A FLEXIBLE OBJECTIVE-CONSTRAINT APPROACH AND A NEW ALGORITHM FOR CONSTRUCTING THE PARETO FRONT OF MULTIOBJECTIVE OPTIMIZATION PROBLEMS

In this article, a novel scalarization technique, called the improved objective-constraint approach, is introduced to find efficient solutions of a given multiobjective programming problem. The presented scalarized problem extends the objective-constraint problem. It is demonstrated that how adding variables to the scalarized problem, can lead to find conditions for (weakly, properly) Pareto optimal solutions. Applying the obtained necessary and sufficient conditions, two algorithms for generating the Pareto front approximation of bi-objective and three-objective programming problems are designed. These algorithms are easy to implement and can achieve an even approximation of (weakly, properly) Pareto optimal solutions. These algorithms can be generalized for optimization problems with more than three criterion functions, too. The effectiveness and capability of the algorithms are demonstrated in test problems.

Post-fire recovery of Puya raimondii, vegetation and birds in the puna of Huascarán National Park, Perú

A large fire of 233 ha in Huascarán National Park in Peru provided an opportunity to compare plant and bird responses in burned and nearby unburned zones of the puna. Heights and live diameters of flagship Puya raimondii rosettes(assigned to four broad developmental phases), plant communities(66 species in 24 families and nine growth forms) and bird communities(77 species in six trophic guilds) were monitored after the fire. Although no mortality was observed, Puya raimondii plants were affected by the fire, losing approximately 60% of their photosynthetic area across all developmental phases, but recovered quickly during the first two years after fire. The comparison of Puya rosette recovery after fire was complicated by the changes in live rosette diameter for unburned plants, which showed plasticity of photosynthetic area linked to seasonal and annual fluctuations in precipitation in this relatively dry environment(decreased by 26% for mature adult plants over the study period). Fire caused an immediate change in the density, biomass and composition of vegetation. Although the species present remained similar, their abundances changed significantly immediately after the fire, with notable reductions in dominant tussock grasses. This provided opportunities for other plants, resulting in higher postfire diversity of plant species, genera, families and growth forms. In turn, the changes in vegetation after fire affected the composition of birds according to their trophic guild. Granivores largely disappeared,generalists were mostly unaffected, and other guilds showed a more complex response. As the vegetation recovered, most displaced birds returned within approximately one year.

APPROXIMATE DUALITY OF g-FRAMES IN HILBERT SPACES

In this article, we introduce and characterize approximate duality for g-frames. We get some important properties and applications of approximate duals. We also obtain some new results in approximate duality of frames, and generalize some of the known results in approximate duality of frames to g-frames. We also get some results for fusion frames, and perturbation of approximately dual g-frames. We show that approximate duals are stable under small perturbations and they are useful for erasures and reconstruction.

On the rate of complete convergence for weighted sums of NSD random variables and an application

In this paper, the complete convergence is established for the weighted sums of negatively superadditive-dependent random variables. As an application, the Marcinkiewicz-Zygmund strong law of large numbers for the random weighted average is also achieved, and a simulation study is done for the asymptotic behaviour of random weighting estimator.

Misuse of prophylactic antibiotics and prevalence of postoperative wound infection in obstetrics and gynecology department in a Sudanese hospital

Purpose: This study was conducted to audit prophylactic antibiotic use and to quantify the rate of wound infection. Methods: Across-sectional prospective study was conducted in the Obstetrics and Gynecology Department in Khartoum Teaching Hospital, Sudan during March 1st to 31st October 2010. All Patients (aged >18 years) were included. Results: Overall 725 patients were included. The performed surgical procedures were 751;of these 578 (76.9%) were Caesarean sections. Overall rate of wound infection was 7.8%. The rate of wound infection among patients operated on for caesarean section and abdominal hysterectomy was 8.3%, and 9.2%, respectively. Multivariate logistic analysis showed that body mass index [BMI] ≥ 30 kg/m2 OR 2.1, 95% CI (1.1 - 4.0), (P = 0.019) was the major independent risk factor for occurrence of wound infection. Evaluation of prescriptions’ parameters against the stated criteria showed that 113 (15.8%) patients were given antibiotics with adequate spectrum of activity, 611 (85.3%) given sub-dose/s, 83 (11.6%) received the first preoperative dose/s in a proper time window, and 716 (100%) had prophylaxis for extended duration. Overall conformity to the stated criteria for the evaluation of prescription’s parameters was not achieved in all prescriptions. Conclusions: In this setting, antibiotics were irrationally used and wound infection rate was high, and the situation calls for multiple interventions to correct the situation, through the activation of the infection control committee in the hospital and development of antimicrobial subcommittee to develop policies for the use and auditing of prophylactic antibiotics.

