The position of the planets for the planetary gear systems are in two forms of equally and unequally spaced. This paper investigates free vibration of the planetary gear with unequally spaced planets. The planetary gear set of this study is modeled as a set of lumped masses and springs. Each component such as sun gear, carrier, ring gear and planets possesses three degrees of freedom and is considered as rigid body. Bearing and mesh stiffness are modeled in the form of linear springs. Generally, planet, rotational, translational, distinct and degenerate modes are five vibration modes of the planetary gear systems. The results show that the translational mode for the system with numbers of even equally and unequally spaced planets, is different and rotational and translational modes have the same characteristics for both systems. For the system with numbers of even unequally spaced planets, the natural frequencies of the translational modes have a multiplicity one. When the numbers of the planets of the system are odd and the position of them is unequally spaced, the rotational and planet modes are generated and the natural frequencies of the translational modes do not appear. For the distinct and degenerate modes of the system with unequally spaced planets, the planets only have the rotational motion.

We study the free oscillations of a non-rotating earth-like planet in the presence of a force free magnetic field. The model consists of a solid inner core, a liquid outer core and a solid mantle which is spherically symmetric. The lagrangian displacements are decomposed into scaloidal, poloidal and toroidal components using a gauged version of Helmholtz theorem. These components are identified, with p -, g - and t -modes, respectively. The normal modes of the model are determined using a Rayleigh-Ritz variational technique. The consequence of the presence of the solid parts and the magnetic field is the emergence of pure t -oscillations. The magnetic field, in addition to exciting t -modes, couples the ever present p -and g -modes together. As an application of the model, the real seismic data of the earth is used to calculate eigenvalues and eigenvectors for different modes.

Ptolemy explains his planetary latitude hypothesis in the 13th book of Almagest and for the first time he forced to use inclined circles to explain the planetary movements in latitude. Before it, Ptolemy could explain all the anomalies of planetary movements with two dimensional models, but to explain the movements in latitude, they transform to three-dimensional objects. Although, in his another work, Planetary Hypotheses, Ptolemy considers the spheres to explain the movements of the planets but it seems that in this part of Almagest, due to the need of the hypothesis, he explains the solid orbs independently of Planetary Hypotheses.

Space law is one of the newest and most innovative branches of international law, and along with the activities of space since the 50's, the relevant legal provisions have also been developed, and, in this regard, numerous books and articles have been published in the West. However, Persian legal literature has been slow and inactive. Among the few efforts is the book "International Space Law" by Hussein Navadeh Toupchi. The book includes a variety of sections, including the international law governing space, the legal aspects of space technology, the status of earth orbits, the environmental law, responsibility, dispute settlement and arms control. He attempted to explain each subject in a critical and analytical manner. The present paper, while introducing and editing the contents of the book and its privileges, tries to address the book’ s downsides fairly and specifically addresses issues not addressed in the book.

The fundamental characteristic of Gnosticism is its anti-cosmic attitude and strong duality between God and the material world. This thought requires un-deification of cosmic forces and consideration of the evil and antagonistic actors who control the world, body and psyche of man who are irrelevant to absolutely supreme God, who is beyond this system. In Gnostic thought, these cosmic powers are mainly the rulers of the heavenly planets (archons). In order to achieve salvation, man must be freed from the rule of these archons, and this salvation is not possible without the intervention of God's roar from outside of the cosmic system. At the same time, similar ideas have found their way in the religious texts of Zoroastrianism orthodoxy as well as in Islamic philosophy and mysticism without any contradictions with their basic principles. These anti-cosmic thoughts have found a special and unique resonance in Hafez's poetry through the role of astral spirits in the process of cosmogenesis and the events of the beginning of creation and the existential position of man in relation to these events which has connected Hafez's soteriology with the idea of "splitting the roof of the sky". By comparing Gnostic texts, myths and fundamental ideas with the ideas, themes and symbolism found in Hafez's poetry, this research shows the Gnostic themes of Hafez's poetry and their relationship with his worldview and ontology.

2Astronomers have made predictions based on the study of astrological signs as well as movement of planets and stars and their influence on Earth, and have argued it according to astronomy. This science was initially the exclusive domain of astronomers, but gradually expanded to the field of medicine and treating the patients. The subjects related to the well-known astrological signs (Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, and Pisces) in the zodiac and planets (Saturn, Jupiter, Mars, Sun, Venus, Mercury, and Moon) in the solar system have a special effect according to Persian Medicine. The most important applications included recognizing the suitable moment for medical affairs, including determining the time of symptom onset in patients, composing drugs, prescribing pharmaceutical drugs, medicine consumption at the suitable moment, and finally restoring patient health. Astrological concepts that are more prominent in handwritten texts of three great Iranian sages, Abu Rayhan Biruni, Sayyid Isma‘il Jurjani, and Aqili Shirazi, are those related to predicting auspicious (sa'd) and infelicitous (nahs) moments for medical affairs.

