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Showing papers by "Purdue University published in 1981"


Journal ArticleDOI
TL;DR: This survey summarizes some of the proposed segmentation techniques in the area of biomedical image segmentation, which fall into the categories of characteristic feature thresholding or clustering and edge detection.

1,160 citations


Journal ArticleDOI
TL;DR: A solution procedure is developed that replaces the subproblem by its Kuhn-Tucker conditions and then further transforms it into a mixed integer quadratic programming problem by exploiting the disjunctive nature of the complementary slackness conditions.
Abstract: This paper first presents a formulation for a class of hierarchial problems that show a two-stage decision making process; this formulation is termed multilevel programming and could be defined, in...

969 citations


Journal ArticleDOI
TL;DR: In this article, the authors derived necessary and sufficient conditions for a signal to be invariant under a specific form of median filtering and proved that the form of successive median filtering of a signal (i.e., the filtered output is itself again filtered) eventually reduces the original signal to an invariant signal called a root signal.
Abstract: Necessary and sufficient conditions for a signal to be invariant under a specific form of median filtering are derived. These conditions state that a signal must be locally monotone to pass through a median filter unchanged. It is proven that the form of successive median filtering of a signal (i.e., the filtered output is itself again filtered) eventually reduces the original signal to an invariant signal called a root signal. For a signal of length L samples, a maximum of \frac{1}{2}(L - 2) repeated filterings produces a root signal.

793 citations


Journal ArticleDOI
TL;DR: It is shown that key distribution protocols with timestamps prevent replays of compromised keys and have the additional benefit of replacing a two-step handshake.
Abstract: The distribution of keys in a computer network using single key or public key encryption is discussed. We consider the possibility that communication keys may be compromised, and show that key distribution protocols with timestamps prevent replays of compromised keys. The timestamps have the additional benefit of replacing a two-step handshake.

