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Botvynovska, Svitlana, Zhanetta Levina, and Hanna Sulimenko. "IMAGING OF A HYPERBOLIC PARABOLOID WITH TOUCHING LINE WITH THE PARABOLAL WRAPPING CONE." Management of Development of Complex Systems, no. 48 (December 20, 2021): 53–60. http://dx.doi.org/10.32347/2412-9933.2021.48.53-60.
The paper is dedicated to architectural structures modeling by means of computer-graphics. Images on the monitor represent perspective. That’s why the images could be assessed from the most convenient points as viewer’s position is considered to be the perspective center. Non-rectilinear profile makes the structure the most impressive. The hyperbolic paraboloid surface is researched. Parabolas and hyperbolas are the only forms of its sections except for tangent planes cases. Parabolas as contact lines are reviewed. Hyperbolic paraboloid is an infinite surface that’s why only a portion of it could be modeled. Four link space zigzag ({4l} indicator) is its best representation. In such case the non-rectilinear profile should be represented as a curve of second order semicircular arc. Modeling of a limited section does not affect the final modeling because the {4l} representation makes the depiction of all surface in that frame of axis that have the identified hyperbolic paraboloid looks like a cone. The paper’s objective is development of imaging technique using parabolic contact lines to design hyperbolic paraboloid surface and applicable to several surfaces of the same construction. To do so, parameter analysis of the task is conducted, the applicable theory is identified, and the hyperbolic paraboloid imaging technique using the set profile line in the form of any curve of second order is conducted, namely the imaging technique for contact parabola and the set of hyperbolic paraboloids which it set forth. The set of plans that may contain the parabolic contact line set is two-parameter. However, in general, the position of those planes is remains unknown. Thus, the task is as follows: find the third point of the plane that intersects the given wrapping cone along the parabola when the two points are given. These two points must belong to the same forming line on the cone. The imaging requires 7 parameters whereas the hyperbolic paraboloid has 8 parameters. That’s why with one parabolic contact line and given wrapping cone of the second order one-parameter set of hyperbolic paraboloids could be imaged. The paper shows how to image the contact line if the profile line is given as a parabola, ellipse, or hyperbola. The portion of one hyperbolic paraboloid may imaged when the parameters are aligned and any other bisecant of same perspective line of shape. Two portions of parabola conjugated due to the joint wrapping cone hyperbolic paraboloid imaging is demonstrated.
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Zhu, Yuanchao, Dazhao Zhang, Yanlin Lai, and Huabiao Yan. "Shape adjustment of "FAST" active reflector." Highlights in Science, Engineering and Technology 1 (June 14, 2022): 391–400. http://dx.doi.org/10.54097/hset.v1i.493.
Abstract. In this paper, the relevant working principle of "FAST" Chinese Eye is studied, and a mathematical model is established to solve the equation of the ideal paraboloid. The ideal paraboloid model is obtained by rotating the paraboloid around the axis in the two-dimensional plane. On this basis, the specific solutions of each question are discussed, and the parabolic equation, the receiving ratio of the feed cabin to the reflected signal, the numbering information and coordinates of the main cable node and other parameters are obtained. This paper for solving directly above the benchmark of spherical observation of celestial bodies when ideal parabolic equation, according to the geometrical optics to knowledge should be clear all the signals of the incoming signal after the ideal parabolic will converge to the focal point of basic rules, then through converting ideal parabolic model of ideal parabolic equation in a two-dimensional plane, An optimization model was established to minimize the absolute value of the difference between the arc length and the arc length of the parabola in the diameter of 300 meters. The known conditions were substituted into Matlab to solve the equation of the ideal parabola by rotating the parabola around the axis: . In order to determine the ideal paraboloid of the celestial body, a new spatial cartesian coordinate system is first established with the line direction between the celestial body and the spherical center as the axis, so that the observed object is located directly above the new coordinate system. The same model in question 1 is established to obtain the vertex coordinates of the ideal paraboloid at this time. Then the vertex coordinates are converted to the coordinates in the original space cartesian coordinate system by rotation transformation between space cartesian coordinate systems. The solution of its vertex coordinates (-49.5287, -37.0203, -294.1763).
