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Dissertations / Theses on the topic 'Weight formulas'
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1
Tang, Mei-po. "Weight gain and methods of feeding a retrospective cohort study of the Hong Kong Chinese infants /." Click to view the E-thesis via HKUTO, 2004. http://sunzi.lib.hku.hk/hkuto/record/B31972214.
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Tang, Mei-po, and 鄧美寶. "Weight gain and methods of feeding: a retrospective cohort study of the Hong Kong Chinese infants." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2004. http://hub.hku.hk/bib/B31972214.
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Ratiborský, Pavel. "Konstrukční návrh trubkového rámu Formule Student." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2014. http://www.nusl.cz/ntk/nusl-231389.
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This thesis deals with the design of the tubular frame for the Formula Student car competition. The first part is a brief introduction to the competition and used variants of frames. The main part starts with a list of restrictions by the rules and other necessary installation components. The central part is devoted to the draft modifications and their assessment in terms of torsional stiffness by FEM analysis. The final section presents the resulting frame design with respect to the required properties. The work is concluded final evaluation.
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Moshiri, Maryam. "Truck Size and Weight Analysis for the Development of a European Bridge Formula." PIARC World Road Congress, 2011. http://hdl.handle.net/1993/9148.
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The research analyzes the bridge load stress effects resulting from international bridge formulae and truck size and weight regulations in Europe. This is done with a view to identifying issues that may need to be considered in the development of a European Bridge Formula (EUBF) conforming to European Directive truck configurations for the regulation of truck size and weight limits associated with international travel between European Union (EU) member states.
The level of efficiency of bridge formulae vary depending on the design criteria used in the development of the formula, the compatibility to the jurisdiction’s infrastructure and truck fleet characteristics, and the method of implementation as part of the regulation and by operators in the trucking industry. The EUBF should limit imposed critical bending moment and shear stresses on single and continuous span bridges of varying lengths (5, 20, and 50 metres) in accordance to design live loads specified in the Eurocode. The analysis of bridge load effects imposed by European Directive truck configurations in this research, provide the basis for the development of a EUBF.
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Li, Huajie. "Contributions to the relative trace formula of Guo-Jacquet." Thesis, Université de Paris (2019-....), 2020. http://www.theses.fr/2020UNIP7080.
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On établit des formules des traces globale et locale pour les espaces symétriques infinitésimaux de Jacquet-Guo. On prouve également quelques résultats locaux concernant la comparaison de termes semi-simples réguliers qui sont des intégrales orbitales pondérées non invariantes. Cette thèse contient cinq chapitres. Dans le chapitre 1, on rappelle les motivations et énonce nos principaux résultats. Notre travail s'inspire d'une conjecture de Jacquet-Guo, qui est un exemple dans le programme de Langlands relatif, et des problèmes analytiques apparaissant dans l'approche par la formule des traces relative. Dans le chapitre 2, on établit une variante infinitésimale de la formule des traces de Jacquet-Guo pour le cas de (GL (2n, D), GL (n, D) ⨉GL (n, D)). Elle est une sorte de formule sommatoire de Poisson obtenue par un analogue de la troncature d'Arthur. On décrit les termes semi-simples réguliers comme des intégrales orbitales pondérées explicites. Dans le chapitre 3, on établit une formule similaire et a une description similaire des termes semi-simples réguliers pour le cas d'une algèbre centrale simple contenant une extension quadratique. De plus, on énonce et prouve le lemme fondamental pondéré grâce aux travaux de Labesse sur le changement de base pour GL(n). Dans le chapitre 4, on établit une formule des traces locale invariante infinitésimale de Jacquet-Guo sur un corps p-adique en suivant les travaux de Waldspurger et Arthur. Au cours de la démonstration, on obtient également une formule des traces locale non invariante infinitésimale, la finitude de Howe pour les intégrales orbitales pondérées et la représentabilité de la transformée de Fourier des intégrales orbitales pondérées. Dans le chapitre 5, avec les résultats des chapitres précédents, on adopte la stratégie de Waldspurger sur le transfert endoscopique pour prouver certaines relations entre transformées de Fourier des intégrales orbitales pondérées locales invariantesWe establish global and local trace formulae for infinitesimal symmetric spaces of Guo-Jacquet. We also prove several local results concerning the comparison of regular semi-simple terms which are noninvariant weighted orbital integrals. This thesis contains five chapters. In Chapter 1, we recall the motivations and state our main reults. Our work is inspired by a conjecture of Guo-Jacquet, which is an example in the relative Langlands programme, and analytic problems appearing in the relative trace formula approach. In Chapter 2, we establish an infinitesimal variant of Guo-Jacquet trace formula for the case of (GL (2n, D), GL (n, D) ⨉GL (n, D)). It is a kind of Poisson summation formula obtained by an analogue of Arthur’s truncation. We describe regular semi-simple terms as explicit weighted orbital integrals. In Chapter 3, we estabilish a similar formula and have a similar description of regular semi-simple terms for the case of a central simple algebra containing a quadratic extension. Moreover, we state and prove the weighted fundamental lemma thanks to Labesse’s work on the base change for GL(n). In Chapter 4, we establish an infinitesimal invariant local trace formula of Guo-Jacquet over a p-adic field by following works of Waldspurger and Arthur. During the proof, we also obtain an infinitesimal noninvariant local trace formula, Howe’s finiteness for weighted orbital integrals and the representability of the Fourier transform of weighted orbital integrals. In Chapter 5, with the results in previous chapters, we adopt Waldspurger’s strategy on the endoscopic transfer to prove some relations between Fourier transforms of invariant local weighted orbital integrals
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Contractor, Yateesh Jaykishan. "Evaluation of a new bridge formula for regulation of truck weights." Texas A&M University, 2005. http://hdl.handle.net/1969.1/2551.