787 citations


Book
01 Jan 1981
TL;DR: In this article, the authors present a survey of the history of the American Revolution in terms of the New World ENCOUNTERS, pre-conquest, 1607-1608, and the Second War of Independence, 1788-1800.
Abstract: Maps, Figures, and Tables A Note to My Fellow Teachers A Personal Welcome to Students Acknowledgments Supplements About the Authors CHAPTER 1: NEW WORLD ENCOUNTERS, PRECONQUEST-1608. Diverse Cultures: De Vaca's Journey Through Native America Native Americans Before the Conquest. Conditions of Conquest. West Africa: Ancient and Complex Societies. Europe on the Eve of Conquest. Spain in the Americas. The French Claim Canada. The English Take Up the Challenge. Conclusion: Campaign to Sell America. CHAPTER 2: ENGLAND'S NEW WORLD EXPERIMENTS 1607-1732. Profit and Piety: Competing Visions for English Settlement. Breaking Away: Decisions to Move to America A "New" England in America. Diversity in the Middle Colonies. Planting the Southern Colonies. Conclusion: Living with Diversity. CHAPTER 3: PUTTING DOWN ROOTS: OPPORTUNITY AND OPPRESSION IN COLONIAL SOCIETY, 1619-1692. Families in an Atlantic Empire. Social Stability: New England Colonies of the Seventeenth Century. The Challenge of the Chesapeake Environment. Race and Freedom in British America. Blueprint for Empire. Colonial Political Revolt. Conclusion: Foundations of an Atlantic Empire. CHAPTER 4: EXPERIENCE OF EMPIRE: EIGHTEENTH-CENTURY AMERICA, 1680-1763. Constructing an Anglo-American Identity: The Journal of William Byrd. Tensions in the Backcountry. Spanish Borderlands of the Eighteenth Century. The Impact of European Ideas on American Culture. Religious Revivals in Provincial Societies. Clash of Political Cultures. Century of Imperial War. Conclusion: Rule Britannia? CHAPTER 5: THE AMERICAN REVOLUTION: FROM ELITE PROTEST TO POPULAR REVOLT, 1763-1783. Moment of Decision: Commitment and Sacrifice. Structure of Colonial Society. Eroding the Bonds of Empire. Steps Toward Independence. Fighting for Independence. Conclusion: Preserving Independence. CHAPTER 6: THE REPUBLICAN EXPERIMENT, 1783-1788. A New Political Morality. Defining Republican Culture. Stumbling Toward a New National Government. "Have We Fought for This?" Whose Constitution? Struggle for Ratification. Conclusion: Success Depends on the People. CHAPTER 7: DEMOCRACY AND DISSENT: THE VIOLENCE OF PARTY POLITICS, 1788-1800. Force of Public Opinion. Principle and Pragmatism: Establishing a New Government. Hamilton's Plan for Prosperity and Security. Charges of Treason: The Battle over Foreign Affairs. Popular Political Culture. The Adams Presidency: Politics of Mistrust. Conclusion: Danger of Political Extremism. CHAPTER 8: REPUBLICAN ASCENDANCY: THE JEFFERSONIAN VISION, 1800-1814. Limits of Equality. The Republic Expands. Jefferson as President. Race and Dissent Under Jefferson. Embarrassments Overseas. The Strange War of 1812. Conclusion: The "Second War of Independence." CHAPTER 9: NATION BUILDING AND NATIONALISM, 1815-1825. A Revolutionary War Hero Revisits America in 1824. Expansion and Migration. Transportation and the Market Economy. The Politics of Nation Building after the War of 1812. Conclusion: The End of the Era of Good Feeling. CHAPTER 10: THE TRIUMPH OF WHITE MEN'S DEMOCRACY, 1824-1840. Democratic Space: The New Hotels. Democracy in Theory and Practice. Jackson and the Politics of Democracy. The Bank War and the Second Party System. Heyday of the Second Party System. Conclusion: Tocqueville's Wisdom. CHAPTER 11: SLAVES AND MASTERS, 1793-1861. Nat Turner's Rebellion: A Turning Point in the Slave South. The World of Southern Blacks. White Society in the Antebellum South. Slavery and the Southern Economy. Conclusion: Worlds in Conflict. CHAPTER 12: THE PURSUIT OF PERFECTION, 1800-1861. Redeeming the Middle Class. The Rise of Evangelicalism. Domesticity and Changes in the American Family. Reform Turns Radical. Conclusion: Counterpoint on Reform. CHAPTER 13: AN AGE OF EXPANSIONISM, 1830-1861. The Spirit of Young America. Texas, Manifest Destiny, and the Mexican-American War. Internal Expansionism and the Industrial Revolution. Conclusion: The Costs of Expansion. CHAPTER 14: THE SECTIONAL CRISIS, 1846-1861. Brooks Assaults Sumner in Congress. The Compromise of 1850. Political Upheaval, 1852-1856. The House Divided, 1857-1860. Conclusion: Explaining the Crisis. CHAPTER 15: SECESSION AND THE CIVIL WAR, 1860-1865. The Emergence of Lincoln. The Storm Gathers. Adjusting to Total War. Fight to the Finish. Effects of the War. Conclusion: An Organizational Revolution. CHAPTER 16: THE AGONY OF RECONSTRUCTION, 1863-1877. Robert Smalls and Black Politicians During Reconstruction. The President versus Congress. Reconstructing Southern Society. Retreat from Reconstruction. Reunion and the New South. Conclusion: Henry McNeal Turner and the "Unfinished Revolution." Appendix Glossary Credits Index

699 citations


Journal ArticleDOI
01 Jan 1981-Nature
TL;DR: A natural selection model for sex ratio control in a spatially variable environment and predictions of sex ratio alteration as a function of environmental change are tested in laboratory experiments with two parasitic wasps.
Abstract: We develop a natural selection model for sex ratio control in a spatially variable environment. Predictions of sex ratio alteration as a function of environmental change are tested in laboratory experiments with two parasitic wasps. Field data from a variety of other organisms also support the model. Finally, we discuss possibilities and difficulties for testing this type of evolutionary model.

663 citations


Journal ArticleDOI
01 Mar 1981
TL;DR: The Nursing Stress Scale consists of 34 items that describe situations that have been identified as causing stress for nurses in the performance of their duties and provides a total stress score as well as scores on each of seven subscales that measure the frequency of stress experienced by nurses inThe hospital environment.
Abstract: Despite increased recognition of the stress experienced by hospital nursing staffs and its effects on burnout, job satisfaction, turnover, and patient care, few instruments exist that can be used to measure stress. This paper describes the development of an instrument, the Nursing Stress Scale (NSS). It consists of 34 items that describe situations that have been identified as causing stress for nurses in the performance of their duties. It provides a total stress score as well as scores on each of seven subscales that measure the frequency of stress experienced by nurses in the hospital environment. The Nursing Stress Scale was administered to 122 nurses on five hospital units. Factor analysis indicated seven major sources of stress that closely paralleled the conceptual categories of stress on which the scale was based. Test-retest reliability as well as four measures of internal consistency indicated that the Nursing Stress Scale and its seven subscales are reliable. Validity was determined by correlating the total score from the Nursing Stress Scale with measures of trait anxiety, job satisfaction, and nursing turnover hypothesized to be related to stress. In addition, the ability of the scale to differentiate hospital units and groups of nurses known to experience high levels of stress resulting in staff turnover was examined.

