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Academic literature on the topic 'Knots and links (in high dimensions)'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Knots and links (in high dimensions)"

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Songhafouo Tsopméné, Paul Arnaud, and Victor Turchin. "Rational homology and homotopy of high-dimensional string links." Forum Mathematicum 30, no. 5 (2018): 1209–35. http://dx.doi.org/10.1515/forum-2016-0192.

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AbstractArone and the second author showed that when the dimensions are in the stable range, the rational homology and homotopy of the high-dimensional analogues of spaces of long knots can be calculated as the homology of a direct sum of finite graph-complexes that they described explicitly. They also showed that these homology and homotopy groups can be interpreted as the higher-order Hochschild homology, also called Hochschild–Pirashvili homology. In this paper, we generalize all these results to high-dimensional analogues of spaces of string links. The methods of our paper are applicable i

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OOGURI, HIROSI. "TOPOLOGICAL LATTICE MODELS IN FOUR DIMENSIONS." Modern Physics Letters A 07, no. 30 (1992): 2799–810. http://dx.doi.org/10.1142/s0217732392004171.

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We define a lattice statistical model on a triangulated manifold in four dimensions associated to a group G. When G= SU (2), the statistical weight is constructed from the 15j-symbol as well as the 6j-symbol for recombination of angular momenta, and the model may be regarded as the four-dimensional version of the Ponzano-Regge model. We show that the partition function of the model is invariant under the Alexander moves of the simplicial complex, thus it depends only on the piecewise linear topology of the manifold. For an orientable manifold, the model is related to the so-called BF model. Th

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OGASA, EIJI. "LOCAL MOVE IDENTITIES FOR THE ALEXANDER POLYNOMIALS OF HIGH-DIMENSIONAL KNOTS AND INERTIA GROUPS." Journal of Knot Theory and Its Ramifications 18, no. 04 (2009): 531–45. http://dx.doi.org/10.1142/s0218216509007014.

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As analogues of the well-known skein relations for the Alexander and the Jones polynomials for classical links, we present three relations that hold among invariants of high dimensional knots differing by "local moves". Two are for the Alexander polynomials and the other is for the Arf-invariants, the inertia group and the bP-subgroup.

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Díaz, Juan Pablo, Gabriela Hinojosa, and Alberto Verjosvky. "Cubulated moves for 2-knots." Journal of Knot Theory and Its Ramifications 28, no. 01 (2019): 1950008. http://dx.doi.org/10.1142/s0218216519500081.

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In this paper, we prove that given two cubical links of dimension two in [Formula: see text], they are isotopic if and only if one can pass from one to the other by a finite sequence of cubulated moves. These moves are analogous to the Reidemeister and Roseman moves for classical tame knots (links) of dimensions one and two, respectively.

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DURUMERIC, OGUZ C. "LOCAL STRUCTURE OF IDEAL KNOTS, II CONSTANT CURVATURE CASE." Journal of Knot Theory and Its Ramifications 18, no. 11 (2009): 1525–37. http://dx.doi.org/10.1142/s0218216509007609.

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The thickness, NIR (K) of a knot or link K is defined to be the radius of the largest open solid tube one can put around the curve without any self intersections of the normal discs, which is also known as the normal injectivity radius of K. For C1,1 curves K, [Formula: see text], where κ(K) is the generalized curvature, and the double critical self distance DCSD (K) is the shortest length of the segments perpendicular to K at both end points. The knots and links in ideal shapes (or tight knots or links) belong to the minima of ropelength = length/thickness within a fixed isotopy class. In thi

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KEARTON, C., and S. M. J. WILSON. "SIMPLE NON-FINITE KNOTS ARE NOT PRIME IN HIGHER DIMENSIONS." Journal of Knot Theory and Its Ramifications 12, no. 02 (2003): 225–41. http://dx.doi.org/10.1142/s0218216503002408.

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It has long been known that in high dimensions tbere are examples of irreducible knots which are not prime. Here we show that in fact there are no prime simple knots in high dimensions, with the possible exception of those whose homology is finite. In particular, the result holds for all simple (2q - 1)-knots, q > 1.

