Computer Science and Mathematics

Abstract: We use Random Matrix Theory to analyze the impact of COVID-19 on the correlation structure of the agricultural futures market, using daily returns for 56 futures from various countries around the world before, during, and after COVID. For each of the three time periods, we build correlation matrices of the daily returns, and we examine the matrices’ entries, eigenvalues, and eigenvectors. We find that agricultural futures exhibited stronger collective behavior during COVID than before or after it. We also find clustering based on geographic location, with there being one cluster in the West (North America, South America, Europe) and one in the East (Asia, Oceania), which show predominantly opposite-signed loadings relative to the dominant market mode; since pre-pandemic times, the East has gained weight in the market while the West has lost it. On top of regional clustering, we also find independent exchange-level clustering, where futures tend to be more correlated with futures in its same exchange than any other. Our results demonstrate how Random Matrix Theory can reveal both transient changes in collective behavior and longer-term structural patterns in an interconnected global market.

Abstract: Optimization through a discrete forward solver can introduce constitutive bias into recovered memory kernels, even when fitted trajectories appear accurate. We characterize this discretization-induced bias and assess how independent validation exposes it and nested-solver correction reduces it. A local perturbation analysis separates noise, discretization, and smooth regularization contributions to estimation error. An inverse-crime-free protocol combines independently generated observations, independent forward evaluation, and nested-grid Richardson correction. Four synthetic benchmark families comprise 5480 completed runs, with 20 paired seeds per stochastic condition. Matched-discretization controls yielded nearly exact kernel recovery despite substantial forward state errors relative to the continuous reference. Independent observations exposed systematic resolution-dependent kernel errors. In the exponential benchmark, corrected kernel error decreased at approximately order 1.89, compared with 1.14 for coarse inversion; the manufactured KWW benchmark gave a corrected endpoint rate of approximately 1.54. Correction also improved multiscale and constrained nonparametric recovery, but benefits diminished under noise, sparsity, and misspecification. Accurate Prony kernel recovery coexisted with substantial fast-mode parameter error. Raw forward defects did not reliably estimate kernel error, and fractional and numerical correction orders differed in the tested scheme. These findings support independent forward validation and numerical-convergence assessment as essential components of credible memory-kernel discovery.

Abstract: The Al-Refai--Darus criterion guarantees univalence of a normalized function \( f \) when a weighted sum of \( |(z/f)^{(k)}(0)| \), \( 2\le k\le n-1 \), and of \( \sup|(z/f)^{(n)}| \) does not exceed \( 1 \). For \( n\ge3 \) we study the subclass \( \mathcal C_n \) with \( a_2=\dots=a_n=0 \), in which the whole allowance goes to the \( n \) th derivative. The map \( f\mapsto(z/f)^{(n)} \) is a bijection of \( \mathcal C_n \) onto a closed ball of \( H^\infty \), which turns extremal problems into problems for bounded analytic functions. We prove sharp growth, distortion, covering-radius and coefficient bounds with the \( (n+j) \)-fold symmetric extremal functions \( z/(1+cz^{n+j}) \); the exact region of \( (a_{n+1},a_{n+2}) \), whose boundary is attained by M\"obius parameters written in closed form; and an exact radius for dilations of products \( f_1f_2/z \), sharp both for Aksentev's inequality and for univalence. The \( n \)-fold symmetric members of \( \mathcal C_n \) correspond to \( g(z^n) \) with \( g \) in the same ball, which gives the exact region of \( (a_{n+1},a_{2n+1}) \). For the larger class defined by \( a_2=0 \) and the criterion we obtain sharp bounds as well. The comparison with \( n \)-fold symmetric univalent functions records a gap; it is not a sharpening of known results.