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The current bridge formula, Federal Bridge Formula B (BFB), established in
1974 to protect bridges against excessive overstress, is very restrictive on long
combination vehicles due to an 80,000 lb gross vehicle weight limit. Without this limit
the formula will not be able to protect bridges in the cases of longer trucks. A formula
developed by the Texas Transportation Institute (T.T.I.) called the TTI-HS20 Formula
addresses these issues. This formula, developed especially for bridges designed for the
HS-20 truck, eliminates the need for the 80,000 lb limit.
A generic formula developed to protect H15 and HS-20 bridges (James et al.,
1986) was evaluated in a previous study (James and Zhang, 1991). The approach to
evaluating the TTI-HS20 Formula follows the approach outlined in James and Zhang,
1991. Information was collected on two important elements: a set of test bridges
representative of the lightest continuous bridges, and a set of test truck configurations
representative of real truck traffic with a focus on long combination vehicles.
Critical weights of the selected trucks for the representative bridges are
calculated and plotted against the TTI-HS 20 formula and other proposed formulas. A
final recommendation as to whether this formula should be adopted nationwide is made.
7
KUNIBA, ATSUO, and TOMOKI NAKANISHI. "Bethe Equation at q=0, Moebius Inversion Formula, and Weight Multiplicities: II. X_n case." Elsevier Science B.V, 2002. http://hdl.handle.net/2237/10056.
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Kuniba, Atsuo, and Tomoki Nakanishi. "Bethe Equation at q=0, Möbius Inversion Formula, and Weight Multiplicities: I. sl(2) case." Springer Verlag, 2000. http://hdl.handle.net/2237/10057.
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Zýková, Petra. "Scoring rules -- pokročilé hlasovací systémy s pořadím kandidátů." Master's thesis, Vysoká škola ekonomická v Praze, 2017. http://www.nusl.cz/ntk/nusl-359345.
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This thesis deals with ranked advanced voting systems. The aim is to determine the overall winner and the ranking of candidates based on voters' preferences. The thesis utilises basic voting systems - plurality rules, lexicographical and Borda's method - as well as advanced voting systems with the application of DEA models, specifically DEA/AR model, DEA/AR exclusion model (including variations with penalties), and Llamazares-Peňa model. Compromise programming is used to obtain common vector of weights. The models and their use are demonstrated on Formula One Grand Prix results from season 2016. Formula One World Drivers' Championship and Formula One World Constructors' Championship are being investigated.
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Ueda, Masaru. "The decomposition of the spaces of cusp forms of half-integral weight and trace formula of Hecke operators." 京都大学 (Kyoto University), 1987. http://hdl.handle.net/2433/86379.
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KUNIBA, ATSUO, TOMOKI NAKANISHI, and ZENGO TSUBOI. "The Bethe Equation at q=0, The Mobius Inversion Formula, and Weight Multiplicities: III. The X^{(r)}_N case." Springer Verlag, 2002. http://hdl.handle.net/2237/10054.
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Ortigas, Galindo Jorge. "Invariants algébriques et topologiques des courbes et surfaces à singularités quotient." Thesis, Pau, 2013. http://www.theses.fr/2013PAUU3011/document.
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Le but principal de cette thèse de doctorat est l'étude de l'anneau de cohomologie du complément d'une courbe algébrique réduite dans le plan projectif pondéré complexe dont les composantes irréductibles sont des courbes rationnelles (avec ou sans points singuliers). En particulier, des représentants holomorphes (rationnels) sont obtenus pour les classes de cohomologie. Pour atteindre notre objectif, il est nécessaire de développer une théorie algébrique des courbes sur des surfaces avec des singularités quotient et d'étudier des techniques pour calculer certains invariants particulièrement utiles à travers des Q-résolutions plongéesThe main goal of this PhD thesis is the study of the cohomology ring of the complement of a reduced algebraic curve in the complex weighted projective plane whose irreducible components are all rational (possibly singular) curves. In particular, holomorphic (rational) representatives are found for the cohomology classes. In order to achieve our purpose one needs to develop an algebraic theory of curves on surfaces with quotient singularities and study techniques to compute some particularly useful invariants by means of embedded Q-resolutions
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Škaloud, Martin. "Návrh alternativní konstrukce rámu formulového vozu." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2012. http://www.nusl.cz/ntk/nusl-230197.
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The diploma work focuses on the proposal of formula car support frame type alternative designed for international students´ competition Formula Student. As a first is this competition shortly described. Following basic information about possible support frame in competition, the rules description for the frame from thin-walled profiles as well as for composite structure. As the other are shown the most used material types by the tube frames. Continues the practical (design) part of the work. The work continues in construction/design part. Here are mentioned the requirements for the frame creating, calculation of each torsion strength and construction proposal including creating the analysis model. In the final part is realize the simulation in FEM program and simply described the alternative proposal together with the evaluation.
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Gishe, Jemal Emina. "A finite family of q-orthogonal polynomials and resultants of Chebyshev polynomials." [Tampa, Fla] : University of South Florida, 2006. http://purl.fcla.edu/usf/dc/et/SFE0001620.
