Open Access. Powered by Scholars. Published by Universities.®
- Discipline
-
- Physical Sciences and Mathematics (3675)
- Engineering (974)
- Mathematics (804)
- Chemistry (626)
- Analysis (604)
-
- Other Mathematics (593)
- Environmental Sciences (536)
- Earth Sciences (427)
- Oceanography and Atmospheric Sciences and Meteorology (377)
- Social and Behavioral Sciences (359)
- Computer Sciences (272)
- Civil and Environmental Engineering (263)
- Education (256)
- Life Sciences (250)
- Arts and Humanities (247)
- Applied Mathematics (232)
- Electrical and Computer Engineering (199)
- Chemical Engineering (197)
- Mechanical Engineering (175)
- Physics (167)
- Geology (131)
- Oceanography (121)
- Psychology (106)
- Petroleum Engineering (97)
- Astrophysics and Astronomy (88)
- Business (83)
- Music (73)
- Agriculture (66)
- Medicine and Health Sciences (62)
- Philosophy (60)
- Keyword
-
- Education (321)
- Engineering (271)
- Mathematics (231)
- General (113)
- Chemistry (89)
-
- Louisiana (87)
- Physics (78)
- Chemical (73)
- Business administration (69)
- Economics (62)
- Psychology (62)
- Biology (57)
- Agriculture (54)
- Machine learning (54)
- Gulf of Mexico (45)
- Gravitational waves (42)
- Curricula (38)
- Modeling (38)
- Course catalogs (37)
- General catalogs (37)
- Gumbo (37)
- Gumbo yearbook (37)
- La.) (37)
- Louisiana State University (Baton Rouge (37)
- Louisiana state university (37)
- Lsu yearbook (37)
- Physical (37)
- University archives (37)
- Yearbook (37)
- Computer science (36)
- Publication Year
- Publication
-
- Faculty Publications (2672)
- LSU Doctoral Dissertations (2329)
- LSU Master's Theses (1894)
- LSU Historical Dissertations and Theses (1612)
- Communications on Stochastic Analysis (432)
-
- Honors Capstones (265)
- Journal of Stochastic Analysis (160)
- Seminar on Continuity in Semilattices (102)
- LSU General Catalog (53)
- 1650-1850: Ideas, Aesthetics, and Inquiries in the Early Modern Era (46)
- Gumbo Yearbook (37)
- Clinical Research Faculty Publications (35)
- Publications (29)
- LSU Agricultural Experiment Station Reports (27)
- LSU Faculty Senate Publications (26)
- 2026 LSU Symposium on Control, Learning, and Intelligent Systems (17)
- Civil War Book Review (16)
- Population and Public Health Science Faculty Publications (14)
- Taboo: The Journal of Culture and Education (14)
- Division of Basic Science Faculty Publications (11)
- Components (10)
- Louisiana Agriculture (9)
- College of Engineering Patents (7)
- Reports (6)
- LSU AgCenter Bulletins (5)
- Research Magazine (5)
- Spark! Innovations in Early Childhood Education: A Research-to-Practice Journal for Educators (5)
- Student Senate Enrolled Legislation (5)
- Data (4)
- E-Textbooks (4)
- Publication Type
- File Type
Articles 7831 - 7860 of 9882
Full-Text Articles in Entire DC Network
Ecological Structure Of Estaurine Fish Communities: Habitat Linkages Among Dominant Species Groups In Terminos Lagoon, Mexico., Ana Laura Lara-Dominguez
Ecological Structure Of Estaurine Fish Communities: Habitat Linkages Among Dominant Species Groups In Terminos Lagoon, Mexico., Ana Laura Lara-Dominguez
LSU Historical Dissertations and Theses
Terminos Lagoon in the southern Gulf of Mexico has 5 ecological subsystems: (1) fluvial lagoon systems (FLS) with permanent river discharge, low salinity, high turbidity and nutrients. (2) Central basin (CB) between marine and river conditions, intermediate salinity and variable transparency. (3) Inner littoral of Carmen Island (ILCI) with strong marine influence, high transparency and extensive seagrass meadows. (4) Carmen inlet (Estero Pargo, ESP) with a net outflow of water and high turbidity. (5) Puerto Real inlet (PR) with a net inflow of waters, high transparency and seagrasses. During a 15-month sampling, 13,691 individuals of 79 different species were collected …
Multiscale Analysis For Characterization Of Remotely Sensed Images., Wei Zhao
Multiscale Analysis For Characterization Of Remotely Sensed Images., Wei Zhao
LSU Historical Dissertations and Theses
In this study we addressed fundamental characteristics of image analysis in remote sensing, enumerated unavoidable problems in spectral analysis, and highlighted the spatial structure and features that increase information amount and measurement accuracy. We addressed the relationship between scale and spatial structure and the difficulties in characterizing them in complex remotely sensed images. We suggested that it is necessary to employ multiscale analysis techniques for analyzing and extracting information from remotely sensed images. We developed a multiscale characterization software system based on an existing software called ICAMS (Image Characterization And Modeling System), and applied the system to various test data …