Abstract: We study boundedness, stability, asymptotic stability, and robustness for the nonlinear distributed-delay equation \( x'(t) = -\int_{t-r(t)}^{t}a(t,s)g(x(s))\,ds +p(t,x(t))+f(t), \) where the delay is bounded and may vary with time. The analysis is based on a direct dissipative decomposition of the distributed-delay term together with Lyapunov and Halanay-type comparison estimates. In contrast with fixed-point approaches based on a uniform contraction condition, the present method separates the instantaneous dissipative contribution from a memory remainder controlled by the first absolute moment of the kernel. No derivative of the delay is used. We first obtain a priori bounds under an integrable growth majorant and then establish exponential asymptotic stability under a uniform dissipation-versus-memory gap. A variable-coefficient Halanay inequality is developed to treat nonuniform dissipation and yields explicit decay estimates of the form \( |x(t)| \leq \norm{\phi}_\infty \exp\left( -\eta\int_0^t\lambda(s)\,ds \right). \) State-dependent perturbations and external forcing are also included, yielding ultimate bounds and convergence under vanishing forcing. For the elementary equation \( x'(t)=-c\int_{t-r}^{t}x(s)\,ds, \) our criterion gives exponential asymptotic stability whenever \( cr^{2}<2 \), whereas the contraction condition in Burton's fixed-point result requires \( cr^{2}<1 \). Thus the Lyapunov/comparison method applies on the nonempty parameter range \( 1\leq cr^{2}<2 \) where that contraction criterion fails. The exact characteristic stability boundary for this example is \( cr^{2}=\pi^{2}/2 \), indicating the remaining gap between the present sufficient condition and the sharp linear threshold.

Abstract: This paper examines the nonlinear transient response of porous FGM sandwich beams with elastically restrained ends under thermal environments. Using a refined higher-order shear deformation theory (HSDT), two configurations are analyzed: symmetric and asymmetric cross-sections with temperature-dependent properties and varied porosity distributions. In asymmetric structures, conventional strong-form approximations omit the boundary moments caused by bending–extension coupling and thermal effects. To address this methodological gap, a multi-term weak-form Galerkin approach is developed, retaining end moments and arbitrary support locations. The formulation is rigorously validated against exact linear solutions and independent nonlinear finite element models. Results demonstrate that section symmetry dictates the validity of strong-form approximations. For asymmetric beams, ignoring thermal bending leads to an overestimation of peak deflections at elevated temperatures, with deviations amplifying when supports act at the neutral surface. Comprehensive parametric evaluations further elucidate the governing influence of end restraint, porosity, layer thickness, foundation stiffness, and initial imperfections on the dynamic response.

Abstract: This study develops a direct Hilbert--Schmidt analysis for classical and sequential conformable fractional boundary value problems arising in fixed-point formulations. For the classical problem of order \( \gamma\in(1,2] \), factorizing the Green kernel before squaring preserves a cancellation that is lost in termwise estimates. This yields the exact expression \( \mathcal H_1=(b-a)^{2\gamma}/(3\gamma(4\gamma^2-1)) \), which is finite for every \( \gamma>1 \) and shows that the apparent singularity at \( \gamma=3/2 \) in the previously used representation is removable. Combined with a uniform kernel estimate and Rus's two-metric fixed point theorem, the result extends the corresponding uniqueness criterion to the full natural range \( \gamma\in(1,2] \). We also prove that this Hilbert--Schmidt criterion is strictly less restrictive than the Banach contraction criterion throughout that interval. For the sequential conformable kernel, we derive a compact closed form for the squared Hilbert--Schmidt norm, establish the exact square-integrability threshold \( \delta>1/4 \), and determine analytically the crossover order \( \delta^*=(\sqrt{65}-5)/8 \) between the Hilbert--Schmidt and Banach-type bounds. Numerical comparisons quantify the improvement in the admissible Lipschitz constant, and a nonlinear example with \( \gamma=1.25 \) demonstrates a regime in which the Banach condition fails while the full-range two-metric criterion guarantees uniqueness. The results show that preserving cancellation in singular-looking Green kernels can materially sharpen fixed-point criteria for fractional boundary value problems.