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Acharya, Aviseka, Sonja Brungs, Yannick Lichterfeld, Jürgen Hescheler, Ruth Hemmersbach, Helene Boeuf, and Agapios Sachinidis. "Parabolic, Flight-Induced, Acute Hypergravity and Microgravity Effects on the Beating Rate of Human Cardiomyocytes." Cells 8, no. 4 (April 14, 2019): 352. http://dx.doi.org/10.3390/cells8040352.
Functional studies of human induced pluripotent stem cell (hiPSC)-derived cardiomyocytes (hCMs) under different gravity conditions contribute to aerospace medical research. To study the effects of altered gravity on hCMs, we exposed them to acute hypergravity and microgravity phases in the presence and absence of the β-adrenoceptor isoprenalin (ISO), L-type Ca2+ channel (LTCC) agonist Bay-K8644, or LTCC blocker nifedipine, and monitored their beating rate (BR). These logistically demanding experiments were executed during the 66th Parabolic Flight Campaign of the European Space Agency. The hCM cultures were exposed to 31 alternating hypergravity, microgravity, and hypergravity phases, each lasting 20–22 s. During the parabolic flight experiment, BR and cell viability were monitored using the xCELLigence real-time cell analyzer Cardio Instrument®. Corresponding experiments were performed on the ground (1 g), using an identical set-up. Our results showed that BR continuously increased during the parabolic flight, reaching a 40% maximal increase after 15 parabolas, compared with the pre-parabolic (1 g) phase. However, in the presence of the LTCC blocker nifedipine, no change in BR was observed, even after 31 parabolas. We surmise that the parabola-mediated increase in BR was induced by the LTCC blocker. Moreover, the increase in BR induced by ISO and Bay-K8644 during the pre-parabola phase was further elevated by 20% after 25 parabolas. This additional effect reflects the positive impact of the parabolas in the absence of both agonists. Our study suggests that acute alterations of gravity significantly increase the BR of hCMs via the LTCC.
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Stojanov, V. V., S. J. Jgalli, and V. O. Stojanov. "THE CONSTITUENT ELEMENTS STRUCTURES COVERING OF HYPERBOLIC PARABOLOID." ACADEMIC JOURNAL Series: Industrial Machine Building, Civil Engineering 1, no. 48 (March 27, 2017): 54–61. http://dx.doi.org/10.26906/znp.2017.48.769.
Hypar is a hyperbolic paraboloid representing translational ruled developable anti classical surface, i.e., the surface of negative Gaussian curvature. Shaping of the parabolic elements corresponds to buckling of the shell and the main tensile forces are arranged in the ascending direction of parabolas, and the main compression force - in the direction of the descending parabola. Composite materials are formed from the combination of two or more layered materials, each having very different properties. ANSYS Composite PrepPost software provides all the necessary functionality for the analysis of layered composite structures. The paper discloses a possibility of using for shell covering negative curvature. Design solutions into constituent elements structures and computations such structures are presented.
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Hayah, Ni, Bakri Mallo, and I. Nyoman Murdiana. "PROFIL PEMAHAMAN KONSEP MATEMATIKA DITINJAU DARI GAYA KOGNITIF FIELD INDEPENDENT (FI) DAN FIELD DEPENDENT (FD)." Aksioma 8, no. 2 (September 24, 2019): 137–50. http://dx.doi.org/10.22487/aksioma.v8i2.210.
