Measure functions

2017 ◽  
Author(s):  
Lucas Champollion
Keyword(s):  
One Dimension ◽  
Measure Function ◽  
Monotonicity Constraint ◽  
The Difference ◽  
Water Entity

This chapter explains the linguistic relevance of the difference between extensive measure functions like volume and intensive measure functions like temperature, as illustrated by the pseudopartitives thirty liters of water vs. thirty degrees Celsius of water (Krifka 1998, Schwarzschild 2006). Subsuming these previous accounts, stratified reference correctly predicts the monotonicity constraint: such constructions disallow measure functions that generally return the same value on an entity and on its parts. For example, in order for *thirty degrees Celsius of water to be acceptable, it would have to describe a water entity whose parts are colder than itself; but there are no such entities. Stratified reference relativizes unboundedness to just one dimension or measure function at a time. This makes it possible to account for examples like five feet of snow even though not every part of a five-foot layer of snow is less than five feet high.

Limit theorems and absorption problems for quantum radom walks in one dimension

2002 ◽  
Vol 2 (Special) ◽  
pp. 578-595
Author(s):  
N. Konno
Keyword(s):  
Random Walks ◽  
Limit Theorems ◽  
The Other ◽  
One Dimension ◽  
Unitary Matrices ◽  
Quantum Random Walks ◽  
One Dimensional ◽  
The Difference ◽  
The One

In this paper we consider limit theorems, symmetry of distribution, and absorption problems for two types of one-dimensional quantum random walks determined by $2 \times 2$ unitary matrices using our PQRS method. The one type was introduced by Gudder in 1988, and the other type was studied intensively by Ambainis et al. in 2001. The difference between both types of quantum random walks is also clarified.

Measuring stuff and process

2019 ◽  
pp. 37-60
Author(s):  
Alexis Wellwood
Keyword(s):  
Central Thesis ◽  
Measure Function ◽  
Mass Nouns ◽  
Subsequent Chapter ◽  
Verb Phrases ◽  
Monotonicity Constraint ◽  
Function Selection

This chapter begins the book’s survey of non-canonical comparatives, and suggests a degree-based interpretation of the expression “much” which occurs implicitly as a morphosyntactic part of “more”, and explicitly in phrases like “as much” and “too much”. Focusing on comparatives targeting mass nouns like “mud” and atelic verb phrases like “run (in the park)”, a primary goal of this analysis is to capture both the variability and constraints (especially a hypothesized “monotonicity constraint”) on measure function selection in such cases. In line with the central thesis of the book, this chapter emphasizes the role that the order-theoretic properties (when present) of a predicate plays in fixing the available dimension(s) for comparison in a given nominal or verbal comparative. The success of this analysis suggests considering whether it can apply to the canonical comparatives, which is explored in the subsequent chapter.

scholarly journals Generation of families of spectra in PT -symmetric quantum mechanics and scalar bosonic field theory

2013 ◽  
Vol 371 (1989) ◽  
pp. 20120049 ◽  
Author(s):  
Steffen Schmidt ◽  
S. P. Klevansky
Keyword(s):  
Field Theory ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Complex Analysis ◽  
One Dimension ◽  
Quantum Mechanical ◽  
Bosonic Field ◽  
Symmetric Quantum ◽  
The Difference ◽  
Do So

This paper explains the systematics of the generation of families of spectra for the -symmetric quantum-mechanical Hamiltonians H = p 2 + x 2 (i x ) ϵ , H = p 2 +( x 2 ) δ and H = p 2 −( x 2 ) μ . In addition, it contrasts the results obtained with those found for a bosonic scalar field theory, in particular in one dimension, highlighting the similarities to and differences from the quantum-mechanical case. It is shown that the number of families of spectra can be deduced from the number of non-contiguous pairs of Stokes wedges that display symmetry. To do so, simple arguments that use the Wentzel–Kramers–Brillouin approximation are used, and these imply that the eigenvalues are real. However, definitive results are in most cases presently only obtainable numerically, and not all eigenvalues in each family may be real. Within the approximations used, it is illustrated that the difference between the quantum-mechanical and the field-theoretical cases lies in the number of accessible regions in which the eigenfunctions decay exponentially. This paper reviews and implements well-known techniques in complex analysis and -symmetric quantum theory.

