{"component": "clause", "props": {"groups": [{"snippet": "composition factors of L4(a, 1, 0, 0)\u2297 V2 V4\u2217 We now apply the main result from the previous section to deduce a result about the existence of composition factors of tensor products. Before we do that let us recall some results from the literature. We wish to understand the weights of an irreducible F GLn(F)-module Ln(\u03bb) and to do so we will need the following result from [62].", "size": 2, "samples": [{"hash": "jNuuAX46zSu", "uri": "/contracts/jNuuAX46zSu#an-example", "label": "End User License Agreement", "score": 25.5995893224, "published": true}, {"hash": "ftkqMOIrTmk", "uri": "/contracts/ftkqMOIrTmk#an-example", "label": "End User License Agreement", "score": 25.5995893224, "published": true}], "snippet_links": [{"key": "main-result", "type": "clause", "offset": [63, 74]}, {"key": "let-us", "type": "clause", "offset": [201, 207]}], "hash": "9b07dc5afdf7901edf80d965d20edef3", "id": 1}, {"snippet": "the relay service", "size": 2, "samples": [{"hash": "lOmIFwlyAgJ", "uri": "/contracts/lOmIFwlyAgJ#an-example", "label": "Grant Agreement", "score": 28.1156741958, "published": true}], "snippet_links": [{"key": "relay-service", "type": "clause", "offset": [4, 17]}], "hash": "874eabf1e8c1d5b34aafa19d2e069cb5", "id": 2}, {"snippet": "Tilting \u2587\u2587\u2587\u2587\u2587\u2587\u2587\u2587\u2587\u2587 series\u200c As an example, we shall now discuss an interesting explicit example of the convergent tilting isomorphism Theorem 5.3.3, namely the p-adic \u2587\u2587\u2587\u2587\u2587\u2587\u2587\u2587\u2587\u2587 family. Let K be a perfectoid field extension of Qcyc. Let n : Z\u00d7 \u2192 &\u00d7 be a weight with n(\u00b5p\u22121(Zp)) = 1. Recall from [18], \u00a72.1 that the (p-depleted) p-adic \u2587\u2587\u2587\u2587\u2587\u2587\u2587\u2587\u2587\u2587 series of weight n is defined as follows: Denote by \u03b6\u2217 the p-adic zeta-function of [19] B.1, this is a pseudo-measure on Zp\u00d7 with a pole at n = 1. More precisely, under the usual identification of the Iwasawa algebra of 1 + qZp with Zp[[T ]], we may regard \u03b6\u2217 as an element of the fraction field of Zp[[T ]]. By a Theorem of \u2587\u2587\u2587\u2587\u2587\u2587\u2587, [54], Th\u00b4eor`eme 16, \u03b6\u2217 is then of the form", "size": 1, "samples": [{"hash": "2CZmbrmeWtx", "uri": "/contracts/2CZmbrmeWtx#an-example", "label": "End User License Agreement", "score": 22.8952772074, "published": true}], "snippet_links": [{"key": "the-p", "type": "clause", "offset": [155, 160]}, {"key": "extension-of", "type": "clause", "offset": [213, 225]}, {"key": "field-of", "type": "definition", "offset": [635, 643]}], "hash": "2a897e2630663299435abb250dafa794", "id": 3}, {"snippet": "A parent contacts school because their child has sent a text or called during school hours explaining that they have been placed in detention. It is totally", "size": 1, "samples": [{"hash": "6hlomvpi4Xp", "uri": "/contracts/6hlomvpi4Xp#an-example", "label": "Device Usage Agreement", "score": 31.6657997933, "published": true}], "snippet_links": [{"key": "a-parent", "type": "definition", "offset": [0, 8]}, {"key": "during-school-hours", "type": "clause", "offset": [71, 90]}], "hash": "3a21c7a47ee6662f988b4d883bcd8443", "id": 4}, {"snippet": "has 4 ECTS and is registered on the Provider-led Full Induction Programme. They will be charged: \u00a3450 for each ECT.. The total charge is \u00a31,800. This is paid in two instalments- one per year. In Year 1 the payment is: \u00a31,000. In Year 2 the payment is \u00a3800.", "size": 1, "samples": [{"hash": "bEb95JacBqa", "uri": "/contracts/bEb95JacBqa#an-example", "label": "Service Level Agreement", "score": 33.600103213, "published": true}], "snippet_links": [{"key": "the-provider", "type": "clause", "offset": [32, 44]}, {"key": "total-charge", "type": "clause", "offset": [121, 133]}, {"key": "per-year", "type": "definition", "offset": [182, 190]}, {"key": "year-1", "type": "clause", "offset": [195, 201]}, {"key": "the-payment", "type": "clause", "offset": [202, 213]}, {"key": "year-2", "type": "definition", "offset": [229, 235]}], "hash": "a01ba6ac3611b52306d8d64f332358f5", "id": 5}, {"snippet": "Decentralization of educational governance systems\n1 E.g. WTO-World