in environments characterized by nonlinear dependencies, structural breaks, and parameter uncertainty. Beyond its empirical performance, the WSE model provides a theoretically grounded bridge between information theory and risk management, with strong potential for applications in algorithmic allocation, index construction, and regulatory settings where diversification and stability are essential. Moreover, the integration of informational weighting schemes highlights the capacity of WSE to incorporate both statistical properties and market microstructure signals, thereby enhancing its practical relevance for real-world investment decision-making. Full article

This review examines scientific and engineering strategies for adapting bituminous and asphalt concrete materials to the highly diverse climates of Central Asia. The region’s sharp gradients—from arid lowlands to cold mountainous zones—expose pavements to thermal fatigue, photo-oxidative aging, freeze–thaw cycles, and wind abrasion. Existing climatic classifications and principles for designing thermally and radiatively resilient pavements are summarized. Special emphasis is placed on linking binder morphology, rheology, and climate-induced transformations in composite bituminous systems. Advanced characterization methods—including dynamic shear rheometry (DSR), multiple stress creep recovery (MSCR), bending beam rheometry (BBR), and linear amplitude sweep (LAS), supported by FTIR, SEM, and AFM—enable quantitative correlations between phase composition, oxidative chemistry, and mechanical performance. The influence of polymeric, nanostructured, and biopolymeric modifiers on stability and durability is critically assessed. The review promotes region-specific material design and the use of integrated accelerated aging protocols (RTFOT, PAV, UV, freeze–thaw) that replicate local climatic stresses. A climatic rheological profile is proposed as a unified framework combining climate mapping with microstructural and rheological data to guide the development of sustainable and durable pavements for Central Asia. Key rheological indicators—complex modulus (G*), non-recoverable creep compliance (Jnr), and the BBR m-value—are incorporated into this profile. Full article

Deep clustering aims to discover meaningful data groups by jointly learning representations and cluster probability distributions. Yet existing methods rarely consider the underlying information characteristics of these distributions, causing ambiguity and redundancy in cluster assignments, particularly when different augmented views are used. To address this issue, this paper proposes a novel information-principled deep clustering framework for learning invariant, redundancy-reduced, and discriminative cluster probability distributions, termed ICIRD. Specifically, ICIRD is built upon three complementary modules for cluster probability distributions: (i) conditional entropy minimization, which increases assignment certainty and discriminability; (ii) inter-cluster mutual information minimization, which reduces redundancy among cluster distributions and sharpens separability; and (iii) cross-view mutual information maximization, which enforces semantic consistency across augmented views. Additionally, a contrastive representation mechanism is incorporated to provide stable and reliable feature inputs for the cluster probability distributions. Together, these components enable ICIRD to jointly optimize both representations and cluster probability distributions in an information-regularized manner. Extensive experiments on five image benchmark datasets demonstrate that ICIRD outperforms most existing deep clustering methods, particularly on fine-grained datasets such as CIFAR-100 and ImageNet-Dogs. Full article

In this paper, we introduce and investigate new subclasses of analytic bi-univalent functions defined via Caputo fractional derivatives with boundary rotation constraints. Utilizing the generalized operator ${\mathcal{C}}_{\mathsf{ȷ}}^{\varrho }$, which encompasses and extends classical operators such as the Salagean differential operator and the Libera–Bernardi integral operator, we establish sharp coefficient estimates for the initial Taylor Maclaurin coefficients of functions within these subclasses. Furthermore, we derive Fekete–Szegö-type inequalities that provide bounds on the second and third coefficients and their linear combinations involving a real parameter. Our approach leverages subordination principles through analytic functions associated with the classes ${\mathcal{T}}_{\varsigma }\left(\xi \right)$ and ${\mathcal{R}}_{\Omega }^{\mathsf{ȷ},\varrho }(\vartheta ,\varsigma ,\xi )$, allowing a unified treatment of fractional differential operators in geometric function theory. The results generalize several known cases and open avenues for further exploration in fractional calculus applied to analytic function theory. Full article

