Mathematical Modeling and Evaluation of Reliability Parameters Based on Survival Possibilities under Uncertain Environment

In this article,mathematical modeling for the evaluation of reliability is studied using two methods.One of the methods,is developed based on possibility theory.The performance of the reliability of the system is of prime concern.In view of this,the outcomes for the failure are required to evaluate with utmost care.In possibility theory,the reliability information data determined from decision-making experts are subjective.The samemethod is also related to the survival possibilities as against the survival probabilities.The other method is the one that is developed using the concept of approximation of closed interval including the piecewise quadratic fuzzy numbers.In this method,a decision-making expert is not sure of his/her estimates of the reliability parameters.Numerical experiments are performed to illustrate the efficiency of the suggested methods in this research.In the end,the paper is concluded with some future research directions to be explored for the proposed approach.

Modified DS np Chart Using Generalized Multiple Dependent State Sampling under Time Truncated Life Test

This study presents the design of a modified attributed control chart based on a double sampling(DS)np chart applied in combination with generalized multiple dependent state(GMDS)sampling to monitor the mean life of the product based on the time truncated life test employing theWeibull distribution.The control chart developed supports the examination of the mean lifespan variation for a particular product in the process of manufacturing.Three control limit levels are used:the warning control limit,inner control limit,and outer control limit.Together,they enhance the capability for variation detection.A genetic algorithm can be used for optimization during the in-control process,whereby the optimal parameters can be established for the proposed control chart.The control chart performance is assessed using the average run length,while the influence of the model parameters upon the control chart solution is assessed via sensitivity analysis based on an orthogonal experimental design withmultiple linear regression.A comparative study was conducted based on the out-of-control average run length,in which the developed control chart offered greater sensitivity in the detection of process shifts while making use of smaller samples on average than is the case for existing control charts.Finally,to exhibit the utility of the developed control chart,this paper presents its application using simulated data with parameters drawn from the real set of data.

Multifunctional HDPE/Cu biocidal nanocomposites for MEX additive manufactured parts: Perspectives for the defense industry

In this study, we investigated the performance improvement caused by the addition of copper(Cu)nanoparticles to high-density polyethylene(HDPE) matrix material. Composite materials, with filler percentages of 0.0, 2.0, 4.0, 6.0, 8.0, and 10.0 wt% were synthesized through the material extrusion(MEX)3D printing technique. The synthesized nanocomposite filaments were utilized for the manufacturing of specimens suitable for the experimental procedure that followed. Hence, we were able to systematically investigate their tensile, flexural, impact, and microhardness properties through various mechanical tests that were conducted according to the corresponding standards. Broadband Dielectric Spectroscopy was used to investigate the electrical/dielectric properties of the composites. Moreover, by employing means of Raman spectroscopy and thermogravimetric analysis(TGA) we were also able to further investigate their vibrational, structural, and thermal properties. Concomitantly, means of scanning electron microscopy(SEM), as well as atomic force microscopy(AFM), were used for the examination of the morphological and structural characteristics of the synthesized specimens, while energy-dispersive Xray spectroscopy(EDS) was also performed in order to receive a more detailed picture on the structural characteristics of the various synthesized composites. The corresponding nanomaterials were also assessed for their antibacterial properties regarding Staphylococcus aureus(S. aureus) and Escherichia coli(E. coli) with the assistance of a method named screening agar well diffusion. The results showed that the mechanical properties of HDPE benefited from the utilization of Cu as a filler, as they showed a notable improvement. The specimen of HDPE/Cu 4.0 wt% was the one that presented the highest levels of reinforcement in four out of the seven tested mechanical properties(for example, it exhibited a 36.7%improvement in the flexural strength, compared to the pure matrix). At the same time, the nanocomposites were efficient against the S. aureus bacterium and less efficient against the E. coli bacterium.The use of such multi-functional, robust nanocomposites in MEX 3D printing is positively impacting applications in various fields, most notably in the defense and security sectors. The latter becomes increasingly important if one takes into account that most firearms encompass various polymeric parts that require robustness and improved mechanical properties, while at the same time keeping the risk of spreading various infectious microorganisms at a bare minimum.

