In the recent past, the application of various types of passive dampers (e.g., yielding metallic dampers) has become a common practice for improving seismic performance of the under-construction buildings and rehabilitation of existing constructions. In this study, a new elliptical metallic damper was introduced to improve the seismic behavior of existing steel structures. Among other parameters, geometrical characteristics are known to affect the seismic performance of the constructions rehabilitated with the proposed elliptical damper. Accordingly, the performance of the proposed damper was investigated through accurate numerical studies on various types of dampers considering various damper dimensions, ellipse major and minor axes length-to-plate thickness ratios, and placements of elliptical shear diaphragm. To study the proposed elliptical damper in terms of its effect on the seismic behavior of rehabilitated buildings, three benchmark structures with 3, 9, and 20 stories were used. Further, far-field and near-field earthquake records were used to undertake nonlinear dynamic analyses. In this work, the proposed elliptical damper was verified by the Abaqus finite-element software, and nonlinear time-history analyses were conducted in the SAP2000 software to check for seismic performance of rehabilitated structural frames with the considered damper. Results of the nonlinear dynamic analyses indicated the appropriate performance of the proposed elliptical damper in terms of reducing the seismic responses of the rehabilitated structures and suitable behavior of the proposed elliptical damper in dissipating the imposed earthquake energy to the structures. Based on these results, upon rehabilitation with the proposed damper, the 3-, 9-, and 20-story structures exhibited smaller maximum lateral roof displacements by 66, 64, and 31%, respectively.

In this paper, an approximate solution of required velocity with final position constraint is derived using a piecewise linear gravity assumption for elliptical earth model. In this approach, the total flight time is divided into several time intervals and the gravitational acceleration is assumed to be linear at each interval. The solution gives an explicit relation in terms of the current position vector, desired final position and flight time in three dimensions. The accuracy and computational burden of the method are obtained numerically in terms of the number of time intervals, and compared with linearized solution and Zarchan's iterative algorithm. Numerical solution shows that the present method has better accuracy than the two mentioned approaches with the same computational burden up to a range angle of 18 deg for minimum energy trajectory in an elliptical earth model. The presented method can be extended for two or multi-body problem and also for the computation of sensitivity matrix of required velocity.

Thin revolved shells, in particular doubly-curved shells, are of interest in many engineering applications.In this research, linear and nonlinear buckling analyses (with consideration of geometrical non-linearity) are performed on two different types of elliptical shells known as Oblate and Prolate which are under external hydrostatic pressure. These shells are made of homogeneous steel. ABAQUS (a well-known finite element software) is used for performing the simulations. Several important parameters affecting the buckling behaviour of these revolved elliptical shells are investigated in detail.These include the ratio between minor and major radii, the percentage of nonlinear buckling value and the shell thickness magnitude on buckling load capacity. The results show the significant effect of shell geometrical dimensions, the magnitude of nonlinear buckling value as an initial imperfection and the shell thickness variations on the buckling load capacity. Finally, it is also observed that the Oblate shell results in a remarkable reduction in the load capacity compared to the other shell type used in this study.To verify the validity of the results, a comparison is made between the present FEM results and the available theoretical studies and good agreement is obtained.

Background: The 131I radioisotope is used for diagnosis and treatment of hyperthyroidism and thyroid cancer. In optimized Iodine therapy, a specific dose must be reached to the thyroid gland with minimum radiation to the cervical spine, cervical vertebrae, neck tissue, subcutaneous fat and skin. Dose measurement inside the alive organ is difficult, therefore the aim of this research was dose calculation in the organs by MCNPX code.Materials and Methods: First of all, the input file for MCNPX code has been prepared to calculate F6 and F8 tallies for ellipsoidal thyroid lobes with long axes is tow times of short axes which the 131I is distributed uniformly inside the lobes. Then the code has been run for F6 and F8 tallies for variation of lobe volume from 1 to 25 milliliters. From the output file of tally F6, the gamma absorbed dose in ellipsoidal thyroid, spinal neck, neck bone, neck tissue, subcutaneous fat layer and skin for the volume lobe variation from 1 ml to 25 ml have been derived and the graphs are drew. As well as, form the output of F8 tally the absorbed energy of beta in thyroid and soft tissue of neck is obtained and listed in the table and then absorbed dose of bate has been calculated.Results: The results of this research show that for constant activity in thyroid, the absorbed dose of gamma decreases about 88.3% in thyroid, 6.9% at soft tissue, 19.3% in adipose layer and 17.4% in skin, but it increases 32.1% in spinal of neck and 32.3% in neck bone when the lobe volume varied from 1 to 25 milliliters. For the same situation, the beta absorbed dose decreases 95.9% in thyroid and 64.2% in soft tissue.Conclusion: For the constant activity in thyroid by increasing the thyroid volume, absorbed dose of gamma in thyroid and soft tissue of neck, adipose layer under the skin and skin of neck decreased, but it increased at spinal of neck and neck bone. Also, by increasing of the lobe volume in constant activity, the beta absorbed dose reduced. Therefore, whatever the thyroid lobe is small the administered value of 131I increased to induce the suitable dose.

