Changes In Notation Research Articles

Biot-consistent framework for wave propagation with macroscopic fluid and thermal effects

SUMMARY In principle, wave propagation in porous media can simultaneously trigger macroscopic fluid flow and thermal flow, which can be described by Biot's poroelasticity and Lord–Shulman thermoelasticity, respectively. The physical processes of those effects are significantly different, but phenomenologically, they can lead to identical wave attenuation and dispersion and are hard to be distinguished. By using Biot's virtual concept entropy flow, the Biot-consistent General Linear Solid (the GLS) framework and matrix notation, a rigorous and convenient tool is provided to reveal the similarities and disparities between poroelasticity and thermoelasticity. By using the same framework, a Biot-consistent thermo-poroelastic model is proposed to consider macroscopic effects of fluid and thermal flows simultaneously in an elegant way. These similarities allow us to directly translate many of the available results in poroelasticity to thermoelasticity and vice versa by a simple change of notation. The disparities indicate a fundamental difference in physical mechanisms. Plane-wave analysis shows that the primary P-wave modes of thermoelasticity and poroelasticity are all GSLS-equivalent (Generalized Standard Linear Solid) and can be identical if the model parameters are selected properly. However, the corresponding slow-wave modes have significantly different phase velocity dispersion although the attenuation spectra of which are identical. Such a surprising result can be explained by the GSLS non-equivalence of the slow-wave modes and the fundamentally different mechanisms. As expected, the thermo-poroelastic model predicts four wave modes, which are the fast- and slow-P, temperature (T wave) and S waves. Two attenuation peaks due to, respectively, the thermal- and fluid-flow effects are predicted for the fast-P wave. The slow-P wave mode due to fluid flow is influenced by the thermal effects, but the T wave seems unaffected by the fluid flow. The thermo-poroelastic model is then applied to laboratory observations at 200–106 Hz for the brine-saturated tight sandstone under 35 MPa effective pressure. The unified model provides a convenient framework for studying geothermal exploration, thermal-enhanced oil recovery and other applications involving temperature variations within the porous rock.

История и типология нотолинейных певческих манускриптов: репертуар и внешний вид богослужебных нотных книг

This article examines the notolinear handwritten collections that existed in the church singing practice of Russia from the second half of the XVII century to the revolution. A brief historical digression is given that characterizes the external features of manuscripts in the XVII, XVIII, XIX centuries, describes the change in notation in singing books. The classification of handwritten singing collections is proposed. The characteristics of the most important singing centers of Moscow, St. Petersburg and the province are given. The question is raised about the importance of ownership records, allowing to trace the ownership of the manuscript to a particular temple, the owner, to determine the time of creation of the manuscript. We are talking about the repertoire preserved in the singing collections of different historical periods.

Generations of Reason: A Family's Search for Meaning in Post-Newtonian England

Generations of Reason: A Family's Search for Meaning in Post-Newtonian England

Urban Developments in Late Antique and Medieval Rome: Revisiting the Narrative of Renewal ed. by Gregor Kalas and Ann van Dijk