BAS-ADAM:An ADAM Based Approach to Improve the Performance of Beetle Antennae Search Optimizer

In this paper,we propose enhancements to Beetle Antennae search(BAS)algorithm,called BAS-ADAIVL to smoothen the convergence behavior and avoid trapping in localminima for a highly noin-convex objective function.We achieve this by adaptively adjusting the step-size in each iteration using the adaptive moment estimation(ADAM)update rule.The proposed algorithm also increases the convergence rate in a narrow valley.A key feature of the ADAM update rule is the ability to adjust the step-size for each dimension separately instead of using the same step-size.Since ADAM is traditionally used with gradient-based optimization algorithms,therefore we first propose a gradient estimation model without the need to differentiate the objective function.Resultantly,it demonstrates excellent performance and fast convergence rate in searching for the optimum of noin-convex functions.The efficiency of the proposed algorithm was tested on three different benchmark problems,including the training of a high-dimensional neural network.The performance is compared with particle swarm optimizer(PSO)and the original BAS algorithm.

Direct Derivation of the Comma 3-Vertex in the Full String Basis

The interacting comma 3-vertex for the bosonic open string in the full string basis is derived using the half string overlap relations directly. Thus avoiding the coherent states technique employed in earlier derivations. The resulting form of the interacting 3-vertex turns out to be precisely the desired expression obtained in terms of the full string oscillator modes. This derivation establishes that the comma 3-vertex and Witten’s 3-vertex are identical and therefore are interchangeable.

On the Implementation of Exponential B-Splines by Poisson Summation Formula

Polynomial splines have played an important role in image processing, medical imaging and wavelet theory. Exponential splines which are of more general concept have been recently investigated.We focus on cardinal exponential splines and develop a method to implement the exponential B-splines which form a Riesz basis of the space of cardinal exponential splines with finite energy.

Designing Adaptive Multiple Dependent State Sampling Plan for Accelerated Life Tests

A novel adaptive multiple dependent state sampling plan(AMDSSP)was designed to inspect products from a continuous manufacturing process under the accelerated life test(ALT)using both double sampling plan(DSP)and multiple dependent state sampling plan(MDSSP)concepts.Under accelerated conditions,the lifetime of a product follows the Weibull distribution with a known shape parameter,while the scale parameter can be determined using the acceleration factor(AF).The Arrhenius model is used to estimate AF when the damaging process is temperature-sensitive.An economic design of the proposed sampling plan was also considered for the ALT.A genetic algorithm with nonlinear optimization was used to estimate optimal plan parameters to minimize the average sample number(ASN)and total cost of inspection(TC)under both producer’s and consumer’s risks.Numerical results are presented to support the AMDSSP for the ALT,while performance comparisons between the AMDSSP,the MDSSP and a single sampling plan(SSP)for the ALT are discussed.Results indicated that the AMDSSP was more flexible and efficient for ASN and TC than the MDSSP and SSP plans under accelerated conditions.The AMDSSP also had a higher operating characteristic(OC)curve than both the existing sampling plans.Two real datasets of electronic devices for the ALT at high temperatures demonstrated the practicality and usefulness of the proposed sampling plan.

