Computation of sum of squares polynomials from data points

We propose an iterative algorithm for the numerical computation of sums of squares of polynomials approximating given data at prescribed interpolation points. The method is based on the definition of a convex functional $G$ arising from the dualization of a quadratic regression over the Cholesky factors of the sum of squares decomposition. In order to justify the construction, the domain of $G$, the boundary of the domain and the behavior at infinity are analyzed in details. When the data interpolate a positive univariate polynomial, we show that in the context of the Lukacs sum of squares representation, $G$ is coercive and strictly convex which yields a unique critical point and a corresponding decomposition in sum of squares. For multivariate polynomials which admit a decomposition in sum of squares and up to a small perturbation of size $\varepsilon$, $G^\varepsilon$ is always coercive and so it minimum yields an approximate decomposition in sum of squares. Various unconstrained descent algorithms are proposed to minimize $G$. Numerical examples are provided, for univariate and bivariate polynomials

A comparison of high cycle fatigue methodologies

To evaluate alternate turbopump development (ATD) high cycle fatigue (HCF) methodology, a comparison was made with the space shuttle main engine (SSME) methodology. This report documents the comparison and evaluates ATD's HCF system

STS-26 solid rocket booster post flight structural assessment

A post flight assessment of the Space Shuttle's Solid Rocket Boosters was conducted at the John F. Kennedy Space Center in Florida after the launch of STS-26. The two boosters were inspected for structural damage and the results of this inspection are presented. Overall, the boosters were in good condition. However, there was some minor damage attributed to splash down. Some of this damage is a recurring problem. Explanations of these problems are provided

Effect of loading rate on the mechanical response of vascular graft

Tato bakalářská práce se zabývá cévními náhradami a jejich mechanickou odezvou při zatěžování. Pozornost je soustředěna na analýzu mechanické odezvy kolagenní trubice, jako jedné ze složek cévní náhrady. K analýze je využit extenzně-inflační test. V závěru práce jsou pak diskutovány výsledky tohoto testu.This bachelor thesis deals with vascular grafts and their mechanical response during loading. It focuses on analyzing the mechanical response of the collagen tube, as one of the components of vascular graft. An extension-inflation test is used for the analysis. At the end the results of this test are discussed

On the adverbialization of Polish indefinite quantifiers of nominal origin : a diachronic study of "trochę" "a bit", "odrobinę" "a bit", and "masę" "a lot"

Na podstawie danych diachronicznych, wyekstrahowanych głównie z dostępnych źródeł leksykograficznych i korpusów historycznych języka polskiego, w niniejszym artykule podjęta zostaje próba ustalenia, czy początkowe stadium adwerbializacji odrzeczownikowych liczebników nieokreślonych obejmuje modyfikację zakresu, modyfikacja stopnia zaś jest zjawiskiem późniejszym. Wyniki analizy ewolucji statusu funkcjonalnego polskich określników ilościowych trochę, odrobinę oraz masę wskazują, że zanim wymienione jednostki zyskały status adwerbialnych modyfikatorów stopnia, funkcjonowały one jako przysłówki duratywne lub frekwentatywne. W swoich najwcześniejszych poświadczeniach przysłówkowych w badanym materiale omawiane kwantyfikatory informują bowiem o długości lub częstotliwości akcji denotowanej przez towarzyszący im predykat werbalny bądź - jeśli dany czasownik koduje zdarzenie punktowe - o długości stanu będącego rezultatem owego zdarzenia. Dopiero kolejny etap ich uprzysłówkowienia przejawia się współwystępowaniem z predykatami skalarnymi, tj. czasownikami leksykalizującymi skalę stopnia, przymiotnikami i przysłówkami stopniowalnymi, jak również okolicznikami w postaci fraz przyimkowych. Wyjątek stanowi tu liczebnik masę, ponieważ nie rozwinął on (jeszcze) regularnych użyć intensyfikujących.Based on diachronic data extracted chiefly from the available lexicographic sources and historical corpora of Polish, this paper aims at determining whether the initial stage of the adverbialization of indefinite quantifiers of nominal origin typically involves extent modification, degree modification being a posterior development. The results of an investigation into the evolution of the functional status of the commonly used quantifiers trochę 'a bit', odrobinę 'a bit', as well as masę 'a lot' indicate that prior to establishing themselves as degree modifiers, the items function as extent modifiers, i.e. duratives or frequentatives. In their earliest adverbial attestations recorded in the analysed material, the quantifiers at issue modify the duration or frequency of the action denoted by the associated verbal element, or, if the pertinent verb encodes a punctual event, the duration of the resultant state, and only later do they start to combine with scalar predicates, i.e. degree verbs as well as gradable adjectives and adverbs, including adverbials in the form of prepositional phrases. Exceptional in this respect is masę 'a lot', as it (still) appears incapable of serving as a degree intensifier