Numerical Solution of the Distributed-Order Fractional Bagley-Torvik Equation

In this paper, two numerical methods are proposed for solving distributed-order fractional Bagley-Torvik equation.This equation is used in modeling the motion of a rigid plate immersed in a Newtonian fluid with respect to the nonnegative density function. Using the composite Boole's rule the distributedorder Bagley-Torvik equation is approximated by a multi-term time-fractional equation, which is then solved by the GrunwaldLetnikov method(GLM) and the fractional differential transform method(FDTM). Finally, we compared our results with the exact results of some cases and show the excellent agreement between the approximate result and the exact solution.

THE EXPONENTIAL OF QUASI BLOCK-TOEPLITZ MATRICES

The matrix Wiener algebra,W_(N):=M_(N)(W)of order N>0,is the matrix algebra formed by N×N matrices whose entries belong to the classical Wiener algebraWof functions with absolutely convergent Fourier series.A block-Toeplitz matrix T(a)=[A_(i,j)]i,j≥0is a block semi-infinite matrix such that its blocks A_(i,j) are finite matrices of order N,A_(i,j)=A^(r,s) whenever i-j=r-s and its entries are the coefficients of the Fourier expansion of the generator a:T→M_(N)(C).Such a matrix can be regarded as a bounded linear operator acting on the direct sum of N copies of L^(2)(T).We show that exp(T(a))differes from T(exp(a))only in a compact operator with a known bound on its norm.In fact,we prove a slightly more general result:for every entire function f and for every compact operator E,there exists a compact operator F such that f(T(a)+E)=T(f(a))+F.We call these T(a)+E′s matrices,the quasi block-Toeplitz matrices,and we show that via a computation-friendly norm,they form a Banach algebra.Our results generalize and are motivated by some recent results of Dario Andrea Bini,Stefano Massei and Beatrice Meini.

CHARACTEIZATIONS OF WOVENT g-FRAMES AND WEAVING g-FRAMES IN HILBERT SPACESS AND C^(*)-MODULES

In this paper,using Parseval frames we generalize Sun’s results to g-frames in Hilbert C^(*)-modules.Moreover,for g-frames in Hilbert spaces,we present some characterizations in terms of a family of frames,not only for orthonormal bases.Also,we have a note about a comment and a relation in the proof of Proposition 5.3 in[D.Li et al.,On weaving g-frames for Hilbert spaces,Complex Analysis and Operator Theory,2020].Finally,we have some results for g-Riesz bases,woven and P-woven g-frames.

Numerical scheme to solve a class of variable–order Hilfer–Prabhakar fractional differential equations with Jacobi wavelets polynomials

In this paper,we introduced a numerical approach for solving the fractional differential equations with a type of variable-order Hilfer-Prabhakar derivative of orderμ(t)andν(t).The proposed method is based on the Jacobi wavelet collocation method.According to this method,an operational matrix is constructed.We use this operational matrix of the fractional derivative of variable-order to reduce the solution of the linear fractional equations to the system of algebraic equations.Theoretical considerations are discussed.Finally,some numerical examples are presented to demonstrate the accuracy of the proposed method.