De Haas-Van Alphen Effect Measurements On Cerium-Lanthanum-M-Indium (M = Cobalt, Rhodium, Iridium) Alloys., Umit Alver
De Haas-Van Alphen Effect Measurements On Cerium-Lanthanum-M-Indium (M = Cobalt, Rhodium, Iridium) Alloys., Umit Alver
LSU Historical Dissertations and Theses
The de Haas van Alphen (dHvA) effect, which measures the oscillatory component of the magnetization, in several CexLa1-x MIn5 (M = Rh, Co, Ir) alloys for 0 ≤ x ≤ 1 has been studied in detail using torque, pulse field and field modulation techniques. The frequencies, associated extremal cross sectional areas of the Fermi surface and effective masses of each sample throughout each of the series are reported. The energy band calculations of CeRhIn5, CeCoIn5 and CeIrIn5 assume that the 4f electrons in Ce are completely delocalized and these electrons make a significant contribution to the topology of the Fermi …
The Synthesis Of Deuterated Arylamine Dna Adducts For Use In The Development Of An Isotope Dilution Lc/Ms/Ms Method, Philip Dmitri Olsen
The Synthesis Of Deuterated Arylamine Dna Adducts For Use In The Development Of An Isotope Dilution Lc/Ms/Ms Method, Philip Dmitri Olsen
LSU Doctoral Dissertations
Polycyclic aromatic amines (arylamines) are a class of chemical carcinogens that are prevalent in environmental and industrial settings. In order to study the mechanism of their toxicity a quantitative and qualitative detection method was developed to measure the C8-adenine adducts of benzidine and 2-aminofluorene in DNA samples. To do this a novel synthetic method using a palladium catalyst was developed to prepare authentic and deuterated arylamine adducts to serve as standards. These standards were then used to develop a high performance liquid chromatography, electrospray, tandem mass spectrometry, isotope dilution, detection method. To demonstrate the validity of this method two spike …
Analysis Of Near-Infrared Dye-Labeled Sanger Sequencing Fragments With Gel Electrophoresis Using The Time-Resolved Flourescence Lifetime Indentification Methods, Suzanne Jeanel Lassiter
Analysis Of Near-Infrared Dye-Labeled Sanger Sequencing Fragments With Gel Electrophoresis Using The Time-Resolved Flourescence Lifetime Indentification Methods, Suzanne Jeanel Lassiter
LSU Doctoral Dissertations
The research presented in this dissertation involves the identification of sequencing fragments with time-resolved methods. For this application, near-infrared heavy-atom tricarbocyanine dyes were developed in our laboratory, which can be excited with a single laser and emission collected using a single detection channel. The dyes have four spectroscopically unique, but relatively short lifetimes that can be altered by the intramolecular heavy-atom they contain. The work described here involves the optimization of dye-primer chemistry for preparing Sanger sequencing reactions for longer reads and the optimization of the separation matrix for capillary gel electrophoresis that produces favorable statistical analysis of the aforementioned …
Bounding The Wild Set (Counting The Minimum Number Of Wild Primes In Hilbert Symbol Equivalent Number Fields), Marius M. Somodi
Bounding The Wild Set (Counting The Minimum Number Of Wild Primes In Hilbert Symbol Equivalent Number Fields), Marius M. Somodi
LSU Doctoral Dissertations
This dissertation makes a contribution to the study of Witt rings of quadratic forms over number fields. To every pair of algebraic number fields with isomorphic Witt rings one can associate a number, called the minimum number of wild primes. The situation is particularly nice when this number is 0; often it is not 0. Earlier investigations have established lower bounds for this number. In this dissertation an analysis is presented that expresses the minimum number of wild primes in terms of the number of wild dyadic primes. This formula not only gives immediate upper bounds, but can be considered …
Artin-Schreier Families And 2-D Cycle Codes, Cem Guneri
Artin-Schreier Families And 2-D Cycle Codes, Cem Guneri
LSU Doctoral Dissertations
