Rectangular Projection Research Articles

THE RESEARCH OF IMPLEMENTATION OF NUMERICAL RIGOROUS MATHEMATICAL METHODS WITH THE PARAMETER OF THE MEMBERS NUMBER IN THE TAYLOR SERIES

The current level of development of geoinformation technologies makes it possible to determine the cartometric properties of terrain objects with a user-defined accuracy. The author of this paper proposes a mathematical model that allows to implement the function of converting geodetic coordinates into rectangular flat Gauss-Kruger projections in a software environment based on the setting of the parameter of the number of members in the Taylor series, adjusting the accuracy of the coordinate transformation and their dimension. The purpose of this work is to implement a mathematical model of a numerical approximate computer method of converting geodetic coordinates into flat rectangular Gauss-Kruger projections. The results of this study will also be used to create functions for converting coordinates from rectangular flat Gauss-Kruger projections to geodetic coordinates and from one 6-degree zone of the Gauss-Kruger projection to another, taking into account the parameter of the number of members in the Taylor series. The proposed mathematical models are recommended to be implemented in the MATLAB or PhyCharm using the necessary libraries. The following studies will focus on determining the areas and lengths of objects located in two or more 6-degree zones of the Gauss-Kruger projection.

Аxonometric transformations of a complex drawing

When drawing up technical drawings, it is sometimes necessary to have visual representations along with images of objects in the orthogonal projection system. For such images, the method of axonometric projection is used (axonometry is a Greek word, literally translated as measurement along the axes; axon means axis, metreo means measuring). The essence of the axonometric projection method: an object, together with the axes of rectangular coordinates to which it is assigned in space, is projected onto a certain plane so that none of its coordinate axes is projected onto it at a point. In this case, the object itself is projected onto this projection plane in three dimensions. In this case, the dimensions of the object in axonometric projections along all three axes are distorted. The change in linear dimensions along the axes is characterized by the distortion indices (coefficients) along the axes. The distortion index is the ratio of the length of a segment on the axonometric axis to the length of the same segment on the corresponding axis of the rectangular coordinate system in space. The purpose of this paper is to construct an axonometric projection of a circle located in the plane of general position using classical methods of descriptive geometry - methods of transforming a complex drawing. Axonometry stands alone in descriptive geometry, which is due to the theoretical multitude of approaches in which the coordinate system is a model of geometric space. Certain difficulties in mastering axonometry are related not only to this but also to its insufficient methodological support. Thus, in the definition of axonometric projection, the standards do not contain key phrases about the orientation of the object and the associated coordinate system relative to the projection direction, which should not be parallel to any coordinate axis. There is no clarity about axonometric planes, their location relative to the main planes in rectangular projection. The article describes a method for constructing an axonometric projection of a circle located in the plane of general position relative to the planes formed by axonometric axes. An example of constructing an ellipse - a projection of a circle for a projecting plane - is given, which can be extended to the conditions of the plane of general position without fundamental changes. The proposed article can be recommended for students who study descriptive geometry and engineering graphics courses in depth, and can also be useful for young teachers as a supportive material in working with students.

Projection and Barrier Lyapunov-Based Controller Update Laws in MRAC Structure for Flexible Satellite Launch Vehicles

This paper investigates adaptive flight control design strategies which are robust to a wide range of both parametric and non-parametric uncertainties for a highly non-linear, time-varying and under-actuated launch vehicle system. In general, scheduled PID controllers are designed for the rigid body dynamics of the launch vehicle and structural filters/compensators are used to stabilize underactuated dynamics such as slosh and flexibility. In this work, two stable Lyapunov-based adaptive controllers are designed with full-state feedback. In the first controller, adapted gains are constrained to be within the limits defined by the user using a rectangular projection operator. In the second controller, tracking error is also constrained using a barrier Lyapunov function. States of the under-actuated dynamics and rigid body dynamics are estimated from the noisy attitude and attitude rate measurements using an extended Kalman filter. Tracking and regulation control studies are conducted to show the efficiency of the proposed controller update laws using different command signals.