Relativistic versus nonrelativistic Hartree–Fock calculations: solvable examples in one dimension

1989 ◽  
Vol 67 (6) ◽  
pp. 583-586 ◽  
Author(s):  
D. B. Mitchell ◽  
Y. Nogami ◽  
N. D. Whelan
Keyword(s):  
Binding Energy ◽  
Interaction Strength ◽  
One Dimension ◽  
Contact Interactions ◽  
One Dimensional ◽  
Hartree Fock ◽  
Relativistic Interaction ◽  
Lorentz Scalar ◽  
The Difference

Relativistic and nonrelativistic one-dimensional systems of particles of the same mass interacting through instantaneous contact interactions are considered. For the relativistic interaction, we assume a combination of a Lorentz scalar and a vector. The mass and interaction strength are chosen such that the deuteron is simulated; the relativistic and nonrelativistic "deuteron" models have the same binding energy and practically the same structure. The relativistic and nonrelativistic Hartree–Fock equations can both be solved analytically. For certain combinations of the Lorentz scalar and vector interactions, the difference between the relativistic and nonrelativistic results can be appreciable.

The Origin of the Moon

1962 ◽  
Vol 14 ◽  
pp. 149-155 ◽  
Author(s):  
E. L. Ruskol
Keyword(s):  
Chemical Composition ◽  
Solar System ◽  
The Moon ◽  
The Earth ◽  
The Difference ◽  
Origin Of The Moon

The difference between average densities of the Moon and Earth was interpreted in the preceding report by Professor H. Urey as indicating a difference in their chemical composition. Therefore, Urey assumes the Moon's formation to have taken place far away from the Earth, under conditions differing substantially from the conditions of Earth's formation. In such a case, the Earth should have captured the Moon. As is admitted by Professor Urey himself, such a capture is a very improbable event. In addition, an assumption that the “lunar” dimensions were representative of protoplanetary bodies in the entire solar system encounters great difficulties.

Influence of Cell Wall Composition on the Fossilisation of Bacteria and the Implications for the Search for Early Life Forms

1997 ◽  
Vol 161 ◽  
pp. 491-504 ◽  
Author(s):  
Frances Westall
Keyword(s):  
Cell Wall ◽  
Life Forms ◽  
Cation Binding ◽  
Positive Bacterium ◽  
Gram Positive ◽  
Gram Positive Bacteria ◽  
Transmission Electron ◽  
Hydrothermal Sediments ◽  
Identification Of Bacteria ◽  
The Difference

AbstractThe oldest cell-like structures on Earth are preserved in silicified lagoonal, shallow sea or hydrothermal sediments, such as some Archean formations in Western Australia and South Africa. Previous studies concentrated on the search for organic fossils in Archean rocks. Observations of silicified bacteria (as silica minerals) are scarce for both the Precambrian and the Phanerozoic, but reports of mineral bacteria finds, in general, are increasing. The problems associated with the identification of authentic fossil bacteria and, if possible, closer identification of bacteria type can, in part, be overcome by experimental fossilisation studies. These have shown that not all bacteria fossilise in the same way and, indeed, some seem to be very resistent to fossilisation. This paper deals with a transmission electron microscope investigation of the silicification of four species of bacteria commonly found in the environment. The Gram positiveBacillus laterosporusand its spore produced a robust, durable crust upon silicification, whereas the Gram negativePseudomonas fluorescens, Ps. vesicularis, andPs. acidovoranspresented delicately preserved walls. The greater amount of peptidoglycan, containing abundant metal cation binding sites, in the cell wall of the Gram positive bacterium, probably accounts for the difference in the mode of fossilisation. The Gram positive bacteria are, therefore, probably most likely to be preserved in the terrestrial and extraterrestrial rock record.

