Showing papers by "University of Maryland, College Park published in 1973"

The finite element method with Lagrangian multipliers

Abstract: The Dirichlet problem for second order differential equations is chosen as a model problem to show how the finite element method may be implemented to avoid difficulty in fulfilling essential (stable) boundary conditions. The implementation is based on the application of Lagrangian multiplier. The rate of convergence is proved.

Nonlinear generalized Langevin equations

Abstract: Exact generalized Langevin equations are derived for arbitrarily nonlinear systems interacting with specially chosen heat baths. An example is displayed in which the Langevin equation is nonlinear but approximately Markovian.

On the existence of invariant measures for piecewise monotonic transformations

Abstract: A class of piecewise continuous, piecewise C transforma­tions on the interval [0,1] is shown to have absolutely continuous invariant measures.

Unified Lepton-Hadron Symmetry and a Gauge Theory of the Basic Interactions

Abstract: An attempt is made to unify the fundamental hadrons and leptons into a common irreducible representation $F$ of the same symmetry group $G$ and to generate a gauge theory of strong, electromagnetic, and weak interactions. Based on certain constraints from the hadronic side, it is proposed that the group $G$ is SU(4\ensuremath{'}) \ifmmode\times\else\texttimes\fi{} SU(4\ensuremath{''}), which contains a Han-Nambu-type SU(3\ensuremath{'}) \ifmmode\times\else\texttimes\fi{} SU(3\ensuremath{''}) group for the hadronic symmetry, and that the representation $F$ is (4,4*). There exist four possible choices for the lepton number $L$ and accordingly four possible assignments of the hadrons and leptons within the (4,4*). Two of these require nine Han-Nambu-type quarks, three "charmed" quarks, and the observed quartet of leptons. The other two also require the nine Han-Nambu quarks, plus heavy leptons in addition to observed leptons and only one or no "charmed" quark. One of the above four assignments is found to be suitable to generate a gauge theory of the weak, electromagnetic, and SU(3\ensuremath{''}) gluonlike strong interactions from a selection of the gauges permitted by the model. The resulting gauge symmetry is $\mathrm{SU}{({2}^{\ensuremath{'}})}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{({3}^{\ensuremath{'}\ensuremath{'}})}_{L+R}$. The scheme of all three interactions is found to be free from Adler-Bell-Jackiw anomalies. The normal strong interactions arise effectively as a consequence of the strong gauges $\mathrm{SU}{({3}^{\ensuremath{'}\ensuremath{'}})}_{L+R}$. Masses for the gauge bosons and fermions are generated suitably by a set of 14 complex Higgs fields. The neutral neutrino and $\ensuremath{\Delta}S=0$ hadron currents have essentially the same strength in the present model as in other $\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ theories. The mixing of strong- and weak-gauge bosons (a necessary feature of the model) leads to parity-violating nonleptonic amplitudes, which may be observable depending upon the strength of SU(3\ensuremath{''}) symmetry breaking. The familiar hadron symmetries such as SU(3\ensuremath{'}) and chiral $\mathrm{SU}{({3}^{\ensuremath{'}})}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{({3}^{\ensuremath{'}})}_{R}$ are broken only by quark mass terms and by the electromagnetic and weak interactions, not by the strong interactions. The difficulties associated with generating gauge interactions in the remaining three assignments are discussed in Appendix A. Certain remarks are made on the question of proton and quark stability in these three schemes.

Angle Detection on Digital Curves

Abstract: A simple parallel procedure for selecting significant curvature maxima and minima on a digital curve is described.

Recurrent outbreaks of measles, chickenpox and mumps i. seasonal variation in contact rates

Abstract: London, W. P. (Mathematical Research Branch, National Institute of Arthritis, Metabolism, and Digestive Diseases, Bethesda, Md. 20014) and J. A. Yorke. Recurrent outbreaks of measles, chickenpox and mumps. I. Seasonal variation in contact rates. Am J Epidemiol 98:453-468, 1973. —Recurrent outbreaks of measles, chickenpox and mumps in cities are studied with a mathematical model of ordinary differential delay equations. For each calendar month a mean contact rate (fraction of susceptibles contacted per day by an infective) is estimated from the monthly reported cases over a 30to 35-year period. For each disease the mean monthly contact rate is 1.7 to 2 times higher in the winter months than in the summer months; the seasonal variation is attributed primarily to the gathering of children in school. Computer simulations that use the seasonally varying contact rates reproduce the observed pattern of undamped recurrent outbreaks: annual outbreaks of chickenpox and mumps and biennial outbreaks of measles. The two-year period of measles outbreaks is the signature of an endemic infectious disease that would exhaust itself and become nonendemic if there were a minor increase in infectivity or a decrease in the length of the incubation period. For populations in which most members are vaccinated, simulations show that the persistence of the biennial pattern of measles outbreaks implies that the vaccine is not being used uniformly throughout the population.

