scholarly journals On Erdős-Sós Conjecture for Trees of Large Size

10.37236/5405 ◽  
2016 ◽  
Vol 23 (1) ◽  
Author(s):  
Agnieszka Goerlich ◽  
Andrzej Żak
Keyword(s):  
Average Degree ◽  
Arbitrary Integer ◽  
Large Size ◽  
Special Cases ◽  
Tree Packing

Erdős and Sós conjectured that every graph $G$ of average degree greater than $k-1$ contains every tree of size $k$. Several results based upon the number of vertices in $G$ have been proved including the special cases where $G$ has exactly $k+1$ vertices (Zhou), $k+2$ vertices (Slater, Teo and Yap), $k+3$ vertices (Woźniak) and $k+4$ vertices (Tiner). We further explore this direction. Given an arbitrary integer $c\geq 1$, we prove Erdős-Sós conjecture in the case when $G$ has $k+c$ vertices provided that $k\geq k_0(c)$ (here $k_0(c)=c^{12}{\rm polylog}(c)$). We also derive a corollary related to the Tree Packing Conjecture.

Structural aspects of the hydrolysis products of metal alkoxides and metal trialkylsilyloxides

1969 ◽  
Vol 47 (22) ◽  
pp. 4101-4111 ◽  
Author(s):  
J. W. Lorimer ◽  
D. E. G. Jones
Keyword(s):  
Metal Oxide ◽  
Complex Structure ◽  
Theoretical Models ◽  
Degree Of Polymerization ◽  
Average Degree ◽  
Degree Of Hydrolysis ◽  
Special Cases ◽  
Plausible Mechanism ◽  
Branched Chains ◽  
Structural Aspects

The average degree of polymerization [Formula: see text] depends on the average degree of hydrolysis [Formula: see text] as[Formula: see text] over a large range of [Formula: see text] for all metal oxide alkoxides and oxide trialkylsilyloxides that have been formed by hydrolysis and examined in solution. A number of general theoretical models are developed which permit quantitative interpretation of the parameters a and b. Mixtures of linear or branched chains in proportions governed wholly or partly by the degree of polymerization of the unhydrolyzed alkoxide can explain all the data on oxide alkoxides in solution in their corresponding alcohol, and the model leads to a plausible mechanism for disproportionation. Similar models with more complex structure can be involved in the metal oxide trialkylsilyloxides. Heterogeneity in the composition of the repeating units or in the number of metal–oxygen–metal bridges between successive repeating units can also be significant for both oxide alkoxides and oxide trialkylsilyloxides. Models involving cyclic chains are possible, but steric effects make them improbable in many cases. Mixtures of chains with equal average degrees of hydrolysis for each type of chain have been assumed in previous analyses, but are shown to be special cases of the more general model.

scholarly journals Calculating the average natural recharge in large areas as a factor of their lithology and precipitation

2011 ◽  
Vol 8 (3) ◽  
pp. 4753-4788 ◽  
Author(s):  
E. Sanz ◽  
I. Menéndez Pidal de Navascués ◽  
C. Távara
Keyword(s):  
Groundwater Resources ◽  
Annual Rainfall ◽  
Hard Rocks ◽  
Large Size ◽  
Special Cases ◽  
Catchment Areas ◽  
The World ◽  
Universal Values ◽  
Recharge Rates ◽  
Natural Recharge

Abstract. In an area as large as Spain, it is shown by statistical inference on a sample of 875 springs (with discharges greater than 10 l s−1), whose average flow, lithology and catchment areas are known, and which were grouped into regions of contrasting rainfall, that the average annual recharge is a fixed fraction of annual rainfall for each lithology. Recharge rates have thus been established with respect to rainfall for six lithological groups of different permeability: sands, gravels and generally alluvial formations 8.3%; conglomerates, 5.6%; sandstones, 7.3%; limestone and dolomite 34.3%; marls, marly limestones, silts and clays, 3.3%; and hard rocks, 1.3%. Since Spain can be considered to be representative, given its large size and a highly varied lithology, topography and rainfall, these recharge rates with respect to rainfall are probably quasi-universal values, which can be used to estimate the average recharge or average groundwater resources of large regions in any part of the world (except in special cases such as areas that have permafrost). In any case, the recharge rates can be adapted for each region according to its particular characteristics. Rainfall and lithology data are abundant, and so the method can be widely used to calculate hydraulic balances. The method has been applied to the Duero basin in Spain and to other European countries (Portugal, Ireland and Italy), obtaining recharge results that are very similar to those calculated by other methods.

Constructing Trees in Graphs whose Complement has no K2,s

2002 ◽  
Vol 11 (4) ◽  
pp. 343-347 ◽  
Author(s):  
EDWARD DOBSON
Keyword(s):  
Average Degree ◽  
Minimal Degree ◽  
Maximal Degree ◽  
Special Cases

We show that, if G is a graph of order n with maximal degree Δ(G) and minimal degree δ(G) whose complement contains no K2,s, s [ges ] 2, then G contains every tree T of order n−s+1 whose maximal degree is at most Δ(G) and whose vertex of second-largest degree is at most δ(G). We then show that this result implies that special cases of two conjectures are true. We verify that the Erdös–Sós conjecture, which states that a graph whose average degree is larger than k−1 contains every tree of order k+1, is true for graphs whose complement does not contain a K2,4, and the Komlós–Sós conjecture, which states that every graph of median degree at least k contains every tree of order k+1, is true for graphs whose complement does not contain a K2,3.