Structuring, Motions and Shapes of Corona Emission Line Profiles

1994 ◽  
Vol 144 ◽  
pp. 421-426
Author(s):  
N. F. Tyagun
Keyword(s):  
Emission Line ◽  
Filling Factor ◽  
Direct Relationship ◽  
Coronal Plasma ◽  
Line Of Sight ◽  
Line Profiles ◽  
The Difference ◽  
Yellow Line ◽  
Red Line

AbstractThe interrelationship of half-widths and intensities for the red, green and yellow lines is considered. This is a direct relationship for the green and yellow line and an inverse one for the red line. The difference in the relationships of half-widths and intensities for different lines appears to be due to substantially dissimilar structuring and to a set of line-of-sight motions in ”hot“ and ”cold“ corona regions.When diagnosing the coronal plasma, one cannot neglect the filling factor - each line has such a factor of its own.

Difference Fourier Analysis of Glucose Embedded and Frozen Hydrated Purple Membrane

1982 ◽  
Vol 40 ◽  
pp. 74-75
Author(s):  
Jules S. Jaffe ◽  
Robert M. Glaeser
Keyword(s):  
Purple Membrane ◽  
Data Set ◽  
High Resolution Data ◽  
X Ray ◽  
X Ray Crystallography ◽  
Fourier Techniques ◽  
Versus Protein ◽  
The Difference ◽  
Difference Fourier ◽  
Ideal Method

Although difference Fourier techniques are standard in X-ray crystallography it has only been very recently that electron crystallographers have been able to take advantage of this method. We have combined a high resolution data set for frozen glucose embedded Purple Membrane (PM) with a data set collected from PM prepared in the frozen hydrated state in order to visualize any differences in structure due to the different methods of preparation. The increased contrast between protein-ice versus protein-glucose may prove to be an advantage of the frozen hydrated technique for visualizing those parts of bacteriorhodopsin that are embedded in glucose. In addition, surface groups of the protein may be disordered in glucose and ordered in the frozen state. The sensitivity of the difference Fourier technique to small changes in structure provides an ideal method for testing this hypothesis.

Destruction of Actin Filaments by Osmium Tetroxide

1977 ◽  
Vol 35 ◽  
pp. 466-467
Author(s):  
P. Maupin-Szamier ◽  
T. D. Pollard
Keyword(s):  
Actin Filaments ◽  
Time Course ◽  
Osmium Tetroxide ◽  
Rabbit Muscle ◽  
Muscle Actin ◽  
Sodium Phosphate Buffer ◽  
Transmission Electron ◽  
The Difference ◽  
Rates Of Decay ◽  
Short Time

We have studied the destruction of rabbit muscle actin filaments by osmium tetroxide (OSO4) to develop methods which will preserve the structure of actin filaments during preparation for transmission electron microscopy.Negatively stained F-actin, which appears as smooth, gently curved filaments in control samples (Fig. 1a), acquire an angular, distorted profile and break into progressively shorter pieces after exposure to OSO4 (Fig. 1b,c). We followed the time course of the reaction with viscometry since it is a simple, quantitative method to assess filament integrity. The difference in rates of decay in viscosity of polymerized actin solutions after the addition of four concentrations of OSO4 is illustrated in Fig. 2. Viscometry indicated that the rate of actin filament destruction is also dependent upon temperature, buffer type, buffer concentration, and pH, and requires the continued presence of OSO4. The conditions most favorable to filament preservation are fixation in a low concentration of OSO4 for a short time at 0°C in 100mM sodium phosphate buffer, pH 6.0.

Reconstruction of Objects from their Projections Using Orthogonal Functions

1973 ◽  
Vol 31 ◽  
pp. 268-269
Author(s):  
Elrnar Zeitler
Keyword(s):  
Unit Area ◽  
Three Dimensional ◽  
One Dimension ◽  
Spatial Density ◽  
Dimensional Representation ◽  
Orthogonal Functions ◽  
Object A ◽  
Plane Normal ◽  
Dimensional Object ◽  
Spatial Density Distribution

Considering any finite three-dimensional object, a “projection” is here defined as a two-dimensional representation of the object's mass per unit area on a plane normal to a given projection axis, here taken as they-axis. Since the object can be seen as being built from parallel, thin slices, the relation between object structure and its projection can be reduced by one dimension. It is assumed that an electron microscope equipped with a tilting stage records the projectionWhere the object has a spatial density distribution p(r,ϕ) within a limiting radius taken to be unity, and the stage is tilted by an angle 9 with respect to the x-axis of the recording plane.

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