Number Of Subdivisions Research Articles

Seeds of Amazonian plants

Seeds of Amazonian plants

Trees whose 2-domination subdivision number is 2

A set \(S\) of vertices in a graph \(G = (V,E)\) is a \(2\)-dominating set if every vertex of \(V\setminus S\) is adjacent to at least two vertices of \(S\). The \(2\)-domination number of a graph \(G\), denoted by \(\gamma_2(G)\), is the minimum size of a \(2\)-dominating set of \(G\). The \(2\)-domination subdivision number \(sd_{\gamma_2}(G)\) is the minimum number of edges that must be subdivided (each edge in \(G\) can be subdivided at most once) in order to increase the \(2\)-domination number. The authors have recently proved that for any tree \(T\) of order at least \(3\), \(1 \leq sd_{\gamma_2}(T)\leq 2\). In this paper we provide a constructive characterization of the trees whose \(2\)-domination subdivision number is \(2\).

Strain Life Analysis at Low-Cycle Fatigue on Concentrically Braced Steel Structures with RHS Shape Braces

The seismic performance of concentrically braced frame systems, with braces designed in order to buckle inelastically under a severe earthquake loading, mainly depends on the hysteretic response of the steel braces. As observed in past earthquakes and in experimental programs available in the literature, rectangular hollow section shape braces are more susceptible to early fatigue failures compared to other section shapes. This research, in particular, is focused on the evaluation of the hysteretic response of rectangular hollow section shape braces through appropriate low-cycle fatigue model implemented in a fiber-based element computer program. Firstly, the main influence regarding the number of integration points, number of subdivisions for single brace members, and initial camber on the local response of fiber-based inelastic beam-column element models based on force formulation is investigated. Secondly, the peak strain distribution is used to calibrate the input parameters of the low-cycle fatigue material model. Several data obtained from past experimental programs developed at the Universities of Montreal, Washington, and Calgary are also considered. Finally, an eight-story steel building is designed in order to evaluate the performance levels through incremental time history analyses.

L’autorité du discours: recherches sur le statut des textes et la circulation des idées dans l’Europe des Lumières by Franck Salaün

them; for instance, Romestaing takes up the discussion of the humanization of animals in each part. Some repetition is, perhaps, inevitable in a monothematic study; to be fair, each discussion approaches the motif from a slightly different angle, thereby reminding us that any narrative element may be viewed from multiple perspectives. Unfortunately, too, the study suffers at times from a somewhat choppy presentation; while part 1 forms a more or less coherent whole, the second and third parts are scattershot in places. In the last two thirds of the work, the reader is met with a series of chapters divided into a distracting number of subsections strung together with little transition or continuity. This ostensible attempt to guide the reader only highlights the frequently disjointed presentation. That said, Romestaing makes good use of extant scholarship and critical theory to enhance his analysis. An astute reader, he is at the top of his game when he analyses passages from key novels such as Regain. The comparisons between Giono’s narrative techniques and those of his predecessors provide a solid base for Romestaing’s analysis. For Giono, “l’identité est physique” (219), so it is not surprising that he creates physiognomic portraits à la Balzac. The parallels Romestaing draws between Le hussard sur le toit and Rabelais’s Pantagruel are especially intriguing; both authors, he argues, present us with “ le triomphe du bas corporel, le renversement carnavalesque du monde humain en un monde monstrueux de déjections et d’obscénités” (155). Baudelaire and Huysmans, moreover , inspire Giono to change the sense of smell “en une extraordinaire ‘faculté d’information spatiale’; mieux même: en une faculté de jouissance de l’espace” (24–25). Because of the link between bodily sensation and emotion, one would expect that Giono and Proust would be kindred spirits, yet Romestaing asserts that Giono is an “Anti-Proust:” “si les deux écrivains s’enracinent de la même manière dans le vécu et s’intéressent particulièrement aux mystères de la perception humaine, ils le font chacun en privilégiant l’un le temps, l’autre l’espace” (202). In Giono’s récits, then, physiological sensations “va[lent] autant que le déroulement du récit” (138). Despite the occasional lack of narrative flow, Romestaing’s work makes it clear that le corps gionien is essentially a stage for Giono’s brand of humanism, the means by which he calls into question man’s “condition terrestre” (14). What the reader takes away from the study is the conviction that Giono’s intent in showcasing the body is to recast Descartes’s cogito in physiological terms: “Je perçois donc je suis” (248). University of Arkansas Kathy Comfort SALAÜN, FRANCK. L’autorité du discours: recherches sur le statut des textes et la circulation des idées dans l’Europe des Lumières. Paris: Champion, 2010. ISBN 978-2-7453-20247 . Pp. 456. 85 a. Understanding the objective of Franck Salaün’s current work presents as much a challenge as pinpointing the arguments he details to support his aim. Ostensibly, he examines where certain thinkers and writers of the Lumières obtain their authority to speak as authorities themselves. Throughout the text, he poses many questions that typically serve as pedagogical devices aimed at assisting readers uncover so-called “truths” exposed in various literary genres of the day. In fact, the questions might distract and further confuse readers to the extent that 566 FRENCH REVIEW 85.3 they may find themselves searching for discrete answers instead of concentrating on just the material itself. The best use of his work, perhaps, is as a reexamination of the major philosophical and intellectual trends and ideas of the period as expressed by specific authors in both their obscure and celebrated writings. The question of newfound authorial and textual legitimacy that reverberated throughout eighteenth-century Europe is incorporated in Salaün’s study; it does not seem to reflect the raison d’être of the text. Salaün approaches his subject by creating twenty-six distinct chapters that are almost equally divided into four major sections. The first one concerns the nature of Enlightenment thought, that...

