A metric space is a set X where we have some way of measuring the distance between two points. Ex... more A metric space is a set X where we have some way of measuring the distance between two points. Exercise 1: Let's look at a few ideas before being more specific about this. Do each of the following. a. X = the set of all students in Analysis. Come up with an idea for a way to measure the distance between the students. You really don't need to know the answer to the distance between student x and student y, just brainstorm ideas.
Title page for ETD etd-08142006-110101. Type of Document, Dissertation. Author, Pitts, George Gus... more Title page for ETD etd-08142006-110101. Type of Document, Dissertation. Author, Pitts, George Gustav. URN, etd-08142006-110101. Title, Domain decomposition and high order discretization of elliptic partial differential equations. Degree, Ph. D. Department, Mathematics. ...
T HERE was published some years since a salutiferous Edict, which for the obviating of the danger... more T HERE was published some years since a salutiferous Edict, which for the obviating of the dangerous Scandals of the present Age, imposed a seasonable Silence upon the Pythagorean Opinion of the Mobility of the Earth." These are the opening words of Galileo's preface to his Dialogue on the World Systems. One would be tempted to repeat them almost word for word today, apropos of certain contemporary philological research. The invisible edict or "trend" to which we refer has decreed that the whole development of Greek mathematics and astronomy must be condensed into a rather short interval of time around 4oo B.C., so that almost all the mathematics, astronomy, and music theory of the "so-called Pythagoreans" becomes contemporary with Plato and his successors. There are several schools which find this new viewpoint particularly congenial. One is the massed power of Platonic and Aristotelian scholarship, which tends unconsciously to see the classical landscape through the eyes of its favorite authors, and is always willing to convert a debt owed by them to one owed to them. A second one is a school of hypercritical philologists, starting with Eva Sachs 1 and continuing through Erich Frank's Plato und die Sogenannten Pythagoreer (I923), a book we shall presently examine in more detail, and in the last papers of the late WV. A. Heidel. Finally, there is the recent school of scientific historians which has attempted to trace the connection between Babylonian and Greek mathematics. Of their work we may cite the papers of 0. Neugebauer, K. Reidemeister, and B. L. van der Waerden.2 Relying on Frank, these authors have dismissed the entire tradition about early Greek mathematics, and supplanted it either with a most improbably late transference of Babylonian mathematics to Greece in the Vth century, or else have tried to fill the gap with speculations, conceived certainly in a true and subtle mathematician's spirit, derived from conjectural traces in Euclid and Plato. Possibly they were attracted by the company of various modern philologists, who have been trapped into accepting some of Frank's destructive arguments without noticing their intimate dependence upon his unacceptable alternative. So Cherniss, on p. 386 of his Aristotle's Criticism of the Presocratics, says that Frank's invalidation of the fragments of Philolaos "makes it superfluous to restate the overwhelming case against them." We are led back, then, to Erich Frank as the author who carries, more than any other, the responsibility for the present hypercritical sentiment. A scrutiny of his book is therefore in order. Frank's general thesis is this: There is no Greek science in any real sense before Anaxagoras and Democritus. "Anaxagoras was the first to formulate the principle of modern science, by distinguishing the subjective-psychological world-image in his opti-
branes. This resistance may be reduced by the simultaneous application of antibiotic and ultrasou... more branes. This resistance may be reduced by the simultaneous application of antibiotic and ultrasound. This The objective of this research was to elucidate the hypothesis was confirmed in our experiments with P. factors effecting the permeability of cell membranes aeruginosa exposed to erythromycin. ᧠1997 Academic Press of gram-negative bacteria toward hydrophobic com-Key Words: Pseudomonas aeruginosa; membrane pounds. Ultrasound treatment, cell age, and the phase permeability; spin probe; EPR; gram-negative bactestate of phospholipid membranes were considered. ria; ultrasound; cell age. Spin-labeling EPR method was used to quantify the penetration and distribution of a lipophilic spin probe, 16-doxylstearic acid (16-DS), in Pseudomonas aeruginosa cell membranes. This bacterium was chosen be-Antibacterial drugs attack microorganisms by incause of its reported resistance to the action of hyterfering with biosynthesis of DNA, proteins, or cell drophobic antibiotics caused by the low permeability wall components. In response, bacteria develop resisof the outer cell membrane for hydrophobic comtance to the drugs by limiting the permeability of cell pounds. EPR spectra were collected from cell pellets walls, enzymatically deactivating the drugs, or syntheand cell lysates. The overall spin probe uptake was sizing the proteins that pump the drugs out of the cells. measured in 10% SDS-cell lysates. Lysis with 0.6% SDS Bacterial resistance is a problem with the b-lactam revealed the fraction of the probe located in membrane sites readily accessible to the surfactant. The and aminoglycoside antibiotics. Therefore, the introresults indicated a structural heterogeneity of P. aeru-duction of new drugs to which bacteria have not become ginosa membranes, with the presence of structurally resistant, has become an urgent problem. ''stronger'' and ''weaker'' sites characterized by differ-Gram-negative bacteria are known to be highly resisent susceptibility to the SDS treatment. The intracellutant to the action of hydrophobic antibiotics because of lar concentration of 16-DS was higher in insonated a low permeability of their outer cell membranes to cells and increased linearly with the sonication power. hydrophobic compounds (1). Thus, gram-negative bac-EPR spectra indicated that ultrasound enhanced the teria are not expected to develop resistance to the hypenetration of the probe into the structurally stronger drophobic antibiotics that do not penetrate their cell sites of the inner and outer cell membranes. The effect walls. We hypothesize that if the permeability of gramof ultrasound on the cell membranes was transient in negative bacteria toward common hydrophobic antibithat the initial membrane permeability was restored otics is enhanced, the bacteria will become much more upon termination of the ultrasound treatment. These susceptible to the antibiotic. We hypothesize that ultraresults suggest that the resistance of gram-negative sound can be used to enhance the membrane permebacteria to the action of hydrophobic antibiotics was ability. caused by a low permeability of the outer cell mem-Ultrasound is currently used in medical practice for diagnostic and therapeutic purposes. A recent and rela-1 To whom correspondence and reprint requests should be adtively new application of ultrasound is in drug delivery.