Low-rank robust online distance/similarity learning based on the rescaled hinge loss.

An important challenge in metric learning is scalability to both size and dimension of input data. Online metric learning algorithms are proposed to address this challenge. Existing methods are commonly based on Passive/Aggressive (PA) approach. Hence, they can rapidly process large volumes of data with an adaptive learning rate. However, these algorithms are based on the Hinge loss and so are not robust against outliers and label noise. We address the challenges by formulating the online Distance/Similarity learning problem with the robust Rescaled Hinge loss function. The proposed model is rather general and can be applied to any PA-based online Distance/Similarity algorithm. To achieve scalability to data dimension, we propose low-rank online Distance/Similarity methods that learn a rectangular projection matrix instead of a full Mahalanobis matrix. The low-rank approaches not only reduce the computational cost but also keep the discrimination power of the learned metrics. Also, current online methods usually assume training triplets or pairwise constraints exist in advance. However, this assumption does not hold, and generating triplets using available batch sampling methods is both time and space consuming. We address this issue by developing an efficient, yet effective robust one-pass triplet construction algorithm. We conduct several experiments on datasets from various applications. The results confirm that the proposed methods significantly outperform state-of-the-art online metric learning methods in the presence of label noise and outliers by a large margin.

Robust Adaptive Control Laws for a Winged Re-entry Vehicle

The flight control system for reusable launch vehicles has to work for an extensive flight envelope ranging from hypersonic to subsonic Mach numbers. Since the plant dynamics are highly nonlinear, time-varying, and coupled, classical controllers are designed for large stability margins about the linearised points. This limits the performance of the classical controller, and the design process is iterative and time-consuming. Hence adaptive controllers are designed to handle such complex systems using a standard quadratic Lyapunov function. The existing parameter update laws of the model reference adaptive control system are not robust to bounded disturbances and unmodelled dynamics. Hence this paper proposes modified controller parameter update laws using a rectangular projection operator and barrier Lyapunov function, ensuring robustness to structured and unstructured uncertainties. The rectangular projection-based control law provides that the controller parameters remain within the specified upper and lower limits, whereas the barrier Lyapunov-based controller maintains the trajectory also within the specified error limit. The effectiveness of the proposed update laws is demonstrated for the automatic landing phase of a reusable launch vehicle.

EXPLOITABLE EDGE ANALYSIS FOR FREE FLOW VEHICLE PLATE LOCALIZATION

In Malaysia, vehicle recognition system (VRS) such as vehicle plate recognition and counting, is rapidly growing and applied in many areas such as to identify vehicle identities for the law enforcement by authorities and electronic toll collection by highway agencies. Uncovering the region of interest in chaotic illumination environment at free flow road makes localizing license plate is critical process of VRS. Available edge vertical projection claimed to be robust to illumination, however, it tends to create false edges and sensitive to noises that can hinder the recognition performance. Thus, this research aims to propose a license plate localization method that based on exploitable edge analysis.comprising four main steps, namely pre-processing, rectangular blob searching, analysis and the vertical rectangular blobs projection. It calculates total and exploit edge information at y axis of the image. The proposed method is then tested on the European number plate datasets i.e. Baza Slika which contains about 167 vehicle images and Ondrej which contains about 97 vehicle images. The experimental results show that the proposed method outperforms the Ondrej method by obtaining accuracy of 95% on Baza Slika dataset and slightly lower by an accuracy of 91% on the Ondrej dataset. Then, the proposed method tested on the Malaysia vehicle dataset namely Tol Sungai Long data set which contains about 584 images of different illumination conditions, i.e. 297 images in the morning, 140 images in the afternoon and 147 images in the night. The proposed method outperforms other approaches with accuracy of 91.24%, 93.57% and 75.51% in the morning, evening and night respectively.

