Solving a parabolic PDE with nonlocal boundary conditions using the Sinc method

In this paper, the problem of solving the parabolic partial differential equations subject to given initial and nonlocal boundary conditions is considered. We change the problem to a system of Volterra integral equations of convolution type. By using Sinc-collocation method, the resulting integral equations are replaced by a system of linear algebraic equations. The convergence analysis is included, and it is shown that the error in the approximate solution is bounded in the infinity norm by the condition number of the coefficient matrix multiplied by a factor that decays exponentially with the size of the system. Some examples are considered to illustrate the ability of this method.     

Cryptography in Hierarchical Coded Caching: System Model and Cost Analysis

The idea behind network caching is to reduce network traffic during peak hours via transmitting frequently-requested content items to end users during off-peak hours. However, due to limited cache sizes and unpredictable access patterns, this might not totally eliminate the need for data transmission during peak hours. Coded caching was introduced to further reduce the peak hour traffic. The idea of coded caching is based on sending coded content which can be decoded in different ways by different users. This allows the server to service multiple requests by transmitting a single content item. Research works regarding coded caching traditionally adopt a simple network topology consisting of a single server, a single hub, a shared link connecting the server to the hub, and private links which connect the users to the hub. Building on the results of Sengupta et al. (IEEE Trans. Inf. Forensics Secur., 2015), we propose and evaluate a yet more complex system model that takes into consideration both throughput and security via combining the mentioned ideas. It is demonstrated that the achievable rates in the proposed model are within a constant multiplicative and additive gap with the minimum secure rates.     

MOF-Based Mycotoxin Nanosensors for Food Quality and Safety Assessment through Electrochemical and Optical Methods

Mycotoxins in food are hazardous for animal and human health, resulting in food waste and exacerbating the critical global food security situation. In addition, they affect commerce, particularly the incomes of rural farmers. The grave consequences of these contaminants require a comprehensive strategy for their elimination to preserve consumer safety and regulatory compliance. Therefore, developing a policy framework and control strategy for these contaminants is essential to improve food safety. In this context, sensing approaches based on metal-organic frameworks (MOF) offer a unique tool for the quick and effective detection of pathogenic microorganisms, heavy metals, prohibited food additives, persistent organic pollutants (POPs), toxins, veterinary medications, and pesticide residues. This review focuses on the rapid screening of MOF-based sensors to examine food safety by describing the main features and characteristics of MOF-based nanocomposites. In addition, the main prospects of MOF-based sensors are highlighted in this paper. MOF-based sensing approaches can be advantageous for assessing food safety owing to their mobility, affordability, dependability, sensitivity, and stability. We believe this report will assist readers in comprehending the impacts of food jeopardy exposure, the implications on health, and the usage of metal-organic frameworks for detecting and sensing nourishment risks.     

Preparation and photodeposition of Fe–S/TiO2@PEG nanoparticles for methylene blue and Evans blue

Here, iron, sulfur and poly(ethylene glycol) doping to TiO₂ nanoparticles toward the effect on photodegradation of the methylene blue (MB) and Evans blue (EB) was investigated. The present nanostructured photocatalysts displayed notable catalytic activity for the decomposition of colorants in water under visible light irradiation. The photocatalytic reaction constants of different samples were determined for EB and MB to be 0.007, 0.008, 0.009 and 0.01, 0.026, 0.021 1/min, respectively. The values of optical band gap for pure TiO₂, Fe–S/TiO₂, and Fe–S/TiO₂@PEG were estimated to be 3.21, 2.75, and 2.81, respectively. X-ray analysis was performed and correlated with BET, Fe–SEM, and TEM results. The lattice structure was studied by W–H (Williamson–Hall) and H–W (Halder–Wagner) methods with a different assumption in the isotropic and homogenous nature. The results revealed that the SSP model shows the most accuracy and adaption to determine the lattice structure.