abstrak: Penelitian ini bertujuan untuk mendeskripsikan pemahaman konsep matematika siswa kelas XI SMA Negeri 2 Dampelas dalam menyelesaikan soal pada subpokok bahasan parabola ditinjau dari gaya kognitif Field Independent (FI) dan Field Dependent (FD). Jenis penelitian ini adalah penelitian kualitatif. Subjek dalam penelitian ini terdiri dari satu siswa yang bergaya kognitif FI dan satu siswa yang bergaya kognitif FD. Hasil dari penelitian ini yaitu saat menyajikan masalah, subjek FI dan FD menuliskan hal-hal yang diketahui dan ditanyakan. Selanjutnya dalam mengklasifikasi unsur-unsur parabola, subjek FI mengelompokkan unsur-unsur parabola menurut bentuk parabolanya yaitu parabola horizontal terbuka ke kanan. Kemudian dalam memberi contoh dan non-contoh pada setiap unsur-unsur parabola, subjek FI memberikan contoh dan non-contoh dari setiap unsur-unsur parabola yang diberikan. Kemudian menyajikan masalah persamaan parabola dalam representasi matematis, subjek FI dan subjek FD menyajikan persamaan parabola kedalam bentuk persamaan umum parabola. Kemudian menggunakan, memanfaatkan dan memilih prosedur tertentu dalam menentukan persamaan parabola, subjek FI menggunakan dan memilih persamaan umum parabola horizontal dan subjek FD menggunakan persamaan umum parabola walaupun subjek tidak mengetahui jenis persamaan umum parabola yang digunakan. Kemudian subjek FI menjelaskan kembali prosedur yang digunakan serta memberikan alasannya dengan menggunakan bahasanya sendiri dan subjek FD menjelaskan kembali prosedur yang digunakan walaupun dalam proses penyelesaiannya siswa belum memahami dengan baik langkah-langkah yang harus digunakan.
Kata Kunci: Profil; Pemahaman konsep matematika; Parabola;
abstract: This study aims to describe the understanding of mathematical concepts of class XI students of SMA 2 Dampelas in solving problems on the subject of the parabolic discussion reviewed from cognitive style of the Independent Field (FI) and Field Dependent (FD). This type of research is qualitative research. The subjects in this study consisted of one student who was in the cognitive style of FI and one student in the cognitive style of FD. The results of this study are when presenting a problem, FI and FD subject write things that are known and asked. Furthermore, in classifying parabolic elements, FI subjects classify parabolic elements according to their parabolic forms, namely horizontal parabola open to the right. Then in giving examples and non-examples of each parabolic element, the FI subject gives examples and non-examples of each parabolic element given. Then presenting the problem of parabolic equations in mathematical representations, the subject FI and subject FD present the parabolic equation in the form of a general parabolic equation. Then using, utilizing and selecting a particular procedure in determining the parabolic equation, FI subject uses and selects the general horizontal parabolic equation and the FD subject uses the general parabolic equation even though the subject does not know the type of general parabolic equation used. Then the FI subject explains the procedure used again and gives the reason using its own language and the FD subject explains the procedure used even though in the process of completion students do not understand the steps that must be used properly.
Keywords: Profile; Understanding of mathematical concepts; Parabolic
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Wang, Yanbo, Yingchang Xiong, Jianming Hao, Jiaqi He, Yuchi Liu, and Xinpeng He. "Active Control Model for the “FAST” Reflecting Surface Based on Discrete Methods." Symmetry 14, no. 2 (January 27, 2022): 252. http://dx.doi.org/10.3390/sym14020252.
Radio telescopes are important for the development of society. With the advent of China’s Five-hundred-meter Aperture Spherical radio Telescope (FAST), adjusting the reflector panel to improve the reception ability is becoming an urgent problem. In this paper, an active control model of the reflector panel is established that considers the minimum sum of the radial offset of the actuator and the non-smoothness of the working paraboloid. Using the idea of discretization, the adjusted position of the main cable nodes, the ideal parabolic equation, and the expansion of each actuator are obtained by inputting the elevation and azimuth angle of the incident electromagnetic wave. To find the ideal parabola, a univariate optimization model is established, and the Fibonacci method is used to search for the optimal solution h=−0.33018 (offset in the direction away from the sphere’s center) and the focal diameter ratio f=0.4671 of the parabolic vertex. The ideal two-dimensional parabolic equation is then determined as x2−555.25z−166757.2=0, and the ideal three-dimensional paraboloid equation is determined to be z=(x2+y2)/555.25−300.33018. Moreover, the amount of the nodes and triangular reflection panels are calculated, which were determined to be 706 and 1325, respectively. The ratio reception of the working paraboloid and the datum sphere are 9.434% and 1.3898%, respectively. The latter is calculated through a ray tracing simulation using the optical system modeling software LightTools.