Head pose estimation is the main step of the face recognition process. Finding a method which can be fully automated and capable of responding to different poses in all aspects, has created a challenge for this topic. Compared to face detection and recognition, which have been the primary focus of face-related vision research, the head pose estimation is an inter processing step during the implementation of programs in machine vision systems. In this paper, a new algorithm is presented which first the face region is extracted from 3D head image and then the feature vectors that strongly influence the human perception of head pose and these are extremely salient cues regarding the orientation of the head are extracted. Finally, the extracted vectors are trained as input to the classifiers for comparing and differentiating features. In this paper, the Support vector Machines (SVM), the Radial Basis Function neural network classifier (RBF) and the K-nearest neighbor (KNN) methods were used to train feature vectors and data classification. The algorithm was tested on Frav3D and Gavab databases. Finally the experimental results of 98.48 percent of correct estimates which obtained from KNN method, indicate considerable enhancement compared to previous methods.

Let's denote $\mathcal{S}^{\ast}(f_c)$ as a family of analytic functions $f(z)=z+a_2z^2+a_3z^3+\cdots$ in the open unit disk $\mathbb{D}$ that satisfy the following relation for $c\in (0,1)$:$$\frac{zf'(z)}{f(z)}\prec f_c(z)=\frac{1}{\sqrt{1-cz}}, \quad z\in\mathbb{D}.$$First, we introduce the analytic functions $f_c(z)$ and examine their starlike and positivity properties of the real part. Then, we obtain their images in the open unit disk $\mathbb{D}$, which are Cassini ovals. Cassini ovals, due to their properties, have applications in solving various problems in fields such as geometry, physics, and mathematics. These curves are used in studying the motion of waves and electromagnetic waves in interstellar spaces, as well as in the design of engineering structures such as telescopes. In this article, with the help of integrals, we investigate the structure of mappings in this family and some properties including maximum and minimum moduli, bounds of the real part of these functions. Moreover, we obtain the relationships between the defined geometric ranks with this family, including the order of starlikeness and order of strong starlikeness.1. IntroductionLet $\mathcal{A}$ be a set of analytic functions of the form $f(z)=z+a2z^2+a3z^3+\cdots$ in the open unit disc $\mathbb{D}:=\left\{z\in\mathbb{C}\colon |z|<1\right\}$. A function $f\in\mathcal{A}$ is called univalent if it is one-to-one. In [5], two classes of starlike and convex functions with order $0\le \beta<1$ are defined as follows:\begin{equation}\label{starlike-convex}\mathcal{S}^{\ast}(\beta):=\left\{f\in\mathcal{A}\colon \Re\left(\frac{zf'(z)}{f(z)}\right)>\beta\right\},\quad \mathcal{K}(\beta):=\left\{f\in\mathcal{A}\colon zf'(z)\in\mathcal{S}^{\ast}(\beta)\right\}.\end{equation}Similarly, in [2], the class of functions called strongly starlike with order $0<\alpha\le 1$ is defined as:\[\mathcal{SS}^{\ast}(\alpha)=\left\{f\in\mathcal{A}\colon \left|\mathrm{Arg}\frac{zf'(z)}{f(z)}\right|<\frac{\alpha \pi}{2}\right\}.\]If $f$ and $g$ are two analytic functions in $\mathbb{D}$, we say that $f$ is subordinate to $g$ \cite{Dur}, denoted by $f\prec g$, if and only if there exists an analytic function $w$ with $w(0)=0$ such that for all $z\in\mathbb{D}$:\[\left|w(z)\right|<1, \quad f(z)=g(w(z)).\]If $g$ is univalent, we have:\[f(z)\prec g(z) \Longleftrightarrow f(0)=g(0),\quad f(\mathbb{D})\subset g(\mathbb{D}).