Theory Of Equations Research Articles

Effect of Food Storage Conditions on Shelf-Life in Uganda

Purpose: The aim of the study was to investigate effect of food storage conditions on shelf-life in Uganda
 Methodology: This study adopted a desk methodology. A desk study research design is commonly known as secondary data collection. This is basically collecting data from existing resources preferably because of its low cost advantage as compared to a field research. Our current study looked into already published studies and reports as the data was easily accessed through online journals and libraries.
 Findings: The shelf-life of food products is influenced by factors like temperature, humidity, and microbial activity, making proper food storage crucial for combating food spoilage and waste, especially in regions with high food insecurity. A World Bank survey highlighted that low access to essential goods was primarily due to financial constraints and rising prices, with a significant portion of the population experiencing food insecurity. Recent developments in food storage include the use of natural antimicrobials, nanotechnology applications, advanced pathogen detection methods, improved storage management practices, and biotechnological processes for waste conversion. These advancements aim to extend food product shelf life, reduce spoilage, enhance food safety, and contribute to food security in Uganda.
 Unique Contribution to Theory, Practice and Policy: Arrhenius equation theory, water activity theory & oxidation theory may be used to anchor future studies on effect of food storage conditions on shelf-life in Uganda. Create user-friendly, informative food labels that clearly highlight allergen information and provide consumer-friendly guidance on reading labels. Mandate standardized allergen labeling formats and allocate funding for public awareness campaigns on allergen safety.

Research of rigid-flexible coupling dynamics model for riser-LMRP/BOPs-wellhead system

The deepwater drilling riser system is the most vulnerable part of the offshore drilling operation. Understanding its dynamic response under complex marine environment is crucial for ensuring drilling safety. However, the coupling mechanism between the riser and LMRP/BOPs is not well understood in existing analysis models of riser system dynamic response. In this paper, a theoretical model for the rigid-flexible coupling dynamics of multi-scale riser-LMRP/BOPs-wellhead system is proposed to reveal the coupling mechanism between the riser and LMRP/BOPs. Considering the characteristics of flexible riser and rigid LMRP/BOPs as well as the nonlinear coupling effect between conductors and soil, a rigid-flexible coupling dynamics model of the riser-LMRP/BOPs-wellhead system is established based on the theory of rigid-flexible coupling dynamics and Lagrange equation, which is numerically solved by the Newmark method. To verify the correctness of the proposed model, a simulation model of the riser-LMRP/BOPs-wellhead system is applied, which is modelled by the combination of pipe and mass elements. The research results demonstrate that the numerical results of the proposed theoretical model agree with the simulation results of the coupling system, thus verifying the correctness of the proposed model and revealing the rigid-flexible coupling mechanism between the riser and LMRP/BOPs.

Problem of Determining the Density of Sources in a Multidimensional Heat Equation with the Caputo Time Fractional Derivative

In this paper, we propose a new formula for representing the solution of the third initial-boundary value problem for multidimensional fractional heat equation with the Caputo derivative. This formula is obtained by the continuation method used in the theory of partial differential equations with integer derivatives. The Green’s function of the problem is also constructed in terms of the Fox H- function. Involving the results of solving a direct problem and the overdetermination condition, a uniqueness theorem for the definition of the spatial part of the multidimensional source function is proved.

Periodic solutions to a class of quasi-variational evolution equations

We study a time-periodicity problem for a class of abstract nonlinear evolution equations associated with subdifferential operators depending on both time and the unknown. Assuming time-periodicity for the subdifferential operator, we prove the existence of a periodic solution using the abstract theory of time-dependent subdifferential evolution equations and its generalization. We provide application examples for quasilinear parabolic variational inequalities with time-periodic constraints of non-local time-delay or memory type depending on the unknown.

Fitting quantum noise models to tomography data

The presence of noise is currently one of the main obstacles to achieving large-scale quantum computation. Strategies to characterise and understand noise processes in quantum hardware are a critical part of mitigating it, especially as the overhead of full error correction and fault-tolerance is beyond the reach of current hardware. Non-Markovian effects are a particularly unfavourable type of noise, being both harder to analyse using standard techniques and more difficult to control using error correction. In this work we develop a set of efficient algorithms, based on the rigorous mathematical theory of Markovian master equations, to analyse and evaluate unknown noise processes. In the case of dynamics consistent with Markovian evolution, our algorithm outputs the best-fit Lindbladian, i.e., the generator of a memoryless quantum channel which best approximates the tomographic data to within the given precision. In the case of non-Markovian dynamics, our algorithm returns a quantitative and operationally meaningful measure of non-Markovianity in terms of isotropic noise addition. We provide a Python implementation of all our algorithms, and benchmark these on a range of 1- and 2-qubit examples of synthesised noisy tomography data, generated using the Cirq platform. The numerical results show that our algorithms succeed both in extracting a full description of the best-fit Lindbladian to the measured dynamics, and in computing accurate values of non-Markovianity that match analytical calculations.