trade Organization, OECD-Organization for Economic Cooperation and Development, GATT- General Agreement on Tariff and Trade, IMF-International Monetary Fund, EU-European Union (especially \u2018the Inner Market\u2019 and the \u2018Europe 2020\u2019 statement) and the World Bank.", "size": 1, "samples": [{"hash": "k3iQMeLJDBa", "uri": "/contracts/k3iQMeLJDBa#an-example", "label": "Grant Agreement", "score": 22.8288843258, "published": true}], "snippet_links": [{"key": "world-trade-organization", "type": "definition", "offset": [62, 86]}, {"key": "cooperation-and-development", "type": "clause", "offset": [119, 146]}, {"key": "general-agreement", "type": "definition", "offset": [154, 171]}, {"key": "international-monetary-fund", "type": "clause", "offset": [197, 224]}, {"key": "european-union", "type": "clause", "offset": [229, 243]}, {"key": "the-world-bank", "type": "clause", "offset": [312, 326]}], "hash": "0b50579556f731a5a2a462dbb2e086b7", "id": 6}, {"snippet": "Title your file \u2018Current Will\u2019 and upload a copy of your current Will (e.g. made in 2009). You can replace it later when you make a new Will (e.g. in 2016) for no extra fee.", "size": 1, "samples": [{"hash": "k4zARHjab06", "uri": "/contracts/k4zARHjab06#an-example", "label": "Other Documents", "score": 18.476386037, "published": true}], "snippet_links": [{"key": "a-copy-of", "type": "clause", "offset": [42, 51]}], "hash": "370831bf20f0e247c6518fd0367436c0", "id": 7}, {"snippet": "Mr \u2587\u2587\u2587\u2587\u2587 is a programmer. He works in Slovakia and Austria for a company based in Slovakia. He is living in Austria, from where he performs telework (telework) for his Slovak employer 2 days a week (40%) and the remaining 3 days he works from the employer's office in Slovakia (60%).", "size": 1, "samples": [{"hash": "4b5m7ZoEHtz", "uri": "/contracts/4b5m7ZoEHtz#an-example", "label": "Framework Agreement", "score": 29.0874679543, "published": true}], "snippet_links": [{"key": "living-in", "type": "definition", "offset": [98, 107]}, {"key": "a-week", "type": "definition", "offset": [191, 197]}, {"key": "the-employer", "type": "definition", "offset": [243, 255]}], "hash": "43c80edac9b3bdb3be9bb556a9fd4365", "id": 8}, {"snippet": "Remember the example of \u2587\u2587\u2587\u2587 working on his presen- tation at the beginning of this paper. When he enters the meeting room, his digital assistant automatically discov- ers the projector and the SlideInterpreter component of his presentation application tries to connect to the Slide- Figure 4: Projector example: SlideInterpreter connected with SlideVisualizer Visualizer component of the projector, as shown in fig- ure 4. Unfortunately, there seems to be not enough band- width available on the Bluetooth link between his PDA and the projector to transmit the slide images from the interpreter to the visualizer, from the slideImageOutput port to the slideImageInput port. Indeed, the interpreter produces at fifteen frames per second compressed hi- resolution images, which have a size of about six hun- dred kilobytes on average. Although the visualizer and the interpreter agree on their contract, the system does not due to the limitation of its bandwidth resources. For- tunately, the system is able to perform an automatic opti- mization. It realizes that the interpreter component has a low bandwidth contract on its input port. Indeed, reading the description file for the presentation does not require a large bandwidth, while generating the images that have to be projected on the screen does. Therefore, the sys- tem decides to relocate the interpreter component to the run-time system on the projector hardware. The contract agreement now does get accepted by the system, needing to send only one fifty kilobyte message each two seconds on average. The interpreter component and the visual- izer component now communicate at full speed, almost without limitations. The outgoing bandwidth contract for the slideImageOutput port is (the metric is expressed in milliseconds for ITBM and in kilobytes for MS): avg ITBM = 66.7 avg MS = 600 avg ITBM acc = 5 avg MS acc = 17 var ITBM = 11 var MS = 134 var ITBM acc = 3 var MS acc = 15 max ITBM = 143 max MS = 860 min ITBM = 39 min MS = 400 The outgoing bandwidth