On the effect of pluralization on the numeralization of nouns in English and Polish : a contrastive corpus-based study

On the basis of corpus-derived data, the present paper examines the collocational patterns of the singular and the plural forms of a pair of etymologically and semantically related quantifying nouns (QNs), namely English heap and its Polish equivalent kupa 'heap'. The primary aim is to determine their respective levels of numeralization, operationalized as the frequency of co-occurrence with animate and abstract N2-collocates in purely quantificational uses, in an attempt to establish whether, and to what extent, the addition of the plurality morpheme bears on the grammaticalization of a nominal of this kind into an indefinite quantifier. Following the observations arrived at by Brems (2003, 2011), the hypothesis is that pluralization should yield a facilitating effect on the numeralization of nouns referring to large quantities by amplifying their inherent scalar implications. The results demonstrate that whereas heaps indeed exhibits a higher percentage of such numeralized uses than heap, kupy ‘heaps’ has turned out to be grammaticalized in the quantifying function to a markedly lesser degree than kupa ‘heap’. It is argued that this apparently aberrant behaviour of kupy ‘heaps’ can nonetheless be elucidated in terms of the specificity of numeralization in Polish, since at its advanced, morphosyntactic stage, the process in question affects solely the singular (accusative) forms of QNs

Meningkatkan Kreativitas Anak Melalui Metode Pemberian Tugas di Kelompok B TK An-Nisa Kita Singgani Maku

efektif yang disebabkan guru dalam proses pembelajaran kurang menerapkan penggunaan metode pemberian tugas yang berdampak pada rendahnya kreativitas anak. Tujuan penelitian ini untuk meningkatkan kreativitas anak melalui metode pemberian tugas.Setting penelitian ini yaitu anak kelompok B TK Annisa Kita Singgani Maku yang berjumlah 20 anak terdiri dari laki-laki 10 anak dan 10 anak perempuan. Rancangan penelitian yang digunakan adalah tindakan kelas yang dimulai dari perencanaan,pelaksanaan tindakan, observasi dan refleksi, yang dilakukan dengan 4 kali tindakan dalam 2 siklus. Data dikumpulkan dengan cara observasi, tanya jawab, pemberian tugas dan dokumentasi, serta alat yang digunakan adalah lembar observasi baik untuk aktifitas guru maupun murid.Selanjutnya dianalisa secara persentasi untuk menarik kesimpulan.Kata Kunci : Kreativitas anak dan metode pemberian tuga

On the grammaticalization of partitives into degree adverbs : the case of Polish "odrobina" 'crumb; a little' and Swedish "smula" 'crumb; a little'

Apart from degree adverbs derived from adjectives, such as wysoce 'highly' or starkt 'strongly,' both Polish and Swedish possess a set of grammaticalized partitive nominals which perform the function of degree modification, e.g. odrobina 'crumb; a little' and smula 'crumb; a little,' as used in odrobinę lepszy 'a little better' and vänta en smula 'wait a little,' respectively. Analysing English data, Traugott (2008) observes that in order for such an item to grammaticalize into a degree adverb, it must first acquire the status of an indefinite quantifier, in which case it still co-occurs with nominal collo-cates, yet solely encodes the abstract notion of quantity. Accordingly, this process can be schematized as follows: partitive ('a part/unit of') > quantifier ('a small/large quan-tity of') > degree modifier ('to a small/large degree/extent'). On the basis of linguistic material extracted from a number of lexicographic sources, it is argued here that the validity of the above-described grammaticalization path can likewise be extended to the history of the two aforementioned nouns, viz. the Polish lexeme odrobina 'crumb; a little' and its Swedish counterpart smula 'crumb; a little,' both of which developed the adverbial sense only after having established themselves as vague quantifiers