Another Look at the “Mercator Effect” on Global-Scale Cognitive Maps: Not in Areas but in Directions

The Mercator effect is the widespread and persistent belief among cartographers and others that people’s global-scale cognitive maps are distorted in a particular way because of their exposure to world maps displayed with the common Mercator projection. In particular, such exposure has been claimed to lead people to believe that polar regions, such as Greenland, are much larger than they really are, relative to equatorial regions. Recent studies, however, have found no evidence for a Mercator effect on recalled areas for world regions. Given that a version of the Mercator projection known as the Web Mercator has been used for Web mapping in the last couple of decades, we carried out a replication with samples at two universities, but we also asked respondents to estimate great-circle directions (“as a jet would fly”) from their home city to several other world cities. We again find no support for a Mercator effect on areas estimated from memory, but our novel collection of spherical direction estimates provides clear evidence of a Mercator effect (or that of a similar rectangular projection) on directional beliefs. These results confirm that cognitive maps are not unitary, analogue mental structures but collections of beliefs stored in different formats in separate mental structures that are not necessarily mutually coordinated and integrated. We also introduce a survey of map use that focuses on digital maps and their use for local versus global geographic inquiries.

Моделирование интенсифицированных теплообменников с различной вязкостью сред

Equations are derived for mean friction and heat transfer coefficients to solve problems of updating industrial plants for getting oil fractions based on application of approximate method of modeling momentum and heat transfer in heat exchangers with surface intensifiers. The Dyssler and Van-Driest turbulent boundary-layer model is used for the turbulent viscosity function for a flat smooth wall. An equation for the Stanton number is written using Chilton-Colborne hydrodynamic analogy and agreement with the known analogy is shown. Identical local properties of turbulent motion in a boundary layer on a plate and in a near-wall layer of a tube and the conservative properties of the laws of friction and heat transfer to turbulences, which are taken account of parametrically, are used for modeling momentum and heat transfer in channels with surface intensifiers. An equation for mean tangential stress in channels with intensifiers and, further, an equation for the Nusselt number is derived using a dissipative model. The results of calculations and comparison with the known experimental investigations are given for tubes with surface wire inserts, with spiral finning and rectangular projections for transformer oil at Reynolds numbers 200 < Re <2000. Thus, the adequacy of the developed mathematical model is proved in a wide range of operating and design parameters and thermophysical properties of fluids and gases. Further, the hydraulic resistance of the channel is the key experimental information about the object of modeling. Examples of use of mathematical model for designing and commissioning heat exchangers in petroleum fuels fractionating plants at industrial enterprises in the Russian Federation and abroad are given.

Removal of Deflection and Reconstruction of Foundations of the Historic Museum Building

The displacements and forces were measured and analysed in the jacks on which the structure was rested during the complex renovation. The building was deflected from the vertical and its foundations were damaged. The renovation consisted in lifting the above-ground part of the structure and removing its deflection and then replacing the foundations. The building subject to renovation and investigations dates back to 1902; it is a historical structure and serves as a museum. The building is partially cellared, has two above-ground floors and a rectangular projection with 10.3 m and 10.7 m long sides. The building was vertically deflected by 31 mm/m. 27 hydraulic jacks were installed in order to remove the deflection in the axes of the cellar and foundation walls. With their help, the building was torn apart and then straightened by uneven lifting. After the rectification, the weight of the building was transferred onto a new system of supports transferring the load directly to the ground outside the foundations and the jacks located in the walls’ axes were dismounted. This made it possible to demolish the old stone foundations which were in very poor technical condition. New reinforced concrete strip foundations and foundation walls made of concrete blocks were made in their place. The forces and displacements in the jacks were continuously measured during the rectification. The article presents these measurements and establishes the relationships between the forces in the jacks and the displacements of the elevated building. The scope of the renovation and the innovative structural solutions applied in the construction of the foundations are also presented. The renovation of the deflected structure allowed to avoid demolition of the historic building and its re-assembly. Moreover, with the presented procedure, no damage was caused to the structure’s elements that were being lifted. The measurements of forces and displacements made it possible to determine the parameters of the straightened building.