contract for the slid- eDescription port, on the other hand, is (same metric): avg ITBM = 2000 avg MS = 50 avg ITBM acc = 100 avg MS acc = 5 var ITBM = 450 var MS = 15 var ITBM acc = 10 var MS acc = 3 max ITBM = 15000 max MS = 85 min ITBM = 500 min MS = 10 It is obvious that the second contract is a better can- didate for a low-bandwidth transmission than the first contract. The middleware deals with this problem by executing a component relocation step, so that the high- bandwidth connection is moved from a wireless trans- mission to a local transmission (exchanging messages as local variables). In general, making the architecture more appropri- ate for ad hoc systems involves letting the middleware decide how to distribute the application into its envi- ronment. A possible basis to formulate such decisions might be resource availability: \u201cAllocate components to the most appropriate host, judging by the match be- tween resource consumption and resource availability\u201d. The terms \u2019Cyber foraging\u2019 [9] and \u2019resource harvest- ing\u2019 are generally used to denote this search and al- location of distributed resources. Application reloca- tion is a technique to implement it. When a device is no match for a certian application, it can still handle it through the use of resource harvesting. Once avail- able resources are found in the vicinity, the application is split and parts are relocated onto the resource-rich de- vices in the environment. Intra-application communica- ton (inter-component communication) now goes via the wireless connection between the devices. There is no doubt that resource-awareness is an impor- tant requirement for pervasive computing, but design- ing a designer-friendly solution for implementing this requirement is not an easy task. The Quality Objects framework seems to be putting the implementation bur- den on the side of the application designer. We believe, however, that this task should be made more straight- forward for the application designer by shifting resource allocation and application adaptation strategies towards the middleware. The difficulty, however, is to find al- gorithms that find realistic adaptation strategies without sacrificing the availability of the application by . We conclude that the fine-grained structure of the applica- tion is really required to build flexible applications that suport the dynamic resource management techniques as proposed in this paper.", "size": 1, "samples": [{"hash": "cSQudQxbNYq", "uri": "/contracts/cSQudQxbNYq#an-example", "label": "Design and Run Time Bandwidth Contracts", "score": 19.0, "published": true}], "snippet_links": [{"key": "beginning-of", "type": "clause", "offset": [66, 78]}, {"key": "meeting-room", "type": "clause", "offset": [110, 122]}, {"key": "figure-4", "type": "definition", "offset": [284, 292]}, {"key": "as-shown", "type": "definition", "offset": [400, 408]}, {"key": "to-transmit", "type": "definition", "offset": [546, 557]}, {"key": "the-system", "type": "definition", "offset": [903, 913]}, {"key": "limitation-of", "type": "clause", "offset": [934, 947]}, {"key": "able-to-perform", "type": "clause", "offset": [1002, 1017]}, {"key": "the-description", "type": "clause", "offset": [1154, 1169]}, {"key": "time-system", "type": "clause", "offset": [1387, 1398]}, {"key": "contract-agreement", "type": "definition", "offset": [1430, 1448]}, {"key": "accepted-by", "type": "definition", "offset": [1462, 1473]}, {"key": "contract-for", "type": "definition", "offset": [1702, 1714]}, {"key": "for-ms", "type": "clause", "offset": [1811, 1817]}, {"key": "the-other-hand", "type": "clause", "offset": [2065, 2079]}, {"key": "second-contract", "type": "definition", "offset": [2300, 2315]}, {"key": "first-contract", "type": "definition", "offset": [2382, 2396]}, {"key": "local-variables", "type": "clause", "offset": [2606, 2621]}, {"key": "in-general", "type": "clause", "offset": [2624, 2634]}, {"key": "ad-hoc", "type": "definition", "offset": [2683, 2689]}, {"key": "distribute-the", "type": "clause", "offset": [2744, 2758]}, {"key": "resource-availability", "type": "clause", "offset": [2849, 2870]}, {"key": "the-terms", "type": "definition", "offset": [3003, 3012]}, {"key": "location-of", "type": "definition", "offset": [3111, 