Reviewed by: Urban Developments in Late Antique and Medieval Rome: Revisiting the Narrative of Renewal ed. by Gregor Kalas and Ann van Dijk Douglas Boin Urban Developments in Late Antique and Medieval Rome: Revisiting the Narrative of Renewal. Edited by Gregor Kalas and Ann van Dijk. (Amsterdam: Amsterdam University Press. 2021. Pp. 342. €128,00. ISBN: 9789462989085.) In this model volume of collaborative scholarship, editors Gregor Kalas and Ann van Dijk have assembled an all-star list of scholars to address, in nine master-class case studies, one gradually emerging central question. As imperial Rome’s circle of influence diminished and other global centers of culture and commerce emerged in Asia and the Islamic worlds, with the Italian peninsula growing ever more insular by the minute, how did life in the city of Rome change over the third through twelfth centuries? Under the editors’ orchestration and jointly-authored introduction, the seemingly parochial theme reveals surprising insights into the legacy of Rome’s capacity for “creativity” (p. 26) in art, poetry, architecture, music, ritual and even financial matters, underscoring the city’s legacy of pursuing “productive responses to evolving circumstances” (p. 7). Rome as a symbol of apocalyptic disaster, this is not. Claims of liveliness across any city or community over a long stretch of nearly a thousand years, of course, can easily drain any analysis of historical specificity. The search for stability during a time of change becomes a sentiment just bland enough to keep all problematic or extenuating circumstances out of the scholar’s focus. Too sagacious to settle for trite and tired frameworks, however, editors Kalas and van Dijk have pushed their contributors toward precision, and what emerges here quite sharply is how important the seventh century was, in particular, in marking the gateway toward many of the new social and cultural realities that distinguished the classical city from the medieval one. The century that saw the last meeting of the Roman Senate (p. 28) would witness, as in Erik Thunø’s essay, the indisputable establishment of the popes as “martyr-saint impresarios” in church building, while Dennis Trout’s study of church inspirations under Pope Honorius, whose under-appreciated artistry is rendered by Trout in original verse translations, reveal a papal city “renewed and embarking on a novel course” (p. 162). In a city “deeply committed to curating its past for present purposes,” the seventh century, Trout writes in epigrammatic fashion marked “yet another renaissance” (p. 150). Where the contributors excel—Kristina Sessa on war, finance, and the clergy; Dale Kinney on the nuanced collaboration between lay and ecclesiastical stakeholders in illuminated manuscript production and architectural renovation; Luisa Nardini’s fascinating account of manuscript changes in musical notation, charting the “permeability” of Roman chant, replete with Frankish, Gallican, and Beneventan [End Page 173] influences—is to bring a radical or unorthodox way of seeing old material which asks scholars to consider it anew, to see even this later Rome still shaped by factors beyond its walls, and to study complex processes outside the traditional boundary divisions of time. Jacob Latham’s nod to the Jewish contexts for the study of early Christianity in his essay on public rituals, as well as William North’s discussion of Hebrew Scripture in the eleventh century, shows a welcome sensitivity to religious inclusion in an otherwise excellent volume that misses an opportunity to engage directly with the history and archaeology of Rome’s Jewish community on the eve of the Middle Ages. When the Roman Empire withdrew from its control of Dacia in the third century—a stunning retreat—foreigners threatened the empire’s borders, exposing what would become a lingering issue of who possessed citizenship and whether these rights and judicial protections might be acquired by outsiders. Kalas’s own study of the monuments of the fifth-century city reminds us that Romans frequently lived in a “denial of conflict” (p. 103). In his analysis of the medieval guidebook, the Mirabilia, John Osborne goes a step further. In Rome always lay a “wonderful blend of possible fact and utter fantasy” (p. 209). Douglas Boin Saint Louis University Copyright © 2023 The Catholic University of America Press ...

나손 김동욱 선생의 기녀사: ‘기녀/기생/창기’ 개념의 정의

This article tried to define the concept of ‘Giyeou/Gisaeng/changgi’ focusing on Nason’s “Introduction to the history of Chosun Giyeou (Giyeou and Gisaeng)－A customs-historical approach to the nobles and changgi of Lee dynasty－” published in 1966 by Nason. In particular, the central concept of the thesis can be seen as a Gisaeng, a Changgi, a nobleman, and a history of customs.
 The vocabulary of ‘Gisaeng’ is not difficult to find in East Asian literature.
 Even today, without any change in diachronic notation, it is possible to search for data in East Asia as well. ‘Gisaeng’ is judged to be the most common word.
 In academia, there is a tendency to express mainly as ‘Giyeou’ in the Korea period, and in the case of the Chosun period, it is classified as ‘Gisaeng’.
 In the case of ‘changgi’, there are many examples of use in East Asian literature, and it can be found that the use of ‘changgi’ is mixed in ancient Korean literature. ‘Gisaeng’ is a suffix ‘-saeng’, and its usage has been prominent since the late Chosun Dynasty. Here, ‘live’ means ‘to make a living by some kind of livelihood’. A ‘Giyeou’ can be called a ‘gisaeng’ who is making a living through a company. For example, ‘Yu-saeng’, ‘Seo-saeng’ etc. can be mentioned. It can be speculated that the generic name of ‘Gisaeng’ is from the 15th to 16th centuries in the mid-Chosun period, when Neo-Confucianism was established as the governing ideology.
 Concepts are important in academic concepts. In Nason’s thesis on the history of changgi, generic terms such as ‘gisaeng’, ‘Giyeou’, ‘gagi’, ‘sucheonggi’, ‘gwangi’, and ‘changgi’ are used interchangeably. A concept refers to general knowledge about an object or phenomenon. The generic name of ‘gisaeng’ can be said to be a generic term for a changgi who is making a living in a company. Therefore, the definitions of ‘gisaeng’, ‘Giyeou’, ‘gagi’, ‘sucheonggi’, ‘gwangi’, and ‘Giyeou’ are generic terms that reflected the society of the time.