We start with the study of certain Artin-Schreier families. Using coding theory techniques, we determine a necessary and sufficient condition for such families to have a nontrivial curve with the maximum possible number of rational points over the finite field in consideration. This result produces several nice corollaries, including the existence of certain maximal curves; i.e., curves meeting the Hasse-Weil bound.We then present a way to represent two-dimensional (2-D) cyclic codes as trace codes starting from a basic zero set of its dual code. This representation enables us to relate the weight of a codeword to the number of rational …
Numerical Simulations Of Dynamical Mass Transfer In Binaries, Patrick Michael Motl
Numerical Simulations Of Dynamical Mass Transfer In Binaries, Patrick Michael Motl
LSU Doctoral Dissertations
We present results from investigations of mass transfer instability in close binary star systems. By unstable mass transfer we mean the exchange of material where the response of the binary to the initial Roche lobe overflow causes the donor to loose even more material. Our work is guided by approximate arguments that dictate the stability boundaries for binary star systems. To proceed further one must explicitly treat extended mass and velocity distributions that are both nitially, and through their subsequent evolution in time, self-consistent. In this dissertation, we present the first three-dimensional, fully self-consistent treatment of mass transfer in close …
Making Classical And Quantum Canonical General Relativity Computable Through A Power Series Expansion In The Inverse Cosmological Constant, Rodolfo Gambini, Jorge Pullin
Making Classical And Quantum Canonical General Relativity Computable Through A Power Series Expansion In The Inverse Cosmological Constant, Rodolfo Gambini, Jorge Pullin
Faculty Publications
Casting ordinary general relativity as a perturbative theory in Λ-1 and starting with background theory in which Λ → ∞ allows one to explicitly compute nondegenerate physical quantum states and observables. The technique is applicable in the theory in general and also in mini-super-space models. In the general theory, the calculations are well defined and tractable, but quite involved. This opens up a program for the quantization of the gravitational field that is well defined computationally and allows contact with the physical observables of the theory, a key ingredient in the road to finding a theory with a semiclassical regime …
Land Use Impacts On Atmospheric Carbon Monoxide Consumption By Soils, G. M. King
Land Use Impacts On Atmospheric Carbon Monoxide Consumption By Soils, G. M. King
Faculty Publications
Seasonal analyses of in situ CO fluxes from forested and agricultural soils in Maine and Georgia, and more limited comparisons in Hawai'i indicated that agricultural land use consistently enhanced CO consumption. Soils at an agricultural site in Maine consumed approximately 1.9 g CO m-2 yr-1 while uptake in a nearby mixed forest was about 70% lower, 0.6 g CO m-2 yr-1. A similar trend was observed for sites in Georgia, where annual uptake by agricultural sites was approximately 1.0 g CO m-2 while net emission (about -0.5 g CO m-2) was observed for neighboring pine stands. Net CO fluxes in …
The Large Cosmological Constant Approximation To Classical And Quantum Gravity: Model Examples, Rodolfo Gambini, Jorge Pullin
The Large Cosmological Constant Approximation To Classical And Quantum Gravity: Model Examples, Rodolfo Gambini, Jorge Pullin
Faculty Publications
We have recently introduced an approach for studying perturbatively classical and quantum canonical general relativity. The perturbative technique appears to preserve many of the attractive features of the non-perturbative quantization approach based on Ashtekar's new variables and spin networks. With this approach one can find perturbatively classical observables (quantities that have vanishing Poisson brackets with the constraints) and quantum states (states that are annihilated by the quantum constraints). The relative ease with which the technique appears to deal with these traditionally hard problems opens up several questions concerning how relevant the results produced can possibly be. Among the questions is …
Re: 'Differences In Socioeconomic Status And Survival Among White And Black Men With Prostate Cancer' [1] (Multiple Letters), Jay S. Kaufman, Robert Millikan, Charles Poole, Paul Godley, Richard S. Cooper, Vincent Freeman
Re: 'Differences In Socioeconomic Status And Survival Among White And Black Men With Prostate Cancer' [1] (Multiple Letters), Jay S. Kaufman, Robert Millikan, Charles Poole, Paul Godley, Richard S. Cooper, Vincent Freeman
Faculty Publications
No abstract provided.
