In this paper، we introduce a new five-parameters distribution with increasing، decreasing، bathtub-shaped failure rate، called as the Beta Weibull-Geometric (BWG) distribution. Using the Sterling Polynomials، the probability density function and several properties of the new distribution such as its reliability and failure rate functions، quantiles and moments، Renyi and Shannon entropies، moments of order statistics، mean residual life، reversed mean residual life are obtained. The maximum likelihood estimation procedure is presented in this paper. Also، we compare the results of fitting this distribution to some of their sub-models، using to a real data set. It is also shown that the BWG distribution fits better to this data set.

Suppose that a geometrically distributed number of observations are available from an absolutely continuous distribution function $F$, within this set of observations denote the random number of records by $M$. This is called geometric random record model. In this paper, characterizations of $F$ are provided in terms of the subsequences entropies of records conditional on events ${M geq n}$ or ${M = n}$ in a geometric random record model. Characterization results for symmetric distributions are also presented based on entropies of upper and lower records in a random record model.

The aim of this study is an investigate the effect of design parameters and profile modification on static transmission error and load sharing factor of helical gears using analytical method with Matlab software. In the first step, we define the concept of transmission error that is the source of noise in the gear pair. Then load sharing factor and static transmission error are calculated using the gear mesh stiffness. In this paper the total stiffness of helical gear’s and the load sharing factor is determined using an accumulated integral potential energy method. In the next, results are verified and the effect of design parameters on avarege and pick to pick of the helical gears transmission error and load sharing factor is investigated. This parameter is called macro-geometric parameters of gear pairs. At the end, we write a Matlab code to modify the tip relif of tooth to optimize the load sharing factor and static transmission error. The results of this study show that the simultaneous correction of macro-geometric modifications and profile modification (micro-geometric modifications) cause a more uniform load distribution and significantly reduce the transmission error of the helical gear and consequently reduce the noise and vibration of the gearboxes.

A moderate earthquake (M: 5.1) impacted the urban regions of Malard-Meshkindasht in Alborz province (far west of Tehran) with noticeable crashing of indoor objects that injured people around main shock epicenter in 20 December 2017. In this research, I have used Fibonacci numbers to set 53 years epicenters (IIEES, 1964-2017) based on Perimeter-Area fractal model containing foreshocks, main event and aftershocks onsets. Malard spiral revealed a meaningful geometrical relationship between the recent and recorded earthquakes in catalogue. Several epicenters have been patterned by geometrical angles in self-organized features. Also a set of foreshocks illustrate spiral distributions as well as in aftershocks due to a coherent association with seismic fault systems. Also an integrative spiral has been illustrated in the end of research to realize the hazard of Malard earthquake on NTF. For the time being, there is no inductive case from Malard into NTF because of represented Fibonacci and fractal evidences for this research.    

Fibonacci numbers are famous series in mathematics for introducing golden sequences in natural creatures [1]. In this sequence, each number is found by adding up two numbers before it. Starting with 0 and 1, the sequence goes 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so forth. Written as a rule, the expression is:

Fn = Fn-1 + Fxn-2

(1)

Where, Fn is obtained Fibo-number, and Fn-1, Fn-2 are two sequences before Fn respectively [1].
Both real sets and integer sequences impressed many of natural phenomena, and therefore known as the mathematical keys for terrestrial and infra-terrestrial solutions. For instance, earthquakes have close and meaningful relations with rectangular spiral distributions as a result of spatio-temporal evolution in nature.
A simple sequence of Fibo-numbers is shown as below:1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …, Fn
In above sequence, a ratio of (Fn/Fn-1) gives constant value (golden ratio, Ҩ) equal with 1.618.

Ҩ=Fn/F(n-1) = 1.618

(2)

This ratio has important roles in geosciences such as a main role in earthquake distribution geometrically. From geodynamical points, crustal motions regulate themselves by Ҩ to originate self-organized patterns on the basis of chaos theory [2]. Two types of golden ratios (1/618 and 1/133) are involved in golden shapes such as triangles, golden circles and golden rectangles [3,4]. Also a simple distribution of earthquakes can be seen in Gnomons and circles around the main shock events. Malard circle has two unequal arcs which one of them has golden angle equal with 137.5 degree of angle. The third is golden rectangle which has spiral function to correlate with geological patterns [3]. For example, earthquakes and their focal distributions are relevant process to golden rectangles with affinity to appear in spiral distributions as is it shown in Figure 1.
 