Impact of vaccination on the dynamics of COVID-19:A mathematical study using fractional derivatives

Arrival of a new disease marks a yearlong destruction of human lives and economy in general,and if the disease turns out to be a pandemic the loss is frightening.COVID-19 is one such pandemic that has claimed millions of lives till date.There is a suffering throughout the world due to various factors associated with the pandemic,be it loss of livelihoods because of sudden shutdown of companies and lockdown,or loss of lives due to lack of medical aid and inadequate vaccination supplies.In this study,we develop a six-compartmental epidemiological model incorporating vaccination.The motivation behind the study is to analyze the significance of higher vaccination efficacy and higher rate of population getting vaccinated in controlling the rise in infectives and thereby the untimely demise of various individuals.The work begins with an ordinary differential equation model followed by stability analysis of the same,after which a fractional-order derivative model of the same is formulated and the existence of uniformly stable solution for the system is proved.In addition to this,we present the stability of the equilibria in general for the fractional model framed.The sensitivity analysis of the basic reproduction number along with its correlation with various parameters is presented.In addition to this,sensitivity of certain state variables in the fractional model with respect to different.fractional orders as well with respect to different infection rate is exhibited in this work.Factors related to lockdown and usage of face shields are incorporated in the entire study,and importance of these is highlighted in the study as well.The major takeaway from the study is that mere vaccination will not sufice in eradication of the virus.The vaccine efficacy plays a major role along with other intervention included in the model.The numerical simulations are carried out in MATLAB software using ode45 and fdel2.

Error Analysis of the Nonconforming P1 Finite Element Method to the Sequential Regularization Formulation for Unsteady Navier-Stokes Equations

In this paper we investigate the nonconforming P_(1) finite element ap-proximation to the sequential regularization method for unsteady Navier-Stokes equations.We provide error estimates for a full discretization scheme.Typi-cally,conforming P_(1) finite element methods lead to error bounds that depend inversely on the penalty parameter ∈.We obtain an ∈-uniform error bound by utilizing the nonconforming P_(1) finite element method in this paper.Numerical examples are given to verify theoretical results.

New Concepts on Quadripartitioned Bipolar Single Valued Neutrosophic Graph

The partition of indeterminacy function of the neutrosophic set into the contradiction part and the ignorance part represent the quadripartitioned single valued neutrosophic set.In this work,the new concept of quadripartitioned bipolar single valued neutrosophic graph is established,and the operations on it are studied.The Cartesian product,cross product,lexicographic product,strong product and composition of quadripartitioned bipolar single valued neutrosophic graph are investigated.The proposed concepts are illustrated with examples.

A Novel Multiple Dependent State Sampling Plan Based on Time Truncated Life Tests Using Mean Lifetime

The design of a new adaptive version of the multiple dependent state(AMDS)sampling plan is presented based on the time truncated life test under the Weibull distribution.We achieved the proposed sampling plan by applying the concept of the double sampling plan and existing multiple dependent state sampling plans.A warning sign for acceptance number was proposed to increase the probability of current lot acceptance.The optimal plan parameters were determined simultaneously with nonlinear optimization problems under the producer’s risk and consumer’s risk.A simulation study was presented to support the proposed sampling plan.A comparison between the proposed and existing sampling plans,namely multiple dependent state(MDS)sampling plans and a modified multiple dependent state(MMDS)sampling plan,was considered under the average sampling number and operating characteristic curve values.In addition,the use of two real datasets demonstrated the practicality and usefulness of the proposed sampling plan.The results indicated that the proposed plan is more flexible and efficient in terms of the average sample number compared to the existing MDS and MMDS sampling plans.

Asymptotic solutions for the asymmetric flow in a channel with porous retractable walls under a transverse magnetic field

The self-similarity solutions of the Navier-Stokes equations are constructed for an incompressible laminar flow through a uniformly porous channel with retractable walls under a transverse magnetic field. The flow is driven by the expanding or contracting walls with different permeability. The velocities of the asymmetric flow at the upper and lower walls are different in not only the magnitude but also the direction. The asymptotic solutions are well constructed with the method of boundary layer correction in two cases with large Reynolds numbers, i.e., both walls of the channel are with suction, and one of the walls is with injection while the other one is with suction. For small Reynolds number cases, the double perturbation method is used to construct the asymptotic solution. All the asymptotic results are finally verified by numerical results.