The total domination subdivision number in graphs with no induced 3-cycle and 5-cycle

A set S of vertices of a graph G=(V,E) without isolated vertex is a total dominating set if every vertex of V(G) is adjacent to some vertex in S. The total domination number ? t (G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number $\mathrm{sd}_{\gamma_{t}}(G)$ is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the total domination number. Favaron, Karami, Khoeilar and Sheikholeslami (J. Comb. Optim. 20:76---84, 2010a) conjectured that: For any connected graph G of order n?3, $\mathrm{sd}_{\gamma_{t}}(G)\le \gamma_{t}(G)+1$ . In this paper we use matching to prove this conjecture for graphs with no 3-cycle and 5-cycle. In particular this proves the conjecture for bipartite graphs.

Solving polynomial systems using no-root elimination blending schemes

Searching for the roots of (piecewise) polynomial systems of equations is a crucial problem in computer-aided design (CAD), and an efficient solution is in strong demand. Subdivision solvers are frequently used to achieve this goal; however, the subdivision process is expensive, and a vast number of subdivisions is to be expected, especially for higher-dimensional systems. Two blending schemes that efficiently reveal domains that cannot contribute by any root, and therefore significantly reduce the number of subdivisions, are proposed. Using a simple linear blend of functions of the given polynomial system, a function is sought after to be no-root contributing, with all control points of its Bernstein–Bézier representation of the same sign. If such a function exists, the domain is purged away from the subdivision process. The applicability is demonstrated on several CAD benchmark problems, namely surface–surface–surface intersection (SSSI) and surface–curve intersection (SCI) problems, computation of the Hausdorff distance of two planar curves, or some kinematic-inspired tasks.