Selecting Best Software Vulnerability Scanner Using Intuitionistic Fuzzy Set TOPSIS

Software developers endeavor to build their products with the least number of bugs.Despite this,many vulnerabilities are detected in software that threatens its integrity.Various automated software i.e.,vulnerability scanners,are available in the market which helps detect and manage vulnerabilities in a computer,application,or a network.Hence,the choice of an appropriate vulnerability scanner is crucial to ensure efficient vulnerability management.The current work serves a dual purpose,first,to identify the key factors which affect the vulnerability discovery process in a network.The second,is to rank the popular vulnerability scanners based on the identified attributes.This will aid the firm in determining the best scanner for them considering multiple aspects.The multi-criterion decision making based ranking approach has been discussed using the Intuitionistic Fuzzy set(IFS)and Technique for Order of Preference by Similarity to Ideal Solution(TOPSIS)to rank the various scanners.Using IFS TOPSIS,the opinion of a whole group could be simultaneously considered in the vulnerability scanner selection.In this study,five popular vulnerability scanners,namely,Nessus,Fsecure Radar,Greenbone,Qualys,and Nexpose have been considered.The inputs of industry specialists i.e.,people who deal in software security and vulnerability management process have been taken for the ranking process.Using the proposed methodology,a hierarchical classification of the various vulnerability scanners could be achieved.The clear enumeration of the steps allows for easy adaptability of the model to varied situations.This study will help product developers become aware of the needs of the market and design better scanners.And from the user’s point of view,it will help the system administrators in deciding which scanner to deploy depending on the company’s needs and preferences.The current work is the first to use a Multi Criterion Group Decision Making technique in vulnerability scanner selection.

ON SELECTIONS OF SET-VALUED EULER-LAGRANGE INCLUSIONS WITH APPLICATIONS

We discuss the set-valued dynamics related to the theory of functional equations.We look for selections of convex set-valued functions satisfying set-valued Euler-Lagrange inclusions.We improve and extend upon some of the results in[13,20],but under weaker assumptions.Some applications of our results are also provided.

Local Lyapunov Exponents and characteristics of fixed/periodic points embedded within a chaotic attractor

A chaotic dynamical system is characterized by a positive averaged exponential separation of two neighboring tra- jectories over a chaotic attractor. Knowledge of the Largest Lyapunov Exponent λ1 of a dynamical system over a bounded attractor is necessary and sufficient for determining whether it is chaotic (λ1>0) or not (λ1≤0). We intended in this work to elaborate the connection between Local Lyapunov Exponents and the Largest Lyapunov Exponent where an alternative method to calculate λ1 has emerged. Finally, we investigated some characteristics of the fixed points and periodic orbits embedded within a chaotic attractor which led to the conclusion of the existence of chaotic attractors that may not embed in any fixed point or periodic orbit within it.

PRODUCTS OF RESOLVENTS AND MULTIVALUED HYBRID MAPPINGS IN C AT(0) SPACES

In this article, we introduce and investigate the concept of multivalued hybrid mappings in C AT（0） spaces by using the concept of quasilinearization. Also, we present a new iterative algorithm involving products of Moreau-Yosida resolvents for finding a common element of the set of minimizers of a finite family of convex functions and a common fixed point of two multivalued hybrid mappings in C AT（0） spaces.

P-Bifurcation of Stochastic van der Pol Model as a Dynamical System in Neuroscience

This study aims to determine the phenomenological bifurcation(P-bifurcation)occur-ring in the van der Pol(VDP)neuronal model of burst neurons with a random signal.We observe the P-bifurcation under an intense noise stimulus which would become chaotic transitions.Bursting and spiking simulations are used to describe the causes of chaotic transitions between two periodic phases that are the reason for the neuronal activities.Ran-domness plays a crucial role in detecting the P-bifurcation.To determine the equilibrium points,stability or instability of the stochastic VDP equation,and bifurcation,we use the stochastic averaging method and some related theorems.Apart from theoretical methods,we also examine numerical simulations in the particular case of that stochastic equation that illustrates the outcome of theorems for various noise types.The most striking part of our theoretical findings is that these results are also valid for the Izhikevich-FitzHugh model,Bonhoeffer-van der Pol oscillator in dynamical systems of neuroscience.Finally,we will discuss some applications of the VDP equation in neuronal activity.