Longitudinal change in components of astigmatism and its association with axial length-corneal radius ratio in Chinese young children: the Nanjing Eye Study.

To assess the longitudinal change in components of astigmatism from age 4 to 7years and its association with axial length-corneal radius ratio (AL/CR). Children born between September 2011 and August 2012 in Yuhuatai District of Nanjing were invited to participate in the Nanjing Eye Study for a comprehensive eye examination annually since 2015. The data presented in this paper were obtained in 2016, 2017, and 2019. At each study encounter, noncycloplegic autorefraction and ocular biometric parameters were measured. Changes of total astigmatism (TA), corneal astigmatism (CA), anterior corneal astigmatism (ACA), residual astigmatism (RA), and internal astigmatism (IA) were analyzed in clinical notation (Cyl) and vector notation (J0, J45). Nine hundred fifty-four children (mean ± standard deviation of baseline age: 4.63 ± 0.29years, 53.7% boys) had complete data and were included in this study. Mean slopes of longitudinal changes in Cyl notation were significantly negative for TA, CA, and ACA, but positive for IA. TA, CA, ACA, and RA of J0 notation had a shift toward increasing with-the-rule (WTR) astigmatism and/or decreasing against-the-rule (ATR) astigmatism. TA of J45 notation showed an increase in astigmatism at axis 135° and/or a decrease in astigmatism at axis 45°, while CA and ACA of J45 notation showed an opposite change. Longitudinal changes in ACA and IA were negatively correlated in J0 notation, but not in J45 notation. Based on compensation factor (CF, defined as the minus ratio of IA and ACA), the compensation proportions for J0 in varying degrees (CF: 0.1-2) in 2016, 2017, and 2019 were 91.3%, 93.5%, and 90.0%, respectively, while these for J45 were 74.9%, 76.5%, and 34.6%, respectively. Higher AL/CR increase was associated with less decrease or more increase in CA and ACA of Cyl notation, and a shift toward increasing WTR and/or decreasing ATR in these of J0 notation. The compensatory role of IA was persistent and prominent from 4 to 7years old for J0 notation in Chinese young children. The progression of AL/CR was correlated with astigmatism originated from the cornea.

Invariance of edit-distance to tempo in rhythm similarity

Despite the long history of music psychology, rhythm similarity perception remains largely unexplored. Several studies suggest that edit-distance—the minimum number of notational changes required to transform one rhythm into another—predicts similarity judgments. However, the ecological validity of edit-distance remains elusive. We investigated whether the edit-distance model can predict perceptual similarity between rhythms that also differed in a fundamental characteristic of music—tempo. Eighteen participants rated the similarity between a series of rhythms presented in a pairwise fashion. The edit-distance of these rhythms varied from 1 to 4, and tempo was set at either 90 or 150 beats per minute (BPM). A test of congruence among distance matrices (CADM) indicated significant inter-participant reliability of ratings, and non-metric multidimensional scaling (nMDS) visualized that the ratings were clustered based upon both tempo and whether rhythms shared an identical onset pattern, a novel effect we termed rhythm primacy. Finally, Mantel tests revealed significant correlations of edit-distance with similarity ratings on both within- and between-tempo rhythms. Our findings corroborated that the edit-distance predicts rhythm similarity and demonstrated that the edit-distance accounts for similarity of rhythms that are markedly different in tempo. This suggests that rhythmic gestalt is invariant to differences in tempo.