Flexible paleoclimate age-depth models using an autoregressive gamma process

Radiocarbon dating is routinely used in paleoecology to build chronolo- gies of lake and peat sediments, aiming at inferring a model that would relate the sediment depth with its age. We present a new approach for chronology building (called \Bacon) that has received enthusiastic attention by paleoecologists. Our methodology is based on controlling core accumulation rates using a gamma au- toregressive semiparametric model with an arbitrary number of subdivisions along the sediment. Using prior knowledge about accumulation rates is crucial and in- formative priors are routinely used. Since many sediment cores are currently ana- lyzed, using difierent data sets and prior distributions, a robust (adaptive) MCMC is very useful. We use the t-walk (Christen and Fox, 2010), a self adjusting, robust MCMC sampling algorithm, that works acceptably well in many situations. Out- liers are also addressed using a recent approach that considers a Student-t model for radiocarbon data. Two examples are presented here, that of a peat core and a core from a lake, and our results are compared with other approaches. Past climates and environments can be reconstructed from deposits such as ocean or lake sediments, ice sheets and peat bogs. Within a vertical sediment proflle (core), mea- surements of microfossils, macrofossils, isotopes and other variables at a range of depths serve as proxy estimates or \proxies of climate and environmental conditions when the sediment of those depths was deposited. It is crucial to establish reliable relationships between these depths and their ages. Age-depth relationships are used to study the evolution of climate/environmental proxies along sediment depth and therefore through time (e.g., Lowe and Walker 1997). Age-depth models are constructed in various ways. For sediment depths containing organic matter, and for ages younger than c. 50,000 years, radiocarbon dating is often used to create an age-depth model. Cores are divided into slices and some of these are radiocarbon dated. A curve is fltted to the radiocarbon data and interpolated to obtain an age estimate for every depth of the core. The flrst restriction to be considered is that age should be increasing monotonically with depth, because sediment can never have accumulated backwards in time (extraordinary events leading to mixed or reversed sediments are, most of the time, noticeable in the stratigraphy and therefore such cores are ruled out from further analyses). Moreover, cores may have missing sections, leading to ∞at parts in the age depth models.

A new ALS model for dilute polymer solutions in flows with strong shear components

Ghosh et al. (J Rheol 46:1057–1089, 2002) developed a new model for dilute polymer solutions in flows with strong extensional components. The model based on introducing an adaptive length scale (ALS) as an internal variable was developed to reproduce the fine-scale physics of the Kramers chain. The ALS model describes the polymer molecule as a set of identical segments in which each segment represents a fragment of the polymer that is short enough so that it can sample its entire configuration space on the time scale of an imposed deformation and therefore stretch reversibly. As the molecule unravels, the number of the segments decreases, but the maximum length of each segment increases, so that the constant maximum contour length of the molecule is preserved. Though the single-segment-based ALS model accounts for the orientability of the polymer molecules, it cannot describe the internal motions of the molecules due to the lack of internal nodes. Hence, in this work we consider the more realistic chain (multi-segments) model composed of Nseg springs connected linearly. The model presented in this work is an extension of the ALS model developed by Ghosh et al. (J Rheol 46:1057–1089, 2002). We demonstrate that the ALS varies with the flow strength. Specifically, it is found that as the flow strength increases, the ALS decreases. This implies that as the flow strength increases, the polymer molecule is required to divide into finer and finer segments such that each segment can locally equilibrate with the imposed flow. However, there is a critical number of such subdivisions beyond which further subdivision of the polymer molecule is not required to capture the polymer dynamics for a given flow strength. Both shear viscosity and first normal stress coefficient predictions from ALS model show shear thinning behavior with Weissenberg number. In weak flows, the ALS model and the finitely extensible non-linear elastic model exhibit the same behavior.

Nested meshes for numerical approximation of space fractional differential equations

In this study, we use the nested meshes to approximate the space fractional differential equations. Two approaches are used to approximate the second order derivative. It is obvious that the nested meshes method is more effective in solving large scale problems. Matrix building and how to introduce the boundary condition are both presented. Two examples are given to show the effects of the number of subdivisions in each nested interval on the accuracy in different cases of various domain scales.

STATISTICAL ANALYSIS OF HIERARCHICAL SORTING DATA

ABSTRACT Hierarchical sorting is a data collection methodology used in sensory analysis, which consists in asking people to provide a succession of categorization tasks: in the first step, they have to divide the set of objects into groups and in the second step, they can, if they want, subdivide these groups into finer groups, etc., until they judge the final groups of objects to be homogeneous. This article describes a new methodology to analyze these data: multiple factor analysis (MFA). MFA allows balancing the part of each subject into the analysis according to the number of subdivisions provided. MFA provides usual factor analytic representations (object representations) and specific representations (in particular subject representations and levels of hierarchy representations). This method is illustrated with an example in which 89 children performed a hierarchical sorting task on 16 cards. It is conducted with the R SensoMineR package. PRACTICAL APPLICATIONS The aim of this article is to present a new approach of analyzing hierarchical sorting data. We show how the outputs of the proposed methodology can be interpreted using an example. This methodology is particularly helpful if we are interested in the process of sorting used by the subjects.