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Ortmann, Regina. "Uncertainty in Weighting Formulary Apportionment Factors and its Impact on After-Tax Income of Multinational Groups." WU Vienna University of Economics and Business, Universität Wien, 2015. http://epub.wu.ac.at/4609/1/SSRN%2Did2521386.pdf.
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Formulary apportionment is an intensively debated mechanism for allocating tax base within
multinational groups. Systems under which the formula is identical in all jurisdictions and systems
under which jurisdictions can determine the weights on the formula factors individually can be
observed. The latter systems produce uncertainty about the overall tax-liable share of the future group
tax base. Counter-intuitively, I identify scenarios under which increased uncertainty leads to higher
expected future group income. My results provide helpful insights for firms and policy makers
debating the specific design of a formulary apportionment system. (author's abstract)Series: WU International Taxation Research Paper Series
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ALMEIDA, Mariana de Albuquerque. "Investiga??o da resist?ncia ? corros?o do a?o aisi 1020 em meio ?cido na presen?a de tiossemicarbazonas, extratos vegetais e suas formula??es." Universidade Federal Rural do Rio de Janeiro, 2017. https://tede.ufrrj.br/jspui/handle/jspui/2167.
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CAPES
This dissertation presents the evaluation of four thiosemicarbazones, from extracts of species of vegetables Talinum triangulare, Physalis angulata e Theobroma cacao L. besides formulation obtained from the combination extract of thiosemicarbazones vegetables as corrosion inhibitor in the presence of carbon steel AISI 1020. Thiosemicarbazones were obtained with good level of purity, satisfactory throughput and identified by NMR of 1H and 13C. The watery extract of Talinum triangulare was obtained using ultrasound device. The extracts of Physalis angulata species were obtained by maceration in water and the other one in ethyl acetate. The watery extracts of Theobroma cacao L. species were obtained using ultrasound device and decoction and hydroalcoholic extract was obtained by maceration in ethanol:water (80:20). The thiosemicarbazones, the vegetable extracts and their formulation were tested in the presence of corrosion of carbon steel AISI 1020 in solution 1 mol. L-1 of HCl. For this evaluation it was used the gravimetric techinique of weight loss and electrochemical techiniques of potentiodynamic polarization and electrochemical impedance spectroscopy. The results showed that the presence of thiosemicarbazones, as well as, the formulation increased significantly the resistence of carbon steel AISI 1020 in acidic medium. The results obtained in different used essays (weight loss, potentiodynamic polarization and electrochemical impedance spectroscopy) show that these techniques are complementary in relation to the evaluation of corrosion inhibition. The best anti-corrosion efficiency was observed for thiosemicarbazone chloro and hydroxy-substituted and its formulations with the extract of T. triangulare achieving 88% and 87% of efficiency, by electrochemical impedance spectroscopy, respectively.
Nesta Tese ? apresentada a avalia??o de quatro tiossemicarbazonas, dos extratos das esp?cies vegetais Talinum triangulare, Physalis angulata e Theobroma cacao L., al?m de formula??es obtidas pela combina??o extrato vegetal:tiossemicarbazonas, como inibidores de corros?o frente ao a?o carbono AISI 1020 em meio de ?cido cloridr?co. As tiossemicarbazonas foram obtidas com bom grau de pureza, em rendimentos satisfat?rios e, caracterizadas por IV, RMN de ^1H e ^13C. O extrato aquoso de Talinum triangulare foi obtido em aparelho de ultrassom, os extratos da esp?cie Physalis angulata, foram obtidos sob macera??o em ?gua e o outro em acetato de etila; j? os extratos aquosos da esp?cie Theobroma cacao L. foram obtidos em aparelho de ultrassom e decoc??o e, finalmente, o extrato hidroalco?lico foi obtido por macera??o em etanol:?gua (80:20). As tiossemicarbazonas, os extratos vegetais e suas formula??es foram testadas frente ? corros?o de a?o carbono AISI 1020 em solu??o 1mol.L-1 de HCl. Para tal avalia??o foi utilizada a t?cnica gravim?trica de Perda de Massa e as t?cnicas eletroqu?micas de Polariza??o Potenciodin?mica e Espectroscopia de Imped?ncia Eletroqu?mica. Os resultados mostraram que a presen?a de tiossemicarbazonas, bem como, das formula??es aumentam significativamente a resist?ncia do a?o carbono AISI 1020 em ?cido. Os resultados obtidos nos diferentes ensaios utilizados (Perda de Massa, Polariza??o Potenciodin?mica e Espectroscopia de Imped?ncia Eletroqu?mica) mostraram que estas t?cnicas s?o complementares quanto a avalia??o da inibi??o da corros?o. A melhor efici?ncia anticorrosiva foi observada para as tiossemicarbazonas cloro e hidroxi-substitu?das e, para suas formula??es com o extrato da T. triangulare obtendo-se 88% e 87% de efici?ncia por espectroscopia de imped?ncia eletroqu?mica, respectivamente.
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Sutherland, Sarah C. "Characteristics Associated with Neonatal Carnitine Levels: A Systematic Review & Clinical Database Analysis." Thèse, Université d'Ottawa / University of Ottawa, 2013. http://hdl.handle.net/10393/23744.