Análisis de capas PML en una región de campo electromagnético utilizando el Método de Diferencias Finitas en el Dominio del Tiempo

The Finite Difference in Time Domain (FDTD) method is currently one of the most used electromagnetism methods in electromagnetic field simulation, however, in order to obtain reliable results from this simulation it is necessary to have optimal boundary conditions. Perfectly Coupled Layers (PML) is characterized by the decomposition of the transversal field to the direction of propagation in its rectangular projections, and the use of both electrical and magnetic conductivity in the numerical layers for the absorption of electromagnetic fields. The PML layers are characterized by values of permittivity, permeability and conductivity that are assigned to each of the equations according to their position in the region. Because it is the same set of equations there is no need to use connection conditions at the junction of the analysis region with the PML absorption region, which provides a natural transition throughout the region. This paper presents the study of the difference between the calculation region with and without PML layers.

Determination method of dynamic characteristics of mobile terrestrial robotic complex manipulator

A method for determining the dynamic characteristics of the mobile terrestrial robotic complex manipulator is developed. A new concept for finding dynamic characteristics is proposed. It involves determining the manipulator displacement during its “quasi-rigid” movement along with the chassis along the road surface with isolated inequality through a rectangular projection. The manipulator is considered to be undeformed and its position relative to the chassis unchanged. Having considered “quasi-rigid” displacement of the manipulator, the dynamic loads acting on it are defined. At the same time, dynamic deformations of the manipulator corresponding to the “deformation” movement of the manipulator elastic system relative to its position corresponding to the “quasi-rigid” displacement are considered. Based on the proposed concept, a method for determining the dynamic characteristics of the manipulator was developed. It involves the development of a mathematical model of the manipulator when presenting it through a multi-mass dynamic system. The system of dynamics equations is presented as a structural mathematical model by means of which the dynamic characteristics of the manipulator corresponding to the robotic complex displacement along the road with a single irregularity are found. The coefficients of dynamic loads in the elastic system of the manipulator are determined by simulation.

Zachowane baldachimy procesyjne na terenie Małopolski z wieku XVII i XVIII

Baldachimy procesyjne na terenie Małopolski w wieku XVII i XVIII przyjmowały formę dekoracyjnego daszku wykonanego zazwyczaj z tkaniny rozpiętej na stelażu, przymocowanego do ozdobnych drążków, co umożliwiało ich przenoszenie. Przede wszystkim baldachimów używano podczas procesji teoforycznych. Wykonywano je z zasady z nietrwałych materiałów, stąd też zachowało się ich tylko kilka. Na podstawie źródeł archiwalnych oraz zachowanych przykładów baldachimy procesyjne można podzielić ze względu na kształt na dwa rodzaje.Pierwszy, najliczniejszy, stanowią baldachimy o drewnianym lub metalowym stelażu na rzucie prostokąta zbliżonego do kwadratu, zaopatrzone w dwa lub cztery drążki. Drugi to baldachimy owalne na jednym drążku w kształcie parasola. W obu grupach najistotniejszym elementem dekoracyjnym była tkanina rozpięta na stelażu tworząca podniebie oraz dach baldachimu, kształtująca także jego boki za pomocą falbany lub lambrekinu. Podniebie i dach baldachimu wykonywane były zasadniczo z dwóch różnych tkanin. Dach baldachimu najczęściej był płaski, ale występowały także przykłady o dynamicznych formach, czego przykład stanowi baldachim w Kacwinie z drugiej połowy XVIII wieku. Dodatkowo stosowano dekoracyjne uzupełnienia w postaci obszycia galonem, koronką, frędzlą, taśmami i haftem, a także chwostami. Najczęściej drzewce baldachimów były rzeźbione i malowane. Najlepszym przykładem klasycznego baldachimu barokowego stanowi najstarszy zachowany w Małopolsce baldachim z roku ok. 1663 w Polance Wielkiej lub baldachim wykonany z XVII-wiecznej tkaniny w kolegiacie św. Anny w Krakowie. Zdarzało się, że dach baldachimu był obwiedziony ażurowym, bogato rzeźbionym i złoconym obramieniem, jak np. baldachim z trzeciej ćwierci XVIII wieku w Krzywaczce lub w kościele św. Anny w Nowym Targu (2. poł. XVIII w.). Ciekawą grupę tworzyły baldachimy w całości drewniane dekorowane malowaną i złoconą snycerką, które zachowały się na Spiszu, w kościele we Frydmanie (2. poł. XVIII w.), Krempachach (2. poł. XVIII w.) i Trybszu oraz znany ze zdjęć archiwalnych niezachowany baldachim z końca XVIII wieku w Łapszach Niżnych. Zasadniczym elementem dekoracyjnym wymienionych baldachimów jest bogato rzeźbiony i złocony drewniany stelaż, do którego przytwierdzany był dach wykonany z tkaniny bądź z deski.Drugi rodzaj baldachimów w formie rozkładanego i składanego parasola reprezentowała niezachowana obecnie XVIII-wieczna umbella w Bielanach k. Kęt.Powstające w następnych stuleciach baldachimy generalnie przyjęły formę opartą na prostym drewnianym stelażu z tekstylnym dachem i bokami prostymi lub w formie lambrekinu. Spotykane są także rozwiązania, w których do elementów tekstylnych dodawano akcenty snycerskie.