We have investigated the evolution of CDW states and structural phases in a Cu-deficient Cu_1-δTe (δ = 0.016) by employing high-pressure experiments and first-principles calculations. Raman scattering results reveal that the vulcanite structure at ambient pressure starts to change into the Cu-deficient rickardite (r-CuTe) structure from 6.7 GPa, which then becomes fully stabilized above 8.3 GPa. Resistivity data show that T_CDW1 (≈333 K) is systematically suppressed under high pressure, reaching zero at 5.9 GPa. In the pressure range of 5.2–8.2 GPa, a sharp resistivity drop due to superconductivity occurs at the onset temperature T_C = ~2.0–3.2 K. The maximum T_C = 3.2 K achieved at 5.6 GPa is clearly higher than that of CuTe (2.3 K), suggesting the importance of charge fluctuation in the vicinity of CDW suppression. At 7.5 GPa, another resistivity anomaly appears due to the emergence of a second CDW (CDW2) ordering at T_CDW2 = ~176 K, which exhibits a gradual increase to ~203 K with pressure increase up to 11.3 GPa. First-principles calculations on the Cu-deficient Cu₁₁Te₁₂ with the r-CuTe structure show that including on-site Coulomb repulsion is essential for incurring an unstable phonon mode relevant for stabilizing the CDW2 order. These results point out the important role of charge fluctuation in optimizing the pressure-induced superconductivity and that of Coulomb interaction in creating the competing CDW order in the Cu-deficient CuTe system. Full article

In the accurate calculation of the temperature rise and hot spots of transformer windings, considering the inter-turn insulation will lead to a sharp increase in the workload of detailed modeling and a large number of mesh refinements. To address this issue, this paper proposes a calculation method for the equivalent thermal conductivity based on the minimum thermal resistance principle. This method can accurately calculate the equivalent thermal conductivities in the axial and radial directions of the windings. By using the disk windings model under the equivalent thermal conductivity, a temperature field analysis is performed on the actual windings with inter-turn insulation. To validate the method, models considering inter-turn insulation and equivalent models are constructed, and detailed analyses are performed using the empirical formula method and the equivalent method based on the minimum thermal resistance principle, respectively. By comparing the simulation results of the equivalent model and the model considering inter-turn insulation, it is found that the equivalent method based on the minimum thermal resistance principle not only significantly reduces the number of mesh elements but also achieves significantly improved accuracy in the temperature field analysis of the turn-divided model compared to the empirical formula method. Moreover, the winding temperature rise and hot spot positions before and after the equivalence are nearly identical and closer to the experimental results, demonstrating the validity of this method. Full article

The goal of this paper is to give an error analysis of a finite difference method for a time-fractional Black–Scholes equation with weakly singular solutions. The time Gerasimov-Caputo derivative is discretized by the L1 scheme on a graded mesh designed to compensate for the initial singularities, and a standard finite difference method is used for spatial discretization on a uniform mesh. A discrete comparison principle is presented for the fully discrete scheme, and stability and convergence of the scheme in maximum norm are established by constructing some appropriate barrier functions. Furthermore, an $\alpha$-robust pointwise error estimate of the fully discrete scheme on a uniform mesh is given. Finally, some numerical results are presented to show the sharpness of the error estimate. Full article

We present a study based on first-principles calculations of the vibrational and spectroscopic properties of four types of layered boron nitride (BN) polymorphs: e-BN (AA), h-BN (${\mathrm{AA}}^{\prime }$), r-BN (ABC), and b-BN (AB). By using density functional perturbation theory with van der Waals corrections, we calculate phonon frequencies and Raman/infrared (IR) activities at the $\mathsf{\Gamma }$ point and extract specific spectral fingerprints for each stack. In e-BN, we observe a sharp, isolated high-frequency $E^{\prime }$ mode at $1420.9{\mathrm{cm}}^{-1}$ that is active in both Raman and IR. For h-BN, the characteristic Raman $E_{2g}$ line occurs at $1415.5{\mathrm{cm}}^{-1}$. The out-of-plane IR-active $A_{2u}$ branch shows a mid-frequency TO/LO pair at 673.5/$806.6{\mathrm{cm}}^{-1}$, which closely matches experimental results. Rhombohedral r-BN has a strong, coincident Raman/IR high-frequency feature (E) at $1418.5{\mathrm{cm}}^{-1}$, along with a large IR LO partner at $1647.3{\mathrm{cm}}^{-1}$, consistent with observed Raman and IR signatures. Bernal b-BN displays the most complicated pattern. It combines a robust mid-frequency $A_2^{″}$ pair (TO/LO at 697.9/$803.5{\mathrm{cm}}^{-1}$) with multiple high-frequency $E^{\prime }$ modes (TO near 1416.9 and $1428.1{\mathrm{cm}}^{-1}$, each with LO counterparts). These stack-dependent Raman and IR fingerprints match existing experimental data for h-BN and r-BN and provide clear predictions for e-BN and b-BN. The results offer a consistent framework for identifying and interpreting vibrational spectra in layered $s{p}^2$ boron nitride and related materials. Full article