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Newborn screening programs measure analyte levels in neonatal blood spots to identify individuals at high risk of disease. Carnitine and acylcarnitine levels are primary markers used in the detection of fatty acid oxidation disorders. These analytes may be influenced by certain pre/perinatal or newborn screening related factors. The primary objective of this study was to explore the association between these characteristics and levels of blood carnitines and acylcarnitines in the newborn population. The study was composed of two parts: a systematic review and a clinical database analysis of existing newborn screening data. The systematic review results suggested considerable variability across studies in the presence and directionality of associations between analyte levels and birth weight, gestational age, age at time of blood spot collection, type of sample, and storage time. Sex was not significantly associated with carnitine or acylcarnitine levels in neonatal blood. We identified a need to more fully investigate a potential interaction between gestational age and birth weight in regard to analyte levels. The secondary data analyses indicated a statistically significant relationship between analyte levels and all perinatal / infant and newborn screening related factors of interest, but effect sizes were generally small. The interaction between gestational age and birth weight was significant in all models; when further explored through graphical analysis with conditional means, extremely premature neonates stood out as having distinct analyte patterns in relation to birth weight. Variation in the ratio of total acylcarnitine to free carnitine was better accounted for by the perinatal and newborn factors than was variation in any individual carnitine or acylcarnitine, indicating that proportions of carnitine and acylcarnitines may be more important in understanding an individual’s metabolic functioning than individual analyte levels. A low proportion of variation was explained in all multivariate models, supporting the use of universal algorithms in newborn screening and suggesting the need for further large scale empirical research targeted at previously unaccounted for perinatal factors such as birth stress.
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Krishna, Teja G. V. "Weights of highest weight modules over Kac-Moody algebras." Thesis, 2022. https://etd.iisc.ac.in/handle/2005/5886.
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In this dissertation, broadly, we treat the weight-sets of arbitrary highest weight modules (uniformly) over all general complex Kac-Moody Lie algebras $\mathfrak{g}$,
achieving the below.
We obtain a uniform, explicit, cancellation-free and positive formula for the weight-sets of all highest weight modules $V$ (of all highest weights) over all Kac-Moody $\mathfrak{g}$.
Interestingly, our formula for the weights of $V$ involves basic ingredients, namely the independent subsets in the Dynkin diagram of $\mathfrak{g}$ determined by $V$, and nothing else!
Prior to our work, it seems that even for all (non-integrable) simple highest weight $\mathfrak{g}$-modules - despite these being treated for over a half century - their weight-formulas were not known until a few years ago.
Namely, these were written-up in Khare [J. Alg. 2016] and Dhillon-Khare [Adv. Math. 2017 and J. Alg. 2022]; and our general formula recovers the formulas for simples in these papers.
Leaving out general Kac-Moody or even general semisimple settings, given an arbitrary highest weight module $V$ over $\mathfrak{sl}_n(\mathbb{C})$ or in particular $\mathfrak{sl}_4(\mathbb{C})$, even in this case the weights of $V$ were not written down in the literature to the best of our knowledge.
More importantly, our weight-formula naturally drives us to introduce and study a finite family of ``higher order Verma modules" $\mathbb{M}(\lambda,\mathcal{H})$ over Kac-Moody $\mathfrak{g}$, for every highest weight $\lambda\in \mathfrak{h}^*$ and (any) collection $\mathcal{H}$ of independent subsets in the Dynkin diagram of $\mathfrak{g}$.
This family generalizes and includes: all Verma modules $M(\lambda)=\mathbb{M}(\lambda,\emptyset)$ at zeroth order level, and the parabolic Verma modules $M(\lambda,J)=\mathbb{M}(\lambda, \{ \{j\} \ |\ j\in J \})$ (which were introduced and studied by Lepowsky, Kumar, Mathieu,... to name but a few) at first order level.
Importantly, our higher order Verma modules are crucial and universal for weight considerations:
their weight-sets (which are finitely many when we fix their highest weight) are pairwise disjoint and exhaust the weight-sets of all highest weight $\mathfrak{g}$-modules.
In this thesis, we also initiate the study of the characters of these universal modules, by computing them via BGG-type resolutions in certain cases.
Next, a phenomenon in root systems which rewarded us with many applications on the weights side.
First, recall the partial sum property for Kac-Moody root systems: every root of $\mathfrak{g}$ is an ordered sum of simple roots such that each partial sum is also a root.
The course/journey to finding and proving our weight-formula mentioned above begins from proving a parabolic-generalization of this property, which we call as the parabolic partial sum property.
Given a subset $S$ of simple roots, it allows one to write any (positive) root $\beta$ involving some simple roots from $S$ as: an ordered sum of roots, in which each root involves exactly one simple root from $S$ (unit $S$-height roots) and with each partial sum also being a root.
The parabolic partial sum property has been devised in order to obtain a ``minimal" description for the weights of all (non-integrable) highest weight simples, which was posed by Khare.
This thesis exhibits such minimal descriptions as an immediate application of the parabolic partial sum property;
in fact we will more strongly show this property at the level of Lie words for any general Lie algebra graded over any free abelian semigroup.
There is also another generalization of the partial sum property due to Khare and Kumar for highest weight simples in finite type, which we extend to the Kac-Moody setting in this thesis.
There is another notable application of the parabolic partial sum property shown in this thesis. Chari and her coauthors [Adv. Math. 2009 and J. Geom. Phys. 2011] introduced and studied certain combinatorial subsets called weak faces and $(\{2\};\{1,2\})$-closed subsets of finite root systems. This is in order to construct Koszul algebras, study Kirillov-Reshetikhin modules over specializations of quantum affine algebras, and also to classify nilpotent ideals in the parabolic Lie subalgebras of finite type $\mathfrak{g}$, etc.