2012 IEEE Power and Energy Society General Meeting, 2012
ABSTRACT This paper presents potential techniques for automated analysis of various types of data... more ABSTRACT This paper presents potential techniques for automated analysis of various types of data collected in power systems. Diverse recording devices have been widely deployed in modern power systems, and as a result more data have been obtained. It is necessary to extract useful and actionable information from the captured data. This paper focuses on discussing intelligent techniques for automatically analyzing such data, including disturbance classification, fault events correlation, fault type classification, fault cause identification, fault location, generator monitoring and parameter estimation, incipient fault detection, and line parameter estimation.
Abstract This paper describes a method for discretizing general linear two dimensional elliptical... more Abstract This paper describes a method for discretizing general linear two dimensional elliptical PDEs with variable coefficients, Lu= g, which achieves high orders of accuracy on an extended range of problems. The method can be viewed as an extension of the ...
Abstract Three strategies for parallelizing components of the mathematical software package ELLPA... more Abstract Three strategies for parallelizing components of the mathematical software package ELLPACK are considered: an explicit approach using compiler directives available only on the target machine, an automatic approach using an optimizing and parallelizing ...
A metric space is a set X where we have some way of measuring the distance between two points. Ex... more A metric space is a set X where we have some way of measuring the distance between two points. Exercise 1: Let's look at a few ideas before being more specific about this. Do each of the following. a. X = the set of all students in Analysis. Come up with an idea for a way to measure the distance between the students. You really don't need to know the answer to the distance between student x and student y, just brainstorm ideas.
Title page for ETD etd-08142006-110101. Type of Document, Dissertation. Author, Pitts, George Gus... more Title page for ETD etd-08142006-110101. Type of Document, Dissertation. Author, Pitts, George Gustav. URN, etd-08142006-110101. Title, Domain decomposition and high order discretization of elliptic partial differential equations. Degree, Ph. D. Department, Mathematics. ...
T HERE was published some years since a salutiferous Edict, which for the obviating of the danger... more T HERE was published some years since a salutiferous Edict, which for the obviating of the dangerous Scandals of the present Age, imposed a seasonable Silence upon the Pythagorean Opinion of the Mobility of the Earth." These are the opening words of Galileo's preface to his Dialogue on the World Systems. One would be tempted to repeat them almost word for word today, apropos of certain contemporary philological research. The invisible edict or "trend" to which we refer has decreed that the whole development of Greek mathematics and astronomy must be condensed into a rather short interval of time around 4oo B.C., so that almost all the mathematics, astronomy, and music theory of the "so-called Pythagoreans" becomes contemporary with Plato and his successors. There are several schools which find this new viewpoint particularly congenial. One is the massed power of Platonic and Aristotelian scholarship, which tends unconsciously to see the classical landscape through the eyes of its favorite authors, and is always willing to convert a debt owed by them to one owed to them. A second one is a school of hypercritical philologists, starting with Eva Sachs 1 and continuing through Erich Frank's Plato und die Sogenannten Pythagoreer (I923), a book we shall presently examine in more detail, and in the last papers of the late WV. A. Heidel. Finally, there is the recent school of scientific historians which has attempted to trace the connection between Babylonian and Greek mathematics. Of their work we may cite the papers of 0. Neugebauer, K. Reidemeister, and B. L. van der Waerden.2 Relying on Frank, these authors have dismissed the entire tradition about early Greek mathematics, and supplanted it either with a most improbably late transference of Babylonian mathematics to Greece in the Vth century, or else have tried to fill the gap with speculations, conceived certainly in a true and subtle mathematician's spirit, derived from conjectural traces in Euclid and Plato. Possibly they were attracted by the company of various modern philologists, who have been trapped into accepting some of Frank's destructive arguments without noticing their intimate dependence upon his unacceptable alternative. So Cherniss, on p. 386 of his Aristotle's Criticism of the Presocratics, says that Frank's invalidation of the fragments of Philolaos "makes it superfluous to restate the overwhelming case against them." We are led back, then, to Erich Frank as the author who carries, more than any other, the responsibility for the present hypercritical sentiment. A scrutiny of his book is therefore in order. Frank's general thesis is this: There is no Greek science in any real sense before Anaxagoras and Democritus. "Anaxagoras was the first to formulate the principle of modern science, by distinguishing the subjective-psychological world-image in his opti-
