Multiproduct manufacturer-retailer coordinated supply chain with adjustable rate for common parts, delayed differentiation, and multi-shipment

Operating in today’s turbulent and competitive world marketplaces, manufacturers must find the best production scheme and delivery policy to meet timely client’s multiproduct requirements and minimize the total manufacturing-shipment expenses. This study proposes a two-stage delayed differentiation model for a multiproduct manufacturer-retailer coordinated supply chain featuring the adjustable-rate for making common parts and a multi-shipment policy for transporting finished goods. The aim is to help present-day manufacturers achieve their operational goals mentioned above. The mathematical techniques help us build a specific model to explicitly represent the problem and derive its overall operating expense. Then, the convexity of the total expense is verified by Hessian matrix equations. The differential calculus helps derive the cost-minimized fabrication-shipment decision. This study offers an example to demonstrate the applicability and capabilities of our proposed model numerically. The following crucial information has been made available to the managers to facilitate their operating decision makings: (1) the problem’s best fabrication-shipment policy; (2) the collective influence of various common part’s completion rates and values on the problem’s total expenses and optimal fabrication-shipment policy; (3) the impact of various adjustable-rates in stage one on utilization and stage one’s uptime; (4) the details of cost contributors to the problem; and (5) the collective impacts of critical features on the problem’s performance.

Astrophysical Magnetic Fields

Magnetic fields permeate space and affect many major astrophysical phenomena, but they are often ignored due to their perceived complexity. This self-contained introduction to astrophysical magnetic fields provides both a comprehensive review of the current state of the subject and a critical discussion of the latest research. It presents our knowledge of magnetic fields from the Early Universe, their evolution in cosmic time through to their roles in present-day galaxies, galaxy clusters and the wider intergalactic medium, with attention given to both theory and observations. This volume also contains an extensive introduction into magnetohydrodynamics, numerous worked examples, observational and mathematical techniques and interpretations of the observations. Its review of our current knowledge, with an emphasis on results that are likely to form the basis for future progress, benefits a broad audience of advanced students and active researchers, including those from fields such as cosmology and general relativity.

A simulation strategy to determine the mechanical behaviour of cork-rubber composite pads for vibration isolation

The present work aimed to determine the performance of new cork-rubber composites, applying a modelling-based approach. The static and dynamic behaviour under compression of new composite isolation pads was determined using mathematical techniques. Linear regression was used to estimate apparent compression modulus and dynamic stiffness coefficient of compounds samples based on the effect of fillers, cork and other ingredients. Using the results obtained by regression models, finite element analysis (FEA) was applied to determine the behaviour of the same cork-rubber material but considering samples with different dimensions. The majority of the regression models presented R2 values above 90%. Also, a good agreement was found between the results obtained by the presented approach and previous experimental tests. Based on the developed methodology, the compression behaviour of new cork-rubber compounds can be accessed, improving product development stages.

Quantifying the impact of individual and collective compliance with infection control measures for ethical public health policy

Compliance with infectious disease control measures can benefit public health but be burdensome for individuals. This raises ethical questions regarding the value of the public health benefit created by individual and collective compliance. Answering such questions requires estimating the total benefit from an individual’s compliance, and how much of that benefit is experienced by others. This is complicated by “overdetermination” in infectious disease transmission: each susceptible person may have contact with more than one infectious individual, such that preventing one transmission may have no net effect if the same susceptible person is infected later. This article explores mathematical techniques enabling quantification of the impacts of individuals and groups complying with three types of public health measures: quarantine of arrivals, isolation of infected individuals, and vaccination/prophylaxis. The models presented suggest that these interventions all exhibit synergy: each intervention becomes more effective on a per-individual basis as the number complying increases, because overdetermination of outcomes is reduced, Thus additional compliance reduces transmission to a greater degree.

Response surface methodology for optimization studies of hydro-distillation of essential oil from pixie mandarin (Citrus reticulata Blanco) peels

Essential oil extraction technique from mandarin pixie peels by hydro-distillation is optimized by response surface methodology (RSM). Mathematical techniques were used in experimental design to evaluate the impacts of factors that affect the extraction process and improve the yield of the extraction process. A central mixed design based on influencing variables such as water ratio (3–5 mL/g), temperature (110–130 °C) and extraction time (90–150 min) was adopted with essential oil yield as the target function. Correlation analysis of the mathematical regression model showed that the quadratic polynomial model can be used to optimize hydro-distillation of pixie mandarin oil. The results showed that under the optimum extraction conditions, the highest quantity of essential oils was achieved (7.28 mL/100 g materials). In terms of statistical analysis, the significance levels (p-value <0.05) of the model showed that the experimental results had a good impact between factors. The coefficient of determination indicating the match between the experimental value and the predicted value of the model was high (R2>0.9). The chemical composition of the essential oil was analyzed by Gas Chromatography-Mass Spectrometry, revealing the dominance of limonene content (97.667%), which implies that the essential oil of pixie mandarin could be an alternative source of limonene.