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Tang, Hongxin. "Parabolic Detection Algorithm of Tennis Serve Based on Video Image Analysis Technology." Security and Communication Networks 2021 (November 29, 2021): 1–9. http://dx.doi.org/10.1155/2021/7901677.
At present, the existing algorithm for detecting the parabola of tennis serves neglects the pre-estimation of the global motion information of tennis balls, which leads to great error and low recognition rate. Therefore, a new algorithm for detecting the parabola of tennis service based on video image analysis is proposed. The global motion information is estimated in advance, and the motion feature of the target is extracted. A tennis appearance model is established by sparse representation, and the data of high-resolution tennis flight appearance model are processed by data fusion technology to track the parabolic trajectory. Based on the analysis of the characteristics of the serve mechanics, according to the nonlinear transformation of the parabolic trajectory state vector, the parabolic trajectory starting point is determined, the parabolic trajectory is obtained, and the detection algorithm of the parabolic service is designed. Experimental results show that compared with the other two algorithms, the algorithm designed in this paper can recognize the trajectory of the parabola at different stages, and the detection accuracy of the parabola is higher in the three-dimensional space of the tennis service.
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Sharma, N. K., Ashok Kumar Mishra, and P. Rajgopal. "Design of Low-Cost Solar Parabolic Through Steam Sterilization." International Journal of Biomedical and Clinical Engineering 10, no. 1 (January 2021): 50–60. http://dx.doi.org/10.4018/ijbce.2021010104.
The objective of this study is to develop a low cost solar parabolic trough that can be used for steam sterilization of medical instruments in small clinics where electricity is scarce and expensive. On the basis of theoretical concepts of parabola and focus-balanced parabola, the assembly of ribs and reflector sheet with evacuated tube and heat pipe has been done. The parabolic trough has been mounted on a trolley so that it can be moved easily according to direction of sun light. The designed solar parabolic trough was integrated with pressure cooker under various setups and experiments were conducted to test whether sterilization is taking place or not. To validate sterilization process, tests were also conducted by placing the infected medical instruments. The solar parabolic trough developed was able to generate and maintain steam at 121 degrees Celsius at pressure 15 psig (101.3 kN/m2) for 15 minutes. The solar parabolic trough developed was effective in sterilizing the medical instruments.
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Stavek, Jiri. "Newton’s Parabola Observed from Pappus’ Directrix, Apollonius’ Pedal Curve (Line), Newton’s Evolute, Leibniz’s Subtangent and Subnormal, Castillon’s Cardioid, and Ptolemy’s Circle (Hodograph) (09.02.2019)." Applied Physics Research 11, no. 2 (February 25, 2019): 30. http://dx.doi.org/10.5539/apr.v11n2p30.
Johannes Kepler and Isaac Newton inspired generations of researchers to study properties of elliptic, hyperbolic, and parabolic paths of planets and other astronomical objects orbiting around the Sun. The books of these two Old Masters “Astronomia Nova” and “Principia…” were originally written in the geometrical language. However, the following generations of researchers translated the geometrical language of these Old Masters into the infinitesimal calculus independently discovered by Newton and Leibniz. In our attempt we will try to return back to the original geometrical language and to present several figures with possible hidden properties of parabolic orbits. For the description of events on parabolic orbits we will employ the interplay of the directrix of parabola discovered by Pappus of Alexandria, the pedal curve with the pedal point in the focus discovered by Apollonius of Perga (The Great Geometer), and the focus occupied by our Sun discovered in several stages by Aristarchus, Copernicus, Kepler and Isaac Newton (The Great Mathematician). We will study properties of this PAN Parabola with the aim to extract some hidden parameters behind that visible parabolic orbit in the Aristotelian World. In the Plato’s Realm some curves carrying hidden information might be waiting for our research. One such curve - the evolute of parabola - discovered Newton behind his famous gravitational law. We have used the Castillon’s cardioid as the curve describing the tangent velocity of objects on the parabolic orbit. In the PAN Parabola we have newly used six parameters introduced by Gottfried Wilhelm Leibniz - abscissa, ordinate, length of tangent, subtangent, length of normal, and subnormal. We have obtained formulae both for the tangent and normal velocities for objects on the parabolic orbit. We have also obtained the moment of tangent momentum and the moment of normal momentum. Both moments are constant on the whole parabolic orbit and that is why we should not observe the precession of parabolic orbit. We have discovered the Ptolemy’s Circle with the diameter a (distance between the vertex of parabola and its focus) where we see both the tangent and normal velocities of orbiting objects. In this case the Ptolemy’s Circle plays a role of the hodograph rotating on the parabolic orbit without sliding. In the Plato’s Realm some other curves might be hidden and have been waiting for our future research. Have we found the Arriadne’s Thread leading out of the Labyrinth or are we still lost in the Labyrinth?