Abstract: A recent family of methods selects the phase-space reconstruction delay \(\tau\) as the point where a symbolic entropy $H(m,\tau)$ stops growing and saturates, on the premise that this onset marks the decorrelation delay. We prove the premise structurally unsound \emph{within the pairwise-agreement class of symbolic schemes that these methods use}. The agreement symbol is invariant under complementation of the thresholded sign vector, so the effective alphabet has exactly \(2^{m-1}\) symbols and \(H(m,\tau)\in[0,m-1]\), with \(H\to m-1\) for any mixing process. Saturation is therefore an artefact of a ceiling imposed by the symbolisation rather than a property of the dynamics, and the delay read off it is the argument of the approach to a self-imposed asymptote; the law is verified to three decimal places on i.i.d.\ noise. The conclusion is specific to saturation criteria built on pairwise agreement and carries no claim about symbolic entropies of other design, such as permutation entropy, whose alphabet is not complement-degenerate. Testing the family, which comprises SEM, multiscale sample entropy, symbolic and multiscale fuzzy entropy, the C-C method, and low-pass filtered symbolic entropy (LPF-SEM), against average mutual information and false nearest neighbours on five chaotic systems at six noise levels, all with independently verified positive Lyapunov exponents, we find that on clean data LPF-SEM returns delays $1.17$--$4.69$ times the reference and carries the largest bias of the six estimators at every noise level; that the low-pass filter, \emph{doubles} the delay bias ($28.8\to56.4$ samples) rather than reducing it; that the returned delay spans a fortyfold range across the filter's own parameter grid; that the threshold which recovers the reference varies fivefold between systems and does not exist for two of five; and that the dimension output is the method's own fallback constant in $100\%$ of runs for four of five systems. The engineering outcome is counterintuitive and cuts against the theorem's practical weight: on real MFPT bearing data the comparison inverts, the most biased estimator classifying best ($0.930$) and the most accurate one worst ($0.599$). Neither the delay's accuracy nor its length explains it: a sweep at fixed dimension is flat or non-monotone, and the calibrated pair alone reproduces $88\%$ of the winner's score. Saturation-based \emph{pairwise-agreement} entropy criteria should not be used as delay estimators; where only classification accuracy is wanted, LPF-SEM may serve as a black-box feature heuristic, but its \(\tau\) is not the decorrelation delay.

Abstract: Malaria remains a major global public health challenge, with a substantial burden of morbidity and mortality concentrated in sub-Saharan Africa and other tropical and subtropical regions. The complex transmission process involving Plasmodium parasites, Anopheles mosquito vectors, and human hosts makes mathematical modeling an important tool for understanding transmission dynamics and evaluating control strategies. This review provides a comprehensive synthesis of mathematical modeling approaches for malaria transmission and control, including deterministic compartmental models, stochastic models, optimal control frameworks, spatial models, and cost-effectiveness analyses. Particular attention is given to major intervention strategies, including vector control, vaccination, antimalarial treatment, and other integrated control approaches. The review also examines the effects of seasonality, climate variability, drug and insecticide resistance, spatial heterogeneity, and human movement on malaria transmission and intervention outcomes. A bibliography-based keyword frequency analysis and word-cloud visualization are used to identify dominant research themes, followed by a comparative assessment of modeling approaches and intervention strategies. The findings highlight the importance of integrating multiple interventions with context-specific epidemiological and environmental conditions. Overall, mathematical models provide valuable support for optimizing malaria control strategies and addressing important challenges toward malaria elimination.

Abstract: We introduce and study a precise fundamental relation for a class of neutrosophic Lie hyperalgebras. The construction separates two issues which are often conflated in the literature: the classical hypercompositional fundamental relation and the neutrosophic information carried by the elements. An element is represented by a neutrosophic profile (T, I, F) ∈ [0, 1]³, and a profile-compatible relation is imposed on the elementary β-relation before taking its transitive closure. We prove a quotient theorem under an explicit strong regularity hypothesis: the quotient by the resulting relation is a well-defined ordinary Lie algebra and the canonical projection is a good hyperalgebra homomorphism. We then define a quotient-level neutrosophic Baker–Campbell–Hausdorff operation and prove its independence of representatives. In the nilpotent class-two case the formula reduces to the expected finite expression. Several examples are given, including central neutrosophic thickening of a Lie algebra, a Heisenberg-type example, and a matrix realization. Counterexamples show that profile compatibility, strong regularity, and quotient descent cannot be omitted. The resulting framework provides a precise bridge between neutrosophic hyperstructures and classical Lie theory.