Splitting Type Variational Problems with Linear Growth Conditions

Regularity properties of solutions to variational problems are established for a broad class of strictly convex splitting type energy densities of the principal form f : ℝ2 → ℝ, f(ξ1, ξ2) = f1(ξ1) + f2(ξ2), with linear growth. We show that, regardless of the corresponding property of f2, the assumption (t ∈ ℝ) $$ {c}_1{\left(1+\left|t\right|\right)}^{-{\upmu}_1}\le {f}_1^{\hbox{'}\hbox{'}}(t)\le {c}_2,\kern1em 1<{\upmu}_1<2, $$ is sufficient to obtain higher integrability of ∂1u for any finite exponent. We also include a series of variants of our main theorem. In the case f : ℝn → ℝ, similar results hold with the obvious changes in notation. Bibliography: 30 titles.

FeynMaster: A plethora of Feynman tools

FeynMaster is a multi-tasking software for particle physics studies. By making use of already existing programs ( FeynRules, QGRAF, FeynCalc), FeynMaster automatically generates Feynman rules, generates and draws Feynman diagrams, generates amplitudes, performs both loop and algebraic calculations, and fully renormalizes models. In parallel with this automatic character, FeynMaster allows the user to manipulate the generated results in Mathematica notebooks in a flexible and consistent way. It can be downloaded in https://porthos.tecnico.ulisboa.pt/FeynMaster/. Program summaryProgram Title: FeynMasterProgram Files doi:http://dx.doi.org/10.17632/f6yrbk4cm3.1Licensing provisions: CC0 1.0Programming language: Python, Wolfram MathematicaNature of problem: Although different softwares exist that separately handle Feynman rules, Feynman diagrams, loop calculations and renormalization, there seems to be missing a single software to address all those topics in a flexible and consistent way. Indeed, despite the undisputed quality of some of the existing softwares, they usually do not combine an automatic character with the possibility of manipulating the final analytical expressions in a practical way. And although interfaces between different softwares exist, they tend not to be free of constraints, since the notation changes between softwares and a conversion is not totally automatic.Solution method: Using both Python and Wolfram Mathematica to combine FeynRules [1, 2], QGRAF [3] and FeynCalc [4, 5], FeynMaster performs all the above listed tasks, and at the same time allows the user to handle the final results in Mathematica notebooks.Additional comments including restrictions and unusual features: Besides computing the results automatically, FeynMaster generates notebooks that allow the user to act upon them. It also includes a thorough interaction with numerical calculations, as it converts the expressions to LoopTools [6].Algebraic computations only guaranteed up to 2 particles in both the initial and final states. Complex problems may require much computational time. The drawing of Feynman diagrams is only guaranteed to properly work with the diagrams up to 1-loop; moreover, diagrams with more than two particles in the initial or final states, as well as some reducible diagrams, are also not warranted. Due to some problems in LaTeXbreqn package, some lines in PDF outputs may go out of the screen.