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Stability of a mixed additive and cubic functional equation in several variables in non-Archimedean spaces

Consider the functional equation ${\Im_1(f ) = \Im_2(f )\,\,(\Im)}$ in a certain general setting. A function g is an approximate solution of ${(\Im)}$ if ${\Im_1(g)}$ and ${\Im_2(g)}$ are close in some sense. The Ulam stability problem asks whether or not there is a true solution of ${(\Im)}$ near g. In this paper, we achieve the general solution and the stability of the following functional equation $$\begin{array}{ll}f\left(\sum\limits^{n}_{i=1}x_{i} \right)+f\left(\sum\limits^{n-1}_{i=1} x_{i}-x_{n} \right)\\\quad=2f\left(\sum\limits^{n-1}_{i=1}x_{i} \right)+\sum\limits^{n-1}_{i=1}(f(x_{i}+x_{n}) +f(x_{i}-x_{n})-2f(x_{i}))\end{array}$$ for all x _i (i =? 1,2, . . . , n), in non-Archimedean spaces.     

Application of Sinc-collocation method for solving an inverse problem

In this article, the identification of an unknown time-dependent source term in an inverse problem of parabolic type with nonlocal boundary conditions is considered. The main approach is to change the inverse problem to a system of Volterra integral equations. The resulting integral equations are convolution-type, which by using Sinc-collocation method, are replaced by a system of linear algebraic equations. The convergence analysis is included, and it is shown that the error in the approximate solution is bounded in the infinity norm by the norm of the inverse of the coefficient matrix multiplied by a factor that decays exponentially with the size of the system. To show the efficiency of the present method, an example is presented. The method is easy to implement and yields very accurate results.     

From Random Numbers to Random Objects

Many security-related scenarios including cryptography depend on the random generation of passwords, permutations, Latin squares, CAPTCHAs and other types of non-numerical entities. Random generation of each entity type is a different problem with different solutions. This study is an attempt at a unified solution for all of the mentioned problems. This paper is the first of its kind to pose, formulate, analyze and solve the problem of random object generation as the general problem of generating random non-numerical entities. We examine solving the problem via connecting it to the well-studied random number generation problem. To this end, we highlight the challenges and propose solutions for each of them. We explain our method using a case study; random Latin square generation.     

Can restrictions on redemption timing boost profitability of loyalty programs in competitive environments?

Computational Management Science - This research investigates whether it is beneficial for competing firms offering loyalty programs (LPs) to restrict the reward redemption time. We develop a...     

Pore-Scale Network Modeling of Three-Phase Flow Based on Thermodynamically Consistent Threshold Capillary Pressures. I. Cusp Formation and Collapse

We present a pore-scale network model of two- and three-phase flow in disordered porous media. The model reads three-dimensional pore networks representing the pore space in different porous materials. It simulates wide range of two- and three-phase pore-scale displacements in porous media with mixed-wet wettability. The networks are composed of pores and throats with circular and angular cross sections. The model allows the presence of multiple phases in each angular pore. It uses Helmholtz free energy balance and Mayer–Stowe–Princen (MSP) method to compute threshold capillary pressures for two- and three-phase displacements (fluid configuration changes) based on pore wettability, pore geometry, interfacial tension, and initial pore fluid occupancy. In particular, it generates thermodynamically consistent threshold capillary pressures for wetting and spreading fluid layers resulting from different displacement events. Threshold capillary pressure equations are presented for various possible fluid configuration changes. By solving the equations for the most favorable displacements, we show how threshold capillary pressures and final fluid configurations may vary with wettability, shape factor, and the maximum capillary pressure reached during preceding displacement processes. A new cusp pore fluid configuration is introduced to handle the connectivity of the intermediate wetting phase at low saturations and to improve model’s predictive capabilities. Based on energy balance and geometric equations, we show that, for instance, a gas-to-oil piston-like displacement in an angular pore can result in a pore fluid configuration with no oil, with oil layers, or with oil cusps. Oil layers can then collapse to form cusps. Cusps can shrink and disappear leaving no oil behind. Different displacement mechanisms for layer and cusp formation and collapse based on the MSP analysis are implemented in the model. We introduce four different layer collapse rules. A selected collapse rule may generate different corner configuration depending on fluid occupancies of the neighboring elements and capillary pressures. A new methodology based on the MSP method is introduced to handle newly created gas/water interfaces that eliminates inconsistencies in relation between capillary pressures and pore fluid occupancies. Minimization of Helmholtz free energy for each relevant displacement enables the model to accurately determine the most favorable displacement, and hence, improve its predictive capabilities for relative permeabilities, capillary pressures, and residual saturations. The results indicate that absence of oil cusps and the previously used geometric criterion for the collapse of oil layers could yield lower residual oil saturations than the experimentally measured values in two- and three-phase systems.