Coherency loss in γ' precipitates in nickel-base superalloy

1983 ◽  
Vol 41 ◽  
pp. 244-245
Author(s):  
R. A. Ricks ◽  
Angus J. Porter
Keyword(s):  
Lattice Mismatch ◽  
Lattice Parameter ◽  
Nickel Base Superalloy ◽  
Large Size ◽  
The Matrix ◽  
Nimonic 80A ◽  
Interfacial Dislocations ◽  
Nickel Base ◽  
Coherency Loss ◽  
Nimonic 115

During a recent investigation concerning the growth of γ' precipitates in nickel-base superalloys it was observed that the sign of the lattice mismatch between the coherent particles and the matrix (γ) was important in determining the ease with which matrix dislocations could be incorporated into the interface to relieve coherency strains. Thus alloys with a negative misfit (ie. the γ' lattice parameter was smaller than the matrix) could lose coherency easily and γ/γ' interfaces would exhibit regularly spaced networks of dislocations, as shown in figure 1 for the case of Nimonic 115 (misfit = -0.15%). In contrast, γ' particles in alloys with a positive misfit could grow to a large size and not show any such dislocation arrangements in the interface, thus indicating that coherency had not been lost. Figure 2 depicts a large γ' precipitate in Nimonic 80A (misfit = +0.32%) showing few interfacial dislocations.

Electron Beam Damage of Biomolecules Assessed by Energy Loss Spectroscopy

1978 ◽  
Vol 36 (3) ◽  
pp. 61-69
Author(s):  
M. Isaacson ◽  
M.L. Collins ◽  
M. Listvan
Keyword(s):  
Electron Microscopy ◽  
Radiation Damage ◽  
Structural Integrity ◽  
Analytical Electron Microscopy ◽  
High Dose ◽  
Dose Rates ◽  
Special Cases ◽  
Analytical Electron ◽  
Atom Migration ◽  
Beam Damage

Over the past five years it has become evident that radiation damage provides the fundamental limit to the study of blomolecular structure by electron microscopy. In some special cases structural determinations at very low doses can be achieved through superposition techniques to study periodic (Unwin & Henderson, 1975) and nonperiodic (Saxton & Frank, 1977) specimens. In addition, protection methods such as glucose embedding (Unwin & Henderson, 1975) and maintenance of specimen hydration at low temperatures (Taylor & Glaeser, 1976) have also shown promise. Despite these successes, the basic nature of radiation damage in the electron microscope is far from clear. In general we cannot predict exactly how different structures will behave during electron Irradiation at high dose rates. Moreover, with the rapid rise of analytical electron microscopy over the last few years, nvicroscopists are becoming concerned with questions of compositional as well as structural integrity. It is important to measure changes in elemental composition arising from atom migration in or loss from the specimen as a result of electron bombardment.

Decoration technique and surface physics

1978 ◽  
Vol 36 (1) ◽  
pp. 436-437 ◽  
Author(s):  
H. Bethge
Keyword(s):  
Diffusion Path ◽  
Special Importance ◽  
Surface Physics ◽  
Step Structure ◽  
Initial Stage ◽  
Special Cases ◽  
Atomic Surface ◽  
The Mean ◽  
Bulk Structure ◽  
Decoration Technique

Besides the atomic surface structure, diverging in special cases with respect to the bulk structure, the real structure of a surface Is determined by the step structure. Using the decoration technique /1/ it is possible to image step structures having step heights down to a single lattice plane distance electron-microscopically. For a number of problems the knowledge of the monatomic step structures is important, because numerous problems of surface physics are directly connected with processes taking place at these steps, e.g. crystal growth or evaporation, sorption and nucleatlon as initial stage of overgrowth of thin films.To demonstrate the decoration technique by means of evaporation of heavy metals Fig. 1 from our former investigations shows the monatomic step structure of an evaporated NaCI crystal. of special Importance Is the detection of the movement of steps during the growth or evaporation of a crystal. From the velocity of a step fundamental quantities for the molecular processes can be determined, e.g. the mean free diffusion path of molecules.