On The Excluded Minors For Quaternary Matroids, J. F. Geelen, J. G. Oxley, D. L. Vertigan, G. P. Whittle
On The Excluded Minors For Quaternary Matroids, J. F. Geelen, J. G. Oxley, D. L. Vertigan, G. P. Whittle
Faculty Publications
This paper strengthens the excluded-minor characterization of GF(4)-representable matroids. In particular, it is shown that there are only finitely many 3-connected matroids that are not GF(4)-representable and that have no U2, 6-, U4, 6-, P6-, F-7-, or (F-7)*-minors. Explicitly, these matroids are all minors of S(5, 6, 12) with rank and corank at least 4, and P″8, the matroid that can be obtained from S(5, 6, 12) by deleting two elements, contracting two elements, and then relaxing the only pair of disjoint circuit-hyperplanes. © 2000 Academic Press.
Canonical Quantum Gravity In The Vassiliev Invariants Arena: Ii. Constraints, Habitats And Consistency Of The Constraint Algebra, Cayetano Di Bartolo, Rodolfo Gambini, Jorge Griego, Jorge Pullin
Canonical Quantum Gravity In The Vassiliev Invariants Arena: Ii. Constraints, Habitats And Consistency Of The Constraint Algebra, Cayetano Di Bartolo, Rodolfo Gambini, Jorge Griego, Jorge Pullin
Faculty Publications
In a companion paper we introduced a kinematical arena for the discussion of the constraints of canonical quantum gravity in the spin network representation based on Vassiliev invariants. In this paper we introduce the Hamiltonian constraint, extend the space of states to non-diffeomorphism-invariant 'habitats' and check that the off-shell quantum constraint commutator algebra reproduces the classical Poisson algebra of constraints of general relativity without anomalies. One can therefore consider the resulting set of constraints and space of states as a consistent theory of canonical quantum gravity.
Theoretical Prediction Of Nuclear Quadrupole Resonance Spectra Of Aluminum, Bromine And Nitrogen Compounds Via First Principles Calculations, Chris Harwell
LSU Historical Dissertations and Theses
We study the interaction of the electric field gradient (EFG) and the nuclear quadrupole moment of 81Br,27Al, and 14N nuclei via ab initio quantum chemistry calculations. The primary goal is to predict the nuclear magnetic resonance (NMR) spectral parameters of interesting materials and assist in interpretation of their spectra. The calculations predict NMR spectral parameters for:
- 27Al nuclei in andalusite, sillimanite and kyanite - three polymorphs of Al2Si05 - for assigning NMR signals to crystallographic sites, as a zeolite model and studying the effect of structural changes due to temperature (25-1000''C);
- 14N nuclei in …
Classification Of The Lie Bialgebra Structures On The Witt And Virasoro Algebras, Siu Hung Ng, Earl J. Taft
Classification Of The Lie Bialgebra Structures On The Witt And Virasoro Algebras, Siu Hung Ng, Earl J. Taft
Faculty Publications
We prove that all the Lie bialgebra structures on the one sided Witt algebra W1, on the Witt algebra W and on the Virasoro algebra V are triangular coboundary Lie bialgebra structures associated to skew-symmetric solutions r of the classical Yang-Baxter equation of the form r = a ∧ b. In particular, for the one-sided Witt algebra W1 = Der k[t] over an algebraically closed field k of characteristic zero, the Lie bialgebra structures discovered in Michaelis (Adv. Math. 107 (1994) 365-392) and Taft (J. Pure Appl. Algebra 87 (1993) 301-312) are all the Lie bialgebra structures on W1 up …
Iron Acquisition Systems And The Effect Of Iron On Virulence, Amy E. Noles
Iron Acquisition Systems And The Effect Of Iron On Virulence, Amy E. Noles
Honors Capstones
No abstract provided.