These subsets (say subsets of a set $X$) are some discrete analogues/ generalizations of the faces for convex sets (the faces of the convex hull of $X$).
In this thesis, we are concerned with such subsets of $X=$ a weight-set, generalizing the faces for convex hulls of weight-sets.
Using the weak faces for weight-sets of finite-dimensional simples (in finite type) Khare extended the aforementioned results of Chari et al.
Motivated by the applications of these two modern notions to representation theory, we completely classify the weak faces and $(\{2\};\{1,2\})$-closed subsets of weights of all highest weight modules (again uniformly) over all Kac-Moody $\mathfrak{g}$; extending and completing the partial classification results of Chari, Khare, and their co-authors from finite type.
We more strongly show that both these notions are the same as the weights falling on the faces, for the convex hulls of these weight-sets.
This shows the equivalence of these two notions, to the classical faces for the convex hulls of weights (which have been pursued from the 1960s).NBHM Ph.D. Fellowship (Ref. No. 2/39(2)/2016/NBHM/R&D-II/11431) and by a Swarnajayanti Fellowship from the DST and SERB (Govt. of India).
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Chang, Hao-Shong, and 張皓翔. "Some Weighted Sum Formulas of Multiple Zeta Values." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/96594460499471647485.
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碩士國立中正大學
應用數學研究所
103
Many weighted sum formulas of MZVs follow from the decomposition theorem of $n$ products of Riemann zeta values. All these sum formulas contain not only one sum, but several sums which are analogues of the restricted sum formula \[ \sum_{\av{\bss}=m} \zeta(\set{1}^{k}, \seqs{s}{1}{r-1}{r}+1) = \sum_{\av{\boldsymbol{h}}=k+q} \zeta(\seq{h}{1}{2}{k+1}+(m-q)+1). \] In light of the deomposition theorem of $n$ products of MZVs of height one, we are able to eliminate all the restricted sums when $k \geqslant 1$. Therefore the improved sum formulas have only one sum of multiple zeta values. For example, \begin{align*} &\frac{1}{3}\sum_{\av{\bsp}=r} \zeta(p_{1}+2)\zeta(p_{2}+2)\zeta(p_{3}+2) +\sum_{\ell=0}^{r+1} \zeta(1,\ell+2)\zeta(r-\ell+3)+\zeta(1,1,r+4)\\ &=\sum_{\av{\bss}=r+5} \zeta(s_{1}, s_{2}, s_{3}+1) \brac{2^{s_{2}}(3^{s_{3}}-2^{s_{3}})-(2^{s_{3}}-1)}
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Chang, Chiang Chi, and 江奇璋. "Sum formulas of multiple zeta value with even arguments and polynomial weights." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/2z39nx.
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碩士國立中正大學
數學系應用數學研究所
105
\begin{center} \textbf{Abstract} \\[1cm] \end{center} \begin{flushleft} Let \end{flushleft} \begin{center} $E_h(2mn, k)=\sum\limits_{{|\alpha|=n}}\{{\prod\limits_{j=1}^{k} \alpha_j^h}\}\zeta(2m\alpha_1,2m\alpha_2,...,2m\alpha_k)$, \end{center} \begin{flushleft} be sums of multiple zeta value of weight $2mn$ and depth with the weight $\{{\prod\limits_{j=1}^{k} \alpha_j^h}\}$. In this their, we are going to evaluate the cases $h=0, 1, 2, 3$ and $m=1, 2$ when $1\leq k \leq n$. The special case $h=0$ give the evaluations of \begin{center} \begin{center} $E(2n, k)=\sum\limits_{|\alpha|=n}\zeta(2\alpha_1,2\alpha_2...2\alpha_k)$, \end{center} \begin{flushleft} and \end{flushleft} \begin{center} $E(4n, k)=\sum\limits_{|\alpha|=n}\zeta(4\alpha_1,4\alpha_2...4\alpha_k)$, \end{center} \begin{flushleft} which are of particular interest. \end{flushleft} \begin{flushleft} In particular, \end{flushleft} $E(2n,k)=\dfrac{(-1)^{n-k-1}\pi^{2n}}{(2n+1)!}\sum\limits_{j=0}^{n-k}\begin{pmatrix}n-j\\k\end{pmatrix}\begin{pmatrix}2n+1\\2j\end{pmatrix}2(2^{2j-1}-1)B_{2j}$, \begin{flushleft} which is obtained by Hoffman in 2016. \end{flushleft}
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Tlale, Juliet Karabo. "Validation of a simple clinical formula for predicting birth weight in women who are in labour at term." Thesis, 2012. http://hdl.handle.net/10539/11449.