branes. This resistance may be reduced by the simultaneous application of antibiotic and ultrasou... more branes. This resistance may be reduced by the simultaneous application of antibiotic and ultrasound. This The objective of this research was to elucidate the hypothesis was confirmed in our experiments with P. factors effecting the permeability of cell membranes aeruginosa exposed to erythromycin. ᧠1997 Academic Press of gram-negative bacteria toward hydrophobic com-Key Words: Pseudomonas aeruginosa; membrane pounds. Ultrasound treatment, cell age, and the phase permeability; spin probe; EPR; gram-negative bactestate of phospholipid membranes were considered. ria; ultrasound; cell age. Spin-labeling EPR method was used to quantify the penetration and distribution of a lipophilic spin probe, 16-doxylstearic acid (16-DS), in Pseudomonas aeruginosa cell membranes. This bacterium was chosen be-Antibacterial drugs attack microorganisms by incause of its reported resistance to the action of hyterfering with biosynthesis of DNA, proteins, or cell drophobic antibiotics caused by the low permeability wall components. In response, bacteria develop resisof the outer cell membrane for hydrophobic comtance to the drugs by limiting the permeability of cell pounds. EPR spectra were collected from cell pellets walls, enzymatically deactivating the drugs, or syntheand cell lysates. The overall spin probe uptake was sizing the proteins that pump the drugs out of the cells. measured in 10% SDS-cell lysates. Lysis with 0.6% SDS Bacterial resistance is a problem with the b-lactam revealed the fraction of the probe located in membrane sites readily accessible to the surfactant. The and aminoglycoside antibiotics. Therefore, the introresults indicated a structural heterogeneity of P. aeru-duction of new drugs to which bacteria have not become ginosa membranes, with the presence of structurally resistant, has become an urgent problem. ''stronger'' and ''weaker'' sites characterized by differ-Gram-negative bacteria are known to be highly resisent susceptibility to the SDS treatment. The intracellutant to the action of hydrophobic antibiotics because of lar concentration of 16-DS was higher in insonated a low permeability of their outer cell membranes to cells and increased linearly with the sonication power. hydrophobic compounds (1). Thus, gram-negative bac-EPR spectra indicated that ultrasound enhanced the teria are not expected to develop resistance to the hypenetration of the probe into the structurally stronger drophobic antibiotics that do not penetrate their cell sites of the inner and outer cell membranes. The effect walls. We hypothesize that if the permeability of gramof ultrasound on the cell membranes was transient in negative bacteria toward common hydrophobic antibithat the initial membrane permeability was restored otics is enhanced, the bacteria will become much more upon termination of the ultrasound treatment. These susceptible to the antibiotic. We hypothesize that ultraresults suggest that the resistance of gram-negative sound can be used to enhance the membrane permebacteria to the action of hydrophobic antibiotics was ability. caused by a low permeability of the outer cell mem-Ultrasound is currently used in medical practice for diagnostic and therapeutic purposes. A recent and rela-1 To whom correspondence and reprint requests should be adtively new application of ultrasound is in drug delivery.
2012 IEEE Power and Energy Society General Meeting, 2012
ABSTRACT This paper presents potential techniques for automated analysis of various types of data... more ABSTRACT This paper presents potential techniques for automated analysis of various types of data collected in power systems. Diverse recording devices have been widely deployed in modern power systems, and as a result more data have been obtained. It is necessary to extract useful and actionable information from the captured data. This paper focuses on discussing intelligent techniques for automatically analyzing such data, including disturbance classification, fault events correlation, fault type classification, fault cause identification, fault location, generator monitoring and parameter estimation, incipient fault detection, and line parameter estimation.
Abstract This paper describes a method for discretizing general linear two dimensional elliptical... more Abstract This paper describes a method for discretizing general linear two dimensional elliptical PDEs with variable coefficients, Lu= g, which achieves high orders of accuracy on an extended range of problems. The method can be viewed as an extension of the ...
Abstract Three strategies for parallelizing components of the mathematical software package ELLPA... more Abstract Three strategies for parallelizing components of the mathematical software package ELLPACK are considered: an explicit approach using compiler directives available only on the target machine, an automatic approach using an optimizing and parallelizing ...
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Papers by George Pitts