Gamma-Ray Bursts Have Millisecond Variability, Katharine C. Walker, Bradley E. Schaefer, E. E. Fenimore
Gamma-Ray Bursts Have Millisecond Variability, Katharine C. Walker, Bradley E. Schaefer, E. E. Fenimore
Faculty Publications
We have performed searches for isolated flares and for steady flickering in the initial ∼ 1 s of gamma-ray burst light curves on the microsecond to millisecond timescales. Two bursts among our sample of 20 revealed four isolated flares with timescales from 256 to 2048 μs. A wavelet analysis for our sample showed low-level flickering for all bursts on timescales from 256 μs to 33 ms, with the majority of bursts containing rise times faster than 4 ms and 30% having rise times faster than 1 ms. These results show that millisecond variability is common in classical bursts and not …
Economic Implications Of Forest Products Sector Industry Development In Northwest Louisiana (Bulletin #874), David W. Hughes, Richard P. Vlosky
Economic Implications Of Forest Products Sector Industry Development In Northwest Louisiana (Bulletin #874), David W. Hughes, Richard P. Vlosky
LSU AgCenter Bulletins
In this study, industry development opportunities specific to northwestern Louisiana were examined. This publication focuses on the economic impacts of forest products industry development in this region.
Surfaces, Tree-Width, Clique-Minors, And Partitions, Guoli Ding, Bogdan Oporowski, Daniel P. Sanders, Dirk Vertigan
Surfaces, Tree-Width, Clique-Minors, And Partitions, Guoli Ding, Bogdan Oporowski, Daniel P. Sanders, Dirk Vertigan
Faculty Publications
In 1971, Chartrand, Geller, and Hedetniemi conjectured that the edge set of a planar graph may be partitioned into two subsets, each of which induces an outerplanar graph. Some partial results towards this conjecture are presented. One such result, in which a planar graph may be thus edge partitioned into two series-parallel graphs, has nice generalizations for graphs embedded onto an arbitrary surface and graphs with no large clique-minor. Several open questions are raised. © 2000 Academic Press.
On Size, Circumference And Circuit Removal In 3-Connected Matroids, Manoel Lemos, James Oxley
On Size, Circumference And Circuit Removal In 3-Connected Matroids, Manoel Lemos, James Oxley
Faculty Publications
This paper proves several extremal results for 3-connected matroids. In particular, it is shown that, for such a matroid M, (i) if the rank r(M) of M is at least six, then the circumference c(M) of M is at least six and, provided |E(M)| ≥4r(M) - 5, there is a circuit whose deletion from M leaves a 3-connected matroid; (ii) if r(M) ≥4 and M has a basis B such that M\e is not 3-connected for all e in E(M) - B, then |E(M)| ≤3r(M) - 4; and (iii) if M is minimally 3-connected but not hamiltonian, then |E(M)| ≤3r(M) …
Moving Mountains: Serving In 10 States, An Engineer's Final Project Is Battery Wagner, Charles D. Ross
Moving Mountains: Serving In 10 States, An Engineer's Final Project Is Battery Wagner, Charles D. Ross
Civil War Book Review
For several centuries, combat engineers have played a crucial role in battle operations. Yet the typical battles and leaders approach to the Civil War usually pays little attention to this important work. George G. Kundahl attempts to fill the void with Confederate Engineer: Training and Campaign....
On The Non-Uniqueness Of Q-Cones Of Matroids, James Oxley, Geoff Whittle
On The Non-Uniqueness Of Q-Cones Of Matroids, James Oxley, Geoff Whittle
Faculty Publications
Let M be a rank-r simple GF(q)-representable matroid. A q-cone of M is a matroid M′ that is constructed by embedding M in a hyperplane of PG(r,q), adding a point p of PG(r,q) not on H, and then adding all the points of PG(r,q) that are on lines joining p to an element of M. If r(M) > 2 and M is uniquely representable over GF(q), then M′ is unique up to isomorphism. This note settles a question made explicit by Kung by showing that if r(M) = 2 or if M is not uniquely representable over GF(q), then M′ need …
On The 3-Connected Matroids That Are Minimal Having A Fixed Spanning Restriction, Manoel Lemos, James Oxley
On The 3-Connected Matroids That Are Minimal Having A Fixed Spanning Restriction, Manoel Lemos, James Oxley
Faculty Publications
Let N be a minor of a 3-connected matroid M and let M′ be a 3-connected minor of M that is minimal having N as a minor. This paper commences the study of the problem of finding a best-possible upper bound on |E(M′) - E(N)|. The main result solves this problem in the case that N and M have the same rank. © 2000 Elsevier Science B.V. All rights reserved.