Octahedron-based Projections as Intermediate Representations for Computer Imaging: TOAST, TEA, and More.

This paper defines and discusses a set of rectangular all-sky projections that have no singular points, notably the Tesselated Octahedral Adaptive Spherical Transformation (or TOAST) developed initially for the WorldWide Telescope. These have proven to be useful as intermediate representations for imaging data where the application transforms dynamically from a standardized internal format to a specific format (projection, scaling, orientation, etc.) requested by the user. TOAST is strongly related to the Hierarchical Triangular Mesh pixelization and is particularly well adapted to situations where one wishes to traverse a hierarchy of images increasing in resolution. Because it can be recursively computed using a very simple algorithm it is particularly adaptable to use with graphical processing units.

Purification of water from dissolved gases in a film unit with discrete-rough walls

This paper analyzes the use of a highly effective film unit for water purification from dissolved corrosive gases, in order to increase the resource efficiency and reliability of various equipment using water circulation systems at industrial plants and thermal power plants. The unit consists of a vertical bundle of tubes contained in tube grids and operates in the upward co-current gas and liquid in a pipe. The gas moves at a speed of 10 – 30 m/s (strong interaction of phases) and carries a liquid film from the bottom up. In this mode, there is a significant intensification of heat and mass transfer (5 – 15 times) in comparison with counter current. In addition, the inner surface of the tubes may have artificial discrete roughness (rectangular projections), which further increases the effectiveness of the processes. The paper presents the mathematical model and the efficiency calculation results for a film contact device with rough walls at strong phase interaction. The mathematical description is based on the models of the flow structure and the diffusion boundary layer. Expressions are given for calculating the mass transfer coefficient in a turbulent film with co-current gas, as well as parameters of the flow structure model in a contact tube. The main parameters of the equation for calculation of the mass transfer coefficient are the dynamic friction velocity on the interfacial film surface and the dimensionless thickness of the viscous sublayer. The dynamic speed is calculated using the equation of balance of forces in the contact tube, and the dimensionless thickness of the viscous sublayer-based on the known values on the plate adjusted for the phase interaction conditions. The cell model of the flow structure is used, and an expression is obtained for calculating the concentration profile of gas dissolved in water at the height of the pipes. The paper also presents an expression to calculate the number of cells in a complete mixing. The paper presents the calculated and experimental dependences of decarbonization efficiency for tubes with smooth and rough walls. The influence of spacing between roughness elements (projections) on water purification efficiency is shown. Conclusions are made about the design of a unit with a rising film at higher concentrations of dissolved gases in the water.

