IntroductionAs we know, the calculation of hydraulic gradient is highly important in the analysis of steady flow inside rockfill materials. Binomial and exponential relationships are used to calculate the hydraulic gradient based on the non-Darcy flow velocity, and the binomial relationship is more accurate and efficient than the exponential relationship. Since it is necessary to use an exponential relationship in the two-dimensional analysis of non-Darcy flow in coarse porous media, in the past, researchers have provided relationships to calculate the coefficients m and n of the exponential relationship based on the coefficients a and b of the binomial relationship. In some previous studies, Vmax= 1 has been considered, even though the maximum flow velocity depends on the physical characteristics of the pebbles and the characteristics of the flow and is not necessarily equal to one. For this reason, in this research, by designing and equipping the laboratory and recording the laboratory data, the maximum velocity based on the values of a, b and Re of the analytical model of Ahmed and Sunada(1969) is proposed.As mentioned above, various researchers tried to calculate the coefficients of the exponential relationship using the values of a and b in the binomial relationship. One of the most important relationships is presented by George and Hansen (1992) as follows.n=(5a+6bV_max)/(5a+3bV_max ) (1)m=(5a+4bV_max )(4a+3bV_max )/(4(5a+3bV_max ) (V_max )^(n-1) ) (2)Further, by stating that in the coarse-grained porous medium, the slope of the energy line (Sf) is equal to the hydraulic gradient (i), it can be stated that one of the most important parameters in the investigation of the flow in the gravel medium in free flow and under pressure is the calculation of it is a hydraulic gradient. In this research, using the coefficients of the binomial relationship, we presented a solution to calculate the values of m and n in the exponential relationship with better accuracy. Therefore, considering that the exponential relationship is used in the two-dimensional analysis of the non-Darcy flow in porous gravel media, this can play a significant role in reduction of the error of hydraulic gradient calculation.MethodologyIn the current research, the laboratory data recorded in the hydraulic laboratory of the Faculty of Civil Engineering of Zanjan University were used. For this purpose, an attempt was made to design and set up a test device and perform tests on different gravel materials. Experiments were carried out in a laboratory flume with the ability to tilt, with dimensions of 1m×1m and a length of 15m, and the length of 2.2m of the mentioned flume is filled with rockfill. The walls of the flume are made of plexiglass, and to measure the piezometric height along the porous media, 23 piezometers are used on the bottom of the channel, which are arranged at certain distances from each other and along them. The water flow in the channel is created by a pump with a maximum flow capacity of 90 liters per second. In order to create a porous media, three types of rockfill materials with small, medium and large diameters have been used in the experiments. During the tests, to ensure a stable flow, the pump was working for about 10 minutes with the desired flow and after the stability of the flow, the desired parameters were measured. These parameters include the piezometric height at the location of 23 piezometers as well as the water depth at the location of each piezometer. Piezometric values are read using a calibrated table. The water depth was also measured and recorded directly by a ruler.Results and DiscussionSince the exponential relationship is only accurate for a certain range of Reynolds numbers and the user area recommended for this relationship by its providers is only non-quiet flow conditions, therefore, if the exponential relationship is used in the two-dimensional solution of the equations, there will be a large error will enter the calculations. To avoid this problem, various researchers have tried to convert the binomial relationship into an exponential relationship. If the minimum flow velocity Vmin and the maximum flow velocity Vmax in the conversion area of the binomial relationship is in the form of an exponential relationship. In order to convert the two mentioned relations, relations (1) and (2) can be used. According to the conducted tests, in most cases, Vmin is considered zero and Vmax value is assumed to be equal to one, while the maximum flow velocity depends on the physical characteristics of the pebbles and the characteristics of the flow and is not necessarily equal to one. Therefore, Vmax can be calculated from the following relationship according to Ahmed and Sunada's(1969) analytical model and the definition of the Reynolds number as Re=ρVd/μ.V_max=Re_max a/b (3)By using relations (1), (2) and (3), it is possible to take advantage of the accuracy of the binomial relation and the practical property of the exponential relation in the two-dimensional analysis in porous media.If relations (1) and (2) are used in the calculation of the coefficients of the exponential relationship of steady flow in gravel materials, the average relative error between the calculated and recorded hydraulic gradients in the laboratory assuming Vmax=1 (according to previous research) in fine gravel materials, medium and coarse are calculated to be 21.95%, 22.98% and 21.97%, respectively. While if relation (3) is used (the solution presented in the current research), the average relative error values of the hydraulic gradient are equal to 11.39, 14.69 and 19.72%, respectively.ConclusionIn general terms, by using relations (1) and (2) and using the relation proposed in the present study instead of Vmax=1, the average values of the relative error of the hydraulic gradient in fine, medium and coarse rockfill materials have decreased to 10.56, 8.29 and 2.25%, respectively, which indicates the high accuracy and efficiency of the proposed solution.Keywords: Non-Darcy flow, exponential relation, binominal relation, rockfill, hydraulic gradient.