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M.Med. (Obstetrics and Gynaecology), Faculty of Health Sciences, University of the Witwatersrand, 2011Background Estimation of fetal weight during labour at term is frequently done to decide if there is a risk of cephalopelvic disproportion or shoulder dystocia. Estimation of fetal weight by clinical palpation has been shown to be as good as ultrasound in labour at term, giving estimates that are correct to within 10% of the birth weight in 60% to 70% of cases. Symphysis-fundal height (SFH) measurement may offer an easier method of fetal weight estimation, but no simple formula is currently available. The objective of this study was to validate a formula calculated from unpublished work done at Chris Hani Baragwanath hospital, where birth weight in g = 100 (SFH in cm – 5) for term intrapartum measurements. In that study, the formula gave estimates correct to within 10% of the birth weight in 67% of cases. Methods This was a prospective cross-sectional study done on women at term with singleton live cephalic presentations at the Charlotte Maxeke Johannesburg Academic Hospital and Chris Hani Baragwanath Hospital. All participants were in the active phase of the first stage of labour. The author performed abdominal palpation, and measured SFH twice, taking the average of the two measurements as the SFH. Maternal heights, weights, membrane status and level of the head were also recorded. The SFH measurements were transformed into estimated birth weights using the formula, and these were compared with the actual birth weights. 7 Results The researcher assessed 294 women, 289 of them being black African. The mean birth weight was 3221 g and the mean SFH was 37 cm, which equated to a mean estimated birth weight, using the formula, of 3200 g. Simple linear regression between SFH and birth weight gave a correlation coefficient (r) of 0.56. The mean percentage error in fetal weight estimation using the formula was 8.7%. Sixty-five per cent of estimations were found to fall within 10% of the actual birth weight. Fetal weight estimates were best (mean percentage error 6.8%) in the birth weight range of 3000 g to 3499 g, and worst at the extremes of term birth weight. Conclusion The birth weight formula was validated in this study, giving very similar results to those found in the original research that described the formula. The formula may be applied by clinicians in environments that serve populations similar to those that participated in this study.
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Su, Wen-Chi, and 蘇雯綺. "Bernoulli Identities and Weighted Sum Formulas of Multiple Zeta Values." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/94070925693729968758.
Full textAbstract:
碩士國立中正大學
應用數學研究所
103
In this thesis, we will produce some Bernoulli identities through the zeta functions. From the evaluation of the Riemann zeta function at even integers, these Bernoulli identities can be transformed into a linear combination of Riemann zeta values at even integers. Also, using the decomposition theorem of a product of n Riemann zeta values, we can express some symmetric sum of Riemann values at even integers in terms of multiple zeta values. Therefore, we can evaluate some weighted sum formulas of multiple zeta values as linear combinations of n Riemann zeta values for n = 2, 3, 4, 5.
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LIU, YI-RU, and 劉羿汝. "Weighted Sum Formulas from Shuffle Products of Riemann Zeta Values." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/80024797345262779733.
Full textAbstract:
碩士國立中正大學
應用數學研究所
103
The classical Euler decomposition expresses a product of two Riemann zeta values as double Euler sums and it leads to a weighted sum formula among double Euler sums. Through a particular integral representation of Riemann's zeta values, we are able to carry out the shuffle product of $n$ Riemann zeta values. As results, we produce some weighted sum formulas among multiple zeta values of depth 2, 3 and 4. In particular when the depth $n=4$, the weighted sum formula is given by \begin{align*} &\sum_{|\balpha|=k+7}\zeta(\alpha _{1},\alpha_2,\alpha_3,\alpha _{4}+1)\left \{ 2^{\alpha _{2}-1}3^{\alpha _{3}-1}\left ( 4^{\alpha _{4}}-3^{\alpha _{4}} \right ) \right.\\ &\qquad \quad\quad\quad\quad \left. -\left ( 2^{\alpha _{2}+\alpha _{3}-2}+2^{\alpha _{3}-1} \right ) \left ( 3^{\alpha _{4}}-2^{\alpha _{4}} \right )+\left (2^{\alpha _{4}} -1\right )\right \}\\ &-\sum_{|\balpha|=k+6}\zeta(1,\alpha_2,\alpha_3,\alpha _{4}+1)\left \{ 2^{\alpha _{3}-1}\left ( 3^{\alpha _{4}}-2^{\alpha _{4}} \right )-\left (2^{\alpha _{4}} -1\right )\right \}\\ & +\sum_{|\balpha|=k+5}\zeta(1,1,\alpha_3,\alpha_4+1)\left \{ 2^{\alpha _{4}}-1 \right \}-\zeta \left ( 1,1,1,k+5 \right)\\ & =\frac{1}{24}\sum_{\left | \mathbf{a} \right |=k}\zeta(a_{1}+2)\zeta(a_{2}+2)\zeta(a_{3}+2)\zeta(a_{4}+2).
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Hsiao, Hsiu-Ju, and 蕭秀如. "Weighted Sum Formulas of Different Depths of Multiple Zeta Values." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/h2fpyf.