Fast/Major and Slow/Minor pairings in J.S. Bach's Well Tempered Clavier Books 1 and 2

Some studies have found that subjects give higher preference ratings and clearer emotional descriptions to pieces with the tempo/mode pairs fast/major and slow/minor. If these findings are true, one might expect to find a predominance of fast/major and slow/minor pairings in musical literature. This study looks for just such a trend in the canonical work of J.S. Bach's Well Tempered Clavier. Books 1 and 2 together contain 24 Major Preludes, 24 Minor Preludes, 24 Major Fugues and 24 Minor Fugues. We use four different measurements of fast/slow tempo based both on elements within the musical notation as well as the interpretive markings of four different music editors: 1. Attacks Per Beat (APB) - measures the number of subdivisions of each piece 2. Attacks Per Minute (APM) - is the APB of a piece multiplied by the editor's metronome marking 3. Time Signature Distribution and 4. Editor's Tempo Distribution. We find a significant amount of fast/major and slow/minor pairings in Book 1 but not in Book 2.

New enclosure algorithms for the verified solutions of nonlinear Volterra integral equations

This paper is concerned with new algorithms which provide the sharp bounds that are guaranteed to contain the exact solutions of nonlinear Volterra integral equations. We develop new enclosure algorithms based on the interval methods which was first introduced by Moore in [24] together with the Taylor polynomials to improve the accuracy of the scheme by reducing the width of interval solutions. The modified methods calculate a priori bound automatically in parallel with the computation of solutions of integral equations. We will show that the accuracy of the proposed algorithms is dependent on the number of interval subdivisions. Some numerical experiments are also included to demonstrate the validity and applicability of the scheme and showing a marked improvement in comparison with the recent existing numerical results.

香港近五十年《詩經》研究述要

LANGUAGE NOTE | Document text in Chinese; abstract also in English.
 本文敘述近五十年（1955—2007）香港學者研究《詩經》一書的成果。全文依林慶彰主編《經學研究論著目録（1912—1987）》之類目，分《詩經》總論、《詩經》基本問題、國風研究、雅頌研究、語言文字研究、分類研究、《詩經》反映的文化風貌、《詩經》學史研究、比較研究、國外研究等節敘述。基本問題和《詩經》學史又分數小節敘述。結論以爲香港的《詩經》研究，早期以何敬群、潘重規、李雲光等人的成果較豐碩；當代學者則以李家樹的研究成果最受矚目。年輕一輩則以李雄溪、陳致、盧鳴東的研究成果較爲凸出。香港的官方語言是英語，學者的英文水平比中國大陸和臺灣的學者高出許多，應利用此一優勢，多關心歐美的《詩經》研究成果。
 This paper presents the results of the study of Shi jing by Hong Kong scholars over the past 50 years (1955-2007). This paper follows the categorization in Jing Xue Yan Jiu Lun Zhu Mu Lu (1912-1987) 經學研究論著目録 (Bibliography of materials for the study of Chinese classics), which includes general studies, primary issues, study of the Airs, study of the Elegantiae and Eulogies, linguistic and paleographical studies, categories, cultural features reflected in the Odes, history of the study of Shi Jing, comparative studies, study of the Odes outside Hong Kong. The parts of primary issues and the history of the study of Shi Jing are further divided into a number of subsections. The conclusion reached is that Ho Chien-tsung, Pan Chung-kwei and Lee Yun-kuang were leading scholars of the study of Shi Jing in Hong Kong in the old limes, with Lee Kar Shui contributing the most in the field. Lee Hung Kai, Chen Zhi and Lo Ming Tung are the most impressive among the younger generation of Hong Kong scholars. The official language in Hong Kong is English, so compared to scholars from the Mainland and Taiwan, the Hong Kong scholars have a better command of English, and therefore should use this advantage to be more involved in the contribution of the Western sinology to the study of Shi Jing.