Menendez (2000) published a paper on Shannon's entropy in exponential family and discussed some properties of them. He introduced an asymptotic distribution for it. In this paper we present an entropy characterization of general exponential model so that Menendez definition is particular state of it. Also we introduced another asymptotic distribution for (H(^q) - H (q0)),where H (q) is Shannon's entropy of X with distribution ¦q (x) , and ^q is MLE of q.

We introduce a new wrapped exponential distribution named transmuted wrapped exponential (TWE) distribution, for the modeling of circular datasets by using the Transmutation Rank-Map method. This method is employed for the first time for a wrapped distribution with this study. The introduced distribution is more flexible than traditional wrapped exponential distribution. The paper provides the explicit form of important distributional properties of the introduced distribution such as expectation, median, moments, characteristic function, quantile function, hazard rate function and stress-strength reliability. Ré nyi and Shannon entropies are also obtained. The statistical inference problem for the TWE distribution is investigated using maximum likelihood, least squares and weighted least squares and comparative numerical study results are presented. Furthermore, we present a real dataset analysis.

In this paper, a non-linear carrier controller with an exponential carrier generator is designed and simulated for power factor correction (pfc). then, this controller is applied to single phase and three phase rectifier using a boost regulator for PFC. the power factor and its variations are measured by computer simulation against the changes in various loads and switching frequencies and the results are discussed. In order to produce voltages lower than the input voltage, a PFC using a buck regulator is used in rectifiers. However, the buck type PFC produces lower power factor then the boost type. For this reson, a flyback regulator is used as a PFC to produce lower voltage then input voltage. Power factor obtained by computer simulation of Fly back pfc are acceptable and are above 95%.

The spectrum of arbitrary graph of finite order the exponential growth of the resolvent of graph G is one of the most investigated object during the last 50 years. In particular, the resolvent matrix is a matrix with property that all of its eigenvalues are outside the spectra of G. In this paper, we study the exponential growth of the resolvent of graph G. The exponential growth of resolvent energy of graph G was investigated.

Welch & Peers (1963) used a root-information prior to obtain posterior probabilities for a scalar parameter exponential model and showed that these Bayes probabilities had the confidence property to second order asymptotically. An important undercurrent of this indicates that the constant information reparameterization provides location model structure, for which the confidence property was and is well known. This paper examines the role of the scalar-parameter exponential model for obtaining approximate probabilities and approximate confidence levels, and then addresses the extension for the vector-parameter exponential model.

Communication in the presence of a priori known interference at the encoder has gained great interest because of its many practical applications. In this paper, additive exponential noise channel with additive exponential interference (AENC-AEI) known noncausally at the transmitter is introduced as a new variant of such communication scenarios. First, it is shown that the additive Gaussian channel with a priori known interference at the encoder when the transmitter suffers from a fast-varying phase noise can be modeled by the AENC-AEI. Then, capacity bounds for this channel under a non-negativity constraint as well as a mean value constraint on input are derived. Finally, it is shown both analytically and numerically that the upper and lower bounds coincide at high signal to noise ratios (SNRs), and therefore, the capacity of the AENC-AEI at high SNRs is obtained. Interestingly, this high SNR-capacity has a simple closed-form expression and is independent of the interference mean, analogous to its Gaussian counterpart.

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Using the concept of exponential monomial on Sturm–Liouville hypergroups we show that an important subclass of exponential monomials, the class of special exponential monomials has a linear independence property. The result can be reformulated as the linear independence of the derivatives with respect to the parameter of the solutions of eigenvalue problems for second order linear differential equations.

The “technological singularity” is forecasted to occur in 2045. It is a point when non-biological intelligence becomes more intelligent than humans and each generation of intelligent machines re-designs itself smarter. Beyond this point, there is a symbiosis between machines and humans. This co-existence will produce incredible impacts on medicine that its sparkles could be seen in healthcare industry and the future medicine since 2025. Ray Kurzweil, the great futurist, suggested that three revolutions in science and technology consisting genetic and molecular science, nanotechnology, and robotic (artificial intelligence) provided an exponential growth rate for medicine. The “exponential medicine” is going to create more disruptive technologies in healthcare industry. The exponential medicine shifts the paradigm of medical philosophy and produces significant impacts on the healthcare system and patient-physician relationship.