Abstract: Traditional deterministic fish stock assessment methods, such as the swept-area and Kushnarenko techniques, show extreme volatility and numerical singularities under sparse data. This paper presents a multi-species stochastic Bayesian state-space algorithm that fuses heterogeneous catch data across species, years, and age cohorts into a fixed-shape NetCDF4 tensor built on a consensus reference field constructed from 8 deterministic methods, jointly models recruitment, mortality, and removal dynamics for several species through an age-structured cohort architecture, and embeds a discrete Heaviside threshold into the population-balance equations to represent age-dependent predation vulnerability. The model was fitted with the No-U-Turn Sampler in PyMC on a 10-year (2015–2024) dataset for four species in the Kapchagay Reservoir, Kazakhstan. Kapchagay was selected as a representative single-reservoir case study given the material's scope; the broader four-reservoir programme (Zhaysan, Kapchagay, Balkhash, and Lake Samarkand) involves substantially more material and is addressed in separate work. The sampler achieved robust convergence for all species (R̂ ≤ 1.0047, ESS > 750), and comparison against alternative predation specifications evaluated by leave-one-out cross-validation (LOO-CV) showed that the choice of functional form had little effect on estimated stock (within approximately 1% for two of the three alternatives) but materially affected sampler efficiency, favoring the adopted threshold formulation on computational rather than biological grounds. A temporal hold-out test showed that forecasting accuracy two to three years ahead remains substantially lower than the in-sample fit (mean absolute percentage error 59–91%), a gap not resolved by correcting an identified age-1 initialization artifact and treated here as a central, unresolved limitation. The algorithm reconciles divergent deterministic stock estimates into a single state-estimation output that may inform, but does not by itself validate, total allowable catch analysis; both the biological necessity of the predation mechanism and multi-year forecasting accuracy remain open limitations for future work.

Abstract: We introduce a unified framework connecting multi-valued group theory, hypergroup theory, neutrosophic algebra, and Lie theory. The main object of the paper is a neutrosophic Lie multigroup, namely a multi-valued group equipped with a neutrosophic state structure and a compatible infinitesimal Lie structure. The proposed construction has three levels. First, the group multiplication is replaced by a hyperoperation whose values are nonempty subsets. Second, every element is assigned a neutrosophic state describing its degrees of truth, indeterminacy, and falsity. Third, the linearized algebra generated by the multi-valued operation is equipped with a Lie bracket satisfying a neutrosophic compatibility condition. We establish basic algebraic properties, criteria for obtaining ordinary Lie groups as degenerate cases, homomorphism and quotient results, properties of neutrosophic Lie subgroups, and compatibility between hypergroup associativity and the Jacobi identity. Several explicit finite and infinite examples are constructed. We also introduce neutrosophic one-parameter families, neutrosophic adjoint actions, invariant substructures, and a tangent Lie algebra associated with a sufficiently regular neutrosophic Lie multigroup. The paper concludes with a list of problems concerning integration, representation theory, topology, and categorical formulations.

Abstract: The binary Goldbach conjecture states that every even integer greater than 2 is a sum of two primes. This paper studies the smallest prime component of such a representation. For an even integer E, Pmin(E) is defined as the smallest prime p for which E - p is also prime. BOUSSOLE-Pmin combines an ordered FIRST search with an empirical prediction of the likely boundary distance. A longitudinal reference series of 100 selected integers of the form 10^N + 2 was studied up to N = 4000. A separate frozen prediction was then tested on 2000 new integers of the form 10^N + c, using 20 values of N from 20 to 400 and 100 even offsets at each level. The predictive scale was D(E) = log(E) log log(E), with frozen levels 0.258D, 0.790D and 1.088D. Observed coverages were 51.5%, 79.4% and 85.4%. The independent median Pmin/D was 0.24893, close to the frozen median coefficient 0.258, while the upper tail was substantially heavier than predicted. The method therefore uses prediction as a search compass, not as a stopping rule. Finally, Pmin gives a direct reformulation of Goldbach: a future proof can target uniform positivity of the number of prime pairs with the smaller prime restricted to a controlled boundary window.