Reply

Ultrasound evaluation is widely accepted as an accurate tool in the assessment of the fetal head during labor. Several classification systems have been proposed to aid in the assignment of different fetal head positions. In 1998 Gardberg et al.1 classified fetal head position as occipitoanterior and occipitoposterior. In 2002, Sherer et al.2 classified it as occiput anterior (OA), occiput posterior (OP), left or right occiput transverse (LOT and ROT) and left or right occiput anterior or posterior (LOA, ROA, LOP and ROP). In the same year, Akmal et al.3 proposed recording the fetal head position according to a clock-like diagram with 24 divisions. Similar clocks, with 24, 12 and eight divisions were used by Rane et al.4, Zahalka et al.5 and Dupuis et al.6, respectively. Using one of these classification methods should enable the clinician to discern promptly the position of the fetal head in most cases, although any clinician would find it very difficult to analyze the fetal head when it lies in a position of transition (e.g. between OP and OT). Attempts have been made to address these borderline situations by modifying the number of clock subdivisions or, in cases when the fetal head position did not match one of the defined grid lines, the nearest location was given, but we and others3, 6 have been unable to solve the issue as the object of analysis is not punctiform. In our opinion, Drs Eggebo and Salvesen, in their Correspondence, do not help solve, improve or modify the current definition of fetal head position. Their main concern is the division of the Akmal clock and the fact that, in our study, the borderline limits were 02 : 29, 03 : 29, 08 : 29 and 09 : 29 hours instead of the 02 : 30, 03 : 30, 08 : 30 and 09 : 30 hours used by Akmal et al.3. Because the fetal head is not punctiform it appears that the difference in the two models is actually irrelevant in the overall assessment. For the purposes of our study7, the position of the fetal head was allocated within the portion of the clock in which the largest part of the fetal occiput was visualized and, in the Methods section, we clearly state that the clock was divided into 12 sections and not into 720 sections as implied by Drs Eggebo and Salvesen. We acknowledge that it would not be useful to try to differentiate the position of the occiput between, for example, a 02.29 and 02.30-hours position and are aware that it would be equally unhelpful to have the same position of 02.30 hours identifying two different positions. The modifications of the Akmal clock made in our paper were not an attempt to solve the issue of borderline cases, merely representing an interpretation that we believe had no effect on the overall analysis. Regarding the relevance of assessment of fetal head position before and in the first stage of labor, considering the findings of Peregrine et al.8, Akmal et al.9 and Souka et al.10, that the position before and in the first stage of labor is not predictive of fetal head at delivery, the data on which our discussion was focused were position at the second stage of labor. In closing, we recognize the importance of keeping alive the discussion on fetal occiput position in borderline cases, but are not convinced that the criticisms of our study contribute helpfully to the debate. I. Blasi*, V. Vinci*, W. Henrich*, V. Mazza*, * Arcispedale Santa Maria Nuova, Modena and Reggio Emilia University, Reggio Emilia, Italy

Quench Current Measurement for Multi-Sectioned Superconducting Solenoid Coil

The technique of subdivision protection is extensively applied to protect large superconducting solenoid magnets such as accelerator magnets and MRI magnets. The number of subdivision and the parameters of protection circuit are usually decided by the quench simulation results. The accurate current data during quench process is important to verify the quench simulation code and estimate the magnet performance. But not like voltage signal, the acquisition of which just needs to attach a pair of voltage taps on both side of each protection resistor, current signal is very difficult to be obtained from cryogenic environment. This paper presents an algorithm to calculate the quench current from the quench voltage measurement result. By this algorithm the temperature rise history of protection resistor is obtained simultaneously.