記譜法の変化と「南東ヨーロッパ共通の特徴」の創造 : バルトークの民謡研究におけるフォノグラフの役割について

記譜法の変化と「南東ヨーロッパ共通の特徴」の創造 : バルトークの民謡研究におけるフォノグラフの役割について

Notation and Phonological Changes of /ㆍ/(arae a) in Hancheongmungam

이 글은 ㆍ의 비음운화와 관련하여 주목 받아온 『한청문감』(1779)을 대상으로 18세기 말기에 일어난 ㆍ의 표기와 그 변화 양상을 연구하기 위한 것이다. 이를 위해 음절 위치와 선행 자음에 따라 나누어 검토하였다. 다음과 같은 사실을 통해 이 시기에 ㆍ의 제1단계 변화는 어느 정도 확산되었으나 여전히 진행 중이며, 제2단계 변화는 초기의 모습을 띤다고 간주하였다.BR 첫째, 이 자료에서 이전 시기의 ㆍ는 대부분 음절 위치에 관계없이 ㆍ가 여전히 사용되었다. 둘째, 어휘형태소에서 어두 위치에 사용된 ㆍ는 ㅏ로 변화하였다. 또 그 변화에 수반하여 ㅏ가 ㆍ로 교체된 표기도 나타났다. ㆍㅏ 변화를 겪은 예들 중 상당수는 원래의 ㆍ가 그대로 표기된 어형과 공존하였다. ㅏ가 ㆍ로 교체된 예들도 원래의 ㅏ가 그대로 쓰인 어형과 함께 쓰였다. 셋째, 어휘형태소에서 비어두 위치 ㆍ는 ㆍ ㅏ, ㆍㅡ, ㆍㅗ로 변화하였다. 또 그 변화에 수반된 ㅏㆍ, ㅡㆍ, ㅗㆍ 교체 표기가 나타났다. 이들 변화는 16세기부터 시작되어 18세기에는 더욱더 확대된 양상을 보여주었다. 넷째, 문법형태소 대부분은 ㆍㅡ의 변화를 겪었음을 확인하였다. 관형사형 어미 ‘-난’은 선행 모음과 관계없이 ‘-난’으로 쓰였다. 그 외 문법형태소에서 선행 자음이 표기상 ㅎ일 경우 ㆍ와 ㅡ가 함께 쓰였다. 이는 ‘(X)하-’의 보수적 표기가 다른 문법형태소를 표기할 때도 영향을 끼친 것으로 보인다. 다섯째, 어두 위치의 ㆍㅏ 변화는 그 예가 적어 선행 자음과의 관련성을 파악하기 어려웠다. 여섯째, 비어두 위치의 ㆍㅡ 변화는 선행 자음이 모든 자음으로 확대되었음을 확인하였다.

Revision to Modeling Soot Derived from Pulverized Coal

The purpose of this paper is to address a number of concerns that researchers have expressed when implementing the soot model of Brown and Fletcher (10.1021/ef9702207). A more common notation is presented here along with a table of units for clarification. It is the hope of the authors that this notation and associated clarifications will facilitate implementation of this model. Alexander J. Josephson and David O. Lignell have been added as authors in this revision. Some equation and notation changes are presented in this revision. These changes are meant to reflect the original implementation of this model and correct a few minor inconsistencies in the orginal print. As a result, a reader may implement this model from the information given in this revision alone. Validation and simulation results have not changed from the original paper. For clarification, the steady-state Reynolds-averaged Navier− Stokes equations for the conservation of soot mass, tar mass, and soot particle number (eqs 4−6 in the original paper) are changed by assimilating the gas density into the transport source terms.

On clarifying some definitions and notations used for type-2 fuzzy sets as well as some recommended changes

This paper is about some important changes in type-2 fuzzy set (T2 FS) definitions and notations that have occurred during the past 16 years. It summarizes the evolution of how the primary membership (Jx) has been used in both the mathematical descriptions of a T2 FS and its footprint of uncertainty (FOU); discusses notational problems associated with the secondary membership function; explains why and when one should distinguish between the FOU and the domain of uncertainty (DOU); explains why no errors have been introduced into T2 FS computations because of notation; and, it provides recommendations notational changes that can be used by all authors.

Erratum to: Diffusion of Finite-Size Particles in Confined Geometries

The authors note that due to a printer’s error, in the text immediately following Eq. (2a), F(X) = (f(x), . . . , f(x)) should have read F(x) = (f(x1), . . . , f(xN )). They also note that, due to a change in notation during copy editing, the same notation x has inadvertently been used for the (dN)-dimensional argument of P and the d-dimensional argument of p; see for example Eq. (4) and the text immediately before it.