Abstract: Quantum search algorithms provide a quadratic speedup for a broad class of unstructured search problems. In practical settings, however, the classification of a candidate as “good” or “bad” may itself contain uncertainty, indeterminacy, or contradictory information. Neutrosophic sets provide a natural mathematical language for representing such information through independent truth, indeterminacy, and falsity degrees. In this paper we introduce a scalarization framework for neutrosophic quantum search. The central idea is to transform a neutrosophic evaluation N = (T, I, F) into a real-valued utility while preserving the distinction between truth, indeterminacy, and falsity. We introduce a parameterized family of weighted scalarization functions and establish conditions under which these functions are normalized, monotone, continuous, and order-preserving. We then define an optimization criterion for choosing scalarization parameters according to the requirements of a quantum search problem. A neutrosophic quantum oracle is modeled by assigning a neutrosophic evaluation to each computational basis state. The resulting scalarized oracle determines the effective marked-state amplitude. We derive an explicit relationship between scalarized utility and the number of amplitude-amplification iterations. Several scalarization functions, including linear, nonlinear, entropy-sensitive, and indeterminacy-penalized forms, are compared. A theoretical criterion based on discrimination, robustness, and indeterminacy sensitivity is proposed. The resulting framework provides a mathematically explicit bridge between neutrosophic decision theory and quantum amplitude amplification.

Abstract: We develop a mathematical framework for neutrosophic quantum channels by combining the operator-theoretic structure of quantum channels with single-valued neutrosophic information. A quantum channel is conventionally modeled as a completely positive tracepreserving (CPTP) linear map between operator spaces. We retain this physical core and augment it with a neutrosophic state N = (T, I, F), representing truth, indeterminacy, and falsity information associated with a quantum state or a channel description. We define neutrosophic quantum states, neutrosophic quantum channels, their composition, tensor products, Kraus representations, Choi representations, and complementary channels. Several structural results are proved, including closure under composition, a tensor-product construction, and a criterion for compatibility between the quantum and neutrosophic components. A distinction is made between the physical quantum channel and the additional neutrosophic information layer. In particular, an arbitrary neutrosophic scalar multiplying a density operator is not identified with a physical quantum operation. This distinction is essential for preserving positivity, trace normalization, and complete positivity. The resulting theory provides a rigorous mathematical framework for incorporating explicit truth, indeterminacy, and falsity information into quantum information models.

Abstract: We develop a mathematical framework for neutrosophic amplitude amplification and establish convergence results for the associated iterative process. The classical amplitude amplification procedure provides a quadratic improvement over classical repetition for searching for a good state, and its mathematical structure is based on a two-dimensional invariant subspace generated by the good and bad components of a quantum state. We extend this framework by assigning to the success event three quantities representing truth, indeterminacy, and falsity. The resulting neutrosophic amplitude is represented by a triple (T, I, F), where the three components are not required to satisfy the classical probability normalization condition. We introduce neutrosophic success amplitudes, neutrosophic amplification operators, and several notions of convergence. In particular, we prove a convergence theorem for the truth component under contractive neutrosophic perturbations and establish corresponding bounds for the indeterminacy and falsity components. We also study the ideal case, the perturbed case, and the fixed-point regime. The results reduce to the ordinary amplitudeamplification formulas when I = F = 0 and T is identified with the ordinary success probability. Examples are given to illustrate the behavior of the three components during amplification.