Thermal characteristics of longitudinal fin with Fourier and non-Fourier heat transfer by Fourier sine transforms

The quest for high-performance of heat transfer components on the basis of accommodating shapes, smaller weights, lower costs and little volume has significantly diverted the industries for the enhancement of heat dissipation with variable thermal properties of fins. This manuscript proposes the fractional modeling of Fourier and non-Fourier heat transfer of longitudinal fin via non-singular fractional approach. The configuration of longitudinal fin in terms of one dimension is developed for the mathematical model of parabolic and hyperbolic heat transfer equations. By considering the Fourier and non-Fourier heat transfer from longitudinal fin, the mathematical techniques of Fourier sine and Laplace transforms have been invoked. An analytic approach is tackled for handling the governing equation through special functions for the fractionalized parabolic and hyperbolic heat transfer equations in longitudinal fin. For the sake of comparative analysis of parabolic verses hyperbolic heat conduction of fin temperature, we depicted the distinct graphical illustrations; for instance, 2-dimensional graph, bar chart, contour graphs, heat graph, 3-dimensional graphs and column graphs on for the variants of different rheological impacts of longitudinal fin.

Nonviscous Oblique Stagnation Point Flow towards Riga Plate

Purpose. The flow of nonviscous Casson fluid is examined in this study over an oscillating surface. The model of the fluid flow has been inspected in the presence of oblique stagnation point flow. The scrutiny is subsumed for the Riga plate by considering the effects of magnetohydrodynamics. The Riga plate is considered as an electromagnetic lever which carries eternal magnets and a stretching line up of alternating electrodes coupled on a plane surface. We have considered nonboundary layer two-dimensional incompressible flow of the fluid. The fluid flow model is analyzed in the fixed frame of reference. Motivation. The motivation of achieving more suitable results has always been a quest of life for scientists; the capability of determining the boundary layer of flow on aircraft which either stays laminar or turns turbulent has encouraged the researcher to study compressible flow in depth. The compressible fluid with boundary layer flow has been utilized by numerous researchers to reduce skin friction and enhance thermal and convectional heat exchange. Design/Approach/Methodology. The attained partial differential equations will be critically inspected by using suitable similarity transformation to transform these flows thrived equations into higher nonlinear ordinary differential equations (ODE). Then, these equations of motion are intercepted by mathematical techniques such as the bvp4c method in Maple and Matlab. The graphical and tabular representation of different parameters is also given. Findings. The behavior of β and modified Hartmann number M increases by positively increasing the values of both parameters for F η , while ω decreases with increasing the values of ω for F η . The graph of β shows upward behavior for distinct values for both G η and G ′ η for velocity portray. Prandtl number and β for the temperature profile of θ η and θ 1 η goes downward with increasing parameters.

Modern perspectives on near-equilibrium analysis of Turing systems

In the nearly seven decades since the publication of Alan Turing’s work on morphogenesis, enormous progress has been made in understanding both the mathematical and biological aspects of his proposed reaction–diffusion theory. Some of these developments were nascent in Turing’s paper, and others have been due to new insights from modern mathematical techniques, advances in numerical simulations and extensive biological experiments. Despite such progress, there are still important gaps between theory and experiment, with many examples of biological patterning where the underlying mechanisms are still unclear. Here, we review modern developments in the mathematical theory pioneered by Turing, showing how his approach has been generalized to a range of settings beyond the classical two-species reaction–diffusion framework, including evolving and complex manifolds, systems heterogeneous in space and time, and more general reaction-transport equations. While substantial progress has been made in understanding these more complicated models, there are many remaining challenges that we highlight throughout. We focus on the mathematical theory, and in particular linear stability analysis of ‘trivial’ base states. We emphasize important open questions in developing this theory further, and discuss obstacles in using these techniques to understand biological reality. This article is part of the theme issue ‘Recent progress and open frontiers in Turing’s theory of morphogenesis’.

Implementation Of ADFGVX Cipher And RSA On TXT And Doc File Security

In data communication, the aspect of security and confidentiality data is needed. To maintain the security and confidentiality of the data is by using cryptography. Cryptography is the science of mathematical techniques related to aspects of information security such as data confidentiality, data authenticity, data integrity, and authentication data. Text security is done by a hybrid cryptography in a text file that is first performed using ADFGVX Cipher encryption, then the results of ADFGVX Cipher encryption is encrypted using the RSA. Testing primes using the Fermat algorithm. Implementation of the system using C# programming language in Microsoft Visual Studio 2010. The system on RSA was tested with a maximum key length of 256 bits to 32 bits intervals.