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Bloch, W. L. "Extending flows from isolated invariant sets." Ergodic Theory and Dynamical Systems 15, no. 6 (1995): 1031–43. http://dx.doi.org/10.1017/s0143385700009779.

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AbstractLet M be a closed n-dimensional manifold, and let U be a n-dimensional isolating block such that U is smoothly embedded in M. Let φ be a smooth semi-flow on U and let Λ contained in U, be isolated and invariant under φ Then there exists a semi-flow φ′ on M which extends φ such that φ′ is Morse-Smale outside of U, and no new recurrence is introduced in U. The theorem is true for any finite number of pairwise-disjoint Ui. Furthermore, if Λ is hyperbolic, topologically transitive and is the closure of periodic orbits, then φ′ is an Axiom A flow and is Ω-stable. In dimensions two and three

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RAMADEVI, P., T. R. GOVINDARAJAN, and R. K. KAUL. "REPRESENTATIONS OF COMPOSITE BRAIDS AND INVARIANTS FOR MUTANT KNOTS AND LINKS IN CHERN-SIMONS FIELD THEORIES." Modern Physics Letters A 10, no. 22 (1995): 1635–58. http://dx.doi.org/10.1142/s0217732395001769.

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We show that any of the new knot invariants obtained from Chern-Simons theory based on an arbitrary non-Abelian gauge group do not distinguish isotopically inequivalent mutant knots and links. In an attempt to distinguish these knots and links, we study Murakami (symmetrized version) r-strand composite braids. Salient features of the theory of such composite braids are presented. Representations of generators for these braids are obtained by exploiting properties of Hilbert spaces associated with the correlators of Wess-Zumino conformal field theories. The r-composite invariants for the knots

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Galakhov, D., D. Melnikov, A. Mironov, A. Morozov, and A. Sleptsov. "Colored knot polynomials for arbitrary pretzel knots and links." Physics Letters B 743 (April 2015): 71–74. http://dx.doi.org/10.1016/j.physletb.2015.02.029.

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Ferrari, Franco, Jarosław Paturej, Marcin Pia̧tek, and Yani Zhao. "Knots, links, anyons and statistical mechanics of entangled polymer rings." Nuclear Physics B 945 (August 2019): 114673. http://dx.doi.org/10.1016/j.nuclphysb.2019.114673.

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Books on the topic "Knots and links (in high dimensions)"

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1974-, Nelson Sam, ed. Quandles: An introduction to the algebra of knots. American Mathematical Society, 2015.

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Jaco, William H., Hyam Rubinstein, Craig David Hodgson, Martin Scharlemann, and Stephan Tillmann. Geometry and topology down under: A conference in honour of Hyam Rubinstein, July 11-22, 2011, The University of Melbourne, Parkville, Australia. American Mathematical Society, 2013.

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Introduction to 3-maniflods. AMS, 2014.

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Weiss, Meredith L. The Roots of Resilience. Cornell University Press, 2020. http://dx.doi.org/10.7591/cornell/9781501750045.001.0001.

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This book examines governance from the ground up in the world's two most enduring electoral authoritarian or “hybrid” regimes—Singapore and Malaysia—where politically liberal and authoritarian features are blended to evade substantive democracy. Although skewed elections, curbed civil liberties, and a dose of coercion help sustain these regimes, selectively structured state policies and patronage, partisan machines that effectively stand in for local governments, and diligently sustained clientelist relations between politicians and constituents are equally important. While key attributes of t

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Book chapters on the topic "Knots and links (in high dimensions)"

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Behrens, Stefan, Mark Powell, and Arunima Ray. "Context for the Disc Embedding Theorem." In The Disc Embedding Theorem. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198841319.003.0001.

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‘Context for the Disc Embedding Theorem’ explains why the theorem is the central result in the study of topological 4-manifolds. After recalling surgery theory and the proof of the s-cobordism theorem for high-dimensional manifolds, the chapter explains what goes wrong when trying to apply the same techniques in four dimensions and how to start overcoming these problems. The complete statement of the disc embedding theorem is provided. Finally the most important consequences to manifold theory are listed, including a proof of why Alexander polynomial one knots are topologically slice and the existence of exotic smooth structures on 4-dimensional Euclidean space.