Abstract: Quantum computation provides algorithms that exploit superposition, interference, and entanglement to solve certain computational problems more efficiently than known classical algorithms. Two fundamental examples are Shor’s factoring algorithm and Grover’s search algorithm. In practical computational settings, however, information associated with quantum states, oracle responses, and measurements may be uncertain or indeterminate. In this paper, we introduce a mathematical framework for neutrosophic quantum algorithms in which quantum states are supplemented by three independent information components representing truth, indeterminacy, and falsity. We define neutrosophic quantum states, neutrosophic quantum measurements, neutrosophic quantum oracles, and scalarization functions. Using these concepts, we formulate neutrosophic versions of Grover’s search algorithm and Shor’s factoring algorithm. For Grover’s algorithm, the classical binary oracle is generalized to an oracle whose response may carry truth, indeterminacy, and falsity degrees. For Shor’s algorithm, neutrosophic information is incorporated into modular exponentiation, quantum Fourier transformation, measurement, and period estimation. We prove that the proposed construction contains the ordinary quantum algorithms as a special case. We also discuss complexity and indeterminacy propagation. The proposed theory is an information-theoretic mathematical extension of quantum algorithms. It is not intended to modify the physical postulates of quantum mechanics.

Abstract: Concentration polarization at the surface of ion-exchange membranes limits the rate of mass transfer and determines the energy consumption of electrodialysis. Turbulence-promoting spacers and profiling of the membrane surface are the two traditional remedies; however, they are almost always considered separately, and non-conducting spacers shade the membrane and increase the channel resistance. In this work, a two-dimensional mathematical model of ion transport in a flow-through desalination channel is developed on the basis of the coupled Nernst–Planck–Poisson and Navier–Stokes equations in the potentiodynamic mode. Using the Poisson equation instead of the local electroneutrality assumption makes it possible to account for the space-charge region and describe electroconvection "from first principles." Eight channel configurations were compared: a smooth or structured cation-exchange membrane, with or without profiled spacers placed in various positions. It is shown that the structured surface and profiled spacers act synergistically: the spacers direct the solution from the flow core toward the membrane's developed surface relief, and the overall benefit exceeds the sum of the individual effects. The combined design raises the limiting current by a factor of about 1.4, shortens the limiting-current plateau, increases the current at 1.4 V by 40–45%, provides a 35% increase of the active membrane area, a 40% reduction of concentration polarization, a 28% acceleration of desalination, a ×1.5 increase of the ion flux, and a 15% reduction of the working voltage. The main conclusion agrees with an independent 3D multiphysics study supported by experiments with physically manufactured profiled membranes.

Abstract: In the paper, we suggest a definition of the entropy of oriented fuzzy graphs, which characterizes the fuzziness of the sets of vertices and edges and the flows on the graphs. We consider the properties of the suggested entropy and its relations with the Rashevsky entropy of the crisp graphs.

Abstract: In this paper, we study discrete time consensus among a group of nodes capable of communicating with each other and equipped with arbitrary binary valued initial decisions. At each time instant, a subset of the nodes are selected for decision update and for each node, the update is made based on the majority decisions of three further independently chosen \consultation" nodes. We consider the near-critical case where the bias towards the majority decision is very small and a function of the total number of nodes and study the evolution of bias as it progresses through each of the three regimes: small, medium and high. In each case, we obtain high probability estimates for the bias or the minority node fraction to change by a constant factor and finally combine these bounds to establish the overall consensus time. We demonstrate that the overall consensus time is of the same order as the generalized coupon collector problem with high probability, i.e., with probability converging to one as the number of nodes becomes arbitrarily large.

Abstract: Hemoglobin subunit beta (HBB) is essential for balanced hemoglobin assembly, and mutations in its short coding sequence cause severe hemoglobinopathies such as β-thalassemia. Pathogenic variants are not randomly distributed but cluster into mutation regions, forming hotspots that influence structural stability and disease progression. To characterize mutation regions, this study shifts focus from isolated point mutations to contiguous hotspot neighborhoods, defining 26 regions from 109 pathogenic mutation sites in the HBB human protein. Quantitative analyses of amino acid frequencies, polarity distributions, hydropathy n-grams, and intrinsic disorder profiles reveal that hotspots are compositionally robust yet unique: they preserve local stability through overlapping subsequences, while also exhibiting recurrence of signatures in distant non-overlapping fragments. Importantly, sequence homology analysis confirmed no relationship among hotspots, underscoring their uniqueness as ordered arrangements rather than simple sequence similarities. These findings highlight the power of quantitative hotspot analysis in uncovering hidden organizational principles of the HBB human sequence, with implications for predictive diagnostics and future comparative studies across globin families and clinical mutational spectra.