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Petkov, Emiliyan G. "Development and Implementation of NURBS Models of Quadratic Curves and Surfaces." Serdica Journal of Computing 3, no. 4 (January 11, 2010): 425–48. http://dx.doi.org/10.55630/sjc.2009.3.425-448.
This article goes into the development of NURBS models of quadratic curves and surfaces. Curves and surfaces which could be represented by one general equation (one for the curves and one for the surfaces) are addressed. The research examines the curves: ellipse, parabola and hyperbola, the surfaces: ellipsoid, paraboloid, hyperboloid, double hyperboloid, hyperbolic paraboloid and cone, and the cylinders: elliptic, parabolic and hyperbolic. Many real objects which have to be modeled in 3D applications possess specific features. Because of this these geometric objects have been chosen. Using the NURBS models presented here, specialized software modules (plug-ins) have been developed for a 3D graphic system. An analysis of their implementation and the primitives they create has been performed.
Hertz, Erik. "Parabolic Synthesis." Licentiate thesis, Department of Electrical and Information Technology Faculty of Engineering, LTH, Lund University, Lund, Sweden, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-22338.
Many consumer products, such as within the computer areas, computer graphics, digital signal processing, communication systems, robotics, navigation, astrophysics, fluid physics, etc. are searching for high computational performance as a consequence of increasingly more advanced algorithms in these applications. Until recently the down scaling of the hardware technology has been able to fulfill these higher demands from the more advanced algorithms with higher clock rates on the chips. This that the development of hardware technology performance has stagnated has moved the interest more over to implementation of algorithms in hardware. Especially within wireless communication the desire for higher transmission rates has increased the interest for algorithm implementation methodologies. The scope of this thesis is mainly on the developed methodology of parabolic synthesis. The parabolic synthesis methodology is a methodology for implementing approximations of unary functions in hardware. The methodology is described with the criteria's that have to be fulfilled to perform an approximation on a unary function. The hardware architecture of the methodology is described and to this a special hardware that performs the squaring operation. The outcome of the presented research is a novel methodology for implementing approximations of unary functions such as trigonometric functions, logarithmic functions, as well as square root and division functions etc. The architecture of the processing part automatically gives a high degree of parallelism. The methodology is founded on operations that are simple to implement in hardware such as addition, shifts, multiplication, contributes to that the implementation in hardware is simple to perform. The hardware architecture is characterized by a high degree of parallelism that gives a short critical path and fast computation. The structure of the methodology will also assure an area efficient hardware implementation.
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Heyer, Claudius. "Applications of parabolic Hecke algebras: parabolic induction and Hecke polynomials." Doctoral thesis, Humboldt-Universität zu Berlin, 2019. http://dx.doi.org/10.18452/20137.
Im ersten Teil wird eine neue Konstruktion der parabolischen Induktion für pro-p Iwahori-Heckemoduln gegeben. Dabei taucht eine neue Klasse von Algebren auf, die in gewisser Weise als Interpolation zwischen der pro-p Iwahori-Heckealgebra einer p-adischen reduktiven Gruppe $G$ und derjenigen einer Leviuntergruppe $M$ von $G$ gedacht werden kann. Für diese Algebren wird ein Induktionsfunktor definiert und eine Transitivitätseigenschaft bewiesen. Dies liefert einen neuen Beweis für die Transitivität der parabolischen Induktion für Moduln über der pro-p Iwahori-Heckealgebra. Ferner wird eine Funktion auf einer parabolischen Untergruppe untersucht, die als Werte nur p-Potenzen annimmt. Es wird gezeigt, dass sie eine Funktion auf der (pro-p) Iwahori-Weylgruppe von $M$ definiert, und
dass die so definierte Funktion monoton steigend bzgl. der Bruhat-Ordnung ist und einen Vergleich der Längenfunktionen zwischen der Iwahori-Weylgruppe von $M$ und derjenigen der Iwahori-Weylgruppe von $G$ erlaubt.