Full textAbstract:
碩士國立中正大學
數學系應用數學研究所
107
Abstract In this thesis, we introduce the method of using an integral to represent a sum of restricted sums. Also we, via the generating dual function, obtain a weighted sum formulas of different depths of multiple zeta values. If \begin{eqnarray*} T(m,n)&:=&\frac{1}{m!n!}\int_{E_2}\left({\log\frac{1}{1-t_1}}+{\frac{1}{2}}{\log\frac{1-t_1}{1-t_2}}\right)^m\left({\frac{1}{2}}{\log\frac{1-t_1}{1-t_2}}+{\log\frac{t_2}{t_1}}\right)^n\frac{dt_1dt_2}{(1-t_1)t_2}, \end{eqnarray*} then \begin{eqnarray*} T(m,n)&=&\sum_{a+b=m}\sum_{c+d=n}\left({\frac{1}{2}}\right)^{b+c}{b+c\choose b}\sum_{|\pmb{\alpha}| =b+n+1} \zeta(\{1\}^a,\alpha_1,\ldots,\alpha_{b+c},\alpha_{b+c+1}+1)\\ &=&2{\left(1-\frac{1}{{2}^{m+n+1}}\right)}\zeta(m+n+2) \end{eqnarray*} or \begin{eqnarray*} T(m,n)&=& {\bf W}(m,n)\zeta(m+n+2)\\ & &+\sum_{j=1}^{\text{min}\{m,n\}}(-1)^j \sum_{\scriptstyle {|\pmb{c_j}|=m-j \atop |\pmb{d_j}|=n-j}}{\zeta(\,c_{j_{0}}+d_{j_{0}}+2, \ldots , c_{j_{j}}+d_{j_{j}}+2\,){\bf W}(c_{j_{0}},d_{j_{0}})}\\ &=&2{\left(1-\frac{1}{{2}^{m+n+1}}\right)}\zeta(m+n+2), \end{eqnarray*} where $${\bf W}(p,q)=\sum_{b=0}^{p}\,\sum_{c=0}^{q}\left({\frac{1}{2}}\right)^{b+c}{b+c\choose b}.$$
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Soni, Zakiyya. "Comparison of weight estimation formulae in paediatric patients at Chris Hani Baragwanath Academic Hospital." Thesis, 2018. https://hdl.handle.net/10539/25376.
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A research report submitted to the Faculty of Health Sciences, University of the Witwatersrand, in partial fulfilment of the requirements for the degree of Master of Medicine in the branch of Anaesthesiology
Johannesburg, 2017.Background Accurate weight determination is essential in providing optimal care to the paediatric population, as both over- and under-estimation can be detrimental. This study aimed to compare the accuracy and precision of three paediatric weight estimation formulae, the Advanced Paediatric Life support (APLS), the formula used by anaesthetists in academic hospitals affiliated to the University of Witwatersrand (Wits-A), and the Luscombe and Owens (LO) formula, to the measured weight of children at the Chris Hani Baragwanath Academic Hospital (CHBAH) outpatient department. Methods A prospective, contextual, descriptive study design was used with quota sampling. Four hundred children aged 1 - 10 years were recruited for the study. Age, gender, ethnicity, weight and height were recorded. Results On average the APLS formula performed the best with 49 % of estimates within 10% of the actual measured weight (PW10), the lowest mean percentage difference (MPD) of +0.7% and the narrowest 95% limits of agreement. The Wits-A formula followed with a PW10 of 41% and a MPD of -5.2% while the LO formula had a PW10 of 24% and a MPD of -19.4%. Conclusion An accurate and precise weight estimation technique remains elusive and the gold standard is a measured weight. The APLS formula was however found to be the most accurate in the CHBAH population and should be used over the Wits-A formula if a formula has to be used.
LG2018
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Yeh, Mei-Ling, and 葉美伶. "Clustering using Radius-Weighted Means and Analytical Radius-Preserved Formula." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/56316888343680263905.
Full textAbstract:
碩士國立交通大學
多媒體工程研究所
104
As mobile phones and wearable devices get popular, people are developing new habits that are totally different from before. Also, many devices now can collect abundant data more diversified and quickly, and this makes new applications are more various, and the data are often high-dimensional. In this situation, with limited performance of hardware, customized devices are often not easy to analyze data and make real-time responses. The thesis here is based on RWM Approach and Analytical Approach, which are, respectively, related to the “Radius Weighted Mean bisection method” and “Analytical Radius-Preserved Formula”. Both of the proposed approaches can deal with larger high-dimensional data without knowing in advance the number of clusters. When we compare ours with other approaches which also do not require inputting number of clusters, since there is no big difference between ours and others in clustering accuracy, we compare our processing speed with the processing speed of reported methods. Some of these reported methods are full- dimensional clustering, and some use Dimension Reduction of data. In the experiments, we see that the time efficiency of ours are good, as the number of data points increases, or as the dimensions changes. Hence, our approach has better speed and also meets the requirements of real-time responses.
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Chen, Guo-Hua, and 陳國華. "Maximum Weight Approach for Code Synchronization in DS/SS Systems Using Adaptive Constrained Filtering Techniquewith Direct-Delay-Estimation Formula." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/49531247326154293689.
Full textAbstract:
碩士國立中山大學
通訊工程研究所
91
The technique of direct sequence spread spectrum (DS/SS) has been widely used in commercial mobile communication systems. The efficiency of DS/SS system is highly dependent on the accurate and fast synchronization between the incoming and locally generated PN (pseudo-noise) codes. The code synchronization is processed in two steps, acquisition (coarse alignment) and tracking (fine alignment), to bring the delay offset between the two codes. Conventionally, for code synchronization, most of techniques were proposed based on the correlation property of PN codes. Recently, the different approach, by using the adaptive LMS filtering scheme, has been proposed to reduce the hardware complexity and to improve the performance of code synchronization, especially for a long PN code. In this thesis, a new coherent adaptive code synchronization scheme is proposed, where the adaptive constrained LMS (CLMS) algorithm with the maximum tap-weight (MTW) test method is devised for code acquisition. The statistics of weight vector of the proposed CLMS scheme are derived to evaluate the performance, in terms of mean acquisition time (MAT). Analytical and simulation results verify that the proposed scheme for code acquisition outperforms the one using the conventional LMS filtering schemes, under the integer and non-integer time delay cases. Moreover, the setting of threshold value is derived for code acquisition, which is independent of the values of signal-to-noise ratio (SNR) and time delay. Next, the CLMS scheme is proposed associated with the direct delay estimation (DDE) formula for code tracking. This approach does achieve a good delay-tracking performance, which is verified via computer simulation. Simultaneously, the hardware complexity can further be reduced due to that a code-tracking loop implemented by the interpolation method is not required.