Proof and Problem Solving at University Level

Abstract: This paper will be concerned with undergraduate and graduate students' problem solving as they encounter it in attempting to prove theorems, mainly to satisfy their professors in their courses, but also as they conduct original research for theses and dissertations. We take Schoenfeld's (1985) view of problem, namely, a mathematical task is a problem for an individual if that person does not already know a method of solution for that task. Thus, a given task may be a problem for one individual, who does not already know a solution method for that task, or it may be an exercise for an individual who already knows a procedure or an algorithm for solving that task.Keywords: Hungary, mathematics education, mathematics competition, Olympiads, international comparative mathematics education, problem solving, creativity, mathematically talented students.A Continuum of Tasks from Very Routine to Very Non-routineWhile what is a problem depends on what a solver knows, it is possible for most mathematics teachers to judge what is difficult for most students in a given class. Thus, we see mathematical tasks for a given class, such as a calculus class, on a continuum from those that are very routine to those that are genuinely difficult problems (Seiden, Seiden, Hauk, & Mason, 2000). At one end, there are very routine problems which mimic sample worked problems found in textbooks or lectures, except for minor changes in wording, notation, coefficients, constants, or functions that are incidental to the way the problems are solved. Such problems are often referred to as exercises (and might not be considered to be problems at all in the problem-solving literature).The vast majority of exercises in calculus textbooks are of this nature. Lithner (2004) distinguished three possible solution strategies for typical calculus textbook exercises: identification of similarities (IS), local plausible reasoning (LPR), and global plausible reasoning (GPR). In IS, one identifies surface features of the exercise and looks for a similar textbook situation - an example, a rule, a definition, a theorem. Without consideration of intrinsic mathematical properties, one simply copies the procedure of that situation. In LPR, one identifies a slightly similar textbook situation, but one in which a few local parts may differ. The solution strategy is to copy as much as possible from that similar situation, modifying local steps as needed. In GPR, the strategy is mainly based on analyzing and considering intrinsic mathematical properties of the exercise, and using these, a solution is constructed and supported by plausible reasoning. Lithner selected a textbook used in Sweden [Adams' Calculus: A Complete Course (5th ed.), Addison-Wesley], and worked through and classified solution strategies for 598 single-variable calculus exercises. He found 85% IS, 8% LPR, and 7% GPR. Furthermore, he concluded that "it is possible in about 70% of the exercises to base the solution not only on searching for similar situations, but on searching only the solved examples."Moving toward the middle of the continuum, there are moderately routine problems which, although not exactly like sample worked problems, can be solved by well-practiced methods, for example, ordinary related rates or change of variable integration problems in a calculus course.1 Moving further along the continuum, there are moderately non-routine problems, which are not very similar to problems that students have seen before and require known facts or skills to be combined in a slightly novel way, but are "straightforward" in not requiring, for example, the consideration of multiple sub-problems or novel insights. This is the type of problem we used on the non-routine test in our three studies of undergraduate students' calculus problem solving. One of those problems was: Find values of a and b so that the line 2x+3y=a is tangent to the graph of f (x) = bx2 at the point where x=3. …

Language Evolution, Metasyntactically

Currently existing syntactic definitions employ many different notations (usually dialects of EBNF) with slight deviations among them, which prevent efficient automated processing. When changes in such notation are required either due to maintenance activities such as correction or evolution, or because a grammar collection is written in a different notation than the one required by the grammarware toolkit, we speak of metalanguage evolution: i.e., a special language evolution scenario when the language itself does not necessarily evolve, but the notation in which it is written, does. Notational changes need to be propagated to different levels, such as to parsers that used to work with the old notation, to grammars of those notations that served as explanation material, and to the existing grammarbase. The solution proposed in this paper, relies on composing a notation specification and expressing notation changes as transformations of that specification. These transformation steps are coupled to changes in the notation grammar (i.e., grammar for grammars) and to changes in other grammars written in the original notation. This paper explains the general setup of such an infrastructure, with links to the prototypical implementation of the solution.