An Inverse Laplace Transform on Lattice Spacing

An inverse Laplace transform on lattice spacing is introduced as a computational framework of the extrapolation of the strong coupling expansion to the scaling region.We apply the transform to the two-dimensional nonlinear O(N)model at N≥3 and show that the approximation of the continuum limit of the susceptibility agrees with the existing theoretical and Monte Carlo data.

An analytical approach for the fractional-order Hepatitis B model using new operator

In this work,the main goal is to implement Homotopy perturbation transform method(HPTM)involving Katugampola fractional operator.As an example,a fractional order Hepatitis model is considered to analyze the solutions.At first,the integer order model is converted to fractional order model in Caputo sense.Then,the new operator Katugampola fractional derivative is used to present the model.The new such kind of operator is illustrated in Caputo sense.HPTM is described to get the solution of the proposed model using the new kind of operator.Also,there are some analyses about the new kind of operator to prove the efficiency of the operator.

A Proof of the Jacobian Conjecture on Global Asymptotic Stability

Let f∈C^1(R^2, R^2), f(0)=0. The Jacobian Conjecture states that if for any x∈R^2, the eigenvalues of the Jacobian matrix Df(x) have negative real parts, then the zero solution of the differential equation x=f(x) is globally asymptotically stable. In this paper we prove that the conjecture is true.

Analysis of a sex-structured HIV/AIDS model with the effect of screening of infectives

This paper presents a nonlinear sex-structured mathematical model to study the spread of HIV/AIDS by considering transmission of disease by heterosexual contact. The epidemic threshold and equilibria for the model are determined, local stability and global stability of both the “Disease-Free Equilibrium” （DFE） and “Endemic Equilibrium” （EE） are discussed in detail. The DFE is shown to be locally and globally stable when the basic reproductive number R0 is less than unity. We also prove that the EE is locally and globally asymptotically stable under some conditions. Finally, numerical simulations are reported to support the analytical findings.

A proof of the Jacobian conjecture on global asymptotic stability

A classical problem, known as global asymptotic stability Jacobian conjecure or plane Markus-Yamabe conjecture, says that if, the Jacobian matrix Df (x) of f is stable, then the zero solution of the differential equation (1) is globally asymptotically stable. In 1963, Olech proved that the conjecture is equivalent to global injectivity of f,

A Numerical Study of Multiple Solutions for Laminar Flows in a Porous and Moving Channel

In this paper,based on the finite element formulation,we focus on multiple solutions and their evolution with time for a laminar flow in a permeable channel with expanding or contracting walls.Both Newtonian fluid and micropolar fluid are consid-ered.For the Newtonian fluid model,we find that the profile of the unique solution in the case of injection remains the same for long time,which indicates that the solution may be stable.On the other hand,in the case of large suction,the profile of multiple solutions changes in time,which suggests that the multiple solutions may be unstable.Similar behaviors and conclusions are observed for the micropolar fluid model under different boundary parameters.

Detecting Isolate Safe Areas in Wireless Sensor Monitoring Systems

Wireless sensors are deployed widely to monitor space, emergent events, and disasters. Collected realtime sensory data are precious for completing rescue missions quickly and efficiently. Detecting isolate safe areas is significant for various applications of event and disaster monitoring since valuable real-time information can be provided for the rescue crew to save persons who are trapped in isolate safe areas. We propose a centralized method to detect isolate safe areas via discovering holes in event areas. In order to shorten the detection delay, a distributed isolate safe area detection method is studied. The distributed method detects isolate safe areas during the process of event detection. Moreover, detecting isolate safe areas in a building is addressed particularly since the regular detecting method is not applicable. Our simulation results show that the distributed method can detect all isolate safe areas in an acceptable short delay.

Lie Super-bialgebra Structures on the Super-BMS3 Algebra

In t his paper,Lie super-bialgebra st rue tures on the super-BMS3 algebra are considered.It is proved that all such Lie super-bialgebras are triangular coboundary Lie super-bialgebras.The method we use is mainly based on the computation of derivations from the super-BMS3 to the tensor product of its adjoint module.