Introduction:The Seljuk era, was a prosperous time in case of dealing with art; during this time art reached to higher level, as numerous and diverse artworks with cosmological concepts were created, which represents the significance of cosmology in this time. The artists in this era, by considering the position of astronomy and cosmological issues, frequently reflected the relevant concepts and contents as practical decorations and motifs in their works. This study aims to comprehend the concepts of cosmological motifs to target the mutual influence of Seljuk artists on each other while designing these patterns; Therefore, the manner these artists influence each other in designing the planet motifs and their meanings has been addressed in two artworks related to Seljuk era; in this regard, the following questions arises: Which kind of hypertextuality is more likely to be influenced by the design of the target motifs of the planets? And what changes have been made in these motifs while influencing each other? The research aims to understand the manner the design of planets' motifs influence each other and the alterations in the two target works by focusing on the hypertextuality theory of Gerard Genette.Research Method: A descriptive-analytical method has been adopted and the data was collected by using library sources; The results were analyzed relying on a qualitative method.Findings: According to the research findings, the cosmological motifs that appeared in the Seljuk manuscripts are rather compatible with other built-in arts, in the case of decoration, besides considering the cosmological criteria; however, some changes have been made according to the artist's priorities. The artists in the Seljuk era were completely aware of the art developments of their own time and also the previous eras, as they tried their best to improve the art of their time by benefiting from the experiences of other artists.Conclusion: the research finding showed that the planet motifs in «Ajaib al-Makhluqat» (hypertext) which is inspired by the planet motifs in the enamel bowl (pre-text or hypotext) have a transposition or transformation with serious function according to the hypertextuality of Genette. The created transformation in hypertext includes a variety of changes (gender, form, composition, and color). The miniature painter of «Ajaib-ul-Makhluqat» has not simply adopted an imitation attitude in creating a new and independent hypertext, as it has been designed differently.

One of the most important subjects used to decorate the metalwork of the Middle Ages of the Islamic period was astrological images including the constellations, zodiac signs and seven planets. Also, the images of seven planets including the Moon, Mercury, Venus, Sun, Mars, Jupiter and Saturn, in Islamic metalwork have always been depicted in two ways, sometimes in combination with the zodiac signs and sometimes in isolation. In the present study, the second type is considered, which is imaginary. The purpose of this research is to consider and compare the isolated images of seven planets in the works of the three major metalworking schools during twelfth and thirteenth centuries, which are, respectively, Khorasan in the north-east of Iran, the Jazira, north of Mesopotamia, and the north-west of Iran. Because of the differences observed in the iconography of seven planets’ images in the products of these three schools, the following questions raised, including what are the stylistic and iconographic differences between the seven planets’ images of these three metalworking schools and what is the reason for these differences? In this research, we examined three important examples of the metalwork of these schools using descriptive-analytical method and then we compared them. On the island>s metalwork, which used the seven planets’ images for the first time, each of the seven planets have been depicted in human form, sitting cross-legged and bearing their own traditional features, such as Mars that has a head and a sword, Saturn that carries an ax, and Venus that plays a lute. In the Khorasani metalwork, we see some slight changes in the overall illustration of these images and a major change in the iconography of Shams (Sun). Here, like the metalwork of the island, all of them, except for the sun, have a human body and sitting cross-legged. However, the multi-handedness of the seven planets’ images on one hand and existence of more than usual signs on the other hand, has revealed the difference between the iconography of planets’ images of the Jazira and Khorasan. In addition, another significant difference between these designs is in the image of the sun as well as the number of planets. The image of the sun in the metalwork of Khorasan, unlike the metalwork of the Jazira, is not human; instead it is a radiating circle containing three human faces. And in the metalwork of the Khorasan, the fake planet Jozhor is also shown next to the other planets. In the end, we should point out how these designs were drawn in the northwest of Iran where almost all the planets’ forms are similar to the designs of Jazira, showing influences from its seven planets’ form with no iconographic difference between them. The only distraction that can be seen in the seven planets’ images of this area appeared in the image of the sun. Here also, like the metalwork of Khorasan, the sun has not been depicted with a human body and appears with merely a radiating circle. However, the image of the sun in this area just surrounds one human face rather than three. The required data is collected through library research method. The results of the analysis of the findings and evidences suggest that there is a significant relationship between the iconography of the seven planets’ images in the metalwork of twelfth and thirteenth centuries and their geographic origins. Furthermore in the attributes assigned to each of these planets, effects of astronomical or astrological beliefs and perspectives of different geographic origins, which have led to the iconographic differences in their imagery, are evident. In general, it should be noted that the beginning of the illustration of seven planets in Islamic metalwork, based on the earliest sample, is attributed to the metalwork school of Jazira. It seems these images have been transferred from Jazira in the northeast of Mesopotamia to the northeast of Iran, and then from there, they returned to the northwest of Iran and have been depicted on the metalwork produced at the beginning of the Ilkhanid period.

According to the Titus-Bode law, orbits of planets in the solar system obey a geometric progression. Many investigations have been launched to improve this law. In this paper, we apply square and exponential models to planets of solar system, moons of planets, and some extra solar systems, and compare them with each other.

Purpose: The integrated coastal zone management (ICZM) was considered the main way of solving environmental problems. In addition, there are many countries in the world that attempt in providing the human needs to coastal region services in order to the natural border of these zones. The main purpose of this paper is to identify the current situation of pollution in different coastal areas of Mazandaran province and the zoning of areas in terms of environmental pollution. Methodology: In this paper, we first deal with the conceptual framework of ICZM and study the successful examples of its implementation in different countries and compare them from different aspects. Then, in order to implement this project on the west coast of Mazandaran province, we will pay attention to the studies related to environmental pollution. Findings: Findings show that in coastal management, all physical, ecological, social, and economic processes that interact on the coast and the sea should be identified and a certain coordinate between different users at local, national, regional, and international levels must be created. Furthermore, the successful implementation of ICZM requires more attention to the social and economic conditions of the Caspian littoral states. Originality/Value: In this article, we study the characteristics of the west coast of Mazandaran province based on important ecosystems and parameters such as industrial pollutants, soil type, vegetation (sea and land), wildlife, geology, marine topics (water fluctuations, wave characteristics, etc. ) And we analyze the related issues. Finally, in order to implement the ICZM in the west coast of Mazandaran province, from the point of view of environmental pollution, we investigate the distribution of industrial pollutants in the use of coastal lands up to a radius of three kilometers in the Caspian Sea.