Im zweiten Teil wird ein allgemeiner Zerlegungssatz für Polynome über der sphärischen (parahorischen) Heckealgebra einer p-adischen reduktiven Gruppe $G$ bewiesen. Diese Zerlegung findet über einer parabolischen Heckealgebra statt, die die Heckealgebra von $G$ enthält. Für den Beweis des Zerlegungssatzes wird vorausgesetzt, dass die gewählte parabolische Untergruppe in einer nichtstumpfen enthalten ist. Des Weiteren werden die nichtstumpfen parabolischen Untergruppen von $G$ klassifiziert. The first part deals with a new construction of parabolic induction for modules over the pro-p Iwahori-Hecke algebra. This construction exhibits a new class of algebras that can be thought of as an interpolation between the pro-p Iwahori-Hecke algebra of a p-adic reductive group $G$ and the corresponding algebra of a Levi subgroup $M$ of $G$. For these algebras we define a new induction functor and prove a transitivity property. This gives a new proof of
the transitivity of parabolic induction for modules over the pro-p Iwahori-Hecke algebra. Further, a function on a parabolic subgroup with p-power values is studied. We show that it induces a function on the (pro-p) Iwahori-Weyl group of $M$, that it is monotonically increasing with respect to the Bruhat order, and that it allows to compare the length function on the Iwahori-Weyl group of $M$ with the one on the Iwahori-Weyl group of $G$.
In the second part a general decomposition theorem for polynomials over the spherical (parahoric) Hecke algebra of a p-adic reductive group $G$ is proved. The proof requires that the chosen parabolic subgroup is contained in a non-obtuse one. Moreover, we give a classification of non-obtuse parabolic subgroups of $G$.
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Gantz, Christian. "On parabolic bundles." Thesis, University of Oxford, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.320221.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016. Cataloged from PDF version of thesis. Includes bibliographical references (pages 73-75). Let G be a reductive group over a field k = k. Let P be a parabolic subgroup. We construct a functor Groupoid ... is a connected space, which induces an action of generalizing a classical result. It is also a part of a study of natural equivalences between ... for P, Q associated parabolic subgroups. by D. Boger. Ph. D.
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Žúrek, Dan. "Nízkoprofilová směrová anténa." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2016. http://www.nusl.cz/ntk/nusl-242122.
This diploma thesis deals with a study of low-profile directional antennas, followed by design and optimization of parabolic reflector antenna in centimeter and millimeter band. The first part of this work is focused on the analysis of several kinds of directional antennas, mainly on parabolic reflector and on SIW technology, which will be used for final antenna realization. The next part of this project is about the particular concept of the substrate integrated parabolic antenna for 60 GHz ISM band, its simulation and optimization in the CST Microwave Studio software. The final part of this thesis is devoted to the results achieved.
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Taher, Chadi. "Calculating the parabolic chern character of a locally abelain parabolic bundle : the chern invariants for parabolic bundles at multiple points." Nice, 2011. http://www.theses.fr/2011NICE4013.
In this thesis we calculate the parabolic Chern character of a bundle with locally abelian parabolic structure on a smooth strict normal crossings divisor, using the definition in terms of Deligne-Mumford stacks. We obtain explicit formulas for ch_1, ch_2 and ch_3, and verify that these correspond to the formulas given by Borne for ch_1 and Mochizuki for ch_2. The second part of the thesis we take D subset in X is a curve with multiple points in a surface, a parabolic bundle defined on (X, D) away from the singularities can be extended in several ways to a parabolic bundle on a resolution of singularities. We investigate the possible parabolic Chern classes for these extensions.
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Deolmi, Giulia. "Computational Parabolic Inverse Problems." Doctoral thesis, Università degli studi di Padova, 2012. http://hdl.handle.net/11577/3423351.