Optimum processing for delay-vector estimation in passive signal arrays

Abstract: For the purpose of localizing a distant noisy target, or, conversely, calibrating a receiving array, the time delays defined by the propagation across the array of the target-generated signal wavefronts are estimated in the presence of sensor-to-sensor-independent array self-noise. The Cramer-Rao matrix bound for the vector delay estimate is derived, and used to show that either properly filtered beamformers or properly filtered systems of multiplier-correlators can be used to provide efficient estimates. The effect of suboptimally filtering the array outputs is discussed.

Some equations modelling growth processes and gonorrhea epidemics

Abstract: At the present time VD is a major national problem. Essentially we are confronted with several epidemics. This paper is devoted to a study of processess of this nature. It is hoped that understanding of the mathematical nature of these processes willhelp in their control.

The Lunar Laser Ranging Experiment: Accurate ranges have given a large improvement in the lunar orbit and new selenophysical information.

Abstract: The scientific objectives achievable through high-accuracy range measurements to lunar retroreflectors are considered. A specific study of design questions related to the operation of retroreflectors on the lunar surface indicated that a reflector panel containing a number of solid fused silica corner reflectors would be capable of maintaining essentially diffraction limited performance under direct solar illumination. Initial Apollo 11 observations are discussed together with the installation of additional lunar retroreflectors in connection with the Luna 17, Apollo 14, Apollo 15, and Luna 21 missions. Range measurements at the McDonald Observatory are considered along with new results from lunar range data, and prospects regarding future lunar ranging stations.

Morphological patterns in high-intertidal gastropods: Adaptive strategies and their limitations

Abstract: An analysis of shell form in several families of high-intertidal herbivorous gastropods has revealed the existence of morphological gradients. Among tropical littorinids, relative spire height and degree of development of external shell sculpture generally increase interspecifically, and often intraspecifically, from low to high shore levels. This gradient is also evident from temperate to tropical latitudes, and may be modified or overridden by exposure to wave action and other factors. Among acmaeid, patellid, and siphonariid limpets, there is a well-marked interspecific increase in relative shell height with increasing shore level, but latitudinal trends in morphology cannot at present be distinguished. Evidence from both tropical and temperate coasts indicates that limpets found in shaded places tend to have smoother shells than those often exposed to direct sunlight. In the Neritidae, relative shell globosity tends to increase interspecifically from low to high shore levels; most high-shore species have strong shell sculpture, with the base of the shell only slightly excavated. A decrease in the number of neritid species towards higher latitudes is accompanied by selective deletion of globose, strongly sculptured types living at high shore levels. Neritids and some limpets can employ evaporative cooling as a mechanism for temperature regulation. The morphological gradients in these groups reflect a relative increase in the volume of the extravisceral cavity (water reservoir) and a decrease in the area in contact with the substratum, as well as a relative decrease in the rate of water loss, in an upshore direction. Neritids are better adapted than limpets to high temperature and desiccation stresses because of their ability to regulate rate of evaporation and contact between soft parts and substratum. These differences are reflected in the complementary patterns of latitudinal diversity in the two groups. In Littorinidae, which attach to the substratum by a mucus film, the morphological gradients reflect a minimization of water loss and substratum contaet, and a maximization of reflective relative to absorptive surface area.

Recurrent outbreaks of measles, chickenpox and mumps ii. systematic differences in contact rates and stochastic effects

Abstract: Yorke, J. A. and W. P. London (Mathematical Research Branch, National Institute of Arthritis, Metabolism, and Digestive Diseases, Bethesda, Maryland 20014). Recurrent outbreaks of measles, chickenpox and mumps. I I . Systematic differences in contact rates and stochastic effects. Am J Epidemiol 98:469-482, 1973.—The mean monthly contact rates for measles, chickenpox and mumps estimated from the monthly reported cases show systematic differences between the years with many cases and the years with few cases. In New York City, the mean contact rates for chickenpox were different during the years 1931-1945 than during 1946-1960. The clustering of cases within social groups is proposed to account for these differences in the contact rates and for other empirical observations. The irregularity of outbreaks of measles in cities of fewer than two million people can be explained by stochastic effects. Outbreaks of measles in distant large metropolitan areas are highly correlated in time, but the reasons for the correlation are not clear.