\]Given $c\in(0,1)$, analytic functions $f_c$ are defined as follows:(1.2)$$f_c(z):=\frac{1}{\sqrt{1-cz}}=1+\frac{c}{2}z+\frac{3c^2}{8}z^2+\cdots$$in the principal branch of the complex logarithm, where $\log 1=0$. These functions are univalent in $\mathbb{D}$ and map the open unit disc $\mathbb{D}$ into the interior of the Cassinian ovals given by the Cartesian equation:\begin{equation}\label{Cassinian-Ovals}(x^2+y^2)^2-\frac{2}{1-c^2}(x^2-y^2)+\frac{1}{1-c^2}=0,\end{equation}or the polar equation:\begin{equation}\label{Cassinian-Ovals1}r^4-\frac{2r^2 }{1-c^2} \cos(2\theta)=\frac{1}{c^2-1}.\end{equation} 2. Main ResultsIn this section, we will first derive the structure of functions in the class $\mathcal{S}^{\ast}(f_c)$, and then using the stated theorems, we will determine the order of starlikeness and strongly starlikeness of functions in the class $\mathcal{S}^{\ast}(f_c)$. Theorem 2.1. A function $f$ belongs to the class $\mathcal{S}^{\ast}(f_c)$ if and only if there exists a function $p \prec f_c$ such that\begin{equation}\label{thm-1-0}f(z)=z\exp\left(\int_{0}^{z}\frac{p(t)-1}{t}dt\right), \quad z\in\mathbb{D}.\end{equation} If we set $p(z)=f_c(z)$ in theorem (2.1), then we get(2.2) $$F_c(z):=z\exp\left(\int_{0}^{z}\frac{f_c(t)-1}{t}dt\right)=\frac{4z}{(1+\sqrt{1-cz})^2}, \quad z\in\mathbb{D}.$$This function $F_c(z)$ is an extreme function for the class $\mathcal{S}^{\ast}(f_c)$. Figure 2 illustrates the image of the open unit disk $\mathbb{D}$ under the mapping $F_c(z)$ for $c=3/4$. Theorem 2.2. Let $f_c$ be the given function described in (1.2). Then $f_c$ is convex and satisfies the following conditions:\begin{equation}\label{max-min0}\max_{|z|=r<1}\left|f_c(z)\right|=f_c(r),\quad \min_{|z|=r<1}\left|f_c(z)\right|=f_c(-r).\end{equation} In the following theorem, we obtain bounds for the real part and strongly starlike mappings of the functions $f_c$. Theorem 2.3. Suppose $c\in(0,1)$. Then we have the following:(1) \[f_c(\mathbb{D})\subset \left\{w\in\mathbb{C}\colon \frac{1}{\sqrt{1+c}}<\Re(w)<\frac{1}{\sqrt{1-c}}\right\},\](2)\[f_c(\mathbb{D})\subset \left\{w\in\mathbb{C}\colon \left|\mathrm{Arg}(w)\right|<\frac12 \arccos\sqrt{1-c^2}\right\}.\] Theorem 2.4. If $f\in \mathcal{S}^{\ast}(fc)$ and $|z|=r<1$, then the following hold:(1) \[\frac{zf'(z)}{f(z)}\prec \frac{zF'_c(z)}{F_c(z)},\quad \frac{f(z)}{z}\prec\frac{F_{c}(z)}{z},\](2) \[F'_c(-r)\le \left|f'(z)\right|\le F'_c(r),\](3) \[-F_c(-r)\le |f(z)|\le F_c(r),\](4) \[\left|\arg{(f(z)/z)}\right|\le \max{|z|=r}\arg\left(\frac{1}{(1+\sqrt{1-cz})^2}\right),\](5) Either $f$ is a rotation of $F_c$ or\[\left\{w\in \mathbb{C} \colon\ |w|\leq-F_c(-1)=\frac{4}{(1+\sqrt{1+c})^2}\right\}\subsetf(\mathbb{D}),\]where in all cases, the function $F_c$ is defined as per equation (2.2).\end{thm}In the following theorem, we determine the subordination order and strong subordination order for the class of functions $\mathcal{S}^{\ast}(f_c)$. Theorem 2.5. The class of functions $\mathcal{S}^{\ast}(f_c)$ has the following properties:(1) For $0\le \beta\le \frac{1}{\sqrt{1+c}}$, we have\[\mathcal{S}^{\ast}(f_c)\subset \mathcal{S}^{\ast}(\beta).\](2) For $\frac{1}{\pi}\arccos\sqrt{1-c^2}\le \alpha\le 1$, we have\[\mathcal{S}^{\ast}(f_c)\subset \mathcal{SS}^{\ast}(\alpha).\] 3. ConclusionsThe class $\mathcal{S}^{\ast}(f_c)$ consists of functions that can be represented in a specific form involving the function $f_c$, which is a special function related to the starlikeness property. The function $F_c(z)$, derived from $f_c(z)$, is an extreme function for the class $\mathcal{S}^{\ast}(f_c)$ and has specific properties, including convexity and bounds on its maximum and minimum modulus on the unit circle. The presented theorems provide bounds for the real part of the functions $f_c$ and establish relationships related to subordination and strong subordination order for the class of functions $\mathcal{S}^{\ast}(f_c)$. Overall, the obtained theorems and their proofs contribute to understanding the structural properties, order of starlikeness and strongly starlikeness, as well as subordination order within the class of functions $\mathcal{S}^{\ast}(f_c)$, for different values of the parameter $c$.