Anomalous Shape Recognition Using Computer Vision, Chang-Sik Kim
Anomalous Shape Recognition Using Computer Vision, Chang-Sik Kim
LSU Historical Dissertations and Theses
In this research, a new method for anomalous shape recognition, named Curvature-Angular Descriptor (CAD), was written. The CAD generates shape feature vectors from a given curve shape. These vectors can be used to uniquely characterize the shape.
The sweet potato has one of the most irregular shapes of any fruit or vegetable. The Standards for Grades of sweet potato shapes (The Code of Federal Regulation, title 7 Agriculture, 1995) are very subjective. For this reason, the sweet potato was chosen as an anomalous shape for evaluating the CAD. The CAD was applied using two methods for sweet potato shape recognition. …
Alcohol Intake And Mortality: Findings From The National Health Interview Surveys (1988 And 1990), Youlian Liao, Daniel L. Mcgee, Guichan Cao, Richard S. Cooper
Alcohol Intake And Mortality: Findings From The National Health Interview Surveys (1988 And 1990), Youlian Liao, Daniel L. Mcgee, Guichan Cao, Richard S. Cooper
Faculty Publications
The authors used prospective data from two supplemental studies of the National Health Interview Survey, the 1988 Alcohol Supplement and the 1990 Health Promotion and Disease Prevention Supplement, to examine the relation between alcohol intake and mortality. Their study included 17,821 men and 25,874 women aged 40 years or older at baseline; during an average of 6 years of follow-up, 5,540 deaths occurred. The alcohol-mortality relation was U-shaped for men and J-shaped for women. On the basis of categorical analyses adjusted for age, race, smoking, and baseline diseases, men who drank 2 drinks per day had a significantly lower risk …
Grant At Face Value: An Officer's Odyssey From West Point To Appomattox, Geoffrey Perret
Grant At Face Value: An Officer's Odyssey From West Point To Appomattox, Geoffrey Perret
Civil War Book Review
These are good times for Ulysses S. Grant, whose reputation took a beating a generation ago at the hands of William S. McFeely. My own, admittedly admiring, biography was published in 1997, the first volume of Brooks D. Simpson's book has finally appeared, and yet another Grant bio-graphy, by Jean S....
Some Generalizations Of The Kadomtsev-Petviashvili Equations, Michael M. Tom
Some Generalizations Of The Kadomtsev-Petviashvili Equations, Michael M. Tom
Faculty Publications
The question of globalization of solutions of the Cauchy problem for some generalizations of Kadomtsev-Petviashvili equations of the form (ut + upux -Dαxux)x + εuyy = 0, where Dx = (- ∂2x)1/2 and ε = ± 1 is examined. It is shown that for ε = -1 and α ≥ 2, a global estimate on solutions can be derived for large initial data provided that p < 4α/4 + α. A consequence of this is that if a is large enough, the local solution in Hs(ℝ2) can be globally continued. © 2000 Academic Press.
Fleeting Fortunes, Deserted Ranks: What Factors Influenced Georgian Troop Desertion?, Kevin Levin
Fleeting Fortunes, Deserted Ranks: What Factors Influenced Georgian Troop Desertion?, Kevin Levin
Civil War Book Review
Desertion is one of the least understood topics in Civil War studies, though an adequate account of it has implications for several areas of historical research, including life on the home front, morale, and nationalism. The current volume is an important first step in addressing the evolution of de....
Classically Unstable Approximations For Linear Evolution Equations And Applications., Yu Zhuang
Classically Unstable Approximations For Linear Evolution Equations And Applications., Yu Zhuang
LSU Historical Dissertations and Theses
Temporal discretization methods for evolutionary differential equations that factorize the resolvent into a product of easily computable operators have great numerical appeal. For instance, the alternating direction implicit (ADI) method of Peaceman-Rachford for 2-D parabolic problems greatly reduces the simulation time when compared with the Crank-Nicolson scheme. However, just like many other factorized approximation methods that exhibit numerical stability, the ADI method is known to satisfy only the Von Neumann stability condition, a necessary condition that is usually surmised as sufficient in practical cases as pointed out by Lax and Richtmyer. Intensive efforts have been directed to understand the Von …