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Shambaugh, David. "China’s Contemporary Roles in Southeast Asia." In Where Great Powers Meet. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780190914974.003.0005.

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This chapter assesses China’s “contemporary” roles in Southeast Asia. China’s relations with Southeast Asian countries and ASEAN have grown dramatically since the turn of the twenty-first century and have now achieved a high degree of interactions on the eve of 2020. China’s contemporary approach toward Southeast Asia is shaped by multiple factors. Among them, geography is perhaps the most important. China’s geographical proximity facilitates easy access and regular presence. This has led to growing economic interconnectedness, buttressed by transportation links, and this relative proximity also facilitates tourism, academic exchanges, and a regular presence of Chinese officials visiting the region. Through the four dimensions of China’s “toolbox” in Southeast Asia—diplomacy, people-to-people exchanges, commerce, and security—the PRC has established a broad and increasingly deep footprint across all of Southeast Asia.

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Price, Sophia. "9. Feminism." In Political Ideologies. Oxford University Press, 2017. http://dx.doi.org/10.1093/hepl/9780198727859.003.0009.

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This chapter examines the evolution of feminism as an ideology using the analogy of ‘waves’, a term that indicates high points of debate and activism followed by more fallow periods. It first traces the historical origins of feminism from the first to the third wave and a possible fourth. It then considers whether feminism is an ideology in its own right and goes on to identify variants of feminism such as liberal feminism, separatism and political lesbianism/lesbian feminism, transfeminism, revolutionary feminism, eco-feminism, and black feminism. The chapter also explores the links between feminism and other ideological perspectives as well as the connection between the national and global dimensions of feminism and the ways in which feminist ideology has been expressed in political movements and shaped the policies of governments and international organizations. Finally, it tackles the question of whether ‘post-feminism’ has rendered feminism obsolete.

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Bascompte, Jordi, and Pedro Jordano. "Mutualistic Networks in Time and Space." In Mutualistic Networks. Princeton University Press, 2013. http://dx.doi.org/10.23943/princeton/9780691131269.003.0005.

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This chapter reviews the combination of empirical and theoretical work describing the dynamics of mutualistic networks in time and space. It also addresses what components of these networks are time and space invariant. On a daily basis, network assembly is intermediate between preferential and random attachment. In a year-to-year scale, there is a very high turnover in species and interactions across years, and yet the global structure of the network is quite constant. Across space, theoretical models predict that plantanimal interactions increase spatial heterogeneity. The spatial and temporal dimensions are also interesting from a more methodological point of view to assess the effect of sampling effort. Interaction accumulation curves are the equivalent of species accumulation curves used in biodiversity monitoring and can be used to assess the role of sampling effort. But important natural history details explain a fraction of the nonobserved links. Therefore, treating missing interactions as the expected unique result of sampling bias would miss important components of the ecological and (co)evolutionary basis of mutualistic networks.

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van der Zee, Han. "The Role of IT and Planning for IT Value." In Measuring the Value of Information Technology. IGI Global, 2002. http://dx.doi.org/10.4018/978-1-930708-08-2.ch002.

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To determine the value of IT once it has been put into place and used, it is important to understand the context of the application of IT. Basically, the role of IT is to enable strategic change and improve business performance in several dimensions. IT enables the rapid delivery of top-quality, increasingly customized products and services, it supports organizations in meeting high standards in customer care, and it provides the means to compress design and development times in order to be the first to market. IT helps to launch new products more frequently, to explore and enter new markets faster, and to seek new distribution channels. All of these dimensions can give companies a powerful competitive edge, and IT is increasingly woven into them. IT does not stand on its own but contributes to realizing business objectives in today’s competitive, often global environment. To determine the value of IT once it has been put into place and used, it is important to first understand the context of the application of IT since it does not stand on its own but rather contributes to realizing business objectives. The first part of this chapter provides a review of the evolution of the role and application of IT, leading to its role in today’s information-based organization. Secondly, it is obvious that the best value from IT is gained if the “right” investment decisions for IT are made. To make the right decisions about IT in the context of business objectives, organizations need to carry out some form of IT planning. Planning-for-success is therefore the second main subject of this chapter. The evolution of IT planning practices is briefly described, leading to the most important attributes of contemporary, effective IT planning approaches. Finally, the chapter links the distinct roles of IT with the planning and valuation approaches for IT investments in relation to their business purpose.

