We consider rotational hypersurface in the four dimensional Euclidean space. We calculate the mean curvature and the Gaussian curvature, and some relations of the rotational hypersurface. Moreover, we define the third Laplace-Beltrami operator and apply it to the rotational hypersurface.

Hamacher operation which is generalization of the Algebraic and Einstein operation, can widely provide a large number of arithmetical operation with respect to uncertainty information, and Heronian mean can deal with correlations of the input arguments or different criteria and don’t make calculation redundancy, meanwhile, the normal intuitionistic fuzzy numbers (NIFNs) can depict distinctively normal distribution information in practical decision making. In this paper, a multi-criteria group decision-making (MCGDM) problem is researched under the NIFNs environment, and a new MCGDM approach is introduced on the basis of the Hamacher operation. Firstly, according to Hamacher t-conorm and t-norm, some operational laws of NIFNs are presented. Secondly, it is noticed that Heronian mean can’t only once take into account mutual relation between attribute values once, but also consider the correlation between input argument and itself. Therefore, we develop some operators and study their properties in order to aggregate normal intuitionistic fuzzy numbers information, these operators include Hamacher Heronian mean (NIFHHM), Hamacher weighted Heronian mean (NIFHWHM), Hamacher geometric Heronian mean (NIFHGHM) and Hamacher weighted geometric Heronian mean (NIFHWGHM). Furthermore, we apply the proposed operators to the MCGDM problem and present a new method. The main characteristics of this new method involve that: (1) it is suitable to make decision under the normal intuitionistic fuzzy numbers environment and more reliable and reasonable to aggregate the normal distribution information. (2) it utilizes Hamacher operation which can provide more reliable and flexible decision-making results and offer an effective and powerful mathematic tool for the MAGDM under uncertainty. (3) it uses the Heronian mean operator which can considers relationships between the input arguments or the attributes and don’t brings subsequently about redundancy. Lastly, an application is given for showing the feasibility and effectiveness of the presented method in this paper.

The propeller jet from a ship has a significant component directed upwards towards the free surface of the water, which can be used for ice management. This paper describes a comprehensive laboratory experiment where the influences of operational factors affecting a propeller wake velocity field were investigated. The experiment was done on a steady wake field to investigate the characteristics of the axial velocity of the fluid in the wake and the corresponding variability downstream of the propeller. The axial velocities and the variability recorded were time-averaged. Propeller rotational speed was found to be the most significant factor, followed by propeller inclination. The experimental results also provide some idea about the change of the patterns of the mean axial velocity distribution against the factors considered for the test throughout the effective wake field, as well as the relationships to predict the axial velocity for known factors.

In this research paper, a hybrid Artificial Neural Network (ANN)-Fuzzy Logic Control (FLC) tuned Flower Pollination Algorithm (FPA) as a Maximum Power Point Tracker (MPPT) is employed to emend root mean square error (RMSE) of photovoltaic (PV) modeling. Moreover, Gaussian membership functions have been considered for fuzzy controller design. This paper interprets Luo converter occupied brushless DC motor (BLDC) directed PV water pump application. Experimental responses certify the effectiveness of the suggested motor-pump system supporting diverse operating states. Luo converter is newly developed dc-dc converter has high power density, better voltage gain transfer and superior output waveform and able to track optimal power from PV modules. For BLDC speed controlling there is no extra circuitry and phase current sensors are enforced for this scheme. The recentness of this attempt is adaptive neuro-fuzzy inference system (ANFIS)-FPA operated BLDC directed PV pump with advanced Luo converter has not been formerly conferred.

The main objective of this paper is to introduce a further extension of extended (p, q)-beta function by considering two Mittag-Leffler function in the kernel. We investigate various properties of this newly defined beta function such as integral representations, summation formulas and Mellin transform. We define extended beta distribution and its mean, variance and moment generating function with the help of extension of beta function. Also, we establish an extension of extended (p, q)-hypergeometric and (p, q)-confluent hypergeometric functions by using the extension of beta function. Various properties of newly defined extended hypergeometric and confluent hypergeometric functions such as integral representations, Mellin transformations, differentiation formulas, transformation and summation formulas are investigated.