Fig. 1. Spiral function of earthquakes based on a golden rectangular distribution.
AGFD (3-a) is a rectangle that is reproduced by a simple ABCD square (3-b) within a multiple statement as below:

(0.5b)*(51/2) = FD   [Where: FD/CD = 1.618

(3)

Here, a golden geometrical distribution of half century earthquakes is well done by applying Fibonacci numbers into IIEES catalogue. Natural earthquakes usually array in spirals and therefore geoscientists are interested to start a seismic spatial interpretation according to Fractals and Fibo-sequences [2,4,5]. At least, 53 years backgrounds of Malard seismic events (IIEES, since 1964) facilitate this opportunity to answer the question of “where is the next destructive earthquake in regional local scale?”
It means, with a dense and accurate catalogue, scientists will be able to locate the future earthquakes based on geometrical precursors. Also we know that Fibonacci numbers have close impressions to nature as a key for earthquake prediction [3,4]. According to post prediction algorithm, a main shock record such as Malard event (20 Dec., 2017) , not only initialized post seismic processes, but is relevant to long term catalogues as a regional Fibonacci variable. In practice, Alborz seismic databases including location of epicenters [6,7] and structural lineaments [8], have been gridded by GIS facilities to reveal geometrical relationships of the epicenters to illustrate golden peculiarities of Malard earthquakes.            

Malard earthquake (2017-12-20) seems to be initial point for a short range of post seismic events, which many of them should be considered as aftershocks activities. In Figure 2-a, meaningful triangular distribution can be seen in north side of Malard main shock epicenter. Also, an obvious golden circle (within radius lesser than 2 Km from main shock event) can be seen in Figure 2-b as below.
 
Fig. 2, a) two kinds of golden triangles (ordinary and gnomons) in Malard seismic pattern.  b) A symmetric golden circle with approximate radius =1.6 near Malard main shock region.
As a primary result, above mentioned facts indicate to natural seismic resources of Malard-Meshkindasht activities, and as second, a rectangular distribution of magnitudes (M>2, since 1964) give rises to spiral function, which contain two types of post seismic potentials (High and Low PSP) shown in Figure 3.
Malard spiral is a dependent geometrical variable to post seismic events as well as its dependency to foreshocks base on Perimeter-Area fractal applied in catalogue. This spiral is Meridian type with west seen affinity that is centralized by Malard seismic events in Dec. 2017.
 
 Fig. 3, Spiral distribution of Malard earthquakes (Ref. Database: IIEES, 1964-2017)

-This research introduced geometrical fractal analysis of 53 years catalogue (Malard region) as recently active zone in eastern part of Alborz province.
-Rectangular distribution of Malard earthquakes, make an easier and accurate forecasting of future events (usually aftershocks or other seismic activities) that is originated from main resources maybe encircled by golden circles and limited by fractals. 
 
Figure 4. A Fractal separation in random - regular Fibonacci sequences in Malard seismic events (20 Dec. 2017)
In figure 4, forecasted areas (red hatched), have been determined by cross-cutting the isosceles of golden rectangles (Fibo-grids). Therefore, many of Fibo-epicenters are shown on this figure, but few of them are involved with PSP.
- Rectangular distribution of Malard earthquakes makes an accurate way to forecast the future events (aftershocks) originate from main seismic resources by both fractal and Fibo analysis of catalogue.
-For the time being, Malard aftershocks maybe continued toward the west to complete seismic gaps in this cycle (high PSP, Figure 3). Also a rare scenario maybe occurred in west or east directions due to triggering Eshtehard fault or NTF system respectively. Moreover, from geometrical points of view, this scenario is temporary with no longer effects after a monthly reducing in post seismic activities.

In this paper, we consider a three parametric regularly varying generalized Hypergeometric distribution which have been generated by Birth-Death process for describing phenomena in bioinformatics (Danielian and Astola, 2006). Under satisfying some conditions, we obtain the system of likelihood equations which its solution coincides with the maximum likelihood estimators. The given maximum likelihood estimators are the same as some moment estimators.Moreover, an approximate computation of the maximum likelihood estimations for the unknown parameters is given. Using MCMC, simulation studies are proposed. Finally, in order to present applications, some real data sets in bioinformatics are fitted with the model. Based on some important criterions, this model is compared with four other discrete distributions in bioinformatics. We see that the generalized Hypergeometric distribution provides a better fit than four other discrete distributions.