Laplace transformations and sine-Gordon type integrable PDE

It is well known that the Laplace cascade method is an effective tool for constructing solutions to linear equations of hyperbolic type, as well as nonlinear equations of the Liouville type. The connection between the Laplace method and soliton equations of hyperbolic type remains less studied. The article shows that the Laplace cascade also has important applications in the theory of hyperbolic equations of the soliton type. Laplace’s method provides a simple way to construct such fundamental objects related to integrability theory as the recursion operator, the Lax pair and Dubrovin-type equations, allowing one to find algebro-geometric solutions. As an application of this approach, previously unknown recursion operators and Lax pairs are found for two nonlinear integrable equations of the sine-Gordon type.

Non-Lorentzian IIB supergravity from a polynomial realization of SL(2, ℝ)

We derive the action and symmetries of the bosonic sector of non-Lorentzian IIB supergravity by taking the non-relativistic string limit. We find that the bosonic field content is extended by a Lagrange multiplier that implements a restriction on the Ramond-Ramond fluxes. We show that the SL(2, ℝ) transformation rules of non-Lorentzian IIB supergravity form a novel, nonlinear polynomial realization. Using classical invariant theory of polynomial equations and binary forms, we will develop a general formalism describing the polynomial realization of SL(2, ℝ) and apply it to the special case of non-Lorentzian IIB supergravity. Using the same formalism, we classify all the relevant SL(2, ℝ) invariants. Invoking other bosonic symmetries, such as the local boost and dilatation symmetry, we show how the bosonic part of the non-Lorentzian IIB supergravity action is formed uniquely from these SL(2, ℝ) invariants. This work also points towards the concept of a non-Lorentzian bootstrap, where bosonic symmetries in non-Lorentzian supergravity are used to bootstrap the bosonic dynamics in Lorentzian supergravity, without considering the fermions.

Optimal control strategies for water, sanitation, and hygiene in mitigating spread of waterborne diseases

Improving access to water, sanitation and hygiene (WASH) can help to eliminate the root cause of waterborne disease transmission. WASH has the potential to function as a sustained and effective mechanism for controlling enteric diarrheal disease (EDD) over the long term. To address this question, we formulate a mathematical model to study the impact of WASH services on reducing the transmission of waterborne diseases. The model is analyzed using the stability theory of differential equations in order to determine the threshold condition in disease control. We utilize optimal control theory to find the right balance in WASH interventions, ensuring a decrease in waterborne disease over a specific planning period. The total number of EDD cases is minimized when there are specific financial restrictions. To analyze the outcomes, we employed numerical simulations and conducted a sensitivity analysis on different weights in the cost index. Furthermore, we compared the numerical simulations of the optimal solutions and performed multiple regression analyses to gain insights into the impact of control strategies. Our findings reveal that wastewater and sewage treatment (WST) control has the most significant impact. When multiple controls are necessary, WST and drinking water supply (DWS) control provide the most effective combination. These results have significant implications for controlling infectious diseases, especially in developing countries where budgets are typically limited. Implementing these strategies could potentially reduce disease transmission and improve public health outcomes.

On the solutions of universal differential equation

The objective of this work is to give expressions for solutions of universal differential equation and finally, as application, provides the unique grouplike solution, by dévissage, of Knizhnik-Zamolodchikov equation satisfying asymptotic conditions, i.e. solution of KZn can be obtained using solution of KZ n−1 and the noncommutative generating series of hyperlogarithms. These expressions are obtained using the algebraic combinatorics on noncommutative formal series with holomorphic coefficients and a Picard-Vessiot theory of noncommutative differential equations.

Professor Alexandru Șubă on his 70th birthday

Alexandru Șubă is University Professor, Doctor Habilitatus in Mathematical and Physical Sciences. He is a Moldovan mathematician and a remarkable leader of the Moldovan School of Differential Equations, who contributed a lot to the qualitative theory of differential equations and to the education of new generations of highly-qualified specialists. On December 2, 2023, Professor Alexandru Șubă celebrated his 70th anniversary.

Professor Alexandru Șubă on his 70th birthday

Alexandru Șubă is University Professor, Doctor Habilitatus in Mathematical and Physical Sciences. He is a Moldovan mathematician and a remarkable leader of the Moldovan School of Differential Equations, who contributed a lot to the qualitative theory of differential equations and to the education of new generations of highly-qualified specialists. On December 2, 2023, Professor Alexandru Șubă celebrated his 70th anniversary.