A Note on Higher Dimensional p-Variation

We discuss $p$-variation regularity of real-valued functions defined on $[0,T]\times [0,T]$, based on rectangular increments. When $p \gt 1$, there are two slightly different notions of $p$-variation; both of which are useful in the context of Gaussian roug paths. Unfortunately, these concepts were blurred in previous works; the purpose of this note is to show that the afore-mentioned notions of $p$-variations are "epsilon-close". In particular, all arguments relevant for Gaussian rough paths go through with minor notational changes.

“Haehaengchongjae” written in Japanese about the transliteration.-Voiced consonant and ‘tsi/tsu’ of notation changes-

“Haehaengchongjae” written in Japanese about the transliteration.-Voiced consonant and ‘tsi/tsu’ of notation changes-

On Prandtl's Formulas for Supersonic Jet Cell Length

In 1904 Prandtl developed a pioneering small perturbation theory to obtain the well-known “Prandtl Formula” λ = 1.306 d√(( wm/ c)2 − 1) for the wavelength (cell length) of an almost perfectly expanded circular supersonic jet, uniform everywhere and notably so on the bounding streamlines, where d = jet diameter, wm/ c = mean (unperturbed) speed (Mach number) of the jet. To relate to experiment and possibly provide a means of estimating jet speed from cell length measurements, he very tersely made a comparison of the results of his formula with those of Emden's formula, λ = 0.88 d√( R - Rc). This was based on extensive experiments with choked jets, with R = pressure ratio (critical value Rc), He rewrote his formula as λ = 1.306 dw√(( w/c)2 − 1), called herein “Prandtl's Formula II, where now dw = minimum diameter of the nozzle duct, i.e. exit diameter for Emden's choked jets, but the throat diameter of the convergent-divergent nozzle of uniform supersonic jets. He rewrote the foregoing equation, “my relationship,”” clearly considering that the nozzle exit diameter dw for the fully expanded flow would vary (according to the one-dimensional gas flow equations) so as to be consistent with the pressure ratio in Emden's formula. Unfortunately these simple but important notational changes for the comparison were made without comment and appear to have been totally ignored. Then converting his Formula II into Emden's form gave the well-known λ = 1.2 d√( R - Rc), a good approximation over a wide range of R. This fully satisfied Prandtl's objective, the discrepancy (1.2 vs. 0.88) being a constant factor easily taken into account, its magnitude apparently being of no particular significance considering the radically different jet flow structures. The coefficient 1.306 was improved to 1.22 by Pack who was able to compute up to 40 terms of the series solution, for which Prandtl had taken just the first term. Pack also provided the full series solution for the two-dimensional case. The circumstances of the origin of these formulas and their subsequent history over the next half-century are discussed in some detail, but a more general discussion of cell length is beyond the scope of this account.

남자 프로배구 경기에서 득점 과정을 이용한 경기 분석

As the men`s professional volleyball matches being the subject, the goal of this research was placed on examining the notational processes and changes during the set progresses of each matches along with the rate of set scores in analyzing what influences they had on the success and failure of the set. For this research, the 105 regular season matches, the 3 play-offs and 3 championship finals of the 6 participating teams in the 2007-2008 season V-league, adding up to 111 matches and 414 sets were set as subjects to gain the rate of set score and calculate to gain the percentage of the winning probability in accordance to point difference. Also, to verify the difference between the first point and final consequence of the team with the first serve, the chi-squared test was executed. Based on these results, the following conclusions can be achieved. First, during a volleyball match, the winning probability of the team that won the first set displayed to be 80.2% and therefore the effort to win the first set is required more than anything. Secondly, since the winning probability of the team that gains 20 points within a set first, showed to be 88.5% and therefore the team should work to attain 20 point faster than their competing team during a match. Also, when there exists a gap larger than 5 points and it is not during the last set as well as when there exists a gap larger than 6 points during a second technical time out, a alternation of athlete is essential for distributing the physical strength of the athletes and for the preparation of the next set. Third, since the winning probability showed to be high for the team with the first serve to gain the first point, with the exception of the 5th set, the team with the serve should order their serve strongly. Fourth, in a set that does not carry a great difference between the scores, the victory and defeat is judged around the point 23 and therefore, greater amount of concentration is required in the end.