On the total domination subdivision numbers in graphs

Abstract A set S of vertices of a graph G = (V, E) without isolated vertex is a total dominating set if every vertex of V(G) is adjacent to some vertex in S. The total domination number γ t(G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number sdγt (G) is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the total domination number. Karami, Khoeilar, Sheikholeslami and Khodkar, (Graphs and Combinatorics, 2009, 25, 727–733) proved that for any connected graph G of order n ≥ 3, sdγ t(G) ≤ 2γ t(G) − 1 and posed the following problem: Characterize the graphs that achieve the aforementioned upper bound. In this paper we first prove that sdγ t(G) ≤ 2α′(G) for every connected graph G of order n ≥ 3 and δ(G) ≥ 2 where α′(G) is the maximum number of edges in a matching in G and then we characterize all connected graphs G with sdγ t(G)=2γt(G)−1.

Analysis of long-term rainfall trends in India

The study of precipitation trends is critically important for a country like India whose food security and economy are dependent on the timely availability of water. In this work, monthly, seasonal and annual trends of rainfall have been studied using monthly data series of 135 years (1871–2005) for 30 sub-divisions (sub-regions) in India. Half of the sub-divisions showed an increasing trend in annual rainfall, but for only three (Haryana, Punjab and Coastal Karnataka), this trend was statistically significant. Similarly, only one sub-division (Chattisgarh) indicated a significant decreasing trend out of the 15 sub-divisions showing decreasing trend in annual rainfall. In India, the monsoon months of June to September account for more than 80% of the annual rainfall. During June and July, the number of sub-divisions showing increasing rainfall is almost equal to those showing decreasing rainfall. In August, the number of sub-divisions showing an increasing trend exceeds those showing a decreasing trend, whereas in September, the situation is the opposite. The majority of sub-divisions showed very little change in rainfall in non-monsoon months. The five main regions of India showed no significant trend in annual, seasonal and monthly rainfall in most of the months. For the whole of India, no significant trend was detected for annual, seasonal, or monthly rainfall. Annual and monsoon rainfall decreased, while pre-monsoon, post-monsoon and winter rainfall increased at the national scale. Rainfall in June, July and September decreased, whereas in August it increased, at the national scale. Citation Kumar, V., Jain, S. K. & Singh, Y. (2010) Analysis of long-term rainfall trends in India. Hydrol. Sci. J. 55(4), 484–496.

St. Paul and Ecumenism: Justification and All That

AbstractAfter some opening reflections on the place of justification in recent Pauline scholarship, the essential argument is that both Catholic and Lutheran readings of Paul on justification, regardless of their strict exegetical accuracy, serve to articulate key principles of Christian existence under grace which need not only to be conjoined or placed alongside each other but need to be allowed, in the spirit of Receptive Ecumenism, to inform each other. In the Catholic case the need is for an expansion in the direction of a more effective and genuinely Pauline emphasis on the dynamism of grace. There are three sections. First, a detailed exploration, presented in a number of subsections, of the historic theological background to the issues at stake in the ecumenical dialogues and the way in which these might be best conceptualised. Second, situated against this backdrop is a summary exposition of some of the key achievements of the 1999 affirmation of the Joint Declaration on the Doctrine of Justification by the Lutheran World Federation and the Roman Catholic Church. Third, note is taken of some of the criticisms that have been made of the Joint Declaration, identifying the need for receptive ecumenical learning if its best intentions are to be realised. This generic need is illustrated in relation to one area of potential receptive Catholic learning from Lutheranism concerning the effective dynamism of grace and the character of Christian life as confident trust in this as a continually renewed event.

Matchings and total domination subdivision number in graphs with few induced 4-cycles

Matchings and total domination subdivision number in graphs with few induced 4-cycles

Optimal Quantization of Signals for System Identification

In this technical note, we examine the optimal quantization of signals for system identification. We deal with memoryless quantization for the output signals and derive the optimal quantization schemes. The objective functions are the errors of least squares parameter estimation subject to a constraint on the number of subsections of the quantized signals or the expectation of the optimal code length for either high or low resolution. The optimal quantizer has the property that it is coarse near the origin of its output and becomes dense away from the origin in the usual situation. Finally the required quantity of data to decrease the total parameter estimation error, caused by quantization and noise, is discussed.