Nowadays, in metal forming industries, the production of parts with proper thickness distribution and geometric accuracy is very important and significant. In this research, all parts are formed by a new process called two-point incremental forming process using a flexible die. Flexible die, is a die that consists of a number of separate overhead pins that can be adjusted by the height of each pin according to the desired geometry. First, the effect of the thickness (0.5, 1.5, 3 and 6mm) and hardness (60 and 90Shore A) of rubber layers on the two parameters of thickness distribution and geometric accuracy of the formed samples has been studied. The effect of the arrangement of the pins in a flexible die with full and partial layout on the two mentioned parameters has been studied. The results show that the geometric accuracy of the sample formed on the rubber layer with a thickness of 0.5mm has been improved by 78.3% compared to the thickness of 6mm, but the degree of thickness of this workpiece is more than other parts. Geometric accuracy of the workpiece is also improved by 61.77% when using a rubber layer with a hardness of 90Shore A compared to a hardness of 60Shore A, but the thickness distribution of the workpiece is the same. The pins with full arrangement have a better geometric accuracy and thickness distribution than the partial arrangement in a flexible die. Using a multi-step strategy in a flexible die has the disadvantage of wrinkling.

Brace and chord members of a tubular joint always have a degree of geometrical imperfection due to the manufacturing، transportation and installation processes and also the action of various loads during the lifetime of the structure. However، during the analysis and design of tubular joints، geometrical imperfection is not usually taken into account. Considering the geometrical imperfection in the analysis of a tubular joint، can lead to a more realistic prediction of the fatigue life. In this paper، the effect of geometrical imperfection of the brace member and dimensionless geometrical parameters on the stress distribution in tubular T-joints under axial loading is studied. The stress concentration factors (SCF) is used to investigate the stress distribution. The research is focused on the SCF values at the saddle، crown 0˚ and crown 180˚ positions. After the numerical modeling of the considered tubular joints using FEM-based software package ANSYS، verification of the FE models by experimental data، and the extraction of SCFs، a set of parametric equations is presented to calculate the SCFs at the saddle، crown 0˚ and crown 180˚ positions. The results show that the in-plane geometrical imperfection of the brace member can change the SCFs at the crown 0˚ and crown 180˚ positions، but does not have a considerable effect on SCF values at the saddle position.

Machine learning is an application of artificial intelligence that is able to automatically learn and improve from experience without being explicitly programmed. The primary assumption for most of the machine learning algorithms is that the training set (source domain) and the test set (target domain) follow from the same probability distribution. However, in most of the real-world applications, this assumption is violated since the probability distribution of the source and target domains are different. This issue is known as domain shift. Therefore, transfer learning and domain adaptation generalize the model to face target data with different distribution.In this paper, we propose a domain adaptation method referred to as IMage Alignment via KErnelized feature learning (IMAKE) in order to preserve the general and geometric information of the source and target domains. IMAKE finds a common subspace across domains to reduce the distribution discrepancy between the source and the target domains. IMAKE adapts both the geometric and the general distributions, simultaneously. Moreover, IMAKE transfers the source and target domains into a shared low dimensional subspace in an unsupervised manner.Our proposed method minimizes the marginal and conditional probability distribution differences of the source and target data via maximum mean discrepancy and manifold alignment for geometrical distribution adaptation. IMAKE maps the input data into a common latent subspace via manifold alignment as a geometric matching method. Therefore, the samples with the same class labels are collected around their means, and samples with different class are separated, as well. Moreover, IMAKE maintains the source and target domain manifolds to preserve the original data position and domain structure. Also, the use of kernels and mapping data into Hilbert space provides more accurate separation between different classes and is suitable for data with complex and unbalanced structures. The proposed method has been evaluated using a variety of benchmark visual databases with 36 experiments. The results indicate the significant improvements of the proposed method performance against other machine learning and transfer learning approaches.

In this paper, we introduce a family of bivariate generalized Gompertz-power series distributions. This new class of bivariate distributions contains several models such as: bivariate generalized Gompertz -geometric, -Poisson, - binomial, -logarithmic, -negative binomial and bivariate generalized exponental-power series distributions as special cases. We express the method of construction and derive different properties of the proposed class of distributions. The method of maximum likelihood and EM algorithm are used for estimating the model parameters. Finally, we illustrate the usefulness of the new distributions by means of application to real data sets.