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Maher, Barbara A. "Airborne Magnetite- and Iron-Rich Pollution Nanoparticles: Potential Neurotoxicants and Environmental Risk Factors for Neurodegenerative Disease, Including Alzheimer’s Disease." In Advances in Alzheimer’s Disease. IOS Press, 2021. http://dx.doi.org/10.3233/aiad210006.

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Fewer than 5% of Alzheimer’s disease (AD) cases are demonstrably directly inherited, indicating that environmental factors may be important in initiating and/or promoting the disease. Excess iron is toxic to cells; iron overload in the AD brain may aggressively accelerate AD. Magnetite nanoparticles, capable of catalyzing formation of reactive oxygen species, occur in AD plaques and tangles; they are thought to form in situ, from pathological iron dysfunction. A recent study has identified in frontal cortex samples the abundant presence of magnetite nanoparticles consistent with high-temperature formation; identifying therefore their external, not internal source. These magnetite particles range from ∼10 to 150 nm in size, and are often associated with other, non-endogenous metals (including platinum, cadmium, cerium). Some display rounded crystal morphologies and fused surface textures, reflecting cooling and crystallization from an initially heated, iron-bearing source material. Precisely-matching magnetite ‘nanospheres’ occur abundantly in roadside air pollution, arising from vehicle combustion and, especially, frictional brake-wear. Airborne magnetite pollution particles <∼200 nm in size can access the brain directly via the olfactory and/or trigeminal nerves, bypassing the blood-brain barrier. Given their toxicity, abundance in roadside air, and nanoscale dimensions, traffic-derived magnetite pollution nanoparticles may constitute a chronic and pernicious neurotoxicant, and hence an environmental risk factor for AD, for large population numbers globally. Olfactory nerve damage displays strong association with AD development. Reported links between AD and occupational magnetic fields (e.g., affecting welders, machinists) may instead reflect inhalation exposure to airborne magnetic nanoparticles.

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Conference papers on the topic "Knots and links (in high dimensions)"

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Nahmad-Achar, Eduardo. "Physics in higher dimensions, knots, and differentiable structures." In II CINVESTAV-UNAM SYMPOSIUM ON HIGH ENERGY PHYSICS, PARTICLES AND NEUTRINOS IN AN ASTROPHYSICAL CONTEXT: In Honor of Juan Carlos D’Olivo. AIP, 2013. http://dx.doi.org/10.1063/1.4810778.

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Kotzer, Clayton, Marc LaViolette, and William Allan. "Effects of Combustion Chamber Geometry Upon Exit Temperature Profiles." In ASME Turbo Expo 2009: Power for Land, Sea, and Air. ASMEDC, 2009. http://dx.doi.org/10.1115/gt2009-60156.

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The purpose of this research was to investigate the effects of combustion chamber geometry on exit temperature fields using an ambient pressure test rig. The apparatus contained a 120° sector of a combustion section of a Rolls Royce (previously Allison) T56-A-15 gas turbine engine. A thermocouple rake acquired high-resolution temperature measurements in the combustion chamber exit plane. Rig test conditions were set to simulate an engine operating condition of 463 km/h (250 knots) at 7620 m (25000ft) by matching the Mach number, the equivalence ratio and the Sauter mean diameter of the fuel sp

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Bastid, Philippe, and Simon D. Smith. "Numerical Analysis of Contact Stresses Between Mooring Chain Links and Potential Consequences for Fatigue Damage." In ASME 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/omae2013-11360.

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Design codes for offshore mooring systems recommend proof loading chain links to around 70% of the specified breaking load of the chain (API RP 2FP1, Lloyd’s Register). This is primarily to check that the chain will safely resist the service loads and will not excessively elongate. It is assumed that the proof load also generates compressive residual stresses at the interlink contact region and also at the point of the intrados (KT point) where a high stress concentration occurs during tensile loading. Tests have shown that proof loading improves the fatigue performance of chain under cyclic a

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Marras, Alex E., Haijun J. Su, and Carlos E. Castro. "Design of DNA Origami Machines and Mechanisms." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-87848.