Quantum-enhanced machine learning, encompassing both quantum algorithms and quantum-inspired classical methods such as tensor networks, offers promising tools for extracting structure from complex, high-dimensional data. In this work, we study the training dynamics of Matrix Product State (MPS) classifiers applied to three-class problems, using both fashion MNIST and hyperspectral satellite imagery as representative datasets. We investigate the phenomenon of grokking, where generalization emerges suddenly after memorization, by tracking entanglement entropy, local magnetization, and model performance across training sweeps. Additionally, we employ information-theory tools to gain deeper insights: transfer entropy is used to reveal causal dependencies between label-specific quantum masks, while O-information captures the shift from synergistic to redundant correlations among class outputs. Our results show that grokking in the fashion MNIST task coincides with a sharp entanglement transition and a peak in redundant information, whereas the overfitted hyperspectral model retains synergistic, disordered behavior. These findings highlight the relevance of high-order information dynamics in quantum-inspired learning and emphasize the distinct learning behaviors that emerge in multi-class classification, offering a principled framework to interpret generalization in quantum machine learning architectures. Full article

The influence of back-gate (BG) bias on the breakdown voltage (BV) of lateral SOI power devices is investigated using TCAD simulations. A reference SOI-LDMOS structure with BVREF = 73.7 V, optimized based on RESURF and charge-sharing principles, is selected as the baseline for analysis. The BV response to BG bias is shown to fall into three distinct regimes: (i) a linear decrease with increasing magnitude of negative BG bias (−65 V ≤ VG2 ≤ −5 V), (ii) an invariant region where the BV reaches its maximum value (−5 V ≤ VG2 ≤ +10 V), and (iii) a sharp reduction under increasing magnitude of positive BG bias (+10 V ≤ VG2 ≤ +65 V). Qualitative analysis of impact ionization and charge distribution confirms that inversion, depletion, and accumulation conditions in the drift region govern these behaviors. Furthermore, parametric variations in drift doping, drift thickness, and buried oxide thickness reveal significant shifts in the optimum design window, with the buried oxide thickness emerging as a critical factor for ensuring robustness of BV under BG bias. These results provide valuable design guidelines for achieving stable high-voltage performance in practical SOI-LDMOS power devices. Full article

Currently, at least one third of greenhouse gas (GHG) emissions come from the agricultural sector, with meat production making a particularly significant contribution. Therefore, alongside the ongoing efforts to transform transport and cut its emissions, it is essential to adopt urgent measures that limit GHG emissions from food production, consumption and distribution. Without them, the Paris Agreement goal of net-zero GHG emissions by 2050 cannot be met, and the most severe impacts of climate change will not be avoided. In principle, lowering emissions from the global food system may appear simple, as no new technology (for example, electric cars or carbon-neutral fuels) is required to decarbonize transport. However, since meat consumption accounts for the majority of food related GHG emissions, it must be coupled with a sharp reduction in the large-scale production and consumption of animal foods. Encouragingly, a growing number of consumers already choose diets that are both healthy and environmentally sustainable. As meat reduction gains popularity in these groups, plant-based products are expanding in the marketplace, mainly in the form of snacks, pasta, pizzas and especially vegan or vegetarian burgers. Thus, almost spontaneously, components of the Westernized diet, rich in ultra-processed foods, salt, sugar and animal protein, are gradually being replaced by plant-derived nutrients that are healthier and more environmentally friendly. To accelerate this trend, legal measures could be introduced to improve the nutritional quality of widely consumed, low-nutrient snacks and to promote agricultural reforms that encourage the production of nutrient-dense legumes and pseudocereals. Full article

We revisit the Extended Uncertainty Principle (EUP) from an operational viewpoint, replacing wavefunction-based widths with apparatus-defined position constraints such as a finite slit of width $\mathrm{\Delta }x$ or a geodesic ball of radius R. Using Hermitian momentum operators consistent with the EUP algebra, we prove a sharp lower bound on the product of momentum spread and preparation size in one dimension and show that it reduces smoothly to the standard quantum limit as the deformation vanishes. We then extend the construction to dimensions two and three on spaces of constant curvature and obtain the corresponding bound for spherical confinement, clarifying its geometric meaning via an isometry to $S^2$ and $S^3$. The framework links curvature-scale effects to operational momentum floors and suggests concrete tests in diffraction, cold-atom, and optomechanical settings. Full article