Arcs and Curves in Digital Pictures

Abstract: Characterizations of digital “simple arcs” and “simple closed curves” are given. In particular, it is shown that the following are equivalent for sets S having more than four points: (1) S is a simple curve; (2) S is connected and each point of S has exactly two neighbors in S; (3) S is connected, has exactly one hole, and has no deletable points. It follows that if a “shrinking” algorithm is applied to a connected S that has exactly one hole, it shrinks to a simple curve.

Differential Energy Spectra of Low-Energy (<8.5 MeV per Nucleon) Heavy Cosmic Rays during Solar Quiet Times

Abstract: Explorer 47 satellite observations of carbon, oxygen, and heavier nuclei differential energy spectra below 8.5 MeV/nucleon are presented for solar quiet time periods. A dE/dx vs E method for particle identification and energy determination was used. The instrumentation telescope included an isobutane proportional counter, a surface barrier Si detector, and a cylindrical plastic scintillator anticoincidence shield. The observations were performed outside the bow-shock and in the ecliptic plane. Results show an anisotropy of about 25% at 22 degrees west of the sun with a C/O ratio of 0.5 supporting a solar origin. The low energy portions of the C and O spectra have steep negative slopes, and the corresponding power law is given. Peculiarities in the O spectrum are discussed.

A class of nonanalytic automorphic functions

Abstract: In this paper we consider a class of nonanalytic automorphic functions which were first mentioned to A. Selberg by C. L. Siegel. These functions have Fourier coefficients which are closely connected with the Fourier coefficients of analytic automorphic forms, and they are also eigenfunctions of the Laplace operator derived from the hyperbolic metric. We shall show how this latter property gives new results in the classical theory of automorphic forms.

Kinetics of the sodium-dependent transport of gamma-aminobutyric acid by synaptosomes

Abstract: The kinetics of transport of gamma-aminobutyric acid [2,3-3H] by synaptosomes from rat brain was studied by means of a rapid filtration technique. The rate of uptake was proportional to the protein concentration over the range 0.05—0.2 mg of synaptosomal protein per ml. Although apparent allosteric kinetics were observed with sodium, transport followed simple saturation kinetics with respect to GABA and no heterotropic, cooperative effects of GABA on sodium on kinetics were observed. A minimum of three interacting sodium sites is suggested the basis of Hill plots of the sodium data. Both the apparent Km and Vmax for GABA were functions of the sodium ion concentration but the effect of sodium was considerably greater on Vmax than on the apparent Km The Vmax for GABA was 1.1 ± 0.5 nmol.min−1 mg−1 of protein at 95 mm sodium and decreased to 12 per Cent of this value at 19 mm sodium. The apparent Km for GABA increased from 4.0 ± 1.0 μm at 95 mm sodium to 8.4 ± 2.0 μm at 19 mm sodium. Potassium was a noncompetitive inhibitor with respect to GABA and did not affect the apparent cooperativity observed with sodium. These findings are discussed in terms of models of GABA transport.

The Initiation and Control of Free Amino Acid Regulation of Cell Volume in Salinity-Stressed Marine Bivalves

Abstract: 1. Molluscan cells maintain constant volume in decreasing salinities by releasing intracellular free amino acids as osmotic solute. 2. During a salinity decrease both osmotic pressure and ion concentrations decline simultaneously. Either condition might initiate the amino acid release. 3. Under constant osmotic conditions a decrease in Na+, K+ or Cl- concentration in the medium surrounding the isolated bivalve heart, did not result in an amino acid efflux. 4. On the other hand, removal of Ca2+ and Mg2+ resulted in a vigorous amino acid efflux which continued until the divalent ion concentration was restored. 5. The hypo-osmotically induced amino acid efflux could be partially blocked by raising the external divalent ion concentration. Similarly, lanthanum proved to be an effective blocking agent, both in low osmotic pressures and in Ca2+- and Mg2+-free SW. 6. These results show that salinity-induced free amino acid regulation is initiated by a decrease in external osmotic pressure. The time course of the efflux is dependent on external divalent ion concentration. 7. Finally, the site of divalent ion action is at the external membrane surface. 8. A hypothetical membrane model is proposed. Contribution No. 18 from the Tallahassee, Sopchoppy and Gulf Coast Marine Biological Association.