572 citations


Journal ArticleDOI
TL;DR: In this paper, a subsample of 128 firms from Rumelt's 1974 study was updated and utilized to investigate the possibility that market structure variables might model or confound the diversification/performance relationship he reported.
Abstract: SUMMARY This paper incorporates both diversification strategy and market structure variables in a study of corporate economic performance. A subsample of 128 firms from Rumelt's 1974 study was updated and utilized to investigate the possibility that market structure variables might modelrate or confound the diversification/performance relationship he reported. Study results indicate that performance differences could be demonstrated for some of Rumelt's categories, but, across the range of categories, a hypothesis of performance differences was rejected. As expected, categories associated with distinctly high or distinctly low economic performance were also associated with significant differences in a series of market structure variables. Researchers from several disciplines have sought to identify factors which influence corporate economic performance. Strategic management researchers have sought to relate corporate economic performance to the major direction-setting decisions made by the firm. For a new and growing firm, these decisions frequently relate to the degree and manner in which its product line and served market should be extended. For an older firm which wishes to continue to grow, the key decisions generally relate to the degree and manner in which it should diversify into different businesses (Chandler, 1962; Scott, 1971). Starting from a very different perspective, researchers in industrial organization economics have been guided by a conceptual framework which examines possible relationships among (1) the structure of the industry (or industries) in which the firm operates, (2) the conduct of the firms within that industry, and (3) the level of economic performance both of the individual firms and of their associated industries. This effort has yielded an extensive literature, much of which supports the proposition that firm profits are strongly influenced by the structure of the market or markets in which the firm operates (Scherer, 1970). These two streams of research have developed in large measure independently of each other. It is the purpose of the present research to incorporate both diversification strategy and market structure variables in a study of corporate economic performance.

563 citations


Journal ArticleDOI
TL;DR: In this article, the spectral bidirectional reflectance factor was measured on uniformly moist soils over the 0.52 to 2.32 micron wavelength range with a spectroradiometer adapted for indoor use.
Abstract: Surface soil samples from a wide range of naturally occurring soils were obtained for the purpose of studying the characteristic variations in soil reflectance as these variations relate to other soil properties and soil classification. A total 485 soil samples from the U.S. and Brazil representing 30 suborders of the 10 orders of 'Soil Taxonomy' was examined. The spectral bidirectional reflectance factor was measured on uniformly moist soils over the 0.52 to 2.32 micron wavelength range with a spectroradiometer adapted for indoor use. Five distinct soil spectral reflectance curve forms were identified according to curve shape, the presence or absence of absorption bands, and the predominance of soil organic matter and iron oxide composition. These curve forms were further characterized according to generically homogeneous soil properties in a manner similar to the subdivisions at the suborder level of 'Soil Taxonomy'. Results indicate that spectroradiometric measurements of soil spectral bidirectional reflectance factor can be used to characterize soil reflectance in terms that are meaningful to soil classification, genesis, and survey.

563 citations



Journal ArticleDOI
TL;DR: In this article, a device is described that has been used for several years for expression pf pore solution from hardened portland cement pastes and mortars, and methods for the analysis of the resulting small volumes of pore solutions are briefly discussed.

Journal ArticleDOI
01 Jul 1981-Cell
TL;DR: Results from biochemical and immunological studies suggest that xanthine oxidase is similar in the various tissues examined and may serve similar redox functions.

Journal ArticleDOI
TL;DR: In this article, an experimental investigation of operating strategies for a computer-controlled flexible manufacturing system is reported, consisting of nine machines, an inspection station and a centralized queueing area, all interconnected by an automatic material handling mechanism.
Abstract: An experimental investigation of operating strategies for a computer-controlled flexible manufacturing system is reported. The system is a real one, consisting of nine machines, an inspection station and a centralized queueing area—all interconnected by an automatic material-handling mechanism. The operating strategies considered involve policies for loading (allocating operations and tooling to machines) and real-time flow control. A detailed simulation was employed to test alternatives. The results are different from those of classical job shop scheduling studies, showing the dependence of system performance on the loading and control strategies chosen to operate this flexible manufacturing system. Loading and control methods are defined that significantly improve the system's production rate when compared to methods which were previously applied to the system. Finally, some conclusions are presented concerning the control of these automated systems.