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This research introduces DNA origami as a viable approach to design and fabricate nanoscale mechanisms and machines. DNA origami is a recently developed nanotechnology that has enabled the construction of objects with unprecedented nanoscale geometric complexity via self-assembly. These objects are made up of thousands of DNA base-pairs packed into 3D structures with typical dimensions of 10–100nm. The majority of DNA origami research to date focuses on assembly of static 2D or 3D structures. In this work, we aim to extend the scope of DNA origami to include design of objects with kinematicall

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Taylor, Stephen. "From Program Music to Sonification: Representation and the Evolution of Music and Language." In The 23rd International Conference on Auditory Display. The International Community for Auditory Display, 2017. http://dx.doi.org/10.21785/icad2017.060.

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Research into the origins of music and language can shed new light on musical representation, including program music and more recent incarnations such as data sonification. Although sonification and program music have different aims — one scientific explication, the other artistic expression — similar techniques, relying on human and animal biology, cognition, and culture, underlie both. Examples include Western composers such as Beethoven and Berlioz, to more recent figures like Messiaen, Stockhausen and Tom Johnson, as well as music theory, semiotics, biology, and data sonifications by myse

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Purwar, Anurag, Shrinath Deshpande, and Q. J. Ge. "MotionGen: An iOS and Android App for Planar Four-Bar Motion Generation." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-60498.

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MotionGen is an indigenously developed app for Apple iOS and Google Android platforms to help mechanism designers solve planar four-bar motion generation problem. The app is a computer implementation of authors’ recent work in developing a unified framework for the synthesis and simulation of planar four-bar mechanisms for the motion generation problem. Simplicity, high-utility, and wide-spread adoption of planar four-bar linkages have made them one of the most studied topics in Kinematics leading to development of algorithms and theories that deal with path-, function-, and motion generation-

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Daneshfard, Mohammad Sajjad, and A. Zabihollah. "Semi-Active Vibration Control of a Marine Structure With Magnetorheological (MR) Dampers Utilizing LQR Method." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-28860.

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The developing of technology has discovered new materials which have been applied to improve the performance of structures. The researchers have recently increased the attention in controllable fluids and its applications. Magnetorheological (MR) dampers are devices that employ rheological fluids to modify their mechanical properties. Their mechanical simplicity, high dynamic range, lower power requirements, large force capacity, robustness and safe manner operation in case of fail have made them attractive devices to passive, semi-active and active control in mechatronic, civil, aerospace and

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Behjat, Amir, Leighton Collins, Andrew Hoffman, Sharat Chidambaran, Maulikkumar Dhameliya, and Souma Chowdhury. "Conceptual Design and Prototype Development of a Solar-Powered Ground Robot for Energy-Autonomous Operation." In ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/detc2019-98361.

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Abstract This paper presents the conceptual design and fabrication/assembly of an autonomous solar powered small unmanned ground vehicle (UGV) platform for operation in outdoor environments. The contribution lies in the ability of the proposed design to offer uninterrupted operation in terms of endurance, to facilitate educational and research applications that are otherwise challenging to perform with a typical UGV (that needs significant downtime for recharging). A high incident area for solar PV panels is required to be able to support the complete energy needs of a ∼ 46 lb UGV (i.e., fully

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ATKOCIUNIENĖ, Vilma, Alvydas ALEKSANDRAVIČIUS, and Romualdas ZEMECKIS. "Public Policy Impact on Prosperity and Resilience of Farms and Agricultural Companies: Lithuanian Case Study." In Rural Development 2015. Aleksandras Stulginskis University, 2015. http://dx.doi.org/10.15544/rd.2015.128.

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The CAP support is mostly focused on the technological modernization of farms, linked with production intensification, and weakly focused on the farms prosperity and resilience. As a result farmers and managers of agricultural companies are only a slightly motivated to produce added value and high quality food products, to use short food supply chains addressing constantly changing consumer needs, or to pay much attention on issues related to climate change. The paper findings are based on the Lithuanian case study carried out as a part of the international research project “Rethinking the lin

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