Automatic analysis of Kikuchi diffraction patterns

1994 ◽  
Vol 52 ◽  
pp. 900-901
Author(s):  
H. Weiland ◽  
D. P. Field
Keyword(s):  
Electron Beam ◽  
Electron Microscope ◽  
Spatial Resolution ◽  
Relevant Information ◽  
Crystalline Materials ◽  
Large Size ◽  
Transmission Electron ◽  
New Type ◽  
Diffraction Patterns ◽  
Orientation Determination

Recent advances in the automatic indexing of backscatter Kikuchi diffraction patterns on the scanning electron microscope (SEM) has resulted in the development of a new type of microscopy. The ability to obtain statistically relevant information on the spatial distribution of crystallite orientations is giving rise to new insight into polycrystalline microstructures and their relation to materials properties. A limitation of the technique in the SEM is that the spatial resolution of the measurement is restricted by the relatively large size of the electron beam in relation to various microstructural features. Typically the spatial resolution in the SEM is limited to about half a micron or greater. Heavily worked structures exhibit microstructural features much finer than this and require resolution on the order of nanometers for accurate characterization. Transmission electron microscope (TEM) techniques offer sufficient resolution to investigate heavily worked crystalline materials.Crystal lattice orientation determination from Kikuchi diffraction patterns in the TEM (Figure 1) requires knowledge of the relative positions of at least three non-parallel Kikuchi line pairs in relation to the crystallite and the electron beam.

Immunoprobe localization in mammalian embryos

1990 ◽  
Vol 48 (3) ◽  
pp. 32-33
Author(s):  
Patricia G. Calarco ◽  
Margaret C. Siebert
Keyword(s):  
Electron Microscopy ◽  
Endoplasmic Reticulum ◽  
Thin Sections ◽  
Relative Lack ◽  
Large Size ◽  
Mammalian Embryos ◽  
Antigen Localization ◽  
Difficult Challenge ◽  
Lowicryl K4m ◽  
Fertilized Egg

Visualization of preimplantation mammalian embryos by electron microscopy is difficult due to the large size of the ircells, their relative lack of internal structure, and their highly hydrated cytoplasm. For example, the fertilized egg of the mouse is a single cell of approximately 75μ in diameter with little organized cytoskelet on and apaucity ofor ganelles such as endoplasmic reticulum (ER) and Golgi material. Thus, techniques that work well on tissues or cell lines are often not adaptable to embryos at either the LM or EM level.Over several years we have perfected techniques for visualization of mammalian embryos by LM and TEM, SEM and for the pre-embedding localization of antigens. Post-embedding antigenlocalization in thin sections of mouse oocytes and embryos has presented a more difficult challenge and has been explored in LR White, LR Gold, soft EPON (after etching of sections), and Lowicryl K4M. To date, antigen localization has only been achieved in Lowicryl-embedded material, although even with polymerization at-40°C, the small ER vesicles characteristic of embryos are unrecognizable.

Vibration Isolator System for Electron Microscope

1990 ◽  
Vol 48 (1) ◽  
pp. 182-183
Author(s):  
K. Ohi ◽  
M. Mizuno ◽  
T. Kasai ◽  
Y. Ohkura ◽  
K. Mizuno ◽  
...  
Keyword(s):  
Electron Microscope ◽  
Magnetic Fields ◽  
Environmental Conditions ◽  
Vibration Isolator ◽  
Air Conditioners ◽  
Vibration Isolators ◽  
Large Size ◽  
Electron Microscopes

In recent years, with electron microscopes coming into wider use, their installation environments do not necessarily give their performance full play. Their environmental conditions include air-conditioners, magnetic fields, and vibrations. We report a jointly developed entirely new vibration isolator which is effective against the vibrations transmitted from the floor.Conventionally, large-sized vibration isolators which need the digging of a pit have been used. These vibration isolators, however, are large present problems of installation and maintenance because of their large-size.Thus, we intended to make a vibration isolator which1) eliminates the need for changing the installation room2) eliminates the need of maintenance and3) are compact in size and easily installable.

One Size Fits All?

Methodology ◽  
2012 ◽  
Vol 8 (1) ◽  
pp. 23-38 ◽  
Author(s):  
Manuel C. Voelkle ◽  
Patrick E. McKnight
Keyword(s):  
Repeated Measures ◽  
Structural Equation ◽  
Type I Error ◽  
Equation Modeling ◽  
Type I ◽  
Finite Sample ◽  
Traditional Methods ◽  
Repeated Measures Anova ◽  
Special Cases ◽  
Latent Curve

The use of latent curve models (LCMs) has increased almost exponentially during the last decade. Oftentimes, researchers regard LCM as a “new” method to analyze change with little attention paid to the fact that the technique was originally introduced as an “alternative to standard repeated measures ANOVA and first-order auto-regressive methods” (Meredith & Tisak, 1990, p. 107). In the first part of the paper, this close relationship is reviewed, and it is demonstrated how “traditional” methods, such as the repeated measures ANOVA, and MANOVA, can be formulated as LCMs. Given that latent curve modeling is essentially a large-sample technique, compared to “traditional” finite-sample approaches, the second part of the paper addresses the question to what degree the more flexible LCMs can actually replace some of the older tests by means of a Monte-Carlo simulation. In addition, a structural equation modeling alternative to Mauchly’s (1940) test of sphericity is explored. Although “traditional” methods may be expressed as special cases of more general LCMs, we found the equivalence holds only asymptotically. For practical purposes, however, no approach always outperformed the other alternatives in terms of power and type I error, so the best method to be used depends on the situation. We provide detailed recommendations of when to use which method.

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