Теорема Гаусса и Польке-Шварца, как основная теорема параллельной прямоугольной проекции аксонометрической системы

Теорема Гаусса и Польке-Шварца, как основная теорема параллельной прямоугольной проекции аксонометрической системы

NUMERICAL STUDY OF PRESSURE DROP AND HEAT TRANSFER IN A STRAIGHT RECTANGULAR AND SEMI CYLINDRICAL PROJECTIONS MICROCHANNEL HEAT SINK

The heat transfer and pressure drop characteristics of a straight rectangular and semi cylindrical projections microchannel heat sink were investigated. The heat sinks, made of copper, were aligned in row as a cluster of 21 microchannels, 231 µm wide and 713 µm deep. Water was used as cooling fluid and was made to flow through the channels. A three dimensional analysis was done for Reynolds number ranging between 200 to 1000 with constant heat flux of 10 6 W/m 2 defined relative to the platform area of the heat sink. The temperature rise and pressure drop of the fluid in straight microchannel heat sink was evaluated using ANSYS-CFX package and was validated using experimental data. Similar analysis was done for semi cylindrical projections microchannel heat sink by solving the conjugate heat transfer problem. A comparison of heat transfer and pressure drop between rectangular and semi cylindrical projections microchannel was done and the results were laid out. Results shows that heat transfer increases with the use of semi cylindrical projections microchannel heat sink.

Magnetotactic Coccus Strain SHHC-1 Affiliated to Alphaproteobacteria Forms Octahedral Magnetite Magnetosomes.

Magnetotactic bacteria (MTB) are morphologically and phylogenetically diverse prokaryotes. They can form intracellular chain-assembled magnetite (Fe3O4) or greigite (Fe3S4) nanocrystals each enveloped by a lipid bilayer membrane called a magnetosome. Magnetotactic cocci have been found to be the most abundant morphotypes of MTB in various aquatic environments. However, knowledge on magnetosome biomineralization within magnetotactic cocci remains elusive due to small number of strains that have been cultured. By using a coordinated fluorescence and scanning electron microscopy method, we discovered a unique magnetotactic coccus strain (tentatively named SHHC-1) in brackish sediments collected from the estuary of Shihe River in Qinhuangdao city, eastern China. It phylogenetically belongs to the Alphaproteobacteria class. Transmission electron microscopy analyses reveal that SHHC-1 cells formed many magnetite-type magnetosomes organized as two bundles in each cell. Each bundle contains two parallel chains with smaller magnetosomes generally located at the ends of each chain. Unlike most magnetotactic alphaproteobacteria that generally form magnetosomes with uniform crystal morphologies, SHHC-1 magnetosomes display a more diverse variety of crystal morphology even within a single cell. Most particles have rectangular and rhomboidal projections, whilst others are triangular, or irregular. High resolution transmission electron microscopy observations coupled with morphological modeling indicate an idealized model—elongated octahedral crystals, a form composed of eight {111} faces. Furthermore, twins, multiple twins and stack dislocations are frequently observed in the SHHC-1 magnetosomes. This suggests that biomineralization of strain SHHC-1 magnetosome might be less biologically controlled than other magnetotactic alphaproteobacteria. Alternatively, SHHC-1 is more sensitive to the unfavorable environments under which it lives, or a combination of both factors may have controlled the magnetosome biomineralization process within this unique MTB.

Theoretical investigation on a general class of 2D quasicrystals with the rectangular projection method

Abstract We take a theoretical investigation on the reciprocal property of a class of 2D nonlinear photonic quasicrystal proposed by Lifshitz et al. in PRL 95, 133901 (2005). Using the rectangular projection method, the analytical expression for the Fourier spectrum of the quasicrystal structure is obtained explicitly. It is interesting to find that the result has a similar form to the corresponding expression of the well-known 1D Fibonacci lattice. In addition, we predict a further extension of the result to higher dimensions. This work is of practical importance for the photonic device design in nonlinear optical conversion progresses.