This thesis presents a general approach to solve numerically parabolic Inverse Problems, whose underlying mathematical model is discretized using the Finite Element method. The proposed solution is based upon an adaptive parametrization and it is applied specically to a geometric conduction inverse problem of corrosion estimation and to a boundary convection inverse problem of pollution rate estimation. In questa tesi viene presentato un approccio numerico volto alla risoluzione di problemi inversi parabolici, basato sull'utilizzo di una parametrizzazione adattativa. L'algoritmo risolutivo viene descritto per due specici problemi: mentre il primo consiste nella stima della corrosione di una faccia incognita del dominio, il secondo ha come scopo la quanticazione di inquinante immesso in un fiume.
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Bauwe, Anne, and Wilfried Grecksch. "A parabolic stochastic differential inclusion." Universitätsbibliothek Chemnitz, 2005. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200501221.
Stochastic differential inclusions can be considered as a generalisation of stochastic
differential equations. In particular a multivalued mapping describes the set
of equations, in which a solution has to be found.
This paper presents an existence result for a special parabolic stochastic inclusion.
The proof is based on the method of upper and lower solutions. In the deterministic
case this method was effectively introduced by S. Carl.
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Baysal, Arzu. "Inverse Problems For Parabolic Equations." Master's thesis, METU, 2004. http://etd.lib.metu.edu.tr/upload/12605623/index.pdf.
In this thesis, we study inverse problems of restoration of the unknown function in a boundary condition, where on the boundary of the domain there is a convective heat exchange with the environment. Besides the temperature of the domain, we seek either the temperature of the environment in Problem I and II, or the coefficient of external boundary heat emission in Problem III and IV. An additional information is given, which is the overdetermination condition, either on the boundary of the domain (in Problem III and IV) or on a time interval (in
Problem I and II). If solution of inverse problem exists, then the temperature can be defined everywhere on the domain at all instants.
The thesis consists of six chapters. In the first chapter, there is the introduction where the definition and applications of inverse problems are given and definition of the four inverse problems, that we will analyze in this thesis, are stated. In the second chapter, some definitions and theorems which we will use to obtain some conclusions about the corresponding direct problem of our four inverse problems are stated, and the conclusions about direct problem are obtained.
In the third, fourth, fifth and sixth chapters we have the analysis of inverse problems I, II, III and IV, respectively.
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Eberhardt, Jens Niklas [Verfasser], and Wolfgang [Akademischer Betreuer] Soergel. "Graded and geometric parabolic induction." Freiburg : Universität, 2017. http://d-nb.info/113557216X/34.
Escher, Joachim, Patrick Guidotti, Matthias Hieber, Piotr Mucha, Jan W. Prüss, Yoshihiro Shibata, Gieri Simonett, Christoph Walker, and Wojciech Zajaczkowski, eds. Parabolic Problems. Basel: Springer Basel, 2011. http://dx.doi.org/10.1007/978-3-0348-0075-4.
Quittner, Prof Dr Pavol, and Prof Dr Philippe Souplet. Superlinear Parabolic Problems. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-18222-9.
Escher, Joachim, Martin Kohlmann, and Boris Kolev. "Geometric Aspects of the Periodic μ-Degasperis-Procesi Equation." In Parabolic Problems, 193–209. Basel: Springer Basel, 2011. http://dx.doi.org/10.1007/978-3-0348-0075-4_10.
Farwig, R., H. Kozono, and H. Sohr. "Global Leray-Hopf Weak Solutions of the Navier-Stokes Equations with Nonzero Time-dependent Boundary Values." In Parabolic Problems, 211–32. Basel: Springer Basel, 2011. http://dx.doi.org/10.1007/978-3-0348-0075-4_11.
Fattorini, H. O. "Time and Norm Optimality of Weakly Singular Controls." In Parabolic Problems, 233–49. Basel: Springer Basel, 2011. http://dx.doi.org/10.1007/978-3-0348-0075-4_12.
Galdi, Giovanni P., and Mads Kyed. "Asymptotic Behavior of a Leray Solution around a Rotating Obstacle." In Parabolic Problems, 251–66. Basel: Springer Basel, 2011. http://dx.doi.org/10.1007/978-3-0348-0075-4_13.
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