Analyzing the Stability of a <i>n-DOF</i>System with Viscous Damping

In this paper we introduce a numerically stable method for determining the stability of n-DOF system without computing eigenvalues. In this sense, at first we reduce the second-order system to a standard eigenvalue problem with symmetric tridiagonal form. Then we compute the exact inertia by using an algorithm based on floating point arithmetic [1]. Numerical tests report the effectiveness of these methods.

A Review of Water Quality Optimisation Models and Techniques

This paper presents a state of the art review of water quality optimisation models and techniques from early 1970s to date in terms of the model/technique category, model/technique type, purpose and application. The models are categorised into Mathematical Programming Models and Meta-heuristic Programming Models. Similarly, the techniques are categorised into Mathematical Programming Techniques and Meta-heuristic Programming Techniques. The review is concluded by drawing attention to the rare nature of application of interior-point methods to water quality optimisation.

Anomalous Viscosity of Vortex Hall States in Graphene

We study temperature effect on anomalous viscosity of Graphene Hall fluid within quantum many-vortex hydrodynamics. The commonly observed filling fraction, in the range is considered. An expression for anomalous viscosity dependent on a geometric parameter-Hall expansion coefficient is obtained at finite temperatures. It arises from strained induced pseudo-magnetic field in addition to an anomalous term in vortex velocity, which is responsible for renormalization of vortex-vortex interactions. We observed that both terms greatly modify the anomalous viscosity as well as an enhancement of weakly observed v fractions. Finite values of the expansion coefficient produce constant and infinite viscosities at varying temperatures. The infinities are identified as energy gaps and suggest temperatures at which new stable quantum hall filling fractions could be seen. This phenomenon is used to estimate energy gaps of already measured fractional Quantum Hall States in Graphene.

Diagnosing Breast Cancer Accurately Based on Weighting of HeterogeneousClassification Sub-Models

In developed and developing countries, breast cancer is one of the leading forms of cancer affecting women alike. As a consequence of growing lifeexpectancy, increasing urbanization and embracing Western lifestyles, the highprevalence of this cancer is noted in the developed world. This paper aims todevelop a novel model that diagnoses Breast Cancer by using heterogeneous datasets. The model can work as a strong decision support system to help doctors tomake the right decision in diagnosing breast cancer patients. The proposed modelis based on three datasets to develop three sub-models. Each sub-model worksindependently. The final diagnosis decision is taken by the three sub-models independently. The power of the model comes from the diversity checks of patientsand this reduces the risk of wrong diagnosing. The model has been developedby conducting intensive experiments. Several classification algorithms were usedto select the best one in each sub-model. As the final results, the sub-modelaccuracies were 72%, 74% and 97%.

Improving the Cellular Characteristics of Aluminum Foam for Maximum Sound Absorption Coefficient Using Genetic Algorithm

Fabricating of metal foams with desired morphological parameters including pore size,porosity and pore opening is possible now using sintering technology.Thus,if it is possible to determine the morphology of metal foam to absorb sound at a given frequency,and then fabricate it through sintering,it is expected to have optimized metal foams for the best sound absorption.Theoretical sound absorption models such as Lu model describe the relationship between morphological parameters and the sound absorption coefficient.In this study,the Lu model was used to optimize the morphological parameters of aluminum metal foam for the best sound absorption coefficient.For this purpose,the Lu model was numerically solved using written codes in MATLAB software.After validating the proposed codes with benchmark data,the genetic algorithm(GA)was applied to optimize the affecting morphological parameters on the sound absorption coefficient.The optimization was carried out for the thicknesses of 5 mm to 40 mm at the sound frequency range of 250 Hz–8000 Hz.The optimized parameters ranged from 50%to 95%for porosity,0.1 mm to 4.5 mm for pore size,and 0.07 mm to 0.6 mm for pore opening size.The result of this study was applied to fabricate the desired aluminum metal foams for the best sound absorption.The novel approach applied in this study,is expected to be successfully applied in for best sound absorption in desired frequencies.

New Implementation of Reproducing Kernel Method for Solving Functional-Differential Equations

In this paper, we apply the new algorithm of reproducing kernel method to give the approximate solution to some functional-differential equations. The numerical results demonstrate the accuracy of the proposed algorithm.