3122]}, {"key": "distributed-resources", "type": "definition", "offset": [3123, 3144]}, {"key": "the-resource", "type": "definition", "offset": [3427, 3439]}, {"key": "the-environment", "type": "clause", "offset": [3458, 3473]}, {"key": "wireless-connection", "type": "definition", "offset": [3557, 3576]}, {"key": "we-believe", "type": "clause", "offset": [3914, 3924]}, {"key": "resource-allocation", "type": "clause", "offset": [4029, 4048]}, {"key": "and-application", "type": "clause", "offset": [4049, 4064]}, {"key": "availability-of-the-application", "type": "clause", "offset": [4226, 4257]}, {"key": "structure-of-the", "type": "clause", "offset": [4297, 4313]}, {"key": "resource-management", "type": "clause", "offset": [4402, 4421]}], "hash": "91bb5c648ea8f806a848cd7757727633", "id": 9}, {"snippet": "The following shows the points \u2587\u2587\u2587\u2587\u2587 \u2587\u2587\u2587\u2587 would have scored over 3 years of his ELC: 2007-08 23 5 5 .435 x 82 36 2008-09 64 31 26 .890 x 82 73 2009-10 81 35 29 .790 x 82 65 Based on this performance, \u2587\u2587\u2587\u2587\u2587 \u2587\u2587\u2587\u2587, at the end of his ELC, would fall into the 171-180 points (Category 1) position and would at minimum require a contract that pays 2.40 in its 1st year. If \u2587\u2587\u2587\u2587\u2587 \u2587\u2587\u2587\u2587 was given an Offer Sheet it would have to be at more than the 2.40 guaranteed by the minimum 0.50 escalating pay rate, meaning the minimum he could be offered, using the Offer Sheet process, would be 2.90. The Razorbacks would have the choice to either accept a 2nd round draft pick as compensation or match the offer. It should be noted that \u2587\u2587\u2587\u2587\u2587 \u2587\u2587\u2587\u2587 is only being used as an example and would not qualify for this process. Points listed below will be based on an average of points-per-game scored. Example: If a player scores 37 points over 60 games played, his points considered will be: 37 divided by 60 = .616 X 82 GP = 51.5 points rounded up to 52 points scored for that season. Less than 90 points scored over the term of the ELC:", "size": 1, "samples": [{"hash": "dkonsujxsbk", "uri": "/contracts/dkonsujxsbk#an-example", "label": "Entry Level Contract (Elc)", "score": 15.6076956028, "published": true}], "snippet_links": [{"key": "based-on", "type": "clause", "offset": [173, 181]}, {"key": "at-the-end-of", "type": "clause", "offset": [212, 225]}, {"key": "category-1", "type": "clause", "offset": [271, 281]}, {"key": "offer-sheet", "type": "definition", "offset": [391, 402]}, {"key": "guaranteed-by", "type": "clause", "offset": [445, 458]}, {"key": "pay-rate", "type": "definition", "offset": [487, 495]}, {"key": "the-offer", "type": "clause", "offset": [544, 553]}, {"key": "that-\u2587", "type": "clause", "offset": [716, 722]}, {"key": "listed-below", "type": "clause", "offset": [812, 824]}, {"key": "divided-by", "type": "clause", "offset": [974, 984]}, {"key": "term-of-the", "type": "clause", "offset": [1101, 1112]}], "hash": "b07fc5f9b9270c420a68bbbbcd0502b8", "id": 10}], "next_curs": "ClMSTWoVc35sYXdpbnNpZGVyY29udHJhY3Rzci8LEhZDbGF1c2VTbmlwcGV0R3JvdXBfdjU2IhNhbi1leGFtcGxlIzAwMDAwMDBhDKIBAmVuGAAgAA==", "clause": {"title": "An example", "size": 21, "children": [["", ""], ["polynomial-degree", "Polynomial Degree"], ["corrupt-one-subspace", "Corrupt one subspace"]], "parents": [["contract-language", "Contract Language"], ["discussion", "Discussion"], ["results", "Results"], ["diverse-perspectives-and-hopes-on-autonomy-in-school-leadership", "DIVERSE PERSPECTIVES AND HOPES ON AUTONOMY IN SCHOOL LEADERSHIP"], ["educational-governance", "Educational Governance"]], "id": "an-example", "related": [["eye-exam", "Eye Exam", "Eye Exam"], ["long-term-cost-evaluation", "Long Term Cost Evaluation", "Long Term Cost Evaluation"], ["switching-system-hierarchy-and-trunking-requirements", "Switching System Hierarchy and Trunking Requirements", "Switching System Hierarchy and Trunking Requirements"], ["low-census", "Low Census", "Low Census"], ["long-term-cost-evaluation-criterion", "Long Term Cost Evaluation Criterion", "Long Term Cost Evaluation Criterion"]], "related_snippets": [], "updated": "2025-07-07T16:38:45+00:00"}, "json": true, "cursor": ""}}