The concept of neutrosophic number is a significant mathematical tool to deal with real scientific problems because it can tackle indeterminate and incomplete information which exists generally in real problems. In this article, we use neutrosophic numbers (a + bI), where a and bI denote determinate component and indeterminate component respectively. We explore the situations in which the input information is needed to express in terms of neutrosophic numbers. We define score functions and accuracy functions for ranking neutrosophic numbers. We then define a cosine function to determine unknown criteria weights. We define neutrosophic number harmonic mean operators and proved their basic properties. Then, we develop two novel MCGDM strategies using the proposed aggregation operators. We solve a numerical example to demonstrate the feasibility and effectiveness of the proposed two strategies. Sensitivity analysis with variation of “I” on neutrosophic numbers is performed to demonstrate how the preference ranking order of alternatives is sensitive to the change of “I”. The efficiency of the developed strategies is ascertained by comparing the obtained results from the proposed strategies with the existing strategies in the literature.

Accurate and timely rainfall prediction enhances productivity and can aid proper planning in sectors such as agriculture, health, transport and water resources. This study is aimed at improving rainfall prediction using ensemble methods. It first assesses the performance of six convective schemes (Kain–Fritsch (KF); Betts–Miller–Janji´c (BMJ); Grell–Fretas (GF); Grell 3D ensemble (G3); New–Tiedke (NT) and Grell–Devenyi (GD)) using the root mean square error (RMSE) and mean error (ME) focusing on the March–May 2013 rainfall period over Uganda. 18 ensemble members are generated from the three best performing convective schemes (i.e. KF, GF & G3). The performance of three ensemble methods (i.e. ensemble mean (EM); ensemble mean analogue (EMA) and multi–member analogue ensemble (MAEM)) is also analyzed using the RMSE and ME. The EM presented a smaller RMSE compared to individual schemes (EM:10.02; KF:23.96; BMJ:26.04; GF:25.85; G3:24.07; NT:29.13 & GD:26.27) and a better bias (EM:-1.28; KF:-1.62; BMJ:-4.04; GF:-3.90; G3:-3.62; NT:-5.41 & GD:-4.07). The EMA and MAEM presented 13 out of 21 stations & 17 out of 21 stations respectively with smaller RMSE compared to EM thus demonstrating additional improvement in predictive performance. The MAEM is a new approach proposed and described in the study.

This paper presents the results of an experimental investigation about target detecting with passive sonar in Persian Gulf. Detecting propagated sounds in the water is one of the basic challenges of the researchers in sonar field. This challenge will be complex in shallow water (like Persian Gulf) and noise less vessels. Generally, in passive sonar the targets are detected by sonar equation (with constant threshold) which increase the detection error in shallow water. Purpose of this study is proposed a new method for detecting targets in passive sonars using adaptive threshold. In this method, target signal (sound) is processed in time and frequency domain. For classifying, Bayesian classification is used and prior distribution is estimated by Maximum Likelihood algorithm. Finally, target was detected by combining the detection points in both domains using LMS adaptive filter. Results of this paper has showed that proposed method has improved true detection rate about 27% compare other the best detection method.

The main focus when developing software is to improve the reliability and stability of a software system. When software systems are introduced, these systems are used in field environments that are the same as or close to those used in the development-testing environment; however, they may also be used in many different locations that may differ from the environment in which they were developed and tested. In this paper, we propose a new software reliability model that takes into account the uncertainty of operating environments. The explicit mean value function solution for the proposed model is presented. Examples are presented to illustrate the goodness-of-fit of the proposed model and several existing non-homogeneous Poisson process (NHPP) models and confidence intervals of all models based on two sets of failure data collected from software applications. The results show that the proposed model fits the data more closely than other existing NHPP models to a significant extent.