The Anthropomorphous Figurine from Zasullia-Mhar

Among a series of the Early Mediaeval objects found recently on the territory of Poltava Oblast, an anthropomorphous figurine from Zasullia-Mhar is of a special interest. It finds its analogies among the products from the North Caucasus and the Crimea. The bronze amulet is a stylized human figurine with a broken lower part. It has an oval-shaped overhanging head with the depiction of hair and a rectangular projection of shoulders with marked arms. A loop with a hole with a ring made of bronze wire is fastened to the head’s back. A figurine belongs to the 6th—7th century products of the Black Sea and the Caucasus region, Kovalevska/type 1, small bronze or silver one-sided figurines with an average height 4,5 + 0,19 сm and width 1,8 + 0,1 cm. Depiction is male, nude, and phallic. The head is rounded or in cone-shaped headdress. Features are absent or schematic. Shoulders are straight and body is stretched. A line of legs repeats a line of arms. The feet are marked. Eye for hanging is on the back. Similar findings are discovered at the sites of the North Caucasus, the Crimea, and on the coast of the Azov Sea. A series of such items comes from the sites of Dzetyasar culture in the east coast of the Aral Sea. Undoubtedly, the interest in such findings never ceases. Paramount is the creation of a full catalogue of such products which will help to develop their new typological scheme. In addition, a full publication of assemblages in which theseamulets are discovered will help answering the question on the chronology of such adornments’ usage. Among a series of the Early Mediaeval objects found recently on the territory of Poltava Oblast, an anthropomorphous figurine from Zasullia-Mhar is of a special interest. It finds its analogies among the products from the North Caucasus and the Crimea. The bronze amulet is a stylized human figurine with a broken lower part. It has an oval-shaped overhanging head with the depiction of hair and a rectangular projection of shoulders with marked arms. A loop with a hole with a ring made of bronze wire is fastened to the head’s back. A figurine belongs to the 6th—7th century products of the Black Sea and the Caucasus region, Kovalevska/type 1, small bronze or silver one-sided figurines with an average height 4,5 + 0,19 сm and width 1,8 + 0,1 cm. Depiction is male, nude, and phallic. The head is rounded or in cone-shaped headdress. Features are absent or schematic. Shoulders are straight and body is stretched. A line of legs repeats a line of arms. The feet are marked. Eye for hanging is on the back. Similar findings are discovered at the sites of the North Caucasus, the Crimea, and on the coast of the Azov Sea. A series of such items comes from the sites of Dzetyasar culture in the east coast of the Aral Sea. Undoubtedly, the interest in such findings never ceases. Paramount is the creation of a full catalogue of such products which will help to develop their new typological scheme. In addition, a full publication of assemblages in which theseamulets are discovered will help answering the question on the chronology of such adornments’ usage.

Load and frequency interaction effects in dynamic buckling of soft core sandwich structures

The present study is concerned with an analysis of load and frequency interaction effects in the dynamic buckling of sandwich plates and shells with a soft, transversely flexible core. The analysis is based of a general geometrically nonlinear soft-core sandwich model presented and a corresponding extended Galerkin solution strategy presented earlier. In the present study, the formalism is adopted and transformed into an eigenvalue problem. Assuming large transverse average displacements but small amplitudes for the vibration problem, a partially decoupled problem is obtained where in a first step the static buckling and face wrinkling problems can be addressed without consideration of the dynamic problem. In a second step, the dynamic eigenvalue problem can be solved, using the static solution as input parameters. The model is applied in parametric studies on the vibration response of plane and doubly curved sandwich panels with rectangular projection. In all cases, strong interaction effects between the external static preload and the natural frequencies are observed. The development of overall buckling or local face wrinkling instabilities enabled due to the transverse flexibility of the core result in distinct drops of the first natural frequency.