Journal ArticleDOI
TL;DR: In this article, drug release mechanisms from, and diffusion processes in hydrophilic crosslinked polymeric systems were investigated in two macromolecular states: in the glassy and rubbery states during the early part of countercurrent water diffusion, and in the rubbery state after thermodynamic equilibrium between the network and the surrounding dissolution medium (water) was attained.

Journal ArticleDOI
TL;DR: The three-dimensional structure of beef liver catalase has been determined to 2.5 a resolution by a combination of isomorphous and molecular replacement techniques and heavy-atom positions were found using vector search and difference Fourier methods.

Journal ArticleDOI
TL;DR: In this article, the authors examine the factors influencing the formulation and implementation of strategy in new and small firms and show that small businesses vary substantially in their resource positions, the goals of their founders and their potential.

Journal ArticleDOI
TL;DR: The authors found that poor readers may adopt decoding rather than meaning comprehension goals during reading and they are less accurate in applying monitoring skills towards resolving comprehension failures, and this was correlated with poorer comprehension and recall scores.
Abstract: Comprehension and memory skills of fourth grade good and poor readers were compared in two studies Their ability to monitor comprehension of difficult and anomalous information was measured in three ways; by spontaneous self- corrections during oral reading, by directed underlining of incomprehensible words and phrases, and by study behaviors Poor readers engaged in significantly less monitoring on all three measures and this was correlated with poorer comprehension and recall scores An additional metacognitive measure of perceived reading strategy effectiveness indicated that poor readers are often unaware of the negative in- fluences of some strategies The patterns of responses on the multiple measures sug- gest that poor readers may adopt decoding rather than meaning comprehension goals during reading and they are less accurate in applying monitoring skills towards resolving comprehension failures Reading comprehension involves many perceptual and cognitive skills, but a ma- jor component is the ability to monitor one's level of understanding while reading This kind of mental pulse-taking is important because it is a measure of progress towards a reading goal and a signal for comprehension failures Checking com- prehension thus provides a link between the reader's purposes, progress, and behavior In our view of reading as a means-goals problem-solving task, there are three distinct aspects of comprehension monitoring: evaluation, planning, and regulation The evaluation component involves checking one's current state of knowledge while reading and provides answers to questions such as, "Does this make sense? Do I understand this word? Do these ideas fit with previous informa- tion?" If the answer to any of the previous questions is negative, then the reader must generate a plan to rectify the comprehension problem (or, alternatively, change

Journal ArticleDOI
TL;DR: Differences in the frequency of stress among the units investigated suggest 2 additional factors that need to be examined in future studies: structural characteristics of units that affect the amount of role conflict and ambiguity staff experience, and personality characteristics that may attract nurses to specific units.

Journal ArticleDOI
TL;DR: In this article, it is shown that normal wind variations can excite this mode resulting in large oscillatory fluctuations in the drive train torques as well as in the generated electric power.
Abstract: Common in the design of wind turbine generators of the multi-megawatt size is a soft shaft in the low speed part of the drive train. The presence of the soft shaft gives rise to a low frequency torsional mode involving an oscillation where the hub and blades swing relative to the generator. It is shown that normal wind variations can excite this mode resulting in large oscillatory fluctuations in the drive train torques as well as in the generated electric power. Methods of improving the dynamic performance are examined.

Journal ArticleDOI
Gary W. Ladd1
TL;DR: Unlike their control group counterparts, trained children also evidenced significant and lasting gains in classroom peer acceptance and a social learning explanation of behavioral change.
Abstract: Previous research indicates that the consequences of peer isolation or rejection may be severe. The present investigation examined changes in low-accepted children's behavior and peer acceptance resulting from social learning approach to social skill training. Third-grade children responded to a sociometric measure and were later observed on targeted social skills. 36 children with low scores on both criteria were randomly assigned to 1 of 3 experimental conditions: skill training, attention control, and nontreatment control. Children in the training condition were coached in 3 social skills: asking questions, leading, and offering support to peers. Sociometric and observational assessments were conducted upon completion of the experimental procedures and at follow-up. Trained children spent a significantly greater percentage of time engaging in 2 of the 3 trained skills at posttest and follow-up, whereas control group children remained the same or declined. Unlike their control group counterparts, trained children also evidenced significant and lasting gains in classroom peer acceptance. The results are interpreted as support for the intervention's effectiveness and a social learning explanation of behavioral change.