Kelly's Criterion is well known among gamblers and investors as a method for maximizing the returns one would expect to observe over long periods of betting or investing. These ideas are conspicuously absent from portfolio optimization problems in the financial and automation literature. This paper will show how Kelly's Criterion can be incorporated into standard portfolio optimization models. The model developed here combines risk and return into a single objective function by incorporating a risk parameter. This model is then solved for a portfolio of 10 stocks from a major stock exchange using a differential evolution algorithm. Monte Carlo calculations are used to verify the accuracy of the results obtained from differential evolution. The results show that evolutionary algorithms can be successfully applied to solve a portfolio optimization problem where returns are calculated by applying Kelly's Criterion to each of the assets in the portfolio.

An approach to the assessment of probabilistic inference is described which quantifies the performance on the probability scale. From both information and Bayesian theory, the central tendency of an inference is proven to be the geometric mean of the probabilities reported for the actual outcome and is referred to as the “Accuracy.” Upper and lower error bars on the accuracy are provided by the arithmetic mean and the -2/3 mean. The arithmetic is called the “Decisiveness” due to its similarity with the cost of a decision and the -2/3 mean is called the “Robustness”, due to its sensitivity to outlier errors. Visualization of inference performance is facilitated by plotting the reported model probabilities versus the histogram calculated source probabilities. The visualization of the calibration between model and source is summarized on both axes by the arithmetic, geometric, and -2/3 means. From information theory, the performance of the inference is related to the cross-entropy between the model and source distribution. Just as cross-entropy is the sum of the entropy and the divergence; the accuracy of a model can be decomposed into a component due to the source uncertainty and the divergence between the source and model. Translated to the probability domain these quantities are plotted as the average model probability versus the average source probability. The divergence probability is the average model probability divided by the average source probability. When an inference is over/under-confident, the arithmetic mean of the model increases/decreases, while the -2/3 mean decreases/increases, respectively.

In the paper, the authors survey integral representations (including the Lévy--Khintchine representations) and applications of some bivariate means (including the logarithmic mean, the identric mean, Stolarsky's mean, the harmonic mean, the (weighted) geometric means and their reciprocals, and the Toader--Qi mean) and the multivariate (weighted) geometric means and their reciprocals, derive integral representations of bivariate complex geometric mean and its reciprocal, and apply these newly-derived integral representations to establish integral representations of Heronian mean of power 2 and its reciprocal.

In the paper, by virtue of a Lévy–Khintchine representation and an alternative integral representation for the weighted geometric mean, the authors establish a Lévy–Khintchine representation and an alternative integral representation for the Toader–Qi mean. Moreover, the authors also collect an probabilistic interpretation and applications in engineering of the Toader–Qi mean.

Abstract: The aim of this study was to find out the incidence of anemia in pregnant women of Swat District; to analyze the iron variations and its dietary effects.Data were collected during the periods of January – September 2016. The study of samples comprised of 250 pregnant women in the different trimester. Blood sample from each woman was collected and full blood count (FBC) was conducted through Mindray BC-3000 plus hem analyzer for all pregnant individuals. Confirmed anemic cases were then examined for IDA with serum ferritin, serum iron, total iron binding capacity (TIBC) through Randox kit and serum transferrin saturation was estimated by formula (serum ferritin saturation =serum iron ×100/TIBC). The total number of participants in the first trimester were 50, among them 26 women were suffer from iron deficiency anemia (IDA) with 52% weightage of prevalence rate, (mean Hb concentration 9.602 ± 0.87 g/dl). The rates of IDA were 63.3%; ( mean Hb concentration 8.48 ± 1.24 g/dl) and 54%; ( mean Hb concentration 9.18 ± 1.28 g/dl), among 150 and 50 participants in the second and third trimester, respectively. A significant correlation was found between serum ferritin and Hb, serum ferritin against MCV and serum ferritin against MCH. The high prevalence of anemia was found 78.2% in the age group from 26-30 followed by 78.2% in the age group 36-40 years compared to those of other age groups in the second trimester. In this study the prevalence of IDA in third trimester is lower compared to first and second trimester.