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Wang, Jiang-Tom, and 王建棠. "The study of modified formula for the maximum unit weight on the compaction curve of the large grain size soil aggregates." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/28845069051515975392.
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A-Chuan, Tu, and 涂阿絹. "THE DEVELOPMENT OF NEW FORMULA TO REPLACE THE USAGE OF MSG IN SCHOOL LUNCH/EFFECT OF HEALTH-RELATED FITNESS OF INTRVENTION IN INCELUSIVE WEIGHT CONTORL PROGRAM FOR SCHOOLCHILDREN." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/267979.
Full textAbstract:
碩士國立臺灣體育大學
競技運動學系碩士班
97
The problems about overuse of monosodium glutamate (MSG) were prevalent all over the country, especially in school lunch. To improve the overuse of in primary school lunch, we try to develop the substitute for the MSG. The new formula containing tiny amount of sugar, glycerrhetinic acid and about 30% of normal usage in MSG exhibits greater acceptance than that of the MSG only. The score of organoleptic evaluation in new formula was 3.63, however, 3.33 in MSG only. It shown no obvious difference between male and female in gender factor. The score of organoleptic evaluation in children was greater than adults. The children from Kinden garden have the greatest preference for new formula (4.64). The new formula can effectively reduce the usage of MSG in meal. This study was designed to verify the fusion-style weight control program, the students can effectively reducelong-term BMI, the promotion of physical fitness is the effect of sculpture. To improve the efficiency of weigh control program, weight controlling course as inclusions’ intervention was applied to 70 children (41 males and 29 females) with 11 to 12 years old. After intervention of dietary and exercise program by weight controlling course as inclusions’ intervention for three months, the weight of obese group reduced from 53.5 ± 9.9kg to 51.4 ± 12.4kg and that the control group from 37.6±6.1kg to 39.8 ±7.7kg. The flexibility measured by sit-and-reach method has obvious improvement from 26.2 ±7.2cm to 28.9 ±8.9 cm in obese group. However, the cardio-respiratory fitness measured by 800-meter run-walk and muscular endurance measured by sit-ups test have no marked changes. In conclusion, weight controlling course as inclusions’ intervention can effectively loss the weight by well fitness in obese children.
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Kamble, Meghana P. "Design and Analysis of a Composite Monocoque for Structural Performance : a Comprehensive Approach." Thesis, 2019. http://hdl.handle.net/1805/19975.
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Indiana University-Purdue University Indianapolis (IUPUI)Lately numerous studies have been performed to design composite monocoques with high strength and low weight for various student level racing contests. The objective of this paper is to develop an insightful methodology to design and de veloped a light-weight composite monocoque. The monocoque is designed to pass the mandatory static load tests laid down by the International Automobile Feder ation (FIA)Formula 3. These Formula 3 tests are considered the baseline of the desired structural integrity of the composite monocoque. The presented design tech nique emphasises on a monocoque developed for Sports Car Club of America (SCCA) races. The three standard load tests performed on the monocoque are Survival Cell Side test, Fuel Tank test and Side Intrusion test. A sandwich layup of bi-directional woven carbon/epoxy prepreg and aluminium honeycomb is optimized for minimum weight while predicting the unknown properties of layup and ensuring the mono coque doesnt experience failure. The approach intends to achieve minimum weight with high torsional rigidity and is capable of being used for the design and analysis of any kind of formula type composite monocoque.
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Hanna, George T. "Cubature reduction using the theory of inequalities." Thesis, 2002. https://vuir.vu.edu.au/18166/.
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This dissertation is a detailed analysis of two-dimensional integration providing a priori
error bounds in a variety of measures of integrand derivatives. Cubature formulae involving
both function evaluations and one-dimensional integration are furnished and numerical
experiments to investigate the efficacy of the error formulae are performed. Product (and
singular) double integration is investigated.
Two-dimensional rectangular integral inequalities are constructed via embedding two one
dimensional Peano kernels. In one dimension, linear kernels with a parametric discontinuity
furnish "three point" rules where sampling occurs at the boundary and an interior point.
The error is bounded in terms of the Lebesgue norms of the first derivative of the integrand.
In two dimensions for a rectangular region, we find that the rule generalises to three "three
point" rules in each dimension. That is nine sample points and six one dimensional integrals.
The error bound is expressed in terms of norms of the first mixed partial derivative of the
integrand.
These results are further generalised to provide error bounds in terms an arbitrary order
mixed partial derivative of the integrand. That is, error bounds in measures of δfn+m/δtnδsm for some integers n,m>0 where the integrand is f. In this case, we find that the rule involves
both sample points and one-dimensional integrals involving all the partial derivatives of the
integrand up to the stated order.
Finally, we explore product integrands, where the weight ω(•,•) is positive and integrable.
In this case, the rule and the error bound involve moments of the weight. Particular attention
is applied to identifying a priori two dimensional grids for which the error bound
is minimized. Various weights and weight null spaces are explored and cubature formulae
providing "optimal" grids are given.