Book ChapterDOI
S. H. Yang1, C. T. Sun1
31 Jul 1981
TL;DR: In this article, the structural properties of composite laminates with steel balls as the indentor are described and static indentation tests are described for glass/epoxy and graphite-epoxy composite lamination.
Abstract: Static indentation tests are described for glass/epoxy and graphite/epoxy composite laminates with steel balls as the indentor. Beam specimens clamped at various spans were used for the tests. Loading, unloading, and reloading data were obtained and fitted into power laws. Results show that: (1) contact behavior is not appreciably affected by the span; (2) loading and reloading curves seem to follow the 1.5 power law; and (3) unloading curves are described quite well by a 2.5 power law. In addition, values were determined for the critical indentation, alpha sub cr which can be used to predict permanent indentations in unloading. Since alpha sub cr only depends on composite material properties, only the loading and an unloading curve are needed to establish the complete loading-unloading-reloading behavior.

Journal ArticleDOI
TL;DR: The relationship between pulse-arrival times and diastolic blood pressure was measured in 10 anesthetized dogs and it was found that pulse-transit time was found to increase nearly linearly with blood pressure, and pulse-wave velocity increased typically by slightly less than six percent.
Abstract: The relationship between pulse-arrival times and diastolic blood pressure was measured in 10 anesthetized dogs. The pulse-arrival time was measured using the R-wave of the electrocardiogram (ECG) as a time reference. Pulse-transit time was also measured between the carotid and femoral pulses. Blood pressure was raised with epinephrine injected intravenously and lowered with vagal stimulation. In all cases, pulse arrival and transit times decreased with an increase in diastolic pressure for diastolic pressures ranging from 15 to 250 mmHg. The correlation between pulse-arrival time and pressure was poorest when the ECG was used as a timing reference. The best correlation was found with true pulse-transit time and diastolic pressure. When pulse-transit time was used to compute pulse-wave velocity, it was found to increase nearly linearly with blood pressure. From 90–100 mmHg, the pulse-wave velocity increased typically by slightly less than six percent.

Journal ArticleDOI
Siegel1, Kemmerer, Mueller, Smalley, Smith 
TL;DR: PASM as mentioned in this paper is a large-scale multimicroprocessor system for image processing and pattern recognition, which can be dynamically reconfigured to operate as one or more independent SIMD and/or MIMD machines.
Abstract: PASM, a large-scale multimicroprocessor system being designed at Purdue University for image processing and pattern recognition, is described. This system can be dynamically reconfigured to operate as one or more independent SIMD and/or MIMD machines. PASM consists of a parallel computation unit, which contains N processors, N memories, and an interconnection network; Q microcontrollers, each of which controls N/Q processors; N/Q parallel secondary storage devices; a distributed memory management system; and a system control unit, to coordinate the other system components. Possible values for N and Q are 1024 and 16, respectively. The control schemes and memory management in PASM are explored. Examples of how PASM can be used to perform image processing tasks are given.

Journal ArticleDOI
TL;DR: The stochastic model representing the closed boundary is invariant to transformations like sealing, translation, choice of starting point, and rotation over angles that are multiples of 2\pi/N, where N is the number of observations.
Abstract: The analysis of closed boundaries of arbitrary shapes on a plane is discussed. Specifically, the problems of representation and reconstruction are considered. A one-to-one correspondence between the given closed boundary and a univariate or multivariate sequence of real numbers is set up. Univariate or multivariate circular autoregressive models are suggested for the representation of the sequence of numbers derived from the closed boundary. The stochastic model representing the closed boundary is invariant to transformations like sealing, translation, choice of starting point, and rotation over angles that are multiples of 2\pi/N , where N is the number of observations. Methods for estimating the unknown parameters of the model are given and a decision rule for choosing the appropriate number of coefficients is included. Constraints on the estimates are derived so that the estimates are invariant to the transformations of the boundaries. The stochastic model enables the reconstruction of a dosed boundary using FFT algorithms. Results of simulations are included and the application to contour coding is discussed.

Journal ArticleDOI
Sidney Diamond1
TL;DR: In this paper, the influence of flyash on the alkali contents and other characteristics of cement paste pore solutions was investigated by preparing pastes with 30 percent replacement of cement with flyash, hydrating for up to six months, and expressing and analyzing the resulting pore solution.