The Volterra Theory of Integro-Differential Equations

The Volterra Theory of Integro-Differential Equations

Application of Lyapunov–Poincaré method of small parameter for Nash and Berge equilibrium designing in one differential two-player game

The Poincaré small parameter method is actively used in celestial mechanics, as well as in the theory of differential equations and in its important section called optimal control. In this paper, the mentioned method is used to construct an explicit form of Nash and Berge equilibrium in a differential positional game with a small influence of one of the players on the rate of change of the state vector.

Mean-variance reinsurance and asset liability management with common shock via non-Markovian stochastic factors

This paper explores a reinsurance and asset liability management problem in a factor model with dependent risks, considering economic factors as non-Markovian processes impacting the appreciation rate, volatility, and value of liabilities. It encompasses various stochastic volatility (SV) models like Hull-White, Heston, 3/2, and 4/2 models as special cases. The model addresses dependent risks through a common shock in claim number processes. The insurer's aim is to minimize variance in terminal net wealth while achieving a certain expected terminal net wealth, balancing reinsurance, new business, and asset allocation. The paper employs linear-quadratic (LQ) control and backward stochastic differential equation (BSDE) theory to derive both the efficient strategy and the efficient frontier. To illustrate our results, numerical examples are provided in two special cases, the 3/2 and 4/2 SV models.

Applicability of a central force water model to study adsorption in disordered hydrophobic matrices—replica Ornstein–Zernike theory

A simple central force water model to study adsorption in random Lennard-Jones-like matrices has been studied using the replica Ornstein–Zernike integral equation theory in hypernetted-chain (HNC) approximation and in HNC+bridge approximation. The structure of water in obstacle matrices of different sizes was studied, showing that the model appropriately accounts for the hydrophobic hydration. By calculating the chemical potential of water in the model adsorbent, we have constructed the adsorption isotherm. Except for the cases of highly dispersed matrices, water gets excluded from the crowded hydrophobic environment, as expected experimentally.

Simulation of Colloidal Dispersion of Spherical Particles Interacting Via a Linear Combination of Dispersive and Screened Yukawa Potential

We have considered a two-dimensional colloidal dispersion of spherical particles interacting via a linear combination of Hamaker type dispersive potential and screened Yukawa potential. We have compared the pair correlation functions (g(r)) calculated from isothermal isochoric (NVT) Monte Carlo simulation with the PCF obtained by solving PercusYevick (PY) integral equation theory, at six values of reduced densities ranging from 0.03 to 0.11, keeping the relative strength of two types of potential fixed. Structure factors are calculated by Fourier transform of total PCF (h(r)).

Approximation of curve-based sleeve functions in high dimensions

Sleeve functions are generalizations of the well-established ridge functions that play a major role in the theory of partial differential equation, medical imaging, statistics, and neural networks. Where ridge functions are non-linear, univariate functions of the distance to hyperplanes, sleeve functions are based on the squared distance to lower-dimensional manifolds. The present work is a first step to study general sleeve functions by starting with sleeve functions based on finite-length curves. To capture these curve-based sleeve functions, we propose and study a two-step method, where first the outer univariate function—the profile—is recovered, and second, the underlying curve is represented by a polygonal chain. Introducing a concept of well-separation, we ensure that the proposed method always terminates and approximates the true sleeve function with a certain quality. Investigating the local geometry, we study an inexact version of our method and show its success under certain conditions.

Limit Directions of Julia Sets of Entire Functions and Complex Differential Equations

The limiting directions of Julia sets of infinite order entire functions are studied by combining the theory of complex dynamic system and the theory of complex differential equations, in which the lower bound of the measure of limiting direction of Julia set of entire solutions of complex differential equations is obtained.

Almost Automorphic Solutions to Nonlinear Difference Equations

In the present work, we concentrate on a certain class of nonlinear difference equations and propose sufficient conditions for the existence of their almost automorphic solutions. In our analysis, we invert an appropriate mapping and obtain the main existence outcomes by utilizing the contraction mapping principle. As the second objective of the manuscript, we reconsider one of the landmark results, namely the Bohr–Neugebauer theorem, in the qualitative theory of dynamical equations, and we investigate the relationship between the existence of almost automorphic solutions and the existence of solutions with a relatively compact range for the proposed difference equation type. Thus, we provide a discrete counterpart of the Bohr–Neugebauer theorem due to the almost automorphy notion under some technical conditions.

On the Monotonic and Asymptotic Properties of Positive Solutions to Third-Order Neutral Differential Equations and Their Effect on Oscillation Criteria

The monotonic properties of positive solutions to functional differential equations of the third order are examined in this paper. It is generally known that by optimizing the relationships between a solution and its corresponding function, as well as its derivatives, one can improve the oscillation criterion for neutral differential equations. Based on this, we obtain new relationships and inequalities and test their effect on the oscillation parameters of the studied equation. To obtain the oscillation parameters, we used Riccati techniques and comparison with lower-order equations. Finally, the progress achieved in oscillation theory for third-order equations was measured by comparing our results with previous relevant results.