Journal ArticleDOI
TL;DR: A local distance measure is shown to optimize the performance of the nearest neighbor two-class classifier for a finite number of samples using the difference between the finite sample error and the asymptotic error as the criterion of improvement.
Abstract: A local distance measure is shown to optimize the performance of the nearest neighbor two-class classifier for a finite number of samples. The difference between the finite sample error and the asymptotic error is used as the criterion of improvement. This new distance measure is compared to the well-known Euclidean distance. An algorithm for practical implementation is introduced. This algorithm is shown to be computationally competitive with the present nearest neighbor procedures and is illustrated experimentally. A closed form for the corresponding second-order moment of this criterion is found. Finally, the above results are extended to

Journal ArticleDOI
Y.F Tsao1, King-Sun Fu1
TL;DR: A parallel algorithm for three-dimensional object thinning with two approaches, path connectivity and surface connectivity, are presented and criteria to avoid excessive deletion and preserve connectivity are described.

Journal ArticleDOI
TL;DR: The proportion of neurons generated (no longer labeled) on specific embryonic days was determined quantitatively in 18 regions of the midbrain tegmentum in order to label in embryos the proliferating precursors of neurons.
Abstract: Groups of pregnant rats were injected with two successive daily doses of 3H-thymidine from gestational day E12 and 13 (E12 j3) until the day before parturition (E21 k2) in order to label in their embryos the proliferating precursors of neurons. At 60 days of age the proportion of neurons generated (no longer labeled) on specific embryonic days was determined quantitatively in 18 regions of the midbrain tegmentum. The neurons of the oculomotor and trochlear nuclei are generated concurrently on days E12 and 13. There was a mirror image cytogenetic gradient in these nuclei and this was interpreted as the dispersal of neurons derived from a common neuroepithelial source to the medial longitudinal fasciculus. Neurons in three other components of the tegmental visual system are produced in rapid succession after the motor nuclei. In the nucleus of Darkschewitsch peak production time was on day E12 and 13, extending to day E15; in the Edinger-Westphal nucleus the time span was the same but with a pronounced between days E13; finally, the neurons of the parabigeminal nucleus were produced between days E13 and E15 with a peak on day E14. The neurons of the periaqueductal gray were generated between days E13 and 17 with a pronounced ventral-to-lateral and lateral-to-dorsal gradient. In the red nucleus the neurons were produced on days E13 and E14 with a caudal-to-rostral gradient: the cells of the magnocellular division preceding slightly but significantly the cells of the parvocellular division. The neurons of the interpeduncular nucleus originated between days E13 and E15; the peak in its ventral portion was on day E13, in its dorsal portion on days E14 and E15. A ventral-to-dorsal gradient was seen also in both the dorsal and the median raphe nuclei in which neuron production occurred between days E13 and E15. The neurons of the pars compacta and pars reticulate of the substantia nigra were both produced between days E13 and E15 with a modified lateral-to-medial gradient. This gradient extended to the ventral tegmental area where neurons of the pars medialis were produced between days E14 and E16. With the exception of the central gray, neuron production was rapid and relatively early in the structures situated ventral to the midbrain tectum. A comparison of the cytogenetic gradients in the raphe nuclei of the lower and upper medulla, the pontine region, and the midbrain suggests that they originate from at least three separate neuroepithelial sources.

Book ChapterDOI
01 Jan 1981
TL;DR: A survey of Gauss-Christoffel quadrature formulae can be found in this paper, with a discussion of the error and convergence theory of the quadratures.
Abstract: We present a historical survey of Gauss-Christoffel quadrature formulae, beginning with Gauss’ discovery of his well-known method of approximate integration and the early contributions of Jacobi and Christoffel, but emphasizing the more recent advances made after the emergence of powerful digital computing machinery. One group of inquiry concerns the development of the quadrature formula itself, e.g. the inclusion of preassigned nodes and the admission of multiple nodes, as well as other generalizations of the quadrature sum. Another is directed towards the widening of the class of integrals made accessible to Gauss-Christoffel quadrature. These include integrals with nonpositive measures of integration and singular principal value integrals. An account of the error and convergence theory will also be given, as well as a discussion of modern methods for generating Gauss-Christoffel formulae, and a survey of numerical tables.

Journal ArticleDOI
TL;DR: These model-building studies provide plausible